PART0001 (Pulse Compression for Phased Array Weather Radars.)

NCAR/TN-444 NCAR TECHNICAL NOTE _· i May 1999

Pulse Compression for Phased Array Weather Radars

R. Jeffrey Keeler Charles A. Hwang Ashok S. Mudukutore

ATMOSPHERIC TECHNOLOGY DIVISION

i NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER, COLORADO - Pulse Compression for Phased Array Weather Radars NCAR Technical Report

R. Jeffrey Keeler 1, Charles A. Hwang1 and Ashok Mudukutore 2 1National Center for Atmospheric Research* PO Box 3000, Boulder, Colorado 80307 USA

2Colorado State University Fort Collins, Colorado 80369 USA

E-mail: keeler@ucaredu Tel: 303-497-2031 Fax: 303-497-2044

*NCAR is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation Preface

This Technical Report is a reprint of the Final Report from NCAR's Atmospheric Technology Division on work performed from 1991 through 1995 for the FAA Terminal Area Surveillance Systems Program. It details the application of pulse compression waveforms to weather radar, the importance of range time sidelobes, special considerations for FM waveforms, simulations of fluctuating weather targets, and a validation study using the NCAR ELDORA testbed radar. The report was originally written in 1995, but not published until now. A few relevant references have been added when they amplify the work originally performed. rJK May 15, 1999 List of figures

Figure 1.1. Advanced high resolution radarsystem using pulse compression waveform and phased array electronic scanned antenna ...... 2

Figure 2.1. Graphicaldescription of optimal sidelobe suppressionfilter design. The desiredoutput response, dk, is an impulse, but the actual output, yk, has sidelobes...... 6...... 6

Figure 2.2. The integratedsidelobe levels (ISL)for a Barker 13 code with inversefiltering decrease with longerfilter length for zero Doppler...... 7

Figure2.3. Waveforms usedfor compressionfilter tests: Barker 13 (B-13), Pseudo-Noise (PN-15), Linear FM 63 (LinFM), and Nonlinear FM 39 (TanFM). The bandwidth or frequency sweep of each waveform is 1 MHz and the durations are as shown...... 7

Figure 2.4. Impulse responses of MF and Inv lx/2x/3x/5x compressionfilters to a B-13 biphase coded waveform. ...8

Figure2.5. Compressionfilter responsesto B-13 waveformfor MF and Inv-lx/2x3x/S5xfilters. Note reduced sidelobes and extended response as filter length increases ...... 9

Figure2.6. Ambiguityfunction for B-13 and matchedfilter. Sidelobes are uniformly high at -22 dB and main response peak is constant showing negligible Doppler sensitivity ...... 9

Figure 2.7. Ambiguity function of B-13 and Inv-Sx filter. Both ISL and PSL are much lower than the MF response but show extreme Doppler sensitivity. Peak sidelobes at zero velocity are -60 dB...... 10

Figure 2.9. ISL, PSL and Lmm vs. Dopplerfor Pseudo-Noise bi-phase waveform of length 63 for MF, Inv-lx and Inv- 5x fi lters...... 11

Figure 2.10. Ambiguityfunction ofLinFM-63 waveform and Inv-5x filter. Peak sidelobes are 45 to 50 dB down at zero velocity...... 12

Figure 2.11. ISL, PSL and Lmm vs. DopplerforLinFM (BT=63) with MF, Inv-lx and Inv-5x compressionfilters. Data are oversampledoversapled by 2B ...... 2B are

Figure 2.12. Ambiguityfunction of TanFM waveform and Inv-5xfilter. Peak sidelobes are 70 dB down at zero velocity. Co pression ratio is 39 ...... 13

Figure 2.13. ISL, PSL and Lmm vs. Dopplerfor TanFM (BT=39) with the MF, Inv-lx and Inv-5x compressionfilters. Data are oversampled by 2B ...... 13

Figure2.14. Ambiguityfunction of a CC-10 code pairusing MF with a) no cross waveform leakage, and b) 20 db cross w aveform leakage...... 14

Figure3.1. Inv-5x SLSfilter response to a linearchirp waveform under top) optimum sampling conditions (zero phase) and (bottom) the same filter response to all phase shifts (all phase) simulated by 8 times oversampling ...... 16 Figure 3.2. ISL values for Inv-5x compressionfilters with sample-phase offset (shift) for zero-phase SLS filters and all- phase SLSfilters at a Nyquist (IN) sampling rate. The expected ISLfor the APSLS filter is -5.9 dB andfor the ZPSLS filter is -5.8 dB...... 18

Figure 3.3. Probabilitydistribution ofISLsfor both APSLS and ZPSLS Inv-5x filters with IN, 2N, and 5N sampling rates. Expected AP/ZP ISLs are (-5.9/-5.8) for IN, (-20.6/-21.9) for 2N, and (-32.5/-33.3) dBfor 5N sample rates. 18

Figure 4.1. ISL as function of Doppler shift for a point target using the B-13 bi-phase code and MF, IFxl, xS, x7 compressionfilters including two Doppler Tolerant (DT) processing variants...... 21

Figure 4.2. ISL vs. Doppler shiftforfluctuating reflectivity (sv =1 ms, SNR =50 dB) "spike " 100 dB greater than any adjacent range sample. Waveform is B-13 code and filters are the MF, IFxl, x5 and x7, and two DT variants...... 21

Figure 4.3. ISL vs. SNRfor various compressionfilters. Dashed lines represent the correspondingDoppler tolerant filters...... 22

Figure 4.4. Range profile of reflectedpower from a 100 dB reflectivity notch of a hard target with zero velocity. The power in the notch represents the ISL for the B-13 waveform and the selected compressionfilter...... 23

Figure4.5. Range profile of reflectedpower from a 100 dB notch in afluctuating target having zero velocity and width of 2.5 m/s. Power in the notch represents ISLfor the B-13 waveform and the selectedfilter...... 23

Figure 4.6. ISL vs. Doppler velocity for a hard targetfor the B-13 waveform and the selected filter...... 24

Figure 4.7. ISL vs. Doppler velocity for afluctuating targetwith sv=2.5 m/s...... 24

Figure 4.8. ISL vs. Doppler velocity for afluctuating targetwith sv=5.0 m/s...... 25

Figure 4.9. Range profiles of reflected power. The input has a 50 dB reflectivity step...... 25

Figure 4.10. Range profiles of Doppler velocity. The input has a 20 n/s velocity step...... 26

Figure 5.1. Schematic of H PA test...... 27

Figure 5.2. Phase plot of HPA's simple pulse phase response after drift correction...... 28

Figure 5.3. Ground clutter data showing receivedpowerand velocityfor simplefrequency 90 m pulse. Nyquist velocity ( 0.5) corresponds to 8 m/s. Ranges greaterthan 150 are noise only...... 29

Figure 5.4. Ground clutter target using B-13 pulse and Inv-5x filter. Note 11 dB SNR increase and the sidelobe response. Simple and coded peak powers are equal...... 29

Figure 5.5. High reflectivity gradient weather using simple 90 m pulse. Gradientis 50 dB over 2 km range at front and rear of cell. Nyquist velocity is 8 m/s. Radial velocities within the cell are aliased and between 5-12 m/s ...... 30

Figure5.6. Weather echo using B-13 waveform and the Inv-5xfilter. There is discernibleleakage of the sidelobe energy from the strong precipitation echo to outside the cell in both reflectivity and velocity...... 30

Figure 5.7. Snapshot color display of weather data takenfrom the ELDORA testbed radar. Data between 5-23 km at azimuth 332 degrees and elevation 18.5 degrees is detailed in Figure 5.8 ...... 32

Figure 5.8. Range plot of the simple pulse (top pair)and B-13/Inv-5x pulse compression (bottom pair) received echo power and velocity data takenfrom the ELDORA testbed radarshowing the weather in Figure 5.7 at 332 degrees and 5-2 3 km ...... 33 Figure5.9. Spectra of range gate at 18 km showing contaminationof storm velocity ingressing through the sidelobes of the coded pulse. Velocity estimate for the Inv-Sxfiltered pulse is near 0.1 (- 0.8 m/s) butfor the Inv-3x filtered pulse is near -0.15 (- -1.2 m/s) caused by greatersidelobe leakage...... 34 Table of Contents I 1 0 Tnftroductionn...... I.. 1 1.1 Motivation for weather radar pulse compression ...... 1 1.1.1 Weather target characteristics ...... 1...... 1.1.2 Digital technology...... 1 1.2 Pulse compression defined ...... 2 1.3 H igh resolution radar system ...... 2 1.4 FAA/TASS program description ...... 2 2.0 Waveform and filter design...... 4 2.1 Coded w aveform design...... 2.2 Com pression filter design...... 5 2.3 Waveform analysis ...... 6 2.3.1 Bi-phase waveform s...... 8 2.3.2 FM waveforms ...... 11 2.4 C om plem entary codes...... 14 3.0 Sample phase aspects of FM waveforms...... 16 3.1 Sam ple phase problem s...... 16 3.2 Phase mismatch with FM waveforms...... 16 3.3 Optimization over unknown sample phase...... 17 3.3.1 Filter design/modification ...... 17 3.3.2 Performance measure...... 17 3.4 A nalysis...... 17 4.0 Simulation and analysis for fluctuating targets ...... 20 4.1 Simulation of fluctuating weather targets with pulse compression ...... 20 4.2 Doppler tolerant design ...... 20 4.3 Evaluation of ISL ...... 222 4.4 Reflectivity and velocity steps...... 25 5.0 Data acquisition and analysis...... 27 5.1 ELDORA test bed radar description ...... 27 5.2 D ata quality ...... 27 5.3 Point clutter target ...... 29 5.4 Convective weather target ...... 30 5.5 Color display: Snowstorm target...... 32 6.0 Phased array configurations ...... 35

/7 aIt*nnelll: ^n .I

8.0 Acknowledgments ...... 37 9.0 References ...... 38 Appendix A--Ambiguity functions...... 41ff Appendix B--Characterization of the NCAR high power amplifier ...... 42ff Appendix C-Coherent wideband processing of distributed radar targets ...... „.. 43ff Appendix D--Rapid scan Doppler radar development considerations: Part II ...... 44ff Appendix E--Pulse compression polarization waveforms for rapid scan Doppler radar ...... 45ff Appendix F--Rapid scan Doppler radar: the antenna issues...... 46ff Appendix G--Pulse compression waveform analysis for weather radar...... 47ff Appendix H--Pulse compression for weather radar...... 4...... 48ff Appendix I--Sample phase aspects of FM pulse compression waveforms...... 49ff Appendix J--Pulse compression weather radar waveforms ...... 50ff Appendix K--Pulse compression weather radars...... 51ff Pulse Compression for Phased Array Weather Radar

1.0 Introduction

1.1 Motivation for weather radar pulse compression

Small, rapidly evolving aviation weather hazards, such as microbursts, strong gust fronts, and wake vortices happen quickly and can be very dangerous to aircraft. Using weather radar to detect their presence among highly reflective aircraft and ground clutter requires high sensitivity and high spatial resolution. Air traffic control and meteorological communities are demanding radars that also scan the atmosphere at faster rates. Today's mechanically scanned radars cannot track and predict these weather hazards while simultaneously mapping aircraft in a terminal area. Phased- array radar systems can fulfill this need by electronically steering their beams, but with current technology the peak power is so low that these radar systems have poor sensitivity. Pulse compression allows systems to increase sensitivity by transmitting larger average power in a longer coded pulse and then compressing the pulse to achieve high range resolution and subsequently a much faster volumetric scan rate.

Pulse compression techniques are well developed for military and aviation radar applications where scattering is from hard point, not distributed, targets. Application of pulse compression to distributed weather targets was not investigated until the 1970s when Fetter (1970) demonstrated a phase coded transmit pulse and matched filter receiver at McGill University. Gray and Farley (1973) used a phase coded waveform for ionospheric scatter observations. In 1974 Keeler (personal communication) built a Barker phase coded system for an acoustic radar echosonde system, but it was never tested with atmospheric returns. Keeler and Passarelli (1990) have traced the evolution of pulse compression techniques in the weather radar community. In Appendix H, Keeler and Hwang (1995) provide a good summary of their theoretical studies and data validation.

Doppler weather radars can accurately depict the reflectivity and velocity structure of convective storms and other weather phenomena. The WSR-88D (NEXRAD), Terminal Doppler Weather Radar (TDWR) and other conventional weather radar networks require relatively long dwell times (30-100 msec) to acquire enough independent samples for accurately measuring weather parameters. For some operational systems and especially for research systems, the volume scan time and low spatial scan spacing are too coarse to capture the essential features of convective evolution (Carbone et al 1985, Wolfson 1993). Future operational, as well as research, systems will likely require higher space and time resolution measurements than are presently available.

1.1.1 Weather target characteristics

Like other volumetric scatterers, such as insects and refractive index gradients, weather is made up of many small scatterers, each with its own backscatter cross section and velocity. Radar characterization of precipitation is defined in terms of the "radar reflectivity factor" (Z), an average quantity related to the Rayleigh scattering from a dielectric sphere, which, in turn, is related to the radar cross section (a) using the X-4 wavelength dependence (Battan 1973, Doviak and Zrnic 1993). Accurately estimating the backscatter power and velocity in a weak echo region near a strong reflectivity gradient requires that range sidelobes in a pulse compression scheme be minimized so that power from these extended sidelobe regions do not contaminate the desired main lobe (Appendix C: Keeler and Frush 1983a).

1.1.2 Digital technology

Rapid technology developments in digital signal processing components and associated digital filter methods have led to new capabilities in waveform generation and pulse compression filter techniques. In the past, waveforms were designed with the concept of using matched filters to optimize the detectability, or the signal to noise ratio, of radar targets. However, weather radar signals are scattered from targets distributed in range, not point targets, and it is the integrated range sidelobe response that becomes the relevant quantity to optimize rather than the signal to noise ratio. Consequently, more sophisticated and precise designs are needed for these digital sidelobe suppression filters used for weather measurements. Highly precise, real time filters using these techniques are readily implemented with modem digital signal processing (DSP) chips.

May 24, 1999 Page 1 of 52 Pulse Compression for Phased Array Weather Radar

1.2 Pulse compression defined

Pulse compression (PC) is a technique of obtaining higher power and resolution from a low peak power transmitter (Skolnik 1990). A long pulse with wide frequency content has a narrow autocorrelation and compression filter response. The output of the compression filter typically has a high-power main lobe and low sidelobes which we desire to minimize.

1.3 High resolution radar system

Figure 1.1 depicts the two distinct technologies required for higher space and time resolution weather radar measurements (Smith 1974, Keeler and Frush 1983a): 1) a coded wide bandwidth waveform that allows higher range resolution and subsequent larger number of independent estimates within a dwell time, and 2) an electronic step scanned (e- scan) phased array antenna that allows rapid and agile beam movement The wideband waveform allows accurate weather measurements in a short data acquisition time and the e-scan antenna allows rapid beam movement, thereby covering the surveillance volume without inducing scan modulation that degrades the accuracy of the measurements. As as example from aviation weather, convective activity frequently spawns dangerous winds, such as microbursts, that may rapidly form a lethal aviation hazard in an airport terminal area. Weather radar volume scan times of 2.5-10 minutes, characteristic of TDWR and NEXRAD radars, do not have adequate time resolution to acquire data by which an accurate microburst hazard can be forecast. A standard mechanically scanned radar located in the airport would have extreme difficulty in searching an airport terminal area for precursor signatures of aviation hazard and other weather events in a timely fashion. By decreasing the beam dwell time, the volume scan time may be decreased dramatically. Alternatively, spatial resolution of the data may be improved for the same volume scan time by spacing the short dwell time beams more closely in azimuth and elevation. In this report we emphasize waveform design issues of this advanced radar architecture and a few of the feasible phased array configurations previously discussed by Keeler and Frush (1983b), Holloway and Keeler (1993), and Keeler (1994).

Pulse c wav A Phased array antenna

Figure 1.1. Advanced high resolution radarsystem using pulse compression waveform and phased array electronic scanned antenna.

1.4 FAA/TASS program description

The FAA's Terminal Area Surveillance System (TASS) Program has been active in the "advanced weather radar" arena since 1991 and has explored concepts for a multiple function, next generation air traffic and weather surveillance radar. The radar is envisioned as a phased array system capable of detecting, tracking and predicting positions

May 24, 1999 Page 2 of 52 Pulse Compression for Phased Array Weather Radar of all aircraft and hazardous weather phenomena in the airport terminal area. A solid state pulse compression e-scan radar is a promising technology. Various antenna system configurations have been considered, ranging from a single ID e-scan mechanically rotating phased array to multiple fixed face 2D phase scanned active arrays. Dual polarization measurements are also being studied. The FAA is working closely with American and European industry in developing concepts and system designs. Rogers, et al (1997), Buckler (1997), and Tidwell (1997) give detailed sum- maries and status of the TASS program.

May 24, 1999 Page 3 of 52 Pulse Compression for Phased Array Weather Radar

2.0 Waveform and filter design

Pulse compression is a waveform generation and processing technique that simultaneously offers higher range resolution and increased average transmit power over that possible with a typical single frequency pulsed radar waveform. Increasing the bandwidth of the waveform increases the range resolution (and the number of independent samples of the received echo) in a specified range interval. The Signal to Noise Ratio (SNR) of each sample is reduced by the same amount. However, the SNR can be recovered by lengthening the transmit pulse, thereby increasing the average transmitted power (Keeler and Frush 1983a).

2.1 Coded waveform design

Any transmitted waveform has a nominal bandwidth B and nominal pulse length T. The time-bandwidth product BT is a measure of the pulse compression factor. That is, given appropriate receiver filtering, the energy of the pulse can be compressed into an effective pulse length BT times shorter than the actual pulse (Cook and Bernfeld 1967). BT values of 100 (e.g., B=lOx and T=lOx the simple reference pulse) allow space or time resolution to be increased an order of magnitude over existing research or operational weather radars with no decrease in sensitivity.

Let us describe a specific example. The effective range resolution of any waveform is c/2B. For example, a pulse with a 10 MHz bandwidth has a potential range resolution of 15 m whether it is a 100 nsec single frequency pulse, an N- element phase code changing every 100 nsec, or a chirped pulse linearly sweeping through 10 MHz. The output of an appropriate pulse compression filter gives an estimate of the received signal that can be processed to yield independent estimates of reflectivity, velocity, etc. every 15 m in range. These "high resolution" measurements can then be averaged in range to provide coarser range resolution, but providing more accurate measurements. For example, if we average 10 consecutive 15 m measurements, we obtain a processed 150 m range resolution that is about 3 times more accurate than the individual 15 m measurements. Thus, we may use shorter dwell times to achieve the same accuracy as the simple pulse system.

The codedcolength pulse is somewhat arbitrary and is determined by the desired system sensitivity and minimum range of radar coverage. To maintain the same SNR for each range sample as existing systems, we require the same increase in average power as was specified for the increase in pulse bandwidth. Consequently, both the time and the bandwidth should increase by the same factor. Typical BT values of 50-100 seem to fit present measurement needs as well as radar and digital processing technology.

The actual coding of the waveform can take many forms. Phase or frequency codes are preferred over amplitude codes to maximize average power and simplify transmitter design. Bi-phase codes reverse the phase according to a specified binary pattern. For example, Barker codes and Pseudo-Noise (PN, or maximal length) codes are common (Cohen 1987). Quadri-phase, or higher order poly-phase codes (Lewis, et al 1986) are also possible but may offer only limited advantages. Frequency Modulation (FM) codes have always been popular. Linear FM codes are efficient in obtaining large compression ratios and are easily generated and compressed using both analog and digital means (Strauch 1988). Non-linear FM waveforms offer spectrum shaping advantages with reduced sidelobe response while retaining a rectangular waveform and a higher average power than obtained by amplitude shaping the pulse (Famett and Stevens 1990). Simultaneous frequency and amplitude shaping may yield additional improvements but were not investigated in this study.

2.1.1 Application in dual polarization

Dual polarization radars may readily accommodate complementary code pairs. It is possible to utilize two orthogonal polarization channels to transmit the complementary code pair simultaneously, one on each polarization, and obtain extremely low range sidelobes. However, differential scattering and propagation effects and Rayleigh fluctuations with the attendant decorrelation of the returns will degrade the sidelobe cancellation as will incomplete polarization isolation between the co-and cross-polarized channels (Keeler, et al 1993). Leakage, or lack of isolation between the two orthogonal polarizations (and the orthogonal codes), gives a rapid increase in range sidelobes. Even with zero Doppler shift, the sidelobes are unacceptably high. An unknown Doppler shift further limits the achievable sidelobe cancellation.

May 24, 1999 Page 4 of 52 Pulse Compression for Phased Array Weather Radar

2.2 Compression filter design

The joint waveform and compression filter design goal is to determine a waveform having a compression factor of BT = 50-100 and a corresponding compression filter that generates low range sidelobes. The "matched filter" (MF) receiver for any arbitrary waveform is known to be optimum in the sense of maximizing the output SNR but it does not minimize the sidelobe response (Cook and Bernfeld 1967). Since weather targets are distributed in range, the contribution from scatterers at ranges other than that desired enter through the range sidelobes (which we desire to minimize). These range sidelobes occur because of imperfect compression filtering or a meteorological influence of the return echo and can only be minimized in a least squares sense, not eliminated.

Let us define attributes of the compression filter sidelobe and mainlobe responses. In the following three equations, let sj denote sidelobe samples and mk denote the mainlobe samples of the filter response. Also let hj be the coefficients of the sidelobe suppression filter, gk be the coefficients of the matched filter, and r, be the mainlobe peak of the waveform autocorrelation function. Common waveforms and matched filters yield peak sidelobe (PSL) values of only 20- 40 dB below the primary target response, which is not adequate for many weather applications. We define the PSL value as nmax(s) PSL = 2Olo max((EQ 1) ^max(in),

For accurately estimating reflectivities and velocities of weather, which are always distributed in range, we require compressed waveforms having integrated sidelobe (ISL) values at least 40 dB below the main response for Doppler shifts less than 50 m/s. This suppression level should satisfy most convective storm gradients. Typical matched filter ISL ratios are only -10 to -20 dB. We define the ISL as

ISL = 10log --- (EQ2) I k where the mainlobe response samples are taken over the well defined mainlobe for phase codes. The central lobe sample is the only one within ± 1/B seconds of the peak response. However, the mainlobe duration is less well defined for FM waveforms. We have chosen to follow the convention of Ashe, et al (1994) and use + 2.5/B seconds as the width of the mainlobe. Additionally, filtering induces a loss in the SNR from that a matched filter which maximizes the SNR. We desire to keep this mismatch loss (Lmm) well below 1 dB to prevent any undesirable loss in detectability. We define Lmm as

L(max(m,)/AI h 1 i2) L 2010g (EQ3)

Digital sidelobe suppression filters (variously called inverse filters, Wiener filters, deconvolution filters, spiking filters, or whitening filters) are optimal designs that minimize the ISL of the filter response in a least squares sense (Wiener 1942, Rice 1961, Treitel and Robinson 1966, Ackroyd and Ghani 1973). The desired response is an impulse having a time width, tB, equal to the inverse bandwidth of the waveform. Both the PSL and ISL can be suppressed 10's of dB over the MF response at the cost in SNR of a fraction of a dB. Consequently, optimal ISL compression filters tend to be preferred over the MF in the weather application. Adequate ISL suppression typically is limited to relatively small velocities so that the Doppler sensitivity of the waveform design is an important parameter to be assessed.

The sidelobe suppression filter design algorithm used is the deterministic least-squares error method (Roberts and Mullis 1987). For a given input signal xk we want to create the inverse filter h such that its output response Yk is as close as possible to the desired response dk. In Figure 2.1 the waveform xk is a 13 bit Barker code and the ideal response dk is a delta function. However, the actual filter response Yk has finite sidelobes that we desire to minimize. We define the length of the inverse filter in terms of the waveform length. Thus, the inverse filter Inv-5x is five times longer than the waveform.

May 24,1999 Page 5 of 52 Pulse Compression for Phased Array Weather Radar

Xk h IT - LF_- x

Figure 2.1. Graphicaldescription of optimal sidelobe suppressionfilter design. The desired output response, db, is an impulse, but the actual output, y, has sidelobes.

To design the optimal compression filter h, we desire to minimize the integrated sidelobe response over the entire filter response

V(h) = dk-yl 2 (EQ 4)

= X ([dk-(xk® hk)] 2 (EQ 5)

By using matrix differentiation or Lagrangian multipliers, we can obtain the matrix equation

R * h = q (EQ 6)

where R is the autocorrelation matrix of xk and q is the causal part of the crosscorrelation of dk and xk. One way to solve for the filter h is by left multiplying by R-1, which exists because all autocorrelation matrices are positive definite. We used this algorithm to compute the bi-phase coded waveform compression filters.

To compute filter coefficients for FM waveforms, we first sampled the waveform into a discrete array (since FM signals are continuous) and unconstrained the mainlobe to a specified width using the same method as Ashe et al (1994). Basically, it involves omitting the mainlobe elements of Equation 6 and then re-solving for the filter coefficients.

Because the weather velocities are typically limited to a band between + 50 m/s, one can design compression filters to minimize sidelobes over those Doppler velocities (Baden 1992, Cohen 1987) rather than only at a specific velocity. This is accomplished by integrating the R matrix and q vector over all Doppler shifts in this range. Empirical evidence during our research has shown that this filter, optimized for a velocity band symmetric about zero m/s, is generally the same as the one that minimizes sidelobe response only at zero Doppler. Thus, we focus only on filter optimization at zero Doppler velocity.

Increasing the length of the compression filter reduces the ISL. Figure 2.2 shows the ISL as a function of filter length for the Barker-13 code compressed by inverse filters of increasingly larger length for the case of zero Doppler velocity. We shall see that despite the extremely low ISL, the response is extremely sensitive to Doppler shifts.

2.3 Waveform analysis

Waveform resolution characteristics in the range and Doppler domains may be visualized with the "ambiguity function" (Woodward 1953, Rihaczek 1969). This two dimensional function shows the joint response of the compression filter to the transmitted waveform and to targets distributed at ranges and velocities about the desired main response. Mudukutore, et al (1996) give a concise derivation of the ambiguity function.

We may consider the ambiguity function to show the response of a weather target (assumed to be fixed in space during the pulse propagation time) at different Doppler velocities. The response is the same for approaching or receding targets so we show the response to zero velocity at the front of the figure and the response for Doppler velocities up to

May 24,1999 Page 6 of 52 Pulse Compression for Phased Array Weather Radar

-10 ._ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~

...... i ......

-20 ......

-30 ......

_. o . ~~~~~~~~~...... ---0 m ...... -J C) -50 -c t_ ^ _ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i. I . . .. i .

-60

-70

-A0 10 20 30 40 50 60 70 80 90 100 Filter length Figure 2.2. The integratedsidelobe levels (ISL) for a Barker 13 code with inverse filtering decrease with longer filter length for zero Doppler

50 m/s receding back and to the left. Figure 2.6 is the first example of the ambiguity function plot and Appendix A shows a full set of ambiguity functions for all the waveforms and compression filters described in this report. The zero velocity matched filter response is also identically the autocorrelation function of the waveform.

We analyze the four waveforms shown in Figure 2.3 that represent potential coded waveforms for the weather radar measurements:

1) Barker bi-phase (BT=13) code (B-13), which has known sidelobe properties but limited compression ratio,

2) Pseudo-Noise bi-phase (BT=15 and 63) code (PN), which has a larger compression ratio taking values 2M-1,

Barker-13

- 0 5.0x10'° 1.0x10' 1.5x10 Seconds

PsDoB,_noise-15

' - - 5 0 5.0x0' 1.OxlO 1.5x10 wcond*

Linear FM

0 2x X10-x 6x10 seconds

Tongent-Bosed Non-Lineor FM

- - o0 2xO 40-x10 6x10 Figure 2.3. Waveforms usedfor compressionfilter tests: Barker 13 (B-13), Pseudo-Noise (PN-15), Linear FM 63 (LinFM), and Nonlinear FM 39 (TanFM). The bandwidth orfrequency sweep of aach waveform is 1 MHz and the durations are as shown.

May 24, 1999 Page 7 of 52 Pulse Compression for Phased Array Weather Radar

3) Linear FM (BT = 63) code (LinFM), which is a waveform class with arbitrary BT, and

4) Tangent Non-linear FM (BT = 39) code (TanFM), which has a spectrum shaped only by the frequency sweep to reduce sidelobes, but the same time duration and frequency extent as the LinFM waveform with BT = 63.

For each waveform we show the ambiguity function and curves of the integrated sidelobes, peak sidelobe and mismatch loss vs. Doppler for the 3.2 cm wavelength (X-band) radar we used to collect test data. For 10 cm (S-band) and 5 cm (C-band) radars the ambiguity functions and the ISL, PSL and Lmm curves would cover only about the first 30% and 60% of the curves for the same 50 m/s velocity coverage. The waveforms and compression filters are analyzed without any bandlimit filtering so as not to obscure subtle effects in analyzing ideal waveforms and filters. An actual radar would include this filter as well as transmit waveform distortions. These waveform modifications by any bandlimit filtering can be easily included in the compression filter design.

The compression filter impulse responses are instructive to note. Figure 2.4 shows that MF impulse response is, by definition, simply the time reversed transmit waveform, B-13 in this case. In addition, the inverse filter impulse responses are highly tapered at both ends and approximate the MF response near the central region.

0r MF

0^^\r~ _ ___-Invlx

-1

o Inv2x

o Inv3x

--1 . .... ln',v3x

0 20 40 60 80

Figure2.4. Impulse responses of MF and Inv Ix/2x/3x/5x compressionfilters to a Barker 13 biphase coded waveform

2.3.1 Bi-phase waveforms

A bi-phase coded waveform reverses the phase of a single frequency sinusoid at regular "chip" intervals (corresponding to the range resolution c/2B) according to a predetermined sequence. The waveform and filter output are sampled once per chip at the inverse bandwidth sampling interval, tB. A single mainlobe sample and all the sidelobe samples (exclusive of the mainlobe sample) are used in the ISL computation described in Equation 2.

The Barker coded waveform has a time bandwidth product, or compression factor, of 13. Thus, for a given desired range resolution, 13 times more average power (1 ldB) can be transmitted than a simple single frequency pulse having the same range resolution. The Barker codes are known to have unit sidelobe matched filter response. The range sidelobes are basically constant at -22 dB for all velocities up to 50 m/s and the ISL is about -11 dB. Figure 2.5 shows the compression filter output response at Vel = 0 for the MF and several inverse filters of increasing length. The MF sidelobes are consistently high. The inverse filter peak sidelobes become increasingly lower and located farther from the main response as the compression filter length is increased. Cohen and Cohen (1988) describe "near perfect" bi- phase codes that have nearly all the sidelobes of unit amplitude, but extend from lengths 14 to 34. Their performance with inverse filters is not as good as for the B-13 code, but may fit well into some applications.

Figure 2.6 shows the ambiguity function for the Barker-13 code and its matched filter. The sidelobes are high for all Doppler shifts. Although the matched filter has the higher signal-to-noise ratio, the sidelobe response can be improved greatly with inverse filtering. Figure 2.7 shows the ambiguity function for the B-13 waveform with an inverse compression filter, Inv-5x, five times longer than the waveform itself. The peak sidelobes are down about 60

May 24, 1999 Page 8 of 52 Pulse Compression for Phased Array Weather Radar

I 0 A A A. AA l l I I -50 MF -100 0 -50 InvIx- -100 0 -50 Inv2x -100 0 -50 Inv3x -100 0 -50 r~i7~v>~~~.-.. ~ Inv~x -100 0 20 40I- 60 80 Figure 2.5. Compression filter responses to B-13 waveform for MF and Inv-lx/2x/3x/5x filters. Note reduced sidelobes and extended response as filter length increases.

Figure 2.6. Ambiguity function for B-13 and matched filter. Sidelobes are uniformly high at -22 dB and main response peak is constant showing negligible Doppler sensitivity. dB and the ISL is approximately -50 dB at zero velocity. The ambiguity function appears different from textbook plots (e.g., Rihaczek 1969) because we plot only the relatively small weather velocities rather than Mach speeds typical of aviation and military targets.

Figure 2.8 shows the ISL, PSL and Ln, vs. Doppler curves for the B-13 waveform and the MF, Inv-lx and Inv-5x filters. Clearly, the MF is inferior to all the inverse filters. Longer inverse filters give exceptionally low ISL values near Vel=0, but they increase and converge to about -20 dB for larger Doppler shifts.

The longest known Barker code is length 13. Pseudo-Noise (PN) codes occur for lengths 2n-1 and allow larger BT products while having reasonably good autocorrelation sidelobes. Therefore, we considered the PN-15 code (not shown) for comparison with the B-13 code and the longer PN-63 code to compare with the higher compression ratio FM waveforms. We searched all the possible PN-15 and PN-63 sequences to select the ones having the lowest inte-

May 24, 1999 Page 9 of 52 Pulse Compression for Phased Array Weather Radar

Figure 2.7. Ambiguity function ofB-13 and Inv-5x filter. Both ISL and PSL are much lower than the MF response but show extreme Doppler sensitivity. Peak sidelobes at zero velocity are -60 dB.

0 'o

-j a-(I) -S in

0 10 20 30 40 50 Velocity (m/s)

Figure 2.8. Integrated sidelobe level, peak sidelobe level and mismatch loss for Barker-13 waveform. Longerfilters suppress sidelobes, increase loss and show greater Doppler sensitivity. The labels at left are ISL and PSL curves and labels are right are Lmm curves. grated sidelobe autocorrelation sequence. Figure 2.9 shows the ISL, PSL and Lmm vs. Doppler curves for the PN-63 waveform with the MF, Inv-lx and Inv-5x filters. The ISL is only -17 db for the PN-63 code near zero velocity. The PN codes that we have investigated do not have the same low ISL values that are characteristic of the Barker-13 code. The PN-15 curves show extremely high ISL and PSL values and should not be considered for weather radar waveforms (Appendix H: Keeler 1994). Thus, PN waveforms were not considered further in this study.

May 24, 1999 Page 10 of 52 Pulse Compression for Phased Array Weather Radar

20 ...... "''''...... 0 MF

-2 ...... 0 Iex -J 0.a. 7jc______------0 E U) 5x -6 E -20 __ - lxx -....__ ISL PfSL--- 1-8 ___- g mm ......

-40 iJ, I a ll tlJ.l , ,I J lllflllll' l, It dl a alI I I ,I ,,l la -10 0 10 20 30 40 50 Velocity (m/s) Figure 2.9. ISL, PSL and Lmm vs. Doppler for Pseudo-Noise bi-phase waveform of length 63 for MF Inv-lx and Inv-5xfilters.

Urkowitz and Bucci (1992a) have used a large compression ratio concatenated Barker code and long inverse filters that give lower ISL values than these PN codes. We have analyzed only those waveforms that have good pulse compression and autocorrelation properties using the MF response. Since the universe of all possible continuous waveforms is infinite, one might as well start with those that exhibit low ISL for the MF case.

2.3.2 FM waveforms

Frequency modulated (FM or chirp) waveforms represent a different category from the bi-phase waveforms. The FM waveforms have a continuous phase change over the duration of the pulse rather than abrupt phase changes at the "chip" boundaries. This continuous phase change represents a dilemma in the compression filter design. The filter is designed in a deterministic manner based on specific discrete time samples of the transmit waveform. However, the received samples have a phase determined by the actual range to the target and are generally different from those used to design the filter. Therefore, the compression filter is not optimum. It appears that a larger sampling rate than the waveform bandwidth mitigates this effect (Labbit 1995) but the sampling rate and processing loss is correspondingly increased. The FM waveforms in our study were oversampled by a factor of 2 to yield 2BT sample points within the pulse. Thus, the matched and inverse filters have twice as many points as the time-bandwidth product would otherwise dictate. The mainlobe region includes those samples within 6 dB of the mainlobe peak and the sidelobe region includes those points greater than 2 samples away from the mainlobe central sample. Any intermediate samples (between the mainlobe central sample and the side lobes) were left unconstrained using the same optimization approach as Ashe, et al (1994).

Linear FM waveforms have a well defined compression ratio -- it is simply the frequency sweep B (the bandwidth) times the pulse length T (Cook and Bernfeld 1967). However, non-linear waveforms have a less well defined BT. Because non-linear FM (NLFM) waveforms control the frequency sweep to tailor the spectrum shape and yield low MF sidelobes (Farnett and Stevens 1990), the 3 dB Doppler spectrum bandwidth is generally less than the total frequency sweep and is defined by the specific frequency sweep chosen.

The ambiguity function for the LinFM waveform with BT = 63 and a MF (shown in Appendix A) has sidelobes that are high and slowly tapered in range. However, an Inv-5x filter significantly reduces the peak and integrated sidelobes as shown in Figure 2.10. Figure 2.11 shows the ISL, PSL and Lmm vs. Doppler for the LinFM waveform. Inverse filters that are at least 5 times as long as the waveform seem to provide nearly the same sidelobe suppression characteristics as Barker waveforms. However, Lmn values are much larger than for the B-13 code. The LinFM waveform exhibits Lm, values of 3-5 dB whereas the B-13 waveforms are less than 0.5 dB.

May 24, 1999 Page 11 of 52 Pulse Compression for Phased Array Weather Radar

Figure 2.10. Ambiguity function of LinFM-63 waveform and Inv-5xfilter. Peak sidelobes are 45 to 50 dB down at zero velocity.

0 0 MF

MF 2

--20 lx _ m ...... U...... I...... ,...... MP' -.. -4 m ...... ~..~...... ,...... ,...... ,~~~~~~ ......

Q0 0 .2 E U) -6 " 01 2 -40 ISL -8 PSL--- ......

-1n -Du I l* III ...... I ...... I ...... -I -- - -_------10 10 - 20 30 40 50 Velocity (m/s) Figure 2.11. ISL, PSL and Lm vs. Doppler for LinFM (BT=63) with MF, Inv-lx and Inv-5x compressionfilters. Data are oversampled by 2B.

Shaping the spectrum of the FM waveform by using a non-linear frequency sweep reduces the 3 dB bandwidth and the compression ratio. But it also allows reduced mismatch loss over the LinFM waveform as the inverse filter better approximates the MF response. Using a frequency sweep that follows the f = tan(t) curve defined in Ashe, et al (1994) is one particular waveform, TanFM. If we sample this waveform at twice thefrequency sweep (not the 3 dB bandwidth), the ambiguity function is virtually identical to the LinFM example. In this case the mainlobe width is over- constrained to be smaller than tB and the sidelobes are large.

However, if the sampling frequency is reduced to twice the bandwidth of the waveform so the response has a fewer number of points and the mainlobe width is constrained to be tB = 1/B (3dB), then the sidelobes can be further suppressed. This TanFM waveform has a compression ratio of about BT = 39. Figure 2.12 shows the ambiguity function for the Tangent NLFM waveform and Figure 2.13 shows the ISL, PSL and Lmm vs. Doppler curves. The peak and integrated sidelobes are significantly lower than for the LinFM cases but show a stronger Doppler sensitivity near zero velocity. The sidelobe levels indicate that NLFM spectrum shaping contributes significantly to the sidelobe

May 24, 1999 Page 12 of 52 Pulse Compression for Phased Array Weather Radar

Figure 2.12. Ambiguity function of TanFM waveform and Inv-5x filter. Peak sidelobes are 70 dB down at zero velocity. Compression ratio is 39.

m I 'D (n-J a. IL

0 10 20 30 40 50 Velocity (m/s) Figure 2.13. ISL, PSL and Lm vs. Doppler for TanFM (BT=39) with the MF, Inv-lx and Inv-5x compressionfilters. Data are oversampled by 2B. reduction. The mismatch loss is also significantly reduced over the LinFM case. Note that the scaling in Figure 2.13 is 0 to -IdB instead of 0 to -10 dB for the LinFM curves.

Although the non-linear FM waveforms appear to hold promise for low integrated sidelobe waveform design at mod- erate Doppler shifts, it seems extremely plausible that combined amplitude shaping and frequency sweep (phase) shaping of the waveform would give yet better performance. We did not investigate this aspect of waveform design, but combined amplitude and phase shaping might yield a matched filter design that maximizes the SNR while giving very low integrated sidelobes over larger Doppler shifts. At the very least, we expect reduced Doppler sensitivity for the inverse filter because spectral shaping is performed with a combination of phase and amplitude design whereas Doppler sensitivity depends only on the phase characteristics of the waveform. Vinagre, et al (1997) give an example of this combined waveform shaping technique for space-borne meteorological radars where the earth return is especially troublesome.

May 24, 1999 Page 13 of 52 Pulse Compression for Phased Array Weather Radar

2.4 Complementary codes

Complementary codes offer the unique advantage of a zero sidelobe response -- the range sidelobes are cancelled completely at zero Doppler shift. There are always two (biphase) codes in the pair. Assuming that both of these codes can be transmitted, received and matched filtered simultaneously, the summation of two independent responses will produce a return with no sidelobes (Wakasugi and Fukao 1985, Urkowitz and Bucci 1992b). This condition, however, can occur only if there is no Doppler shift and no cross coupling or leakage between the two signals.

In our study, we took several complementary code pairs of varying lengths and tested them for Doppler tolerance. In all, we tested codes of length 4, 10, 26, 32, 52, and 64. Golay (1961) illustrates the procedure to generate small codes and longer codes from the shorter ones. In general, the shorter codes had better Doppler performance. Two sets of length 10 complementary codes were tested. The CC1OA code, {0110101110, 0111111001}, whose ambiguity function is shown in Figure 2.14a, had ISL levels of about 5 dB less than the CCIOB code {1010111100, 1111011001} which is not shown.

Complementary Code 10- No Leakage

I-

Complementary Code 10- 20dB Leakage

Figure2.14. Ambiguity function of a CC-10 code pair using MF with a) no cross waveform leakage, and b) 20 db cross waveform leakage.

May 24, 1999 Page 14 of 52 Pulse Compression for Phased Array Weather Radar

One possible technique of transmitting the two codes simultaneously is using a dual polarization radar in which each of the complementary codes is assigned to orthogonal polarizations (Appendix E: Keeler et al 1993). This technique assures that both echoes have the same Rayleigh fluctuations, thereby rejecting the "common mode" fluctuation noise, because they are transmitted simultaneously and at the same frequency. It should be clear that if different frequencies were used for the two codes, the received echoes from them would be uncorrelated and sidelobe cancellation would be extremely poor.

However, crosspolar propagation and scattering effects generate a cross polar leakage that interferes with the sidelobe cancellation property of complementary codes. Figure 2.14b shows the degradation of the ambiguity function when a typical cross waveform leakage of -20 dB is allowed to contaminate the received waveform prior to compression filtering. Furthermore, using a single transmitter frequently leads to practical difficulties in transmitting two different signals simultaneously. Alternatively, the pulse codes could be spaced sequentially, but we have found that at X-band the decorrelation in time is large enough to cause incomplete sidelobe cancellation. Because of the extreme sensitivity of the sidelobe cancellation process, it is unlikely that even at S-band, sequentially generated complementary code pairs would be an acceptable waveform.

Mudukutore, et al (1996) perform S-band simulations for a polarimetric radar using this bi-phase complementary coded pulse compression scheme. They describe the extreme sensitivity of the ISL to decorrelation in the two codes due to instrumentation leakage and imperfectly correlated propagation and scattering effects of non-spherical hydrometeors. It is difficult to compensate for differential propagation and scattering effects in the two codes. There- fore, this technique needs additional development to determine whether it is a viable way to implement pulse compression on a polarimetric radar.

May 24, 1999 Page 15 of 52 Pulse Compression for Phased Array Weather Radar

3.0 Sample phase aspects of FM waveforms

3.1 Sample phase problems

Compression filtering in the past has typically been implemented with a matched filter (MF) to maximize the SNR of the filtered signal. As noted earlier, frequency modulated (FM) waveforms have different processing requirements than phase coded waveforms since the actual samples are determined by the precise range to the target (or the effective phase of the echo from the extended target) and the FM waveform has continuous, not discrete values.

3.2 Phase mismatch with FM waveforms

A digital sidelobe suppression (SLS) filter can be designed only for discrete sequences -- continuous waveforms must be sampled to be processed digitally. Therefore, we can generate a SLS filter only for a sampled continuous waveform. We can design an optimal compression filter for any specific set of samples, or a "template" waveform. Any of an infinite set of different sequences can result from sampling the same received continuous waveform at arbitrary time delays, or "sample phase", and render a filter designed for a specific sampled sequence non-optimal. We define the sample phase as the actual sample time relative to the template waveform sample times; thus, the sampling function has a sliding phase between 0-360 degrees relative to the template sampling phase from which the compression filter is designed.

The sample phase sensitivity of sidelobe suppression filtering is similar to the Doppler sensitivity. SLS filters are designed for a specific template waveform. When a Doppler shift occurs, the received waveform varies from the template waveform and degrades the sidelobe optimization. The same effect occurs from a shift in the sampling phase. With a zero-phase waveform, i.e. one which is not shifted from the template waveform, the filter will suppress sidelobes optimally. Radar targets can have any sample phase shift with uniform probability. This phase randomness degrades the compression filter response by bringing sidelobes up. Part of this effect is due to having N-1 points in the interpolation rather than N points (Labbit 1995). The N interpolated points do not correlate well with the zero shift template sequence and thus end up being suboptimal.

Although the techniques for developing sidelobe suppression filters has had significant attention, robust modeling of them using FM waveforms has not. Figure 3.1 shows the response of an SLS filter to a Linear FM chirp waveform. The inverse filter used is 5 times (Inv-5x) the length of the linear chirp sequence. The upper response shows the zero phase shift response. As expected, the Inv-5x compression filter produces very low sidelobes. The bottom response shows the composite response when the waveform is oversampled by 8 times and processed by the same filter. The sidelobes of the zero phase response represents the lower bound on the sidelobe envelope and gives an optimistic view of the compression filtering process. The lower figure, in essence, shows the range of possible filter responses

May 24, 1999 Page 16 of 52 Pulse Compression for Phased Array Weather Radar over multiple sampling phases which are unacceptably high for even small deviations from the desired zero sample phase.

3.3 Optimization over unknown sample phase

3.3.1 Filter design/modification

The inverse filter design technique we described in Section 2.3 optimizes the ISL response over a specific "set of samples or sample phase." We call this filter the "zero phase side lobe suppression filter" (ZPSLS). We propose a technique to minimize sidelobes over any arbitrary sampling phase of FM waveforms using a method originally proposed by Baden (1994) for Doppler tolerant design (Appendix I: Hwang and Keeler 1995). Generalizing Equation 6, we integrate the effects of all sample phase shifts into the minimizing matrix equations

R'(O)dO . h = q'(0)dJ . (EQ 7)

R'(0) is an autocorrelation matrix assuming that the template waveform has sample shift of 0. q'(0) is similarly assumed to be a sampled waveform having phase of 0. All phase shifts are uniformly weighted in the design of the filter. However, an SLS filter's strength comes from being the "inverse" for some input waveform. This new filter is now not an inverse of any one waveform, but an inverse over the set of all phase shifts and we call it the "all-phase sidelobe suppression filter" (APSLS). A variation of this approach would be to weight the integral with some positive weighting function w(8) over the phase shifts allowed as shown in Equation 8. However, we did not extend our investigation in this direction.

( R'()w()d0 . h = q'(0)w(0)d0 (EQ 8)

3.3.2 Performance measure

Several performance measures are available for measuring probabilistic distributions: PSL and ISL maximum values, root mean squared (rms) values, expected values, etc. We use the expected logarithmic ISL value over all phase shifts for our performance measure in comparing different compression filters. The expected value should give us a more realistic estimate of how the filter performs, since filter responses (and hence ISL's) will vary depending on the sample phase 0 which is assumed to be uniformly distributed.

3.4 Analysis

Figure 3.2 illustrates ISL responses of two filters generated from a 1 MHz, 20 psec complex linear FM chirp sampled at a Nyquist (IN) rate (defined as one bandwidth, or frequency sweep width -- 1 MHz in this example). The ZPSLS filter achieves a much lower minimum than the APSLS filter, but the APSLS filter maximum is lower than the ZPSLS filter maximum. Thus, the APSLS response is flatter over all possible sample phases, as desired. When the uniform sample-phase distribution of scatterers is applied to ISL distributions over phase shifts, we obtain the probability distributions for ISL values shown in Figure 3.3. The three pairs of responses were generated from the same template FM chirp waveform, but with a Nyquist (1N), twice Nyquist (2N) and quintuple Nyquist (5N) sampling rates. The average or expected ISL value for the APSLS filter is slightly lower than the expected ISL of the ZPSLS filter for the Nyquist (IN) case. However, for the oversampled (2N) and (5N) cases the ZPSLS response is slightly less than the APSLS response. Most previous research has considered only the ISL value under the zero-phase conditions. The zero-phase ISL is really the best case but is insufficient to compare performance of different filters under unknown received phase. Our algorithm is an attempt to lower the expected ISL rather than to lower only the zero-phase ISL. However, we have found that, frequently, minimizing the zero shift response also results in a lower expected ISL over all phases.

May 24, 1999 Page 17 of 52 Pulse Compression for Phased Array Weather Radar

5 . · · I I

I 0

-5

m .c -10 en

-15

-20 -

-25 . , I , , . -200 0 200 Sample-Phase offset in degrees Figure 3.2. ISL values for Inv-5x compression filters with sample-phase offset (shift) for zero-phase SLS filters and all-phase SLS filters at a Nyquist (IN) sampling rate. The expected ISL for the APSLS filter is -5.9 dB andfor the ZPSLSfilter is -5.8 dB.

We compared responses of ZPSLS and APSLS filters by using different sampling rates (IN, 2N, 3N, 4N, and 5N) and different filter lengths. However, filter length had very little effect on the results so only the expected ISL values for the Inverse-5x filter are given. For 1N sampling, the APSLS filters exhibited about 0.1 dB improvement in expected ISL over the ZPSLS filters. However, oversampling twice as fast (2N) improved the expected ISL of the APSLS and ZPSLS filters by about 14 and 15 dB, respectively. Basically, ZPSLS filters have better expected ISL values when oversampling (2N and greater) is used, a result also obtained by Labbit (1995). APSLS filtering does not always yield better expected ISL values but it appears to always decrease the maximum ISL at the extra sample phase shifts. If the measure of performance is lowest maximum ISL over all phases, then the APSLS method scores very well. It also has a narrower range of possible values than the ZPSLS. Figure 3.3 illustrates this difference in range of possible ISL values. For example, using only the Nyquist sample rate (IN, i.e., no oversampling), the range of ISLs for the APSLS is 0 to -13dB depending on the sample phase and the for the ZPSLS is +5 to -22 dB. The expected ISL value is -5.9 and -5.8 dB respectively. However, for a sample rate five times higher than

a 0 a-

-60 -40 -20 0 20 ISL (dB) Figure 3.3. Probability distribution of ISLs for both APSLS and ZPSLS Inv-5xfilters with IN, 2N, and 5N sampling rates. Expected AP/ZP ISLs are (-5.9/-5.8) for IN, (-20.6/-21.9) for 2N, and (-32.5/-33.3) dBfor SN sample rates.

May 24, 1999 Page 18 of 52 Pulse Compression for Phased Array Weather Radar the Nyquist rate (5N), the range of ISLs is -27 to -42 dB for the APSLS and -26 to -47 dB for the ZPSLS filter. The expected value of the ISLs are -32.5 and -33.3 respectively. FM pulse compression systems that cannot tolerate high ISLs should benefit from the APSLS compression filter technique since they have smaller maximum ISL values for the unknown sample phase.

This analysis shows how SLS filtering behaves under a more robust form of modeling. It is generally not desirable to measure performance only in the zero-phase sampling case, especially given that this best case has a very small probability of occurring. The All Phase SLS filtering using the standard sample rate addresses this problem, however the normal SLS filtering with oversampling appears to suppress the sidelobes even more effectively. This, however, is also dependent on the measure of performance used. We have looked only at uniform weighting schemes in the phase integration, but other weighting schemes could yield better results. This theoretical evaluation has not been validated with actual data, only the simulations. We suggest using at least two times the required Nyquist sample rate for the received waveform sampling and the compression filter implementation to maintain low sidelobes over the 0-360 degree range of sample phase. Although the given results apply only to Inverse-5x compression filters, our preliminary results show that the expected ISL values are insensitive to the length of the compression filter. Therefore, we suspect, but have not verified quantitatively, that the Inverse-2x or even the Inverse-lx compression filters will give nearly the same results as the Inverse-5x filters. A future separate report on sampling phase is being prepared which will give a more definitive result.

May 24, 1999 Page 19 of 52 Pulse Compression for Phased Array Weather Radar

4.0 Simulation and analysis for fluctuating targets

4.1 Simulation of fluctuating weather targets with pulse compression

Nearly all previous analyses of sidelobe suppression schemes have assumed hard, non-fluctuation targets. The simulation procedure described in this section differs from previous schemes in that we are modeling afluctuating weather target. This method extends earlier weather target work which assumes that the scatterers are frozen in space during the pulse propagation time. We allow the scatterers to move during the pulse propagation time. Therefore, this simulation procedure models weather systems more accurately, especially for longer pulses at higher transmit frequencies. Additional details of this modeling and validation work can be found in Mudukutore et al (1995a), Mudukutore et al (1995b), and most completely, in Mudukutore et al (1996) and Appendix K: Mudukutore, Chandrasekar and Keeler (1998).

We simulate returns from transmission of a bi-phase coded waveform through a fluctuating medium with properties similar to those of weather targets. The details of the simulation are skipped for brevity. However, to summarize, the simulation procedure yields time records of signals that satisfy the joint distribution properties in range-time and sample-time and is an extension of the procedure described in Chandrasekar et al (1986). The simulation procedure allows for specifying input profiles for reflectivity, velocity, and spectrum-width and the ability to vary the signal-to- noise ratio. The results shown in this section are based on the following assumptions: * Modulation waveform: Barker bi-phase code of length 13 (B-13) * Pulse repetition time = 1 ms * Wavelength X = 10 cm (The previous ambiguity functions were computed for 3.2 cm, X-band.) * Bandwidth B = 1.024 MHz * Transmit pulse-length T = 12.7 jIs. * White noise and fluctuations are added as specified by SNR and Cv.

The following nomenclature is used in this section for the different filters: * MF - Matched Filter of length 13 * IFxl, IFx5, IFx7 - Inverse filters of length 13, 65, 91 (same as Inv-lx, Inv-5x, and Inv-7x) * DT - Doppler tolerant implementation for IFx5.

4.2 Doppler tolerant design

The design procedure discussed in the previous section is optimum for targets with zero Doppler velocity. As the target velocity increases, the sidelobe suppression degrades (i.e., ISL increases), especially with longer filters. Urkowitz and Bucci (1992a) and Bucci and Urkowitz (1993) outline a Doppler tolerant technique which alleviates the sensitivity of the ISL on the target Doppler velocity. They suggest passing the complex received signal through a filter-bank to separate the signal into several Doppler bins. The signal still contains the Doppler phase shift across the pulse, i.e., along the range samples. Each Doppler filter output is then multiplied with a complex exponential term corresponding to its center frequency to compensate for the residual Doppler phase. Thus, all Doppler shifts are translated to small shifts near zero and the sidelobes remain low. Standard sidelobe suppression techniques are then applied to yield a low ISL on the processing channel for which the Doppler shift is smallest. The ambiguity functions in Appendix K: Mudukutore, Chandrasekar and Keeler (1998) show an abrupt rise in range sidelobes for the Doppler tolerant filter implementations at velocities near and beyond the Nyquist velocity, about 25 m/s in this case. These ambiguity functions were generated using the simulation parameters described above and the sidelobes are caused by incorrect Doppler compensation in the Doppler tolerant processing algorithm. Thus, it is important to prevent aliasing when this form of Doppler tolerant compression filtering is employed.

May 24,1999 Page 20 of 52 Pulse Compression for Phased Array Weather Radar

0 -I - I ,I -I - I I,

-10 ...... F ......

-20 ...... *x*......

-30

...... -I -40 cn .Fx . .

-50

..... -60 -. .I 7 ...... ;. ..., ...... /' . . ../I . . . -70

-nn -O U ...... 0 5 10 15 20 25 30 35 40 45 50 Velocity (m/s)

Figure 4.1. ISL asfunction ofDoppler shiftfor a point target using the B-13 bi-phase code and ME IF xl, x5, x7 compressionfilters including two Dop- pler Tolerant (DT) processing variants.

Figure. 4.1 plots the ISL as a function of Doppler velocity between -2Vnyq, and +2Vn for a hard point target. The different dashed patterns correspond to outputs of matched filter (MF), inverse filters of length 13 (IFxl), length 65 (IFx5), length 91 (IFx7) and two Doppler tolerant implementations IFx5-DT and IFx7-DT. The MF yields the highest

I$ I I

-1(0 ~...... I .. :......

-210 ......

-3(0O...... *.... IFx7, .... ,,'".,,,,,,,, IFx5 .,' -o -- 41 0 ...... : ...... /'. ! ...... C, .· . . .Fx.-D. -5(0

l I~~~~~~~~~~~~~~x5 ; -~~~~~~~~~~~~~~~~~~ -60 ...... ,......

-7'

_- _ _ _ -nu) 0 5 10 15 20 25 30 35 40 45 50 Velocity (m/s)

Figure 4.2. ISL vs. Doppler shiftforfluctuating reflectivity (ao =1 m/s, SNR =50 dB) "spike " 100 dB greaterthan any adjacent range sample. Waveform is B-13 code andfilters are the MF: IFxl, x5 andx7, and two DT variants.

May 24, 1999 Page 21 of 52 Pulse Compression for Phased Array Weather Radar

ISL response. As noted, the ISL for the inverse filters improve with increasing filter length. Note the gradual increase in the ISL with larger Doppler velocity for IFx5 and IFx7. The Doppler dependency is removed for the Doppler tolerant filters until the Nyquist velocity is approached. Near Nyquist and at greater (aliased) velocities the Doppler compensation scheme fails and the ISL levels rise sharply.

4.3 Evaluation of ISL

In this section, we demonstrate the application of our simulation procedure by analyzing two problems: 1) evaluation of ISL of various sidelobe suppression techniques for fluctuating weather targets, 2) evaluating the performance of sidelobe suppression techniques in the presence of artificial "spikes" or "notches" in reflectivity and velocity. The ISL for fluctuating weather targets can be evaluated by studying the returns from a profile where the mean-reflectivity level at one range bin is 100 dB above all the other range bins. The range sidelobes due to the echo spill-over from the strong target dominates the power levels in the adjacent range bins. Integrating the power levels in these sidelobes yields a measure of the ISL. The details of this procedure are skipped but the results are presented in Figure 4.2 which shows the ISL as a function of Doppler velocity for the fluctuating weather target having width of 1 m/s and 50 dB SNR. The performance of the Inverse 5x and 7x filters is similar to that shown in Figure 4.1for the hard point target. The ISL performance degrades at velocities near to Vnyq and higher. At these higher velocities, parts of the Doppler spectrum wrap around the Nyquist interval resulting in incorrect Doppler phase compensation in the Doppler tolerant mechanism. The situation gets worse with larger spectrum widths as described in more detail in Appendix K: Mudukutore, et al (1998).

A more interesting feature of the ISL performance in Figure 4.2 is that the minimum ISL values, even at low Doppler shift, are significantly higher than for the high SNR point target ISLs. This behavior suggests that the minimum ISL that can be obtained for any specific inverse filter is limited by the SNR. Apparently the noise creates a random phase and amplitude component to the well defined phase of the coded waveform. The cancellation of the sidelobes in the inverse filter is highly sensitive to these (likely) phase perturbations and cannot suppress the individual and integrated sidelobes properly. Longer inverse filters allow more noise to enter the output and cause more limitation on the longer filters. Figure 4.3 shows the ISL as a function of SNR between 0 and 80 dB of the 100 dB spike. The solid lines represent the outputs of various filters and the dashed lines correspond to their Doppler tolerant counterparts.

-10 ...... i...... i ...... MF......

-20 ......

-30

-40- o (I,

-0

: :i ___ i:______(: ___ _:__ i: ___ _:_ -60 ......

*...... -70

Ont 0 10 20 30 40 50 60 70 80 SNR (dB) Figure. 4.3. ISL vs. SNR for various compression filters. Dashed lines representcorresponding Doppler tolerant filters.

The SNR imposed limitation on the ISL is evident. We can therefore conclude that arbitrarily extending the filter lengths to get improved sidelobe performance is not possible, and is limited by the SNR of the echo.

We suspect the same effect occurs for wider spectrum width fluctuating waveforms. The random phase variations over the filter length do not permit the precise cancellation necessary to reduce the sidelobes to the full suppression if no fluctuations were present. Thus, with pulse compression waveforms the ISL performance of any inverse filter will

May 24, 1999 Page 22 of 52 Pulse Compression for Phased Array Weather Radar

111 ..... i .....j~I....

0 · . - ...... ,., _ # .. -10 ...... '....i '...'

-20 ! . ! · · · · : · .i : ......

30 ,·...... · ...... : . - m ..

| -40 . . . . . B B.~~~~~~~~~~~~~~~~~~~~~~~~~~~

IFxl -50 ,...... I . . . . IFx5 ...... :...... IFx '...... 7 -60

-70

-80 I 0 2 4 6 8 10 12 14 16 18 20 Range Index Figure 4.4. Range profile of reflected power from a 100 dB reflectivity notch of a hard target with zero velocity. The power in the notch represents the ISLfor the B-13 waveform and the selected compressionfilter. be limited by both the SNR and the spectrum width of the returned echo. In Appendix K: Mudukutore, et al (1998) analyzes this effect and gives quantitative results.

Another measure of the ISL for distributed targets can be obtained from an input profile with a constant reflectivity level at all ranges except for a deep reflectivity notch at one of the range bins. Computing the ratio of power level of the compressed signal at the notch (Pnotch) to the mean power level at other ranges (Pother), we have a direct measure of ISL for that waveform and compression filter. However, this procedure does not yield the ISL for hard targets due to the fact that for a fluctuating target, the contributions to the total power at a given range bin from adjacent range bins add up incoherently, as opposed to coherently for a hard target. The ratio Pnotch/Pother then give the ISL for the fluctuating target. Figure 4.4 shows the range profile of reflected power of the compressed signal for such an input profile with a 100 dB notch at the center range bin from hard target. Figure 4.5 shows a similar plot for a fluctuating

...... -10 ~~~~~~~~~~~~~~~~~~~.>~~~~~~~~~~~\ ...... ?

-20 ......

6-30 ...... i...... ,.. ;,...... 0-40 ...... II: i i I·...... MF -50 ...... ; ...... , ...... ,...... e...~.....;..1. ; ...... i...... I...... ~ · · ·...... ~~~~~~~~. i! . !...... ',...... ~u! i..,..i...... i...... i !~~-l-FxSi{.X... -60 .. ~1·, .·.....- · ···.·.·· · · ,I *-''-'''---''-'''''''-'--- · 1--''-----'----· :*-:----.· .. . . . 11 . . - · ...... , , . , -Fx ...... V.. -70 ......

-80 0 2 4 6 8 10 12 14 16 18 20 Range Index Figure 4.5. Range profile of reflectedpower from a 100 dB notch in afluctuating target having zero velocity and width of2.5 rms. Power in the notch representsISL for the B-13 waveform and the selectedfiltert

May 24, 1999 Page 23 of 52 Pulse Compression for Phased Array Weather Radar

target with v = 0, o v = 2.5 m/s and SNR = 80 dB at all ranges except the 100 dB notch. This comparison specifically brings out the power of our simulation algorithm showing the distinction between hard target responses and fluctuating distributed target responses.

As noted, an alternative technique to obtain the ISL for fluctuating targets is by using an input reflectivity profile with a 100 dB spike at the center range bin. The range sidelobes due to the echo spill-over from the spike dominate the power levels in the adjacent range bins. Integrating the power levels in the sidelobes yields a measure of the ISL, which is plotted in Figures 4.6, 4.7, and 4.8 as a function of mean Doppler velocity for (a) hard target, (b) fluctuating target with the Doppler spectrum width set at ov = 2.5 m/s, and (c) fluctuating target with ov = 5.0 m/s, respectively. The SNR for the spike was set at 80 dB. The different dashed patterns represent outputs of different filters.

-5-6

-..·..;...· ; ;...... ··.. · ·...... ·-...;...... -10

-15

-20

MM, C--25 IF*65 IFirS-DT -35 ·········· ····s...... · ,...... :...... ~...... :..,...... -40

-45 ...... ? ...... · '''' ...... ''''~· ·''' ·

-SO -25 -20 -15 -10 -5 0 5 10 15 20 26 Velocity (rms) Figure4.6. ISL vs. Doppler velocityfor a hard targetfor the B-13 waveform and the selectedfilter.

-5

-10 ...... ; ......

...... -15 . . i i i .... M -20 ...... _ ...... _ ...... ' ' ...... :...... S-25 ...... ;...... (nO9 :~~~~ :·" ~ : -30 . . . : : : I--,F~5: ...... IFx .D T .-.. . ~~ ~.~ ~ ~. ~ ~. .~ ~~~~~~~~~.. -35 ~.. .i

-40 _ _ x : : -45

-50 -25 -20 -15 -10 -5 0 5 10 15 20 25 Velocity (n's) Figure 4.7. ISL vs. Doppler velocityfor afluctuating target with cyv=2.5 m/s.

The MF and IFxl yield the highest ISL's and are not sensitive to Doppler shifts owing to their short lengths. The IFx5 yields lower ISL's (- -48 dB at zero Doppler) but the sidelobes are sensitive to Doppler shifts. This sensitivity is reduced for IFx5-DT. However, the performance of IFx5-DT degrades at higher mean velocities (i.e., approaching Vnyq). This is possibly due to the fact that at these higher velocities, parts of the Doppler spectrum wrap around the Nyquist-interval resulting in incorrect Doppler phase compensation. The situation gets worse with larger spectrum- widths. An interesting point to be noted here is that the best ISL that can be obtained by any sidelobe suppression fil-

May 24, 1999 Page 24 of 52 Pulse Compression for Phased Array Weather Radar

O I I I I I I I I

-5

-10 ,...... _ ._...... _, _ ._ ._ ._ ...... _ .. _ . . _ . _ ...... _ ... _. _._. . _ . . ... -15

-20 " MF -J-26 ...... F ...... c( -30 ...... :. . ... ,,--...... IP--T...... IFxS-DT -35

-40 ...... _... -45 .-...... -en -25 -20 -15 -10 -5 0 6 10 15 20 25 Velocity (rrvs) Figure 4.8. ISL vs. Doppler velocity for afluctuating targetwith ao=5.0 m/s. ter is limited by the SNR. This can be explained by the fact that as the coded dispersed waveform propagates through the distributed medium, the fluctuations of the signal occurring at a time-scale corresponding to the range sampling time (inverse bandwidth) are small and do not decorrelate the signal significantly from one range sampling instant to the next. However, the effect of the fluctuating noise is to add a random phase component to the underlying phase modulation of the transmit waveform, thereby degrading the performance of the compression filter on the received signal.

4.4 Reflectivity and velocity steps

Figures 4.9 and 4.10 shows the range profiles of the reflected power and the Doppler velocity at the output of MF, IFx5 and IFx7. The input profile (solid line) consists of gradients in reflectivity and velocity. The difference in reflected-power values on either side of the gradient is 50 dB and the velocity jumps from -10 m/s to +10 m/s. The

Sioan I1 I

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60 ...... ?

......

40 ...... " : I***: IFx5 ' . IFx7

30 , . . .l

v - : I I I 20 I I I I I I I 10 20 30 40 50 60 70 Range Index Figure 4.9. Range profiles of reflected power. The input has a 50 dB reflectivity step.

May 24, 1999 Page 25 of 52 Pulse Compression for Phased Array Weather Radar

15 I I I I· · -

10 i...... - .

5 ...... ~ ...... '"'i...... ! ....-t ..... : ...... i ',I

· ...... input ' :. -.i. . : i./ .i -5 .:'*,,,'A.. i . i :. . :...... i ...... 0 : ...... -- : Fx7 -10

_-IS . ... I -1- 0 10 20 30 40 50 60 70 80 Range Index Figure4.10. Range profiles of Doppler velocity. The input has a 20 m/s velocity step.

SNR at all ranges was set at 60 dB with crv at 2.5 m/s. It can be seen that the performance of the MF is clearly inferior to all the inverse filters. The IFx5 (best ISL -48 dB) does a mediocre job of estimating the Doppler velocity at the gradient. The IFx7 (best ISL ~ -70 dB) does a better job of estimating both the reflected power and Doppler velocity at the gradient. The best performance was given by the IFx7-DT in which case the reflectivity and velocity profiles at the filter output very closely followed the input profiles (not shown).

The simulations described in this section of the report were performed only for the Barker 13 bi-phase coded waveform. In other sections we have investigated FM waveforms. Extending the fluctuating target simulations to cover the FM waveforms, particularly those from the amplitude and frequency tapered NLFM class, would allow a quantitative evaluation of those promising candidate waveforms.

May 24, 1999 Page 26 of 52 Pulse Compression for Phased Array Weather Radar

5.0 Data acquisition and analysis

To validate the waveform analysis, we modified an existing NCAR X-band radar to acquire Barker 13 pulse compression data which were then compressed and analyzed off-line. Both a ground clutter spike case and a high reflectivity weather gradient were chosen for analysis.

5.1 ELDORA test bed radar description

NCAR's 3 cm test radar in Boulder, Colorado has been modified to transmit pulse compression waveforms and record the digitized complex video signal (the in-phase and quadrature samples) for each range gate. The radar uses a digital waveform generator, amplified by a 50 kw travelling wave tube (TWT) amplifier and fed to a 2.4 m diameter Casseg- rain polarization twist antenna with 1 degree beamwidth. The maximum pulse length is 10 isec. The receiver is a conventional low noise coherent system that uses a Digital IF processor to suppress processing distortion that typically exist in analog receivers (Randall 1991). The digitizer operates at a maximum rate of 20 MHz and 12 bits. The Digital IF allows complex video digitizing at 10 MHz rate and a maximum BT = 100. The data are then processed off-line using NCAR-enhanced PV-WAVE processing and plotting routines.

The system was configured to generate the B-13 bi-phase code for 600 nsec (90 m) range samples. The pulse length was therefore 7.8 ilsec (1.17 km). The Digital IF produced a sampled complex data stream at 1.67 MHz rate. Our goal was to point the radar at 1) a strong point ground clutter target, and 2) a convective weather having a strong reflectivity gradient at non-zero velocity and to evaluate the sidelobe suppression capability of the coded waveforms and inverse filter compression processing. Alternating bursts consisting of 32 simple single frequency 90 m rectangular pulses were followed by 32 Barker-13 coded 1170 m rectangular pulses. No clutter filtering was performed on any of the data shown here.

5.2 Data quality

NCAR has collected many cases of pulse compression data taken from the Foothills Lab site. In order to insure a high level of data quality, we have conducted droop tests on NCAR's high power amplifier (HPA). This allows scientists that use the data to understand how much distortion can be attributed to the system and how much can be attributed to theoretical processes (such as SLS pulse compression) or scatterers in the atmosphere. The data from the tests are available in Appendix B but will be summarized in this section.

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Figure5.1 Schematic of HPA test

May 24, 1999 Page 27 of 52 Pulse Compression for Phased Array Weather Radar

The object of our tests was to parameterize the amplitude and phase droop of the system. To this end, we obtained a Tektronic TDS544A Digital Oscilloscope capable of sampling several thousand points at a 1 Gigahertz rate. One observation that we made early on in our preliminary tests was that the different timing references for the scope and the data system caused a phase drift in the data. In order to minimize this effect, (which happened to be a very slow drift) we sent single-frequency pulses before and after our main test pulses. In this way, we bracketed all of the experimental data with pulses that would tell us how much the reference phase was moving. The HPA manufacturer, Applied Systems Engineering, had already provided us with oscilloscope photographs (see Appendix B) to illustrate droop tolerances at the time of its manufacture. So, in a way, we were also trying to compare results on a much higher scale of resolution. Figure 5.1 (same as Figure B-l) is a schematic of our experimental setup. Under usual circum- stances, the output of the HPA would go to the transmitter dish, but in order to simulate a nearby unmoving hard target, we simply looped the signal back to a IF mixer through an attenuator. The post mix signal then went straight to the oscilloscope. The mixer was locked with the signal generator so as only to measure the drift in the HPA. To do some added signal processing and display, we transferred the scope data to PV-Wave. In order to display the data, we filtered the data with a Gaussian-envelope low-pass filter (exp (-t / 800), 128 nanoseconds in width).

At first glance, the raw data shows that there is no measurable amplitude distortion and an extremely low phase droop (Figure B-17). However, our single-frequency pulse shots just before and after show a phase drift in the data. Averag- ing the phase drifts is the best that can be done without some kind of automated timing switch attached to the scope. However, we observed the within-pulse phase shift on the scope to be drifting quite slowly and obtained all the data within a span less than two minutes. Subtracting the interpolated drift from the raw data, Figure 5.2 (same as B-22) reveals an HPA phase droop of 0.5 degrees per microsecond at a still constant amplitude. Figure B-10 to B-22 in Appendix B show more detail. Knowing this, engineers and scientists using this data can model minor corrections in their processing schemes or choose to ignore the phase drift if the pulse length is thought to be relatively short.

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Figure 5.2 Phase plot of HPA's simple pulse phase response after drift correction.

Specifications of the test set-up in Figure 5.1 are: * HPA manufactured by Applied Systems Engineering Serial #2. * Tektronix TDS544A Digital Oscilloscope - 1 Gigasample/second maximum rate. * 7.8 psec pulse - Single frequency (simple) and Barker-13 (coded) bi-phase. * Gaussian Lo-Pass filter - exp (t2 / 800), 128 nanoseconds in width.

May 24, 1999 Page 28 of 52 Pulse Compression for Phased Array Weather Radar

5.3 Point clutter target

The data of interest for the evaluation is the relative backscattered power and the radial velocity for the simple and coded pulses. Figure 5.3 shows the data for the simple pulse plotted for 200 consecutive 90 m range gates from 5 km to 23 km with a strong ground clutter target located on a mountain peak about 16 km to the west. Note the 60 dB difference in the clutter spike at range gate 137 and the noise beyond.

Figure 5.4 shows the same data for the B-13 coded pulse and the Inv-5x filter Because the average power is 11 dB higher than for the simple pulse and the processing gain is normalized to the same peak power for both coded and simple pulses in our processing, the noise level beyond the point clutter is suppressed 11 dB. Thus, the SNR of the point clutter is about 71 dB. The velocity values are still zero mean but are more accurately determined because the SNR has been increased. The power and velocity estimates clearly show the range sidelobe effects with this extremely strong point clutter "flooding" into adjacent range gates.

Figure 5.3. Ground clutter data showing received power and velocityfor simple frequency 90 m pulse. Nyquist velocity (±0.5) corresponds to +8 m/s. Ranges greater than 150 are noise only.

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0. I - . .

4 0.

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...... a.... I...... I 0 50 100 150 Rwq*Cdo Figure 5.4. Ground clutter target using B-13 pulse and Inv-5x filter. Note 11 dB SNR increase and the sidelobe response. Simple and coded peak powers are equal.

May 24, 1999 Page 29 of 52 Pulse Compression for Phased Array Weather Radar

The non-moving clutter power in the first half of the return is the same for the simple and coded pulses. But the sidelobe responses at range gates 107 and 167 are 55 dB down and correspond to those shown 30 samples away from the main response in the lower panel of Figure 5.4. The sidelobes close to the main response that are 35-50 dB down are not predicted by the filter response. These are likely caused by "distortions" in the transmit waveform not compensated in the filter design.

5.4 Convective weather target

Ground clutter has zero velocity and the expected compression filter sidelobes are therefore lowest. Higher velocities that are sometimes associated with strong reflectivity gradients offer a more severe test of pulse compression waveforms on distributed weather targets. Using the simple 90 m pulse waveform Figure 5.5 shows a 49 dB reflectivity transition from a small thunderstorm cell 15 km to the south of the radar on June 2, 1994. Unless the ISL's are 50 db down, the strong echoes within the storm will contaminate the weak echo region outside the cell due to sidelobe leakage at non-zero velocities. Figure 5.6 shows the same storm cell using the B-13 bi-phase coded pulse and the Inv-5x

-1 - - - I

so 4J9dB. 49 dB

G % . 5 50 100 150 20 Rm Co

Figure5.5. High reflectivity gradient weather using simple 90 m pulse. Gradient is 50 dB over 2 km range at front and rear of cell. Nyquist velocity is ±8 m/s. Radial velocities within the cell are aliased and between 5-12 m/s.

I I

Figure5.6. Weather echo using B-13 waveform and the Inv-5x filter. There is discernible leakage of the sidelobe energy from the strong precipitationecho to outside the cell in both reflectivity and velocity.

May 24, 1999 Page 30 of 52 Pulse Compression for Phased Array Weather Radar compression filter. The SNR is increased from 49 dB to 60 dB but the tapered echo near the cell edge (formerly below the noise level) shows strong evidence of sidelobe leakage caused by a combination of the naturally occurring sidelobes at higher velocities and by the aliased velocities. Note that the velocities in the "shoulders" of the cell are similar to the velocities on the nearer portion of the cell. In Appendix J, Keeler et al (1995) show these precipitation echoes overlaid on the same plot.

Mudukutore, et al (1996) show similar convective data with similar results from testing a 5 bit Barker code on the S- band CHILL radar. Bucci, et al (1997) give a detailed analysis of another convective weather event to further validate the effective application of pulse compression for weather radar.

May 24, 1999 Page 31 of 52 Figure 5.7 Snapshot colordisplay of weather data taken from the ELDORA testbed radar.Data between 5-23 km at azimuth 332 degrees and elevation 18.5 degrees is detailed in Figure 5.8

May 11, 1999 Page 32 of 52 Pulse Compression for Phased Array Weather Radar

and the lower pair shows a B-13 bi-phase coded pulse and an Inv-5x compression filter. The snowband occupies the region between 11-16 km (gates labeled at 60-110). The received powers above the noise level match well (2 dB) except at the edges of the snowband having strong reflectivity gradients where sidelobe leakage increases the measured power. The velocity zero-crossing points in both illustrations match reasonably well except that the velocity values in the color image (Figure 5.7) appear to be scaled high by a factor of two and the signs are reversed.

w-i

80 . .. W-b-. . . . .

0 50 100 150 200

May 24, 1999 Page 33 of 52 Pulse Compression for Phased Array Weather Radar

The sidelobe response near the gradients is relatively smooth and its envelope is monotonically decreasing using the Inv-5x compression filter. If we had implemented a Doppler tolerant version of the compression filter, the sidelobes would have increased noticeably when the velocity approached or exceeded the Nyquist velocity of 8 m/s as noted in Section 4. The "noise floor" drops whenever the Barker pulse is applied to the same simple pulse target because the transmit power is increased by 11 dB, thus the SNR is increased by 11 dB.

Other beams from this data set show various combinations of pulse codes and processing techniques. When we add clutter filtering to the process, a barely perceivable improvement occurs in the power level of both the simple and Barker pulses. Velocities and power returns of the Barker pulse data appears to be more stable and less noisy.

Figure 5.9 shows the 32 point power spectrum of the weak echo at about 18 km (near the range gate labeled 150) which is outside the snowband for the B-13 coded pulse for the Inv-5x filter (solid curve) and for the Inv-3x filter (dashed curve). We expect that the Inv-3x filtered signal to be the more contaminated by sidelobe leakage from gates at other ranges. The spectra show how the velocity estimate shifts from near + 0.1 Nyquist velocity for the B-13 / Inv-5x pulse compression system to about - 0.15 Nyquist velocity for the Inv-3x compression with its greater sidelobe leakage. It may be possible to use the spectrum quantitatively to measure the ISL leakage from the strong echo within the cell having one velocity into the weak echo outside the cell having a different velocity but we have not investigated this aspect of the processing.

. . 0 I I. I I I I I -I. I I I I I I I, B-13 /Inv-3x ------B-13 /Inv-5x

-20 -

f *0

-40

I . , I , , . I . I . . . I -60-- 6 ...... I I I I I. . I I [ -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 Nyquist Velocity Figure 5.9. Spectra of range gate at 18 km showing contamination of storm velocity ingressing through the sidelobes of the coded pulse. Velocity estimate for the Inv-5x filtered pulse is near 0.1 (~ 0.8 m/s) but for the Inv-3xfil- tered pulse is near -0.15 (- -1.2 m/s) caused by greater sidelobe leakage.

May 24, 1999 Page 34 of 52 Pulse Compression for Phased Array Weather Radar

6.0 Phased array configurations

The second component of a rapidly scanning weather radar is a phased array antenna capable of step scanning during the dwell time. The antenna beam motion required to cover a hemispheric volume in less than a minute requires scan rates that are past the limit of mechanical feasibility. Furthermore, the scan modulation would cause an excessive width to the receive echoes that the velocity and width errors would be unacceptably large. Therefore, a stepped scan phased array antenna is the preferred system. Phased arrays that electronically scan in 2 dimensions consist of thousands of radiating and receiving elements and the element cost is a dominant factor in considering the feasibility of phased arrays. Alternatively, a 1D phased array requires of order 100 elements and cost is a less critical factor. An operational aviation radar needs may differ only slightly. Holloway and Keeler (1993) in Appendix F discuss a vari- ety of implementation issues.

The phased array antenna radar systems may be designed and built in several different ways. The antenna may be composed of 1) an antenna with fully active transmit - receive (TR) array modules capable of 2D (i.e., both azimuth and elevation) steering of pencil beams, 2) a single, high power transmitter feeding an electronically steered phased array, or 3) separate transmit and receive arrays each optimized for the specific function. Cost and complexity of the design for each application determine the best system.

For weather measurements we require high resolution (space and time) most likely derived from a narrow pencil beam, stepped electronic scan phased array radar system, possibly incorporating pulse compression. For accurate aircraft location and tracking, this same capability provides a functional backup to the standard secondary surveillance radar functions. In both cases, there appear to be three strong options for implementing such a radar. The first two options with variations have been discussed at length during the TASS program. The third option offers a conceptual design that builds on existing fan beam technology by using an affordable, low power receive array to give the high spatial resolution measurements.

1. Fixedfacepencil beam 2D arrays

A multiple face fixed system may be used to cover the desired volume. Three to five faces are adequate to cover a hemisphere with likely narrow beamwidths and aallowable scan geometries. Since the arrays are fixed, they must phase steer in both azimuth and elevation. Thus, a 2D e-scan system using thousands of elements per face is required for a typical narrow pencil beam system. If the elements are capable of both transmitting and receiving, the need and cost of handling high power limits the precision available to the phase shifters. This option requires duplication of each face to the degree that the total system cost rapidly becomes prohibitive for most applications. 2. Rotating pencil beam ID arrays

A much less costly system can be designed if a single array can be rotated for hemispheric coverage assuming that the space and time resolution can be met. Only a single array is necessary since the beams are mechanically steered to all azimuths and only one dimensional elevation phase steering is required. Consequently, only hundreds (not thousands) of high power phase shifter and radiating elements are necessary. Thus, the ID e-scan system is affordable for a much wider range of applications than the multiple fixed face 2D e-scan system. We assume that full elevation coverage can be met by tilting the array(s) up to cover higher elevations outside the e-scan coverage. In Appendix D, Keeler and Frush (1983b) describe system requirements and scan techniques for a rotating ID system that meets many weather applications, and by inference, may meet many aircraft surveillance backup needs too. Extending this concept, we may use two independent antennas operating back to back on the same pedestal that allows doubling the time resolution.

3. Rotating fan & multi-pencil beam ID array

A potentially even more affordable system consists, first, of a rotating vertical fan beam transmitter, formed by very few high power, fixed phase transmitting elements, or by a standard reflector antenna such as the ASR-9. Second, a receive-only phased array forms multiple simultaneous pencil beams in elevation using digital beam forming technology. Because the array is not used for transmitting, we may design the array using low power, high precision phase shifter and achieve extremely low sidelobes. The isolation between the combined fan beam transmitter and multiple low sidelobe receive beams may be as high as isolation using the conventional transmit and receive pencil beams with their attendant 2-way sidelobe isolation between adjacent beams.

May 24, 1999 Page 35 of 52 Pulse Compression for Phased Array Weather Radar

We may consider a system built upon the rotating ASR-9 fan beam aircraft surveillance radar concept. Let the high power fan beams provide the transmit energy at low elevations and add a separate lower power transmitter with a fan beam covering the higher elevations. The required range coverage at high elevation is much less than at low elevations. Separate receive only arrays would cover the low and high elevations separately.

Each receive array would simultaneously form 30-50 vertically stacked multiple beams using digital beam forming techniques at the IF stage of each of about 100 receive element With proper design, the sidelobes of the receive array could reach the 40-50 dB level one-way. The lower stack would provide 1 degree beams while the upper stack could provide 2-3 degree beams and provide the same spatial resolution at the shorter ranges of interest. The entire system would rotate at 5-6 rpm, thereby providing reasonably long dwell times for ground clutter processing. If faster updates were required for aircraft tracking, a second system might be added for back to back coverage and effective 10-12 rpm coverage rate.

Separation of the high power transmit antenna and the digital beam forming, low power receive array avoids the need for higher power (i.e., expensive) TR modules. Relatively long dwell times add clutter rejection and receive sensitivity. Pulse compression techniques can be applied as necessary to achieve range resolution, high average transmit power (radar sensitivity) and increasing the number of independent samples for more accurate weather parameter estimates.

This fan beam transmit / pencil beam receive array concept needs much more thought and development, but in the future it may provide an affordable alternative to the first two system options.

May 24, 1999 Page 36 of 52 Pulse Compression for Phased Array Weather Radar

7.0 Conclusions

Pulse compression is one technique of obtaining the short dwell time necessary to make high space and time resolution weather radar measurements. Range time sidelobes contaminate weather parameter measurements in exactly the same way as antenna sidelobes. We desire to minimize both types of sidelobe responses. We have shown convincing evidence for both point clutter and moving weather targets that pulse compressed waveforms produce the integrated sidelobe leakage predicted by the ambiguity functions and the simulations.

We verified that an inverse filter yields much lower sidelobes than a matched filter for all the waveforms we studied. An inverse compression filter design not only minimizes the integrated sidelobes (which is important for weather applications) but also reduces the peak sidelobes (which is important for point target detection). Thus, the same pulse waveform should be acceptable for both distributed weather targets as well as aircraft point targets. Furthermore, we found that the integrated sidelobe suppression is limited by the signal to noise ratio of the received echo. Thus, only high SNR signals will benefit from longer inverse compression filters.

Extreme Doppler sensitivity even at low weather velocities, even for 10 cm radars, shows the need for Doppler tolerant designs to maintain low integrated range sidelobes. The principal cost of Doppler tolerant processing is additional computational power. Urkowitz and Bucci (1992a) have suggested a robust, processing intensive scheme that will maintain low integrated sidelobes for weather of all velocities. However, this processing scheme cannot properly compensate Doppler when the velocities are aliased and the ISL values rise steeply near the Nyquist velocity.

Our study shows a strong correlation between waveforms having good autocorrelation functions and effective sidelobe suppression with inverse compression filters to an acceptable level for weather radar applications. An inverse filter five or more times longer than the waveform seems adequate for most expected weather gradients. Based on our limited tests the tangent NLFM waveform with an Inv-5x filter gives the best response from our suite of waveforms. Other NLFM waveforms should perform equally well or better. Although we did not study this aspect of NLFM waveform design, it appears that if both frequency and amplitude shaping are employed, additional Doppler tolerance may be available with the same or better low integrated sidelobes. The extended range response of long waveforms and compression filters requires supplemental pulsing techniques for short range coverage (those ranges during which the pulse is being transmitted) that we have not addressed here.

Continuous phase change FM waveforms require oversampling to maintain low sidelobes because the sample phase uncertainty cannot yield the optimum compression filter. Therefore, the processing requirements are generally much higher than with any of the phase codes. The compression sidelobe sensitivity to sampling phase relative to the start of the waveform for FM waveforms is a difficult problem. We have found that by oversampling the waveform and optimizing the oversampled filter, that the sidelobes can be kept to an acceptable level.

Pulse compression can be used with a polarimetric radar for increasing the scan rates by performing range averaging instead of time averaging. If isolation were sufficient between the orthogonal polarimetric channels and scattering depolarization were extremely low, then it might be advantageous to transmit complementary codes on the two polarimetric channels. Practically, we think there is little to gain using this complementary coding technique with polarimetric radar. We did not explicitly study application of pulse compression to bistatic radar system waveforms but all the same advantages and cautions apply to bistatic systems as to the standard monostatic radar systems.

8.0 Acknowledgments

This research is supported by the FAA/TASS Program Office and the US Air Force Office of Scientific Research, NSF (ATM-9413453). We wish to thank Jim Rogers, FAA Terminal Area Surveillance Systems Program Manager, and his program office staff (Lew Buckler, Cam Tidwell, Angela Harris, and Mark Keehan) for their support in the waveform analysis and evaluation effort described in this report, the engineering staff at Lockheed Martin Govern- ment Electronic Systems in Moorestown, NJ (Harry Urkowitz, Nick Bucci, and Jerry Nespor) as well as the LM/GE Corporate Research and Development Center in Schenectady, NY (Jeff Ashe) for technical discussions, the NCAR Remote Sensing Facility technical staff (Eric Loew, Chuck Frush, Mitch Randall, Joe VanAndel, Craig Walther, Joe Vinson, and Jack Good) for the ELDORA testbed radar modifications, operation, and data acquisition, and the admin- istrative staff (Ann-Elizabeth Nash and Jennifer Delaurant) for assistance in preparing this document.

May 24, 1999 Page 37 of 52 Pulse Compression for Phased Array Weather Radar

9.0 References

Ackroyd, M.H. and F. Ghani, 1973: "Optimum mismatched filters for sidelobe suppression," IEEE Trans. Aerospace Electronics, Vol. AES-9, pp 214-218.

Ashe, J.M., R.L. Nevin, D.J. Murrow, H. Urkowitz, N.J. Bucci and J.D. Nespor, 1994: "Range sidelobe suppression of expanded/compressed pulses with droop," IEEE Nat'l Radar Conf., Atlanta, GA, pp 116-122.

Baden, J. M. 1989: "Pulse compression Doppler sensitivity reduction study," Georgia Institute of Technology, Mas- ters Thesis, Atlanta, GA.

Battan, L.J., 1973: Radar Observation of the Atmosphere, Chicago Press, Chicago, IL.

Bucci, N.J., and H. Urkowitz, 1993: 'Testing of Doppler tolerant range sidelobe suppression in pulse compression meteorological radar," IEEE Nat'l Radar Conf., Boston, MA pp 206-211.

Bucci, N.J., H.S. Owen, K.A. Woodward and C.M. Hawes, 1997: "Validation of pulse compression techniques for meteorological functions," IEEE Trans. Geoscience and Remote Sensing. Vol. GE-35, pp 507-523.

Buckler, L.M., 1997: "Use of phased array radars to detect and predict hazardous weather," 28th Conf. on Radar Meteorology, AMS, Austin, TX, pp 262-263.

Carbone, R.E., M.J. Carpenter and C.D. Burghart, 1985: "Doppler radar sampling limitations in convective storms," J. Atmos. and Ocean. Tech., Vol. 2, pp 357-361.

Chandrasekar, V., V.N. Bringi and P.J. Brockwell, 1986: "Statistical properties of dual-polarized radar signals," Proc., 23rd Conf. on Radar Meteorology, AMS, Snowmass, CO, pp 193-196.

Cohen, M.N., 1987: "Pulse compression in radar systems," Chap. 15 in J.L. Eaves and E.K.Reedy (Eds.), Principles of Modem Radar. Von Nostrand Reinhold Company Inc., New York.

Cohen, M.N. and P.E. Cohen, 1988: "Near perfect bi-phase codes and optimal filtering of their range sidelobes," Proc. 18th European Microwave Conf., Stockholm, Sweden, 6 pp.

Cook, C.E. and M. Bemfeld, 1967: Radar Signals -- Introduction to Theorv and Application, Artech House, Boston.

Doviak, R.J. and D.S. Zrnic, 1993: Doppler Radar and Weather Observations, Second Ed., Academic Press, San Diego.

Farnett, E.C. and G.H. Stevens, 1990: "Pulse compression radar," Chap.10 in M.I. Skolnik (Ed.), Radar Handbook., McGraw-Hill, New York.

Fetter, R.W., 1970: "Radar weather performance enhanced by pulse compression;" 14th Conf. Radar Meteorology, AMS, Tucson, AZ, pp 413-418.

Gray, R.W, and D.T. Farley, 1973: "Theory of incoherent scatter measurements using compressed pulses,"' Radio Sci- ence Vol. 8, pp 123-131.

Golay, M.J.E., 1961: "Complementary series," IRE Trans. on Information Theory Vol. IT-17, pp 82-87.

Hwang, C.A. and R.J. Keeler, 1995: "Sample phase aspects of FM pulse compression waveforms," Proc. Int'l Geo- science and Remote Sensing Symposium (IGARSS 95), Florence, Italy, pp 2126-2128.

Holloway, C.L. and R.J. Keeler, 1993: "Rapid scan Doppler radar: the antenna issues," 26th Conf. on Radar Meteorol- ogy, AMS, Norman, OK, pp 393-395.

Keeler, R.J. and C.L. Frush, 1983a: "Coherent wideband processing of distributed radar targets," Proc. Int'l Geo- science and Remote Sensing Symposium (IGARSS-83) San Francisco, CA, pp 3.1-3.5.

May 24, 1999 Page 38 of 52 Pulse Compression for Phased Array Weather Radar

Keeler, R.J. and C.L. Frush, 1983b: "Rapid scan Doppler radar development considerations, Part II: Technology Assessment" 21st Conf. on Radar Meteorology, AMS, Edmonton, Canada, pp 284-290.

Keeler, R.J., C.A. Hwang, V. Chandra and R. Xiao, 1993: "Polarization pulse compression for weather radar," 26t Conf. on Radar Meteorology, AMS, Norman OK, pp 255-257.

Keeler, R.J., 1994: "Pulse compression waveform analysis for weather radar", COST-75 Int'l Seminar on Advanced Weather Radar Systems, Brussels, Belgium, pp 603-614.

Keeler, R.J. and C. A. Hwang, 1995: "Pulse compression for weather radar" IEEE Int'l Radar Conf., Washington, DC, pp 529-535.

Keeler, R.J., C.A. Hwang and E. Loew, 1995: "Pulse compression weather radar waveforms", 27th Conf. on Radar Meteorology, AMS, Vail, CO, pp 767-769.

Keeler, R.J., C. A. Hwang and E. Loew, 1999: "A pulse compression phased array weather radar," J.of Atmos. and Oceanic Tech. to be submitted.

Keeler, R.J. and R.E. Passarelli, 1990: "Signal processing for atmospheric radars," Chap. 20 in Atlas (Ed.), Radar in Meteorology. AMS, Boston, pp 199-229.

Key, E.L., E.N. Fowle and RD. Haggarty, 1959: "A method of sidelobe suppression in phase-coded pulse compression systems," M.I.T Lincoln Lab., Lexington, Tech. Rep. 209.

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Mudukutore, A.S., V. Chandrasekar and R.J. Keeler, 1995b: "Range sidelobe suppression for weather radars with pulse compression: Simulation and evaluation," 27 th Conf. Radar Meteorology, AMS, Vail, CO, pp 763-766.

Mudukutore, A.S., V. Chandrasekar and R.J. Keeler, 1996: "Pulse compression for weather radars", NCAR Tech. Note TN-434 (Reprint of ASM Ph.D. dissertation), Boulder, CO, 90 pp.

Mudukutore, A.S., V. Chandrasekar and R.J. Keeler, 1998: "Pulse compression for weather radars", EEE Trans. Geoscience and Remote Sensing, Vol. GE-36, pp 125-142. Randall, M., 1991: "Digital IF processor for rectangular pulse radar applications," 2 5th Conf. on Radar Meteorology, AMS, Paris, France, pp 871-874.

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May 24, 1999 Page 39 of 52 Pulse Compression for Phased Array Weather Radar

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Urkowitz, H. and N.J. Bucci, 1992b: "Using complementary sequences with Doppler tolerance for radar sidelobe suppression in meteorological radar," Proc. Int'l Geoscience and Remote Sensing Symposium (IGARSS-92), Hous- ton, TX, Vol. 1, 2 pp.

Vinagre, L., H.D. Griffiths and K. Milne, 1997: "Asymmetric pulse compression waveform design for space-borne meteorological radars," Proc. IEE Radar Conference (Radar-97), Edinburgh, Scotland, pp 370-373.

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Wolfson, M., 1993: "Quantifying airport terminal weather surveillance requirements," 26th Conf. on Radar Meteorol- ogy, AMS, Norman, OK, pp 47-49.

Woodward, P.M., 1953: Probability and Information Theory with Applications to Radar, Permagon Press.

May 24, 1999 Page 40 of 52 Pulse Compression for Phased Array Weather Radar

Appendix A: Ambiguity functions

The ambiguity function is an easy way to illustrate the effects of Doppler shift to the mainlobe and sidelobes. The ambiguity function is a 3- dimensional graph with range-time on the x-axis, Doppler velocity on the y-axis and power level on the z-axis. The front of the graph represents the zero Doppler return and behind it are returns with increasing amounts of Doppler shift. This appendix contains many ambiguity functions not referenced in the main text, where only the more interesting and pertinent results were discussed. Here are the ambiguity functions for all the waveforms considered under the effects of matched and inverse filters of length Ix, 2x, 3x, and 5x.

The figure axes are labelled following the same convention as in the main text:

1) the range-time axis (x, to the right) is labeled in units of range-time samples except 0 is the left-most (not central) sample,

2) the Doppler velocity axis (y, to the left and back) is labeled in units of 5 m/s so that the full range is 0-50 m/s at X- band, and

3) the power axis (z, vertical) is measured in power expressed in dB normalized to the peak response. The coding scheme for the figures is:

The first segment defines the receiver compression filter: RM is Receiver Matched filter, R1 is the Inverse lx filter, R3 is the Inverse 3x filter and R5 is the Inverse 5x filter.

The second segment defines the transmit pulse coding: B13 is the Barker 13 bi-phase code, NP14 is the "Near Per- fect" length 14 bi-phase code (Cohen and Cohen 1988), PN15 is the Pseudo-Noise length 15 bi-phase code, LFM13 is the Linear FM code with time-bandwidth product BT = 13, and TFM13 is the Tangent non-linear FM code with time-bandwidth product BT = 13.

Thus, the final example, Figure A-60 labeled R5TFM63, is the ambiguity function for the Tangent FM non-linear FM waveform with BT = 63 and the Inverse 5x receiver compression filter.

May 24, 1999 Page 41 of 52 Hr Cit

-20

-40

-60..

Fig. A-2. Ambiguity Function for a Barker 13 Code with an Inverse lx compression filter (RIB 13). .-60

Fig. A-3. Ambiguity Function for a Barker 13 Code with an Inverse 2x compression filter (R2B 13). o D i 3

Fig. A-4. Ambiguity Function for a Barker 13 Code with an Inverse 3x compression filter (R3B 13). fs5e t )

-40

Fig. A-5. Ambiguity Function for a Barker 13 Code with an Inverse 5x compression filter (R5B13). pf mrJ Itf

-40

-80

Fig. A-6. Ambiguity Function for a Near-Perfect 14 Code with a Matched filter (RMNP14). g,1 N IL.

Fig. A-7. Ambiguity Function for a Near-Perfect 14 Code with an Inverse Ix compression filter (R1NP14). 2 tJ F1-ZI

-40

-60

Fig. A-8. Ambiguity Function for a Near-Perfect 14 Code with an Inverse 2x compression filter (R2NP14). (( I7 IIL

Fig. A-9. Ambiguity Function for a Near-Perfect 14 Code with an Inverse 3x compression filter (R3NP14). Rs JPl9

-80

Fig. A-10. Ambiguity Function for a Near-Perfect 14 Code with an Inverse 5x compression filter (RSNP14). .Vi' r2zl

Fig. A-l 1. Ambiguity Function for a Near-Perfect 28 Code with a Matched lx filter (RMNP28). r I f'J Qi

-20

-40

Fig. A-12. Ambiguity Function for a Near-Perfect 28 Code with an Inverse lx compression filter (R1NP28). "\ IJ 0 2-

Fig. A-13. Ambiguity Function for a Near-Perfect 28 Code with an Inverse 2x compression filter (R2NP28). _40

Fig. A-14. Ambiguity Function for a Near-Perfect 28 Code with an Inverse 3x compression filter (R3NP28). C, - JV

Fig. A- 15. Ambiguity Function for a Near-Perfect 28 Code with an Inverse 5x compression filter (RSNP28). (KczBrp ~ N t

Fig. A-16. Ambiguity Function for a Pseudo Noise 15 Code with a Matched Ix filter (RMPN15). Rl FMwt5

Fig. A-17. Ambiguity Function for a Pseudo Noise 15 Code with an Inverse Ix compression filter (R1PN15). -20

Fig. A-18. Ambiguity Function for a Pseudo Noise 15 Code with an Inverse 2x compression filter (R2PN15). r\"uf j !§

Fig. A-19. Ambiguity Function for a Pseudo Noise 15 Code with an Inverse 3x compression filter (R3PN15). ,5 CSJIV

Fig. A-20. Ambiguity Function for a Pseudo Noise 15 Code with an Inverse 5x compression filter (R5PN15). -8o0

Fig. A-21. Ambiguity Function for a Pseudo Noise 31 Code with a Matched lx filter (RMPN31). Fig. A-22. Ambiguity Function for a Pseudo Noise 31 Code with an Inverse lx compression filter (RiPN31). rj- V I J ) I

Fig. A-23. Ambiguity Function for a Pseudo Noise 31 Code with an Inverse 2x compression filter (R2PN31). Kf 1 I 9

Fig. A-24. Ambiguity Function for a Pseudo Noise 31 Code with an Inverse 3x compression filter (R3PN31). (KS~I.ij-)I '

Fig. A-25. Ambiguity Function for a Pseudo Noise 31 Code with an Inverse 5x compression filter (R5PN31). K M v'tJ b5

Fig. A-26. Ambiguity Function for a Pseudo Noise 63 Code with a Matched Ix filter (RMPN63). Ri PrrJW

Fig. A-27. Ambiguity Function for a Pseudo Noise 63 Code with an Inverse lx compression filter (R1PN63). K,- PIQJ CL7

Fig. A-28. Ambiguity Function for a Pseudo Noise 63 Code with an Inverse 2x compression filter (R2PN63). Fig. A-29. Ambiguity Function for a Pseudo Noise 63 Code with an Inverse 3x compression filter (R3PN63). gs5rhjLf

Fig. A-30. Ambiguity Function for a Pseudo Noise 63 Code with an Inverse 5x compression filter (R55PN63). RML> LF M I3

Fig. A-31. Ambiguity Function for a Linear FM 13 Signal with a Matched lx filter (RMLFM13). RI LFM 1\3

-60

Fig. A-32. Ambiguity Function for a Linear FM 13 Signal with an Inverse lx compression filter (RILFM13). -60I

Fig. A-33. Ambiguity Function for a Linear FM 13 Signal with an Inverse 2x compression filter (R2LFM13). N} LF I-H\ '

- I

Fig. A-34. Ambiguity Function for a Linear FM 13 Signal with an Inverse 3x compression filter (R3LFM13). RS L F 15

-40

Fig. A-35. Ambiguity Function for a Linear FM 13 Signal with an Inverse 5x compression filter (R5LFM13). 'lKMLF . I1

-20o

Fig. A-36. Ambiguity Function for a Linear FM 31 Signal with a Matched lx filter (RMLFM31). t\I LcH'tIj

--1

Fig. A-37. Ambiguity Function for a Linear FM 31 Signal with an Inverse lx compression filter (R1LFM31). kLLr /,' I

-40

-60

Fig. A-38. Ambiguity Function for a Linear FM 31 Signal with an Inverse 2x compression filter (R2LFM31). l3 LI-/vi:'?I

Fig. A-39. Ambiguity Function for a Linear FM 31 Signal with an Inverse 3x compression filter (R3LFM31). 15 - t-[t .1 I

-80o

Fig. A-40. Ambiguity Function for a Linear FM 31 Signal with an Inverse 5x compression filter (R5LFM31). RMl L FPl(c '

- 1

Fig. A-41. Ambiguity Function for a Linear FM 63 Signal with a Matched lx filter (RMLFM63). Nt LLI-/'I^I6

-20

Fig. A-42. Ambiguity Function for a Linear FM 63 Signal with an Inverse Ix compression filter (R1LFM63). t\ L L I- /' !' ?

FIS A

Fig. A-43. Ambiguity Function for a Linear FM 63 Signal with an Inverse 2x compression filter (R2LFM63). K3LffM/ 6

Fig. A-44. Ambiguity Function for a Linear FM 63 Signal with an Inverse 3x compression filter (R3LFM63). IlS U[ 11 U>

Fig. A-45. Ambiguity Function for a Linear FM 63 Signal with an Inverse 5x compression filter (R5LFM63). 0,

Fig. A-46. Ambiguity Function for a Tangent-Based Non-linear FM 13 Signal with a Matched filter (RMTFM 13). ? TFe'"

q."Z

Fig. A-47. Ambiguity Function for a Tangent-Based Non-linear FM 13 Signal with an Inverse lx compression filter (R1TFM13). "F TFM1

-60

-.80

Fig. A-48. Ambiguity Function for a Tangent-Based Non-linear FM 13 Signal with an Inverse 2x compression filter (R2TFM13). \ 1 1 3

-20

Fig. A-49. Ambiguity Function for a Tangent-Based Non-linear FM 13 Signal with an Inverse 3x compression filter (R3TFM13)). R5TF" '3

Fig. A-50. Ambiguity Function for a Tangent-Based Non-linear FM 13 Signal with an Inverse 5x compression filter (R5TFM13). ( Mr-T 5 /

bad,

---- D'-

Fig. A-5 1. Ambiguity Function for a Tangent-Based Non-linear FM 31 Signal with a Matched filter (RMTFM31). lrFA1/3 1

-20

Fig. A-52. Ambiguity Function for a Tangent-Based Non-linear FM 31 Signal with an Inverse lx compression filter (R1TFM31). Z TFr 51

Fig. A-53. Ambiguity Function for a Tangent-Based Non-linear FM 31 Signal with an Inverse 2x compression filter (R2TFM3 1). R3 TFM 51

Fig. A-54. Ambiguity Function for a Tangent-Based Non-linear FM 31 Signal with an Inverse 3x compression filter (R3TFM31). R5TF me I

Fig. A-55. Ambiguity Function for a Tangent-Based Non-linear FM 31 Signal with an Inverse 5x compression filter (R5TFM31). RI T FM 3

-80

Fig. A-56. Ambiguity Function for a Tangent-Based Non-linear FM 63 Signal with a Matched filter (RMTFM63). K I i- VI )

-240

-40

4ZI.~~~~ft

Fig. A-57. Ambiguity Function for a Tangent-Based Non-linear FM 63 Signal with an Inverse lx compression filter (R1TFM63). .T,I F G)

-80o

Fig. A-58. Ambiguity Function for a Tangent-Based Non-linear FM 63 Signal with an Inverse 2x compression filter (R2TFM63). \Tr-'Fmi t3?

,I 1Z. _^ ^ ^ = V

?Ff2

maZI Fig. A-59. Ambiguity Function for a Tangent-Based Non-linear FM 63 Signal with an Inverse 3x compression filter (R3TFM63). I T M4 b 3

Fig. A-60. Ambiguity Function for a Tangent-Based Non-linear FM 63 Signal with an Inverse 5x compression filter (R5TFM63). Pulse Compression for Phased Array Weather Radar

Appendix B: Characterization of the NCAR high power amplifier

The TWT high power amplifier used in these test was built by Applied Systems Engineering (SN 2) for the NCAR Eldora airborne radar system. It has been replaced with a newer model and is available for laboratory testing as we have done here.

Our tests on the High Power Amplifier #2 involved bypassing the antenna and rerouting the signal through a 40 dB attenuator to a digital oscilloscope (Figure B.1). The manufacturer had provided us with photographs illustrating the HPA's droop characteristics at the time of the HPA testing (Figure B.2). These gave us a general idea of what to expect. For the test, we sent 7.8 us single-frequency simple (Figures B.3) and phased-coded (Figure B.4) pulses. For displaying purposes, we processed the data through a lo-pass FIR filter with a Gaussian envelope (Figures B.5, B.6, B.7). This allowed us to look at the amplitude. Before and after the entire experiment, which lasted only a few minutes, we took reference pulses to measure sample drift misalignment (Figure B.8, B.9, and B.10, and B.18, B.19, and B.20). Inside the window between reference pulses, we transmitted Barker-13 phase-coded (Figures B.11, B.12, B.13, and B.14) and simple pulses (Figures B.15, B.16, B.17). The slow phase drift difference between the sampling oscilloscope and the waveform generator influences the phase droop data taken. However, subtracting the average of the reference frames should have cancelled out most of this effect (Figures B.21 and B.22).

May 11,.1999 Page 42 of 52 TO ROOF ANTENNA

12 FEET COAX

EXCITER AND RECEIVER 40 dB

MDC171 HP8672A SIGNAL GENERATOR

DATA DIGITAL SYSTEM SCOPE TECHTRONICS TDS544A

Fig. B-1. Block Diagram of the Measurement System 10 MV/Division

2, c Microseconds/Division

Detected RF: Pulse Width /0 . se ., PRF // i:iz

5 De-rens/D-v- i½r

2r,0 Microsecond/Division

Phase Detector Pulse Width /O usec., PRF /O00 Hz

Fig. B-2. Phase and Amplitude Droop as Measured by the HPA Manufacturer 12(

10C

8C m 60

0 0 2000 4000 6000 8000 1 0000 nano seconds

C) '- 56 () -0

52 0 2000 4000 6000 8000 10000 nano seconds

Fig. B-3. Amplitude of a 7.8 Single Frequency Pulse (Top), Phase Plot Across the Same Pulse (Bottom) te.lb 13a.wfm filtered 140

120

100

80 m T5 60

0 0 2000 4000 6000 8000 10000 nanoseconds

200

L. 0 U) ID

-200 0 2000 4000 6000 8000 10000 nanoseconds Fig. B-4. Amplitude of a 7.8 us Thirteen Bit Barker Encoded Pulse (Top), Phase Plot Across the Same Pulse (Bottom) 3.(

2.6

2.0

c-+

3 1.5 Q- C)-

1.0

0.5

0.0 0 50 100 150 nonoseconds

Fig. B-5. Sample Domain Gaussian Filter Used to Filter All Data Sets 1.(

0.6

-o I:

CU E

0.4

0.2

0.0 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 G Iz

Fig. B-6. Linear Magnitude of the Gaussian Filter in the Frequency Domain (1 Ghz sampling) I

-2(

-4(

-6C

-8C

-100

-120 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 GHz

Fig. B-7. Log Magnitude of the Guassian Filter in the Frequency Domain 1 x 0t

6 8x10

> 0 5

6x105

nv Z.-2-nnn ._ vv . v 4(l00 6000.- -... . . 8000... 10000 nanoseconds

Fig. B-8. Linear Magnitude of the Single Frequency RF Input to the HPA Taken Just Before Figures 10 to 16 TEKOOOT4 118.4

118.2

118.0

117.8 m -U

117.6

117.4

117.2

117.0 0 2000 4000 6000 8000 10000 nanoseconds Fig. B-9. Log Magnitude of the Single Frequency RF Input to the HPA Taken Just Before Figures 11 to 17 TEKOOOT4 -8:

-84

-86

a) -88 a() -0

-90

-- 92

-94 0 2000 4000 6000 8000 10000 nonoseconds Fig. B-10. Phase plot of the Single frequency RF Input to the HPA Taken Just Before Figures 11 to 17. Note: If the Digital Oscilloscopes' Sampling Were Phase Locked to the System Reference, the Phase Plot Would Be Flat f-- TEKOOOT5 1 x10

8xlO5

3-+-U) To

6x10 5 (-lr

4x10 5 0 2000 4-000 6000 8000 10000 nanoseconds Fig. B-l 1. Linear Magnitude of the Thirteen Bit Barker Encoded Pulse Out of the HPA TFKOOOT5 117.C

116.8

116.6

1 16.4 m "o

116.2

116.0

115.8

115.6 0 2000 4-000 6000 8000 10000 nanoseconds Fig. B-12. Log Magnitude of the Thirteen Barker Encoded Pulse Out of the HPA 5'

(n a) L 48 4)

4-2 0 2000 4000 6000 8000 10000 I (111 ('). ('.0( ( I J;

Fig. B-13. Phase Plot of the Thirteen Bit Barker Encoded Pulse Out of the HPA 5C

CY)c- 46 a) -U

42 0 2000 4 000 6000 8000 10000 nanoseconds Fig. B-14. Phase Plot of the Thirteen Bit Barker Encoded Pulse Out of the HPA. (Note: This is Identical to Figure 12 Except the Angles are Plotted Modula 180) R TEKOOOT6 lx10

8x 10

(n 0->

6x10 5

4x1o 5 0 2000 4.000 6000 8000 10000 nanoseconds

Fig. B-15. Linear-Magnitude of the Single Frequency Pulse Out of the HPA TEIKOOOT6 1 17.C

116.8

116.6

116.4 m -o

116.2

116.0

115.8

115.6 0 2000 41000 6000 8000 1000( nanoseconds

Fig. B-16. Log Magnitude of the Single Frequency Pulse Out of the HPA TEKOOOT6 54

(n a) , 48

_0(D

42 0. 2000 4-000 6000 8000 10000 nanoseconds

Fig. B-17. Phase Plot of the Single Frequency Pulse Out of the HPA 1.4x10 6

1.2x106

U) -n 0 >

6 1.0x10

8.0x10 5 0 .2000 1 000 6000 8000 10000 nanoseconds

Fig. B-1 8. Linear Magnitude of the Single Frequency RF Input to the HPA Taken Just After Figures 11 to 17 TEKIOOOT7 121.1

121.2

121.0

120.8

v m V-W,-Nr o0

120.6

120.4

120.2

120.0 0 2000 4-000 6000 8000 10000 nanoseconds

Fig. B-19. Log Magnitude of the Single Frequency RF Input to the HPA Taken Just After Figures 11 to 17 TEKOOOT7 -158

-160

-162

() a) -164- cD 0)

-166

-168

-170 0 2000 41000 6000 8000 10000 nanoseconds Fig. B-20. Phase Plot of the Single Frequency RF Input to the HPA Taken Just After Figures 11 to 17. Note: If the Digital Oscilliscope's Sampling Were Phased Locked to the System Reference, This Phase Plot Would be Flat [(okGOO L*.vvfi- fDr(cCS S _ - . . 180 1-

175

U) an L- I

i 170

1, vex65 L.,- 0 2000 4.000 6000 8000 10000 nanoseconds Fig. B-21. Figure 14 (Phase Plot of the Barker Pulse) Minus the Average of Figures 10 and 20. This Should Remove Most of the "Droop" Caused by the Oscilloscope Not Being Phased Locked tel

175

(n 0) 1_ -o

170

165 n n 0 2000 4.0 00 (UUU00 800 UUU n noseco n ds

Fig. B-22. Figure 17 (Phase Plot of the Single Frequency Pulse) Minus the Average of Figure 10 and 20. This Should Remove Most of the "Droop" Caused by the Oscilloscope Not Being Phased Locked t-rOOr a.t(LP, -- , P-- i . .1I

1l I-

i rn,

Figure B.23: Simple Pulse Initial Loop-Test Data (60-meter gates) showing power (top) and Phase (middle) and Phase-offset (mod 180) (bottom). L-.o- '/-t L - it ) cbcC.

w 0s - Go . a<

PW% ,

: vc I PG ft.) r

u 200 400 Figure B.24: Barker-Coded Pulse: Initial Loop-Test Data showing power (dB top) and Phase (degrees middle) and Phase mod 180 (degrees bottom). t 44oov -tA v ( i

R:F (5• c 60 40

-20

-40 0 50 100 150 200

_ · __ ___ 80 I

-20 _

-40 r I I I I 0 50 100 150 200

Figure B.25 Same Barker data raw (bottom) and pulse-compressed through Inv5O (50 tap LS inverse) filter (top) bct:cv 1"6p, 4¢., cea-f

-i )

Figure B.26 Close up of raw 60-meter gate Barker data showing (top) and Phase (middle) and Phase-offset (mod 180) (bottom). L-- ./ I' w L. Yc.) . -- t

Figure B.27 Close up of raw 90-meter gate Barker data showing (top) and Phase (middle) and Phase-offset (mod 180) (bottom). Pulse Compression for Phased Array Weather Radar

Appendix C: Keeler, R.J. and C.L. Frush, 1983a: "Coherent wideband processing of distributed radar targets," Proc. Int'l Geoscience and Remote Sensing Symposium (IGARSS-83) San Francisco, CA, pp 3.1-3.5.

May 11, 1999 Page 43 of 52 Proceeding of International Geoscience and Remote Sensing Symposium (IGARSS-83) COHERENT WIDEBAND PROCESSING OF DISTRIBU1rEO San Francisco, CA RADAR TARGETS Aug. 31-Sept. 1, 1983

R. Jeffrey Keeler and Charles L. Frush National Center for Atmospheric Researchl Field Observing Facility P.O. Box 3000 Boulder, CO 80307 (303) 497-0642

Abstract Pulse compression has previously been used by Austinl to improve radar reflectivity estimates of Meteorological targets such as precipitation, the McGIll University meteorological radar near atmospheric aerosols, and refractive index Montreal. Krehbiel and Brook 3 at New Mexico fluctuations in the clear air scatter electromagnetic Institute of Mining and Technology have implemented a energy incident upon them. These distributed targets random signal waveform having a 40 MHz bandwidth at produce a received waveform which has a Rayleigh X-band in conjunction with a rapidly scanning antenna distributed amplitude and a uniformly distributed to average out the Rayleigh flucuations. They used a phase. A common belief is that because of these wideband radiometer-type receiver to sum the random perturbations, pulse compression and matched independent fluctuating returns at the various filtering techniques are not effective for coherently frequencies within the pulse, thereby estimating the processing the received signals for Doppler velocity target reflectivity more accurately than if a single measurements. For radar remote sensing we have frequency waveform were used. At Purdue Cooper and analyzed the case of Illuminating distributed targets McGillemZ have described how to use a random signal with a wideband coded waveform and found that coherent waveform for measuring the Doppler spectrum of a gain in the receiver is achievable. In fact, for distributed target return through its sampled reflectivity and velocity estimates both the autocorrelation function. sensitivity and the range resolution of the remote sensor may be simultaneously increased over that of a Our reason for proposing a wide bandwidth radar comparable radar using a single frequency pulsed system is to be able to accurately represent the waveform. reflectivity, velocity and spectral width parameters during a dwell time of only a few pulse repetition Keywords: Meteorological Doppler radar, pulse intervals while maintaining the sensitivity and range compression, distributed targets. resolution of a single frequency pulsed radar. By transmitting a wide bandwidth signal we are able to Introduction obtain a larger number of independent estimates of these spectral parameters in a short dwell time than The concept of using a wideband waveform (i.e., if we transmitted a pulsed sinusoid. The larger mary times wider than the spectru of a simple pulsed number of independent samples obtained by transmitting sinusoid) on a radar system is not new. Military.and over a large frequency range allows us to average out aviation radar designers long ago realized the noise and Rayleigh fluctuations at different advantages in improved sensitivity and range frequencies rather than over a time interval long resolution by using pulse compression techniques for enough to yield the same number of independent system designs that were directed toward point target samples. applications. Radar meteorology targets, however, are distributed throughout the entire pulse volume and the Wideband Waveform Processing returns have characteristics similar to radar system noise. For a pulsed sinusoid transmit pulse, the Radar meteorologists are typically interested in weather targets return a signal that is Rayleigh measurements of radar reflectivity and radial velocity distributed in mplitude and uniformly distributed in plus an indication of the quality of the estimates. phase6 . Because of this randomness there has been a These measureents and others (e.g., spectral width or question of whether weather echoes can be coherently variance) can be derived from measurement of the processed for Ooppler information using standard pulse autocorrelation function of the weather returns at the compression and matched filter techniques. first two values R(O) and R(1) where R(l) is the autocorrelation at a lag of one pulse repetition Coherent processing is defined here to mean the time. IThe total received power is represented by matched filtering operation performed on a returned R(O). By subtracting out a known receiver noise power signal which is assumed to have a known waveform Nr and using the meteorological radar equation, the except for mplitude and phase. We wish to estimate radar reflectivity can be measured. The argument of the amplitude (or power) of the received echo and the the complex value R(1) contains all the necessary rate of change of its phase (its Ooppler frequency information for measuring the Doppler shift of the shift). The assumption is that the scattering return by using the standard pulse pair algorithm. 6 mechanism from some range and over some time Interval The ratio of these two correlation values also returns a waveform to the receiver which is nearly a provides a data quality Indication as well as spectral replica of the transmit waveform except for its width information. Since only the first two lags of mplitude and phase plus an additive noise component. R(s) are needed, the radar need pulse only twice in We will Justify this assumption. each beam. Operationally, the system would dwell for several pulses however. 'NCAR is sponsored by the National Science Foundation

/ Two approaches to wideband waveform design have It is well known that the SNR at the matched filter been considered-a coherent integration approach using output is just pulse compression/matched filter techniques and an incoherent averaging approach using a transmitted comb SNR - E/No of frequencies and a parallel receiver bank. Our (1) purpose here is to compare and contrast these two a PrT/No concepts for the distributed target case Including the presence of ground clutter. where E is the pulse energy, Pr is the received pulse power, Pulse Compression and Distributed Targets T is the pulse duration, and No is the noise spectral power density. If a waveform of bandwidth B is incident on a continuously distributed target of constant mean radar Thus, for point targets the SNR of the processed reflectivity, then returns from target particles signal is simply proportional to the pulse length T. separated by more than c/28 in range are uncorrelated, 2 . 3 that is, they have Independent For distributed targets we obtain the same amplitudes and phases. Conversely, returns from coherent gain and noise dependencies, but the target particles separated by less than c/28 are scattering volume (and therefore, its radar cross correlated with the transmit waveform. As the section) over which coherence is maintained (and its simplest case a pulsed sinusoid 1 psec long has a similarity to a point target exists) decreases with bandwidth B * 1V/ " 1. Hz and returns from slabs the bandwidth of the pulse according to the c/28 slice separated by greater than cs/2 * 150 m are depth. Therefore, the SNR for distributed targets is uncorrelated. A wide bandwidth pulse T sec long proportional to T/B. There will be some additional typically has a bandwidth 8 much greater than t/T. loss because the return scattered from the slice of Only scattering from particles within slices c/28 in atmosphere is not an exact replica of the transmit depth combine through vector addition to produce a pulse. It is apparent that we can trade off scattered waveform correlated with the incident sensitivity for independent range samples by waveform. This Is true because over the depth of each Increasing the bandwidth, but the lost sensitivity can target slice (c/2B) the received phases of the largest be recovered simply by Increasing the and smallest frequencies in the waveform differ by pulse duration. By specifying the pulse bandwidth B less than % radians from their relationship in the and duration T, we can at least in principle, transmit pulse-i.e., the pulse is relatively Independently control both the nuber of samples 1 and undistorted. the SNR. The actual waveform we choose to implement is not important from the view of processing--only its Two important Implications can be made from this bandwidth and duration are important. observation. First, if we collect these measurements over some desired range cell AR, then within AR we An example Illustrates these tradeoffs. Let us have 14 2ARB/c Independent estimates with which to define a reference radar system having a single average out Rayleigh fluctuations and obtain an frequency pulse T - 1 isec long and average our estimate of reflectivity. Only the pulse bandwidth B measurements over AR a 150 meters. We note that B - 1 determines the number of independent samples M. MHz. The return from a given weather target gives a Single frequency pulsed radars rely on dwell time to reference signal to noise ratio (SNRref) and one provide Rayleigh averaging and typical decorrelation sample over the 150 m range cell. We denote the times result in very few independent reflectivity estimator variance (reflectivity, velocity, etc.) as measurements being averaged. A wideband system will, a (SNRref, M " 1). Specifying a new waveform with therefore, provide more Rayleigh averaging in a much B - 10 MHz and T - 10 isec gives a longer, wider shorter dwell time. The Doppler velocity estimates bandwidth pulse. The slice depth is c/2B - 15 m, can, furthermore, be made at a faster rate for the therefore, 10 independent samples are Immediately same accuracy. available for averaging over 150 m. The SNR for each sample is decreased by 10 from a reduction of the The second implication relates to the sensitivity scattering volume depth, but increased by 10 by the of the remote sensor. Radar sensitivity is directly energy in the longer pulse. Thus, the SNR remains the related to the signal to noise ratio (SNR) of the some. The final parameter accuracy is therefore matched filter receiver. Consider a wideband waveform a (SNRref, M - 10). Increasing both B and T allows whose duration T is several times longer than its 10 independent range samples from the slices within AR inverse bandwidth. Slices of the target c/2B in depth during a single pulse, and the SNR of the sample from scatter a composite waveform which, to a first each slice is unchanged from the SNR obtained in the approximation, is an attenuated and phase shifted reference radar. An accurate reflectivity measurement version of the transmit pulse. The received waveform can beimade from one pulse. Velocity and spectral from the entire continuously distributed target is width measurements require two or more pulses to then a superposition of these composite waveforms that measure the particle motion. are scattered from each slice. By passing the received waveform through a filter matched to the Various types of pulse compression waveforms can transmit waveform, we can achieve coherent gain from be used-they all provide coherent gain but some are each slice in the same way that pulse compression gain more desirable than others for various non-processing is achieved for "point" targets. Coherent integration related factors. A waveform coded with a bi-phase in the matched filter Increases the SNR proportional Barker or pseudo-random (shift register) code has a to the pulse energy, or equivalently its duration constant power during the pulse but has range T. 4 The input noise power Increases with the sidelobes that are difficult to suppress. For receiver bandwidth B, but the SNR at the output of the example, the 13 bit Barker code has 11.2 dB range matched filter depends only on the noise power sidelobes for a continuously distributed target. The spectral density No, not the total noise power. 4 random waveform technique of transmitting uncorrelated waveforms every pulse mitigates the second trip echo interference and potentially allows very large Nyquist velocities. However, the peak power limitation on most radar transmitter tubes and the fluctuating pulse power requires using much less than the full average power rating of the tube. An FM chirp waveform with either a linear frequency sweep or a stepped frequency sweep can take advantage of the full power rating of the output device during the pulse (as does the.phase coded waveform), but the range Doppler ambiguity of the chirp waveform may be a problem.

Another effect to be considered is the Velocity decorrelation time of the targets in each coherent slab. For pulse compression processing to be Error 1.0 effective, the point targets within each pulse volume must remain fixed relative to one another at least G°ad during the pulse propagation time through the slab so (m/s) that Raleigh amplitude and phase fluctuations do not destroy the coherence of the return and preclude the -10 0 10 20 matched filter gain we expect. At weather radar frequencies and for spectral widths of less than 20 m/s, the correlation time of the distributed targets SNR is greater than 1 msec. Therefore, the decorrelation due to turbulence is usually not important at microwave frequencies. In fact it is Just this Figure 1. Typical plot of la radial velocity error pulse-to-pulse coherence or stationarity that allows vs. SNR for the number of independent velocity measurements using the pulse pair technique. estimates M - 32 and 14 128. Arrows A and B indicate the difference In performance Accuracy of Measurements and Tradeoffs when the bandwidth of the waveform is increased by a factor of 4 - a 6 dB Zrnic (1979) has shown how the accuracy of radar decrease In SNR.-.. -. meteorological measurements such as reflectivity, velocity and spectral width depend on the number of to reduce urad as shown by arrow A. However, at independent samples M and the per pulse SNR. We have lower SNR's this same tradeoff results in an increased seen that these factors may be Independently Orad (as shown by arrow B) and such a tradeoff would controlled regardless of the pulse compression be unwise. This type of tradeoff for all the desired waveform we choose to Implement. It is generally true easurements needs to be carefully considered in a for all three estimators that the error decreases as radar system design. the SNR increases and that there is a lower error bound caused by a finite spectral width which is Miscellaneous characteristics impossible to improve upon at any SNR. For example, the standard (la) radial velocity error of a signal One distinct advantage of a wideband coded having spectral width w (m/sec) and some signal to waveform is the high range resolution that can be noise ratio SNR and having been averaged over M achieved. By averaging the sub-range gates c/2B independent samples taken Ts seconds apart is given (typically 2-20 a) in range, we may define any by the variance processed range interval AR that we desire. An application of small range gates is the.ability to 2 kw 4wTs , average them to provide cubic resolution volumes by .141 + -S + - T S using variable range gate depths. rad 2MTS XSNR 16x w T SNRj For a single antenna radar system the minimum range of the system is defined by the total pulse Note that as SNR * - , the lower bound on velocity length. Pulses that are relatively long (several variance is 4sec) to maintain sensitivity will have large minimum ranges. However, there are techniques to reduce this 0 7 2ard-rad %14s - (3) loss; a separate short pulse could fill in the very close ranges. and as SNR . 0, Range sidelobe contamination when sensing continuous targets is especially troublesome near high 2 reflectivity gradients associated with a hail shaft, arad ' 3 * (4) for example. In addition, second trip echoes will 32icZ MTKSNRZ cause interference unless precautions are taken to suppress them. Waveforms having small cross-correlation could be used on pulses to suppress may not a qualitative plot of radial velocity second trip echoes, but these same waveforms Fig. 1 shows We desire to Jointly error as a function of SNR for two values of 4. have low range sidelobes. optimize the signal waveforms to achieve From the previous discussion we know that for both low range (autocorrelation) sidelobes as well as (cross-correlation) sidelobes. distributed targets the sensitivity or SNR can be low pulse to pulse traded directly for number of samples M. By 4, can be Long coded waveforms apparently do not introduce Increasing the bandwidth by a factor of M ground clutter. changed from 32 to 128 because the slices are made any special problem in suppressing a 6 dB lower Arn design for a short range radar will require smaller, however, each sample will have simply SNR. At a high SNR (to the far right on the M1 32 special considerations to suppress the clutter to give up 6 dB in sensitivity because of the difficulty in separating weak weather curve) It is reasonable elevation for 4 times the number of samples. The net effect is targets from strong ground clutter at low angles. Comb of Frequencies Processing The last form expresses the pulse in terms of its total bandwidth. The denominator Is Just the slab A straightforward technique of Implementing a depth for the wideband coded waveform having bandwidth wideband radar system to collect data during a short Btotal- Thus, if both radars have the same transmit dwell time is to distribute the total pulsed transmit bandwidth, they yield the same number of Independent power over several different frequencies and process estimates. The S#R of each slab measurement can the returns separately but simultaneously. If these likewise be equlvalenced given the same total signal frequencies are separated by more than the inverse duration T - Nt. pulse length, then independent returns are scattered from the same target volume. These returns can be The difference' n the two methods is that the processed separately to yield Individual reflectivity comb of frequencies approach trades off bandwidth for and Doppler estimates, which In turn can be averaged n given a fixed pulse volume size, AR - cs/2; whereas, to reduce the error in the parameter measurements. the pulse compression matched filter approach trades This type of Incoherent averaging reduces the standard off bandwidth for N by dividing the desired pulse error by /M as demonstrated In Equation (2). volume (range depth AR) into separate slabs c/28 in depth. All the Individual estimates have the same SNR The basic Implementation is a bank of receivers because we Increase the pulse duration T to satisfy that process the comb of frequencies. In effect the sensitivity requirement. Based on these multiple radar receivers share a common antenna and arguments, there Is no preference based on sensitivity front end before splitting the returns Into parallel or number of amples for either processing technique. IF strips and processors. If the different frequency Both approaches have the potential for measuring pulses were transmitted during the same pulse reflectivity and velocity with the same accuracy. Interval, a high peak power amplifier would be required, which is undesirable because of peak power Characteristics of comb of frequencies limitations In an actual radar system. If the pulses were transmitted contiguously, the minimum range would The advantages of the straightforward comb of be large for the same reason as if we transmitted a frequencies approach are many. The transmitter and long coded waveform pulse. But if the different bank of receivers are conceptually simple--the total frequency pulses were transmitted at different PRF's, transmitter bandwidth is of order 1% and the bank of the minimum range would be maintained and, in parallel receivers are composed of simple, addition, a form of velocity unfolding would be commercially available microwave components, many of possible. The various pulses would block reception which are interchangeable. Stocking spares and having during pulse transmission and any following ground redundant parallel channels gives a more reliable, clutter reception Intervals, but they could be timed easily maintainable receiver system than a single, so that no one range would be consistently blocked. complicated, wide bandwidth matched filter design. Unless the clutter Is effectively suppressed by low The bandwidth of the system is easily expandable sidelobe antenna design, the percentage of receiver simply by adding more transmitter energy and blockage might be unacceptably high. additional receiver channels. The basic radar processors are effectively In parallel, although a Equivalence of Processing Techniques time shared processor is certainly possible. The multiple PRF's that are possible allow velocity Averaging the various meteorological parameters unfolding by an Intelligent processor. over a comb of frequencies is equivalent to averaging the parameters obtained from processing pulse The primary disadvantage of the comb of compressed waveforms in the sense that for a given frequencies approach is the aforementioned ground total pulse duration and bandwidth, we obtain the same clutter masking of received echoes when staggered number of estimates (M) each having the same SNR. PRF's are used. Although the receiver is conceptually This is not obvious, but an example should clarify the simple, there are many (10-50) parallel microwave statement. The previous example of B - 10 MHz and components which occupy rack space and cost money. T * 10 psec yielded a variance of Furthermore, the transmitter for a high PRF, long a2 (SNRref, 1 - 10). If instead we transmit 10 pulse duration system has a duty cycle of 5-10 at an separate 1 psec pulses spaced 1 MHz apart so that the average power of around 10 kw. Designing such a total transmit duration is T - Hi - 10 psec and the transmitter may prove to be a challenge. total bandwidth is the same 10 Miz, then by recalling the definition of SNRref (that of s - 1 psec pulse, Suary 1 MHz wide), it is asy to see that the estimator variance is still a(SNRref, 14 10). We have show that pulse compression/matched filtering techniques are effective for distributed This equivalence of the number of samples M is radar tkrgets as well as for point targets. In easy to show generally. If a radar system transmits N particular, these methods may be used in different frequencies having bandwidth Beach "' l/, meteorological radars to more rapidly and more then for a desired range cell dimension of AR, we have accurately acquire reflectivity and velocity 1 independent values, where measurements thn by using a single frequency pulsed ARw sinusoid. Coherent returns from target slices c/2B in u RNZc acR) range can be processed with a filter matched to the transmit pulse to achieve coherent processing gain . ?R (N-Beach) (i.e. SmR Increase). A simple technique that provides the same gain is the comb of frequencies and a bank of c receivers method. ' 2AR (8total ) (7) References

AR/ total 1. Austin, 6. (1974), Pulse compression systems for B total use with meteorological radars, Radio Science, 9. p. 29-33.

I 2. Cooper, 6. and C. McGillem (1978). Doppler spectrum estiatlion for continuously distributed radar targets. Proc. of RADC Spectrum Estimation Workshop, May 24-26, OOC #A054650, p. 273-285. 3.- Krehbiel, P. and M. Brook (1979), A broadband noise technique for fast scanning radar observations of clouds and clutter targets. IEEE Trans. on Geoscience Electronics, GE-17, p. 196-ZO4. 4. Nathanson, F. (1969). Radar Design Principles, McGraw Hill, New York. 5. Zrnic, 0. (1979), Estimation of spectral moments for weather echoes. IEEE Trans, on Geosclence Electronics, GE-17, p. 113-lZa.- 6. Zrnic, D. and R. Doviak (1983), Doppler Weather Radar, Academic Press, New York Pulse Compression for Phased Array Weather Radar

Appendix D:Keeler, R.J. and C.L. Frush, 1983b: "Rapid scan Doppler radar development considerations, Part II: Technology Assessment," 21st Conf. on Radar Meteorology, AMS, Edmonton, Canada, pp 284-290.

May 11, 1999 Page 44 of 52 Reprinted from Preprint Volume: 21st Conference on Radar Meteorology, Septemoer 19-23, 1983, Edmonton, Alta.. Canada. Published by the American Meteorological Society, Boston, Mass. 9.5

RAPID SCAN DOPPLER RADAR DEVELOPMENT CONSIDERATIONS

PART II: Technology Assessment

R. Jeffrey Keeler and Charles L. Frush National Center for Atmospheric Research* Boulder, Colorado 80307

1. INTRODUCTION The beamwidth and range resolution allows the radar to resolve features on the order Radar meteorologists face a difficult of 1-2 km out to 50 km ranges. Wavelengths problem when trying to determine the behavior of between 3 and 10 cm are commonly used for narrow such interesting atmospheric phenomena as convec- beam meteorological radars to keep the antenna tive storms on a scale that leads to an under- size reasonable, and to prevent attenuation caused standing of the dynamic processes that govern by heavy rain from limiting the sensitivity at their genesis and evolution. One serious problem longer ranges. The -10 dBZ sensitivity will allow is that conventional Doppler radars cannot rapidly measuring some clear air echoes. The accuracy scan such features with adequate resolution in a recommendations listed are those that scientists sufficiently short time span to avoid loss of have found to be acceptable for most radar information caused by the rapid evolution and meteorological studies. Given these approximate advection of the process. We believe that a fun- system requirements, it is clear that designing a damental sampling problem exists in the recovery radar system to satisfy them will require of storm kinematic structure from multiple Doppler innovative techniques for estimating the radar observations. Obtaining adequate spatial meteorological parameters in a short sampling over dwell time a large volume in a time interval with the desired accuracy. short enough that spatial and temporal aliasing do not occur is difficult using existing meteoro- The data collection "space" in which we logical radars (Carbone and Carpenter, 1983). are working includes time, frequency, space, and scattering angles from which we may obtain 2. SYSTEM PERFORMANCE REQUIREMENTS independent measurements. Time is the dimension we desire to reduce. There are over 20,000 The basic design criteria for a rapid 1° beams in a hemisphere. Dividing this number scan Doppler radar system were discussed at the of beams by the desired 60 s scan time gives "3 ms Multiple Doppler Radar Workshop (Carbone et al., dwell time for each beam, which allows only a few 1980). The primary recommendation was to utilize samples of amplitude and phase with which to make new technology in wide bandwidth microwave the measurements. Typical weather radar signals components, phased array antennas, and high speed require several tens of independent samples to array processors to improve the data collection achieve the desired accuracy. Therefore, we must rate. Based on the suggestions of the Workshop expand the other dimensions to collect more data attendees, discussions with radar meteorologists in the allocated short dwell time. Using space during the following three years, and the recent diversity (multibeam antennas) and frequency Rapid Scan Doppler Workshop , we believe these diversity (wideband signals or multiple frequency tentative system requirements define a reasonable pulses) allows the more rapid data rate we rapid scan Doppler radar system: desire. Today's microwave antenna and component technology appears to allow Scan time (hemisphere) a maximum of approxi- -1 min mately ten simultaneous Beamwidth beams and "100 MHz band- 0.5-1° width. These factors allow "1000 Range resolution times faster 200-300 m data rate than existing meteorological Wavelength radars; 3-10 cm therefore, an adequate expansion Maximum range of the data rate 50 km is possible. Sensitivity -10 dBZ Accuracy 3. ANTENNA TECHNOLOGY CONSIDERATIONS Reflectivity ±2 dBZ Velocity ±0.5 m s- A serious problem exists with these Pointing ±0.1° system parameters. A maximum range of 50 km means Location Transportable that a large percentage of the low elevation data will be contaminated by ground clutter unless special precautions are taken. Furthermore, if the pulse repetition frequency (PRF) is high *The National Center for Atmospheric Research is (3 kHz), and if the same signal waveform is sponsored by the National Science Foundation. transmitted on each pulse, second trip echo contamination will be a problem. Different 1The Rapid Scan Doppler Workshop was sponsored by pulse-to-pulse coding could reduce the NCAR's Field Observing Facility in Boulder, second trip echo problem, but ground clutter reduction Colorado, on 4-5 April 1983. There is no formal requires special attention. publication at this time. Low sidelobe antenna design would be a standard preventative approach. Ground clutter rejection processing will provide additional suppression. Both clutter notch

284 For conventional scan rates the spectral filtering and spectral domain clutter removal are - l effective in conventional radars with dwell times spread amounts to a small fraction of a m s However, a 3 m C-band antenna scanning at long enough to characterize the narrow band - 1 - 1 clutter input. However, for a rapidly scanning 1000° s causes =10 m s spreading. This radar, the short dwell time per beam (<3 ms) spectral spreading dominates all other mechanisms severely limits the amount of clutter reduction we and seriously reduces the accuracy of velocity and can achieve by processing. Autocorrelation width measurements for scientific purposes. processing used with frequently updated clutter Figure 1 shows the radial velocity error vs the maps has been discussed, but a long dwell time spectrum width of the received signal for a X=5 cm appears necessary for effective suppression. For radar having a PRF = 1 kHz and M=64 pulse pairs the present, we shall concentrate on keeping the being used to estimate the velocity (Zrnic, antenna sidelobes relatively low (<30 dB) by using 1979). These are typical values both for present off-axis reflector sections or planar radars and a rapid scan radar. Spectrum widths either - arrays in combination with low sidelobe tech- >6 m s l for this system have velocity errors >1 m s- 1 at any signal-to-noise ratio (SNR). For niques. The 60 dB two-way suppression will be an - 1 suppress clutter much of a 1° beam, a scan rate <50° s at C-band effective technique to . the time. increases the spectral width by <0.5 m s- Target sources of spectral spreading-e.g., shear, 3.1 Antenna scan requirements and turbulence, fallspeed variations--generally cause constraints spectral widths in excess of 1 m s~ , so the scan induced spread of 0.5 m s- is acceptable. A one min hemispheric scan time for the 20,000 beams requires that a single beam antenna scan at an average rate of =20,000/60 =360° s-1. 3 This is =20 times faster than present meteorological radars. Furthermore, if mechanical con- S- straints produce redundant volume coverage (for 0 S- example, at high elevation angles using an over- 2 head scan), then the scan rate would have to be LOLu larger yet. .- 0 E 0 If we assume an efficient (i.e., non- r> 1 redundant) scan of a single 1° beam, then each beam has -3 ms for its data acquisition interval. A maximum unambiguous range of 50 km requires 333 ps between radar pulses. Therefore, in principle, each beam can integrate received signals 1 2 3 4 5 6 7 8 9 10 for about nine pulses before the beam illuminates - a new pulse volume. When continuously scanning, Spectrum Width (m s ) there will be some loss associated with each beam over the dwell time because the illuminated volume Figure 1. Standard (la) error of velocity is somewhat different for each pulse. At the measurement vs spectral width of Doppler spectrum maximum 50 km range there is an '90% overlap in at SNR of -5, 0, and 20 dB. PRF = 1 kHz, the transmit beam and the received beam for each X = 5 cm, M = 64 pulse pairs. pulse, and all the sample volumes will be smeared in the direction of scan in the same manner as with conventional radars. If a scan faster than 3.2 Antenna designs 360° s 1 is required, the dwell time and overlap for each beam is proportionally decreased. In order to mitigate the fundamental limitation of scan rate broadening, we consider Experiments by Krehbiel and Brook (1979) three antenna scanning mechanisms: 1) a multiple at New Mexico Institute of Mining and Technology beam design that allows the scan rate of each beam have demonstrated that a single beam that scans to be reduced, 2) a scan-back technique in which continuously at =1000° -s 1 is acceptable for the feed or beam steering compensates for the scan reflectivity measurements. However, this rapid motion during the data sampling interval, and 3) scanning introduces a Doppler spread of several an electronic step scan using, for example, a m s 1, which inhibits accurate mean velocity and phased array or phased array feed, such that the effectively prohibits spectral width measure- beam steps its position only between data ments. This limitation is caused by the beam collection intervals. Furthermore, we will shape modulating the returns from the spatial consider two antenna structures, the focusing volume and inducing amplitude fluctuations over reflector antenna and the direct planar array and above the slower Rayleigh fluctuations caused radiator. We dismiss multiple fixed planar arrays by internal motions within the target pulse using 2-D beam steering to cover the hemispheric volume. The scan induced spectral width (ascan) scan area because they are much too expensive. in m s can be simplified from a formula given by Mechanical rotation around one axis is a proven, Nathanson (1969) to reliable technique and allows simple, 1-D electronic steering to cover the desired volume. o = .2wD (1) scan * Multiple beam antenna with w = scan rate in rad s- l A multiple beam antenna can observe D m. = antenna diameter in several directions simultaneously, thereby covering the scan volume with a smaller scan rate

285 per beam and an acceptable spectral spread. Beams Another characteristic of phased arrays can be formed with a lens feed, such as a Rotman used to transmit nonsinusoidal signals is that the lens, or with separate feed horns illuminating a steering angle is a function of the wavelength common reflector. If the N beams are separated in spacing, and therefore, the input frequency. For frequency so that they are simultaneously active, a sufficiently broad band transmit waveform, the the system could achieve a dwell time N times beam is spread depending on the specific frequency larger than a single active beam system, and the components present. A 50 MHz signal at 5 GHz potential for clutter suppression would be (C-band) typically experiences a 1° beam spread in significantly enhanced. addition to the diffraction beam spread. This is probably not acceptable unless we reduce the * Single beam scan-back antenna diffraction beamwidth by using a larger antenna aperture or by designing an array with "time-delay The scan-back technique is a variation steering" in addition to the standard phase on the step scan. In a step scan the beam is steering. Although technologically soluble, this fixed in space during the data collection interval design adds complication, weight, volume, and and rapidly "steps" to the new beam position expense to the antenna. before the new data interval begins. The scan- back motion is used with a continuously and If the antenna feed and transmit rapidly scanning reflector to compensate for the waveform are designed so that the beam spreading beam motion during each data interval. Because effect of the wideband signal is not a limiting the compensation moves the beam only ±1/2 factor, it can be used advantageously to steer the beamwidth from boresight, the beam shape and beam by sweeping the center frequency of the sidelobes are not signficantly degraded even for wideband transmit waveform. A preliminary parabolic reflectors. The scan-back steering can calculation shows that in order for the 1% be performed mechanically by moving the feed to bandwidth not to spread a 1° beam appreciably, a produce a sawtooth deflection of the beam much ±20% frequency sweep is needed to steer the beam like is done with the Robinson scanner (Skolnik, over ±100 (Skolnik, 1980). It appears that 1970). Mechanical limitations in switching speed .frequency scanning a 1% bandwidth 1° beam requires may render this approach impractical. an excessive frequency csweep, and is not practical at 3-10 cm wavelengths. Alternatively, the scan-back may be done. electronically. A simple monopulse feed with high Phased arrays steer the beam by phasing power phase shifters on each side (which is a two the elemental radiators so that constructive element linear array) may be used to electroni- interference produces a beam in the desired cally perform the scan back. A multibeam scan- direction. In this desired direction the back antenna design would both compensate for the projected aperture is always smaller than in the beam motion and decrease the mechanical scan rate. broadside direction and the beam becomes progressively broader as the steering angle * Electronic step-scan antenna increases. At 15° the beam is broadened only 3.5%; and at 30°, 15%. It is easy to see that if A linear array of approximately 100 relatively constant beam size is a ° factor, elements can be used to form a beam 1' wide in electronic steering with a phased array should be the dimension of the array elements. Beam shaping limited to 10 or 20 deg. in the other dimension can be done by using long elements, like a slotted waveguide, thereby Planar array antennas are appealing forming a planar array radiator or by shaping the because all the elements are identical and there linear array feed with a parabolic cylinder main is no aperture blocking by a feed assembly. A reflector. In either case the antenna can be common form of planar array radiator is the electronically steered in elevation while the slotted waveguide, i.e., waveguide in which entire assembly rotates in azimuth at a few tens precisely located slots have been cut to achieve of deg s . If the elevation scan of the array the desired radiation phase and amplitude along is limited (which it typically will be), the whole its length. The technology for fabricating these antenna can be coarsely positioned to as many slotted waveguide planar arrays is mature and elevations as necessary. antennas with extremely low sidelobes (<40 dB) are well within the limits of current technology There are several attractive features of (Schrank, 1983). An example of a planar array is beam steering with the array. Because the beam is shown in Fig. 2. Another type planar radiator almost fixed in space during the data acquisition incorporates the stripline technology in which the interval, there is little loss caused by excess phase shifters, the attenuators, as well as the spectral spreading or by spatial volume smearing. stripline radiators, are built into a slab of The radiated power is distributed over many feed dielectric material. This newer technology needs elements and phase shifters so the entire trans.- to be examined for cost effectiveness and for mitted power does not need to be accommodated at a field maintainability. single point. If one of the feed elements fails, the remainder continues to function so the radia- Another appealing antenna design is the tor has built-in redundancy and degrades "grace- off-axis parabolic cylinder reflector fed by a fully." If the linear array is vertical, it is linear array. There is no feed blockage with this possible to incorporate a predetermined null in structure and large parabolic cylinder reflectors the beam pattern in the direction (elevation) of are relatively easy to manufacture compared to maximum ground clutter. In fact, with sufficient doubly curved reflector surfaces. In this design computing power it is possible to adaptively train a vertical linear array might do rapid ±15° eleva- the antenna sidelobe pattern at each site for tion steering, while the antenna rotates slowly in maximum ground clutter rejection. azimuth at 18° s- (3 rpm). On successive

286 4.1 Wideband waveform processing

Radar meteorologists are typically interested in measurements of radar reflectivity and radial velocity plus an indication of the quality of the estimates. These measurements and others (e.g., spectral width or variance) can be derived from evaluating the autocorrelation function R(r) of the weather returns at the zero and first interpulse period lags, R(O) and R(1). The total receiver power is represented by R(O). By subtracting out a known receiver noise power Nr and using the meteorological radar equation, the radar reflectivity can be measured. The argument of the complex value R(1) contains all the necessary information for measuring the Doppler shift of the return by using the standard Figure 2. Drawing of planar array antenna using pulse pair algorithm (Zrnic and Doviak, 1983). slotted waveguide elements. The serpentine feed The ratio of these two correlation values also is used for frequency scanning (Skolnik, 1970). provides a data quality indication as well as spectral width information. rotations, the antenna is tipped back (or coarse Two approaches to wideband waveform steered in elevation) to three boresight angles of design have been considered--an integration 15°, 45° and 75°. Full hemispheric coverage (when approach using pulse compression/matched filter desired) is achieved with minimal degradation of techniques and an averaging approach using a beam shape and sidelobe levels because of the transmitted comb of frequencies with a parallel small steering angles. The reflector needs to be receiver bank. Our purpose here is to compare and large enough in the electrically scanned direction contrast these two concepts for the distributed to intercept the feed energy at the maximum scan target case including the presence of ground angle. For typical designs, a reflector dimension clutter. of =150X (7.5 m at C-band) is adequate and reasonable to build. A possible disadvantage to 4.2 Pulse compression and distributed any offset parabolic or spherical section is less targets polarization purity than could be achieved with a symmetrically curved antenna. If a waveform of bandwidth B is incident on a continuously distributed target of constant 4. WAVEFORM DESIGN AND SIGNAL PROCESSING mean radar reflectivity, then returns from target particles separated by more than c/2B in range are Radar meteorology targets are distrib- uncorrelated (Cooper and McGillem, 1978; Krehbiel uted throughout the entire pulse volume and the and Brook, 1979); i.e., they have independent returns have characteristics similar to radar amplitudes and phases. Conversely, returns from system noise. For a pulsed sinusoid transmit target particles separated by < c/2B are correlat- pulse, the weather targets return a signal that is ed. As the simplest case a pulsed sinusoid 1 us Rayleigh distributed in amplitude and uniformly long has a bandwidth B = 1/T = 1 MHz and returns distributed in phase (Zrnic and Doviak, 1983). from slabs separated by > cr/2 = 150 m are Because of this randomness, there has been a ques- uncorrelated. tion of whether weather echoes can be coherently processed for Doppler information using standard If we collect these measurements over pulse compression and matched filter techniques. some desired range increment AR, then within AR we Austin (1974) studied pulse compression for wea- have M = 2ARB/c independent estimates with which ther radar reflectivity measurements, but did not to average out Rayleigh fluctuations and obtain an consider the Doppler recovery. estimate of reflectivity. Only the pulse bandwidth B determines the number of independent Our reason for proposing a wide band- samples M. Single frequency pulsed radars rely on width radar system is to accurately represent the dwell time to provide Rayleigh averaging, and reflectivity, velocity, and spectral width para- typical decorrelation times (a few ms) result in meters during a dwell time of only a few pulse very few independent reflectivity measurements repetition intervals. By transmitting a wide being averaged. A wideband system will, there- bandwidth signal, we are able to obtain a larger fore, provide more Rayleigh averaging in a much number of independent estimates of these para- shorter dwell time. The Doppler velocity esti- meters in a shorter dwell time than if we trans- mates can also be made at a faster rate. mitted a pulsed sinusoid. The larger number of independent samples obtained by transmitting over 4.3 Accuracy of measurements and a large frequency range allows us to average out tradeoffs noise and Rayleigh fluctuations at different , frequencies rather than over a time interval long Zrnic (1979) has shown how the accuracy enough to yield the same number of independent of radar meteorological measurements such as samples due to the reorientation of the particles. reflectivity, velocity and spectral width depend on the number of independent samples M and the per pulse SNR. It is generally true for all three estimators that the error decreases as the SNR increases and that there is a lower error bound

287. caused by a finite spectral width, which is long (several us) to maintain sensitivity will impossible to improve upon at any SNR. For have large minimum ranges. However, there are example, the standard (la) radial velocity error techniques to reduce this loss; a separate short of - a signal having spectral width w (m s ) and pulse could fill in the very close ranges. some SNR, and having been averaged over M independent samples taken Ts s apart,is given by Range sidelobe contamination, when the variance sensing continuous targets, is especially troublesome near high reflectivity gradients associated with a hail shaft. In addition, second trip 2 4wT s o= X 7.141 »lw 1+L + 1.(2) echoes will cause interference unless precautions are taken to suppress rad 2MT XSNR 16~ wT SNR them. Waveforms having .s s small cross-correlation could be used to suppress second trip echoes, but these same waveforms may not have low range sidelobes. Figure 3 shows a qualitative plot of radial We desire to jointly optimize the signal waveforms velocity error as a function of SNR for two values to achieve of M. both low range (autocorrelation) sidelobes as well as low pulse-to-pulse (cross-correlation) sidelobes. The sensitivity or SNR can be traded directly for number of samples M. By increasing 4.5 Comb of frequencies the bandwidth by a factor of 4, M can be changed processing from 32 to 128 because the slices are made A straightforward technique smaller; however, each sample will have a 6 dB of implementing a wideband radar system to lower SNR. At a high SNR (to the far right on the collect data during a short dwell time is to distribute M = 32 curve), it is reasonable to give up 6 dB in the total pulsed transmit power sensitivity for 4 times the number of samples. over several different frequencies and process the The net effect is to reduce orad as shown by returns separately but simultaneously. If these arrow A. However, at lower SNR's this same frequencies are separated by more than the inverse tradeoff results in an increased orad (as shown pulse length, then independent returns are by arrow B) and such a tradeoff would be unwise. scattered from the same target volume. These returns can be processed separately to yield individual reflectivity and Doppler estimates, which in turn can be averaged 10 to reduce the error in the parameter measure- .J ments. S.- This type of incoherent averaging reduces a the standard error by /M as demonstrated in Eq. (2).

US The basic implementation 0 1.0 is a bank of receivers that process the comb of frequencies. In effect multiple radar receivers share a common antenna and front end before splitting the returns into 0.1 parallel IF strips and processors. If the different frequency pulses were transmitted during the same pulse interval, a high peak power amplifier would be required, which is undesirable because of peak power limitations in an actual SNR (dB) radar system. If the pulses were transmitted contiguously, the minimum range would be large for the same reason as Figure 3. Typical plot of la radial velocity if we transmitted a long coded waveform pulse. error vs SNR for the number of independent But if the different frequency pulses were transmitted at estimates M = 32 and M = 128. Arrows A and B different PRF's, the minimum range would be indicate the difference in performance when maintained and, in the addition, velocity bandwidth of the waveform is increased by a unfolding would be possible. factor The of 4--a 6 dB decrease in SNR. various pulses would block reception during pulse transmission and any following ground clutter 4.4 Miscellaneous characteristics but they could be timed so that no one range would be consistently blocked. Unless the clutter is effectively One distinct advantage of a wideband suppressed by low sidelobe antenna design, the percentage coded waveform is the high range resolution that of receiver blockage might be unacceptably can be achieved. By averaging the sub-range gates high. c/2B (typically 2-20 m) in range, we may define The comb any processed range interval AR that we desire. of frequencies approach trades off bandwidth for An application of small range gates is the M given a fixed pulse volume ability size, AR to average them to provide cubic resolution = cr/2; whereas, the pulse compression matched filter volumes by using variable range gate depths. approach trades off bandwidth for M by dividing the desired pulse volume (range depth AR) into separate For a single antenna radar system slabs c/2B in depth. Based on the these arguments, minimum range of the system is defined by the there is no preference based on number of samples total pulse length. Pulses that are relatively for either processing technique.

288 4.6 Characteristics of comb of is proportionally increased. A high volume, fast frequencies temporary data storage would be required for buffering the data before transferring it to The advantages of the straightforward permanent storage. At these data rates, video comb of frequencies approach are many. The trans- disk with several Gbytes storage on each disk mitter and bank of receivers are conceptually might conceivably be the final medium. simple--the total transmitter bandwidth is on the order of 1% and the bank of parallel receivers are There are techniques that can be used t. composed of simple, commercially-available micro- reduce the output data rate. We are usually not wave components, many of which are interchange- interested in altitudes >15 km. As a function of able. The bandwidth of the system is easily elevation angle, the processor simply would not expandable simply by adding more transmitter process output data from altitudes >15 km, and the energy and additional receiver channels. The total volume size would be reduced by a factor of basic radar processors are effectively in paral- almost three. Of course the peak rate at low lel, although a time-shared processor is certainly angles remains high, and fast buffering might possible. The multiple PRF's that are possible still be necessary. In many instances fewer bits allow velocity unfolding by the processor. are necessary to code differential reflectivity and velocity between range gates than the absolute The primary disadvantage of the comb of values at each range gate. Zero run encoding frequencies approach is the aforementioned ground would also allow a reduction, but more time and clutter masking of received echoes when different computing effort would be required for decoding PRF's are used. Although the receiver is concep- the data. If the postprocessing trade off is an tually simple, there are many (10-50) parallel acceptable option, then the processor could record microwave components that occupy rack space and the intermediate complex autocorrelation values, cost money. Furthermore, the transmitter for a because all the meteorological and data quality high PRF, long pulse duration system has a duty values are derived from R(0) and R(l). This cycle of 5-10% at an average power of "10 kW. recording option assumes that ground clutter and Designing such a transmitter may prove to be a second trip echoes have been suppressed prior to challenge. the correlation processing. Based on these typical data compression methods, a data rate 5. DATA ACQUISITION AND STORAGE reduction of 2 to 4 appears possible.

The mode of operation in which we Real time display of all the data is visualize the rapid scan radar being used is to certainly not practical, nor is it desirable, from rapidly (but at a low duty cycle) scan an atmos- user assimilation considerations. Because the pheric feature, say a convective storm. Continu- antenna will probably scan the volume in some ous data collection could be counter-productive manner that is nonoptimal for operator viewing, although in some especially interesting meteoro- the display system should be flexible enough to logical cases it certainly would be justifiable. synthesize a viewing surface from the entire Our initial system requirements call for 20,000 volume-scanned data. Viewing surfaces would beams to be scanned in 60 s. Suppose there are include PPI's, CAPPI's, RHI's, as well as any 250 range gates per beam and that 6 bytes of other surfaces that are found to be useful for processed data per range gate are to be recorded. real time or off line display. Experience with The 6 bytes could be the log reflectivity, the rapidly evolving display technology will open velocity, and other values which could be used for up new possibilities in the next few years. data quality indicators and postprocessing data Consequently, this aspect of the rapid scan radar enhancements. Then the processed output data rate system should remain flexible. D is 6. SUMMARY AND CONCLUSIONS 20000 beams 250 range gates 6 bytes D = x x 60 s beam range gate Recommendations from the radar meteorology community, namely the Multiple Doppler = 500 kbytes/s (3) Workshop and the Rapid Scan Doppler Workshop, point to the need for scanning convective storms Although this is a high data rate com- and other mesoscale weather events at a faster pared to present weather radars, it is only 5 rate than presently exists. Errors in derived times higher than the data rate of NCAR's CP-2 wind fields can be reduced by sampling the storm radar when it is collecting at its highest rate. volumes at a spatial and temporal scale appropri- Existing digital tape recorders running at ate to the event being investigated. In this - 1 125 in s at a density of 6250 characters/in are paper, we have identified and discussed the capable of recording at 600-700 kbytes s- depend- critical areas of antenna design and signal ing on record size and other overhead. Each tape processing considerations. A scan and data contains about 160 Mbytes of data, which is over 6 collection rate increase of about 20 would allow complete hemispheric volume scans (30 Mbyte each). significant improvements in experimental studies and wind field synthesis techniques. If we desire higher range resolution data from using a pulse compression scheme, or higher spatial resolution by spatial over-sampling or using a narrower beamwidth, then the data rate

289 7. REFERENCES

Austin, G., 1974: Pulse compression systems for use with meteorological radars. Radio Science, 9, 29-33.

Carbone, R.E., F.I. Harris, P.H. Hildebrand, R.A. Kropfli, L.J. Miller, W. Monginer, R.G. Strauch, R.J. Doviak, K.W. Johnson, S.P. Nelson, P.S. Ray, and M. Gilet, 1980: The Multiple Doppler Radar Workshop, November 1979. Bull. Amer. Meteor. Soc., 61, 1169-1208.

and M.J. Carpenter, 1983: Rapid scan Doppler radar development considerations, Part I: Sampling requirements in convective storms. Preprints, 21st Radar Meteor. Conf., Edmonton, Canada, Amer. Meteor. Soc.

Cooper, G. and C. McGillem, 1978: Doppler spectrum estiamtion for continuously distributed radar targets. Proc. of RADC Spectrum Estimation Workshop, Rome, NY, DDC #A054650, 273-285.

Krehbiel, P. and M. Brook, 1979: A broadband noise technique for fast scanning radar observations of clouds and clutter targets. IEEE Trans. Geoscience Electronics, GE-17, 196-204.

Nathanson, F., 1969: Radar Design Principles. McGraw Hill, New York.

Schrank, H.E., 1983: Low sidelobe phased array antennas. IEEE Ant. and Prop. Soc. Newsletter, 25, 5-9.

Skolnik, M.I. (editor), 1970: Radar Handbook. McGraw Hill, New York.

,1980: Introduction to Radar Systems, McGraw-Hill, New York.

Zrnic, D., 1979: Estimation of spectral moments for weather echoes. IEEE Trans. Geoscience Electronics, GE-17, 113-128.

, and R. Doviak, 1983: Doppler Weather Radar. Academic Press, New York. (In press). Pulse Compression for Phased Array Weather Radar

Appendix E: Keeler, R.J., C.A. Hwang, V. Chandra and R. Xiao, 1993: "Polarization pulse compression for weather radar," 26 th Conf. on Radar Meteorology, AMS, Norman OK, pp 255-257.

May 11, 1999 Page 45 of 52 Reprinted from the preprnt volume of the 26th Intrnatonal Conference on Radar Meteorology, 24-28 May 1993, Norman, OK. Published by the American Meteorological Sodety, Boston, MA. 8.12

PULSE COMPRESSION POLARIZATION WAVEFORMS FOR RAPID SCAN DOPPLER RADAR

R. Jeffrey Keeler and C. Hwang V. Chandrasekar and R. Xiao National Center for Atmospheric Research' Colorado State University ATD - Remote Sensing Facility Electrical Engineering Department Boulder, Colorado 80307 Fort Collins, Colorado 80523

1. INTRODUCTION longer, thereby increasing the average power. Rapid scan Doppler radars can accurately define Any transmitted pulse has a nominal the evolution of convective storms and associated bandwidth, B, and the range resolution of any weather phenomena. Conventional weather radars transmitted pulse has range resolution of c/2B (Keeler require about 50-100 ms dwell time to achieve enough and Frush 1983b). For example, a 10 MHz bandwidth independent samples for accurately measuring pulse has a potential range resolution of 15 m, reflectivity and velocity. Convective systems evolve whether a 100 ns single frequency, an N element rapidly enough and conventional weather radars scan phase code which changes every 100 ns, or a chirped slowly enough that a faster scanning radar is often pulse sweeping through 10 MHz. That is, for these 10 needed (Carbone et al., 1983). A rapid scan research MHz pulses and pulse compression processing weather radar requires two distinct technological (matched filtering), an independent estimate of the efforts to realize a complete system (Keeler and Frush, Rayleigh scattering vector is obtained every 15 meters 1983a): 1) complex waveform design, which is the in range. Consequently, by processing these 15 m subject of this paper, and 2) the electronic step- samples with the pulse pair algorithm, by spectral scanned phased array antenna system, which is techniques, or by any other desired scheme, required to implement a rapid scan radar in its most independent estimates of reflectivity, velocity, width, complete form (Holloway and Keeler, 1993). SNR, etc. every 15 m can be made. These "high Range time sidelobes of pulse compression resolution" estimates can then be averaged to obtain waveforms cause range smearing in strong reflectivity any reduced range resolution. For example, if we gradients (sometimes called "clutter flooding") and average 10 consecutive independent 15 m range must be suppressed. Complementary code waveforms estimates, we obtain a processed 150 m resolution. (Nathanson, 1991) exactly zero these sidelobes if the returns from the code pair arrive at the receiver 3. SIDELOBE SUPPRESSION TECHNIQUES undistorted. However, relative particle motion that The waveform design goal is to find a large occurs between the two coded pulses modifies the compression factor (10-100) and low integrated range transmitted waveforms and exact cancellation is sidelobes at all expected Doppler shifts. Common usually not possible. We propose a complementary waveforms give peak sidelobe (PSL) levels 20-50 dB code waveform pair in which one biphase coded pulse below the primary target response. But for weather is transmitted at horizontal polarization and its targets distributed in range, the important parameter complement is transmitted at vertical polarization. is the integrated sidelobe (ISL) response from all The codes may be transmitted sequentially and their ranges (sidelobes) except the main response. The ISL responses separated by the orthogonal polarizations. may be used as a figure of merit for the weather case. Adding the two responses from the code pair causes Cohen and Baden (1983) demonstrated various the range sidelobes to be suppressed greater than optimization criteria other than minimizing the ISL many other phase coded waveforms. response. Typical ISL values of 10-30 dB are common, but inadequate, for accurately estimating reflectivity 2. DESCRIPTION OF PULSE COMPRESSION and velocities in strong gradients. Digital, sidelobe Pulse compression is a wide bandwidth suppression filters following the matched filter can waveform generation technique that simultaneously suppress the integrated sidelobe power up to 60-70 dB offers increased average transmit power and improved depending on the filter length, but Doppler shifts in range resolution over that offered by a typical single the received signal cause the sidelobes to rise frequency pulsed radar (Keeler and Passarelli, 1990). unacceptably, even for small velocities. Urkowitz and Increasing the bandwidth increases the number of Bucci (1992) describe a Doppler tolerant processing independent samples of the received echo obtainable technique that maintains the integrated sidelobe in a given range interval. It simultaneously decreases response to less than 40 dB at all Doppler shifts. the Signal to Noise Ratio (SNR) of each measurement The resolution characteristics of a specific by the same factor. However, this lost SNR can be waveform may be visualized using the "ambiguity recovered by making the transmit pulse (and the code) function" (Nathanson, 1991), which shows the

The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.

255 ------' .I -- . I- - A r l response ot the matched filter to targets at ranges and Doppler shifts other than the desired response. This response is determined for the specified waveform, and is defined for distributed, as well as point, targets so long as the distributed target may be considered fixed during the pulse propagation time. The sidelobe response at various Doppler shifts is illustrated by cuts along the range axis. For weather targets, the relevant Doppler shifts are ±50 m/s (a few KHz at centimetric wavelengths). Typical textbook drawings show the function out to very large Doppler shifts where the sidelobes are objectionable. Figure 1 shows the ambiguity function for the common 13-bit Barker code on an X-band (3 cm) radar for velocities up to 1000 m/s.

Figure 2. Same as Fig. 1 except Doppler axis covers only relevant weather velocities from 0 to 50 m/s. ISL = -11 dB at all velocities.

In this paper we propose transmitting a complementary code pair, one immediately following the other with minimal time separation, each having orthogonal polarization. A dual receiver system is required to simultaneously receive both waveforms. Appropriately delayed and combined, the waveform pair will show very low sidelobes. The length 10 code looo Hor/Ver example is shown in Fig. 3 and its relevant ambiguity function is shown in Fig. 4. Note this waveform's extreme sensitivity to Doppler shifts near zero, but the integrated sidelobes remain below -29 dB it nc,, llc l rnM- /. x~*fCr a-,11ivolnr vvu.,.ni.iLc: iess Ll[ll. n/3, n/ .

e Figure 1. Ambiguity function for Barker-13 biphase coded waveform. Cod Code Range extent is twice the length of the waveform. Doppler axis I I I I I I extends from 0 to 1000 m/s at3 cm wavelength. The range response I I I at velocity = 0 is the autocorrelation function of the transmitted Horzoni vertical waveform.

Figure 3. Diagram of dual polarization waveform length 10 For weather radars, the velocities of interest are complementary code pair. For a bandwidth of 10 MHz, the horizontal much smaller. Figure 2 shows the same function only and vertical coded pulses are each 1 ps long. for Doppler shifts to 50 m/s. The sidelobes clearly indicate no sensitivity to these Doppler shifts. However, the ISL response is only 11 dB below the main lobe response. A more appropriate class of pulse compression waveforms is the complementary code set (Nathanson, 1991). Complementary code pairs have the property that for an identical scattering response to both pulses and when processed together, the individual sidelobes exactly cancel and the range time sidelobes are identically zero. A distributed target decorrelates in the time between adjacent pulses and the cancellation 5 advantage is reduced. More important, Doppler shifted returns significantly reduce the cancellation for b-c-- - complementary codes.

Figure 4. Ambiguity function of dual polarization complementary code shown in Fig. 3 for 0-50 m/s. ISL is -49 dB at v = 5 m/s, -43 dB at v = 10 m/s, and -29 dB at v = 50 m/s.

257 For a real system, both the target and the may give a significantly better integrated sidelobe antenna will produce a depolarized response which response than the Barker-13 code. The integrated will reduce the sidelobe cancellation. For example, if sidelobe improvement for the biphase codes is more the H-code is the desired signal, then target scatter than 20 dB for relevant weather velocities up to 50 from the V-code will cause a random component in m/s. Contamination from both the cross-polar target the H-code receiver. Furthermore, the antenna will scattering and antenna leakage, and from both group allow a portion of the copolarized scatter from the V- and relative particle motion in the time interval code to leak into the H-code receiver and contaminate between the two codes has not yet been modelled. the copolar H-code return. Precipitation echoes generally have nonzero 60- differential reflectivity (ZDR) and phase (DDP) which causes yet further reduction in sidelobe cancellation. However, we believe these effects can be separately 50 estimated and compensated.

4. SIMULATIONS

"ScatMod" is a relatively simple numerical ? 30 model of the atmospheric scattering that is used to synthesize data for testing various aspects of complex, 20 wideband waveform processing techniques. We have verified this model's operation in one dimension using some basic waveforms with well known properties. 10 Scattered wavelets from a distributed target are coherently combined at the receiver to synthesize the O ( received waveform. A future extention to a two- RAN E dimensional plane of scatterers will obey the 2D equation of continuity to simulate realistic particle Figure 5. Sample of total returned power as Barker code (left) and motions. Digital processing is performed on the I/Q dual polarization complementary code (right) waveforms propagate signals at the model output to estimate atmospheric through reflectivity notch. The power in the notch represent at ranges 100 and 300 the contribution from only the parameters. A statistical analysis integrated sidelobe power. of this data Note that the complementary code performs much better for this basic compared to the known model values allows example, in which the particle velocity and velocity width are both waveform performance evaluation. zero. In Fig. 5 we illustrate a measure of the integrated sidelobe power for the Barker-13 waveform Acknowledgement: This work was supported at a reflectivity notch in which the scattering particles by the FAA Terminal Area Surveillance System have been removed. The notch is imbedded within a Program Office, Jim Rogers, Program Manager. high reflectivity region that has a zero velocity and no velocity width, or relative motion between the two 6. REFERENCES pulses. In the model the only contribution to the Carbone, R.E., M.J. Carpenter and C.D. Burghart, 1985: Doppler radar sampling measured power at the notch is limitations in convective storms. J. Atmos. Ocean. from the sidelobes of Tech., 2, No 3, 357-361. the pulse compressed waveform. The total power Cohen, M. and J.M. Baden, 1983: Pulse Compression Coding Study, drops by about only 9 dB as the filter attempts to Ga. Tech Memo, Project A-3366. measure the low reflectivity notch with the Barker Holloway, C.L. and RJ. Keeler, 1993: Rapid scan Doppler radar: the waveform. The response of the dual polarization antenna issues. Preprints: 26th Conf. on Radar Meteor. Norman, OK, Amer. Meteor. Soc. complementary code to the same reflectivity notch is Keeler, RJ. and CL. Frush, 1983a: Rapid scan Doppler radar much greater because the sidelobes exactly cancel for development considerations. Part 2: Technology assessment. this degenerate atmospheric model. Preprints: 21st Conf. on Radar Meteor., Edmonton, Alberta, Research is continuing with "ScatMod" with Amer. Meteor. Soc., 284-290. Keeler, R.J. and more realistic atmospheric models. We will evaluate CL Frush, 1983b: Coherent wideband processing of distributed radar targets. Digest Int'l Geosc. Remote Sensing new waveforms that may have more robust sidelobe Symp., San Francisco, IEEE, PS-1. characteristics, adaptive sidelobe suppression filters, Keeler, R.J. and R.E. Passarelli, 1990: Signal processing for and further use of polarization to improve waveform atmospheric radars. Proc. of the Battan Memorial Conf. on Radar performance. In the summer of 1993 actual data will Meteor., Boston, Amer. Meteor. Soc., Chap. 20A. Nathanson, F.E., 1991: be collected from a high Radar Design Principles (Second power X-band (3cm) Doppler Ed.), McGraw Hill, N.Y. system to validate and extend model results. Urkowitz, H., and N.J. Bucci, 1992: Doppler tolerant range sidelobe suppression. Digest IGARRS-92, Houston, 5. CONCLUSIONS IEEE. We have shown that the dual polarization complementary code using no Doppler compensation

256 Pulse Compression for Phased Array Weather Radar

Appendix F: Holloway, C.L. and R.J. Keeler, 1993: "Rapid scan Doppler radar: the antenna issues," 26th Conf. on Radar Meteorology, AMS, Norman, OK, pp 393-395.

May 11, 1999 Page 46 of 52 Reprinted from the preprint volume of the 256t InterMaorna Conferenc on Radar Meteorology, 24-28 May 1993, Norman, OK. Published by the American Meteorological Society, Boston, MA. 13.5

RAPID SCAN DOPPLER RADAR: in a continuous manner. This continuous azimuth THE ANTENNA ISSUES rotation will result in only a minor spectral spread of the data. by No attempt is made here to decide upon the Christopher L. Holloway and R. Jeffrey Keeler type of radiating elements to be used in the planar array. The point of this paper is to address para- National Center for Atmospheric Research 1 metric issues like the size of the array, the number Atmospheric Technology Division of elements, the optimum scanning procedure, and P.O. Box 3000, Boulder, CO 80307 number of bits in the phase shifters.

1. INTRODUCTION 2. BASIC ANTENNA ARRAY CONCEPTS The total E-field radiated by N-elements has the Radar meteorologists face the need to obtain information about the development and evolution of following far-field distribution [Balanis, 1982]: rapidly forming atmospheric phenomena like convective storms. This information is needed on a Etotal = [E(single element)] X [AF] (1) spatial and temporal scale, which would lead to a detailed understanding of the dynamic processes where AF is the array factor. This factor is a involved. A few papers in the past have discussed function of the number of elements in an array the concept of a rapid scan radar system [Carbone, and the space between elements. The array factor 1983; Keeler, 1983]. These papers have concen- is what shapes the beam of the array. For the N trated on the type of waveform required for such element array, the array factor can be written as: a radar system. In this paper we address the antenna issues of a rapid scan radar system. Cost N 1 and performance of systems are discussed. AF = E anej(n-l ) (2). Keeler [1983] shows that for many meteorolog- n=l ical applications, the radar needs to scan the entire hemisphere in 60 seconds. In that case over with: 20 000 1° beams are required to cover a hemi- = kbkdsinO + 3 sphere where the dwell time of each beam position is approximately 3 ms. Because of the short dwell where an are the excitation coefficients of the ele- time for each beam position, an antenna array ments, d is the spacing of the elements, 0 is the an- that can be positioned very quickly is needed. An gle measurement perpendicular from the antenna 2 electrically scanned phased array with the follow- face, k = >- and fl is the phase excitation between ing requirements could accomplish this fast scan- the elements. ning rate: beamwidth = 0.5 - 1.0° sidelobes lev- It can be shown that by changing the phase ex- els < -35 dB, gain > 45 dB and a bandwidth citation 3 between the elements the maximum ra- P 100 MHz. diation can be steered in any desired direction. We The antenna concept proposed here is shown in can write i as: Figure 1. For the rapid scan doppler radar system, it is felt that the use of a planar array composed of ¢ = a 1-D electronic elevation scan used in conjunction kd(sin 0 - sin 0o) (3) with a mechanical azimuth scan will be adequate for scanning the entire hemisphere. where O, is the desired scanning direction. Ideally the mechanical scan would scan to dis- The array factor (AF) is a periodic function, crete locations. However, due to the inertia of the and large spacing between the elements will pro- antenna, the mechanical scan must be performed duce more than one main beam in the space between -90° < 0 < 90° (the visible space). The large spacing will allow the waves from each element to add in-phase at additional main beams, called "grating lobes." It can be shown fSkolnik, 3so 1990] that if: d 1 A 1 + Isin |,,I (4) then no grating lobes occur in visible space when the desired beam is scanned over a maximum scan range of 0,9 from broadside (0 = 0). Equation (4) says that if a maximum scan angle is set, then the spacing of the element in the array must be d < A 1+ . in order to illuminate the grating lobes. This equation also provides the maximum angle the antenna can be scanned for eiven 1.6a 5 T %,AL snaciner csiuch thantULt 6.,rbu%1.UL6orta.;Tr lVUVZl-rlrc willWe n-o+tILU Figure 1. Scanning configuration of the planar appear. Another important quantity required for an- array for weather doppler radar. tenna design is the beamwidth. It can be shown The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.

393 1.00- a'7 - Tay I or Dow (n LM--U tforfny Tapper,

L 0.80- I R Po~

c I r. I I 0.60- I I CD I -N=10 I C LL I I 'c I 0.40- I E Il m I~ II ar Il m 1: N=60 0.20- II . a3 -N=ee zl II %I % N=10 " I Nz14e "I I I, I I J~ , I n tnunk · b I : - i I ! ...... - WG.* Go -r - 1--- -- Y - · · - ' V . I. .; - f- FTA -.... 00 -1.0..... 0. 40 1'.20 -b. B -3.00 -1.00 1.00,,, 3.003.I ri , 5 .0000 d/X Figure 2. Illustration of both the effect of element Figure 3. Antenna pattern of a Taylor designed spacing and the number of elements on a beam- current distribution. width. very low sidelobe design include: reduced gain, [Balanis, 1982] that for an N element array with increased beamwidth, increased design tolerance, the element spacing of d, the beamwidth for a and increased cost. scanning array Various techniques are used to design the de- is given by: sired sidelobes. The two most common techniques are the Chebyshev polynomials procedure and the e 0 cos- [cos 0 -0.4434 4 } Taylor procedure. In this design study the Tay- -cos- 1 [cos 0o + 0.443Nd J ) lor procedure was used for 100 elements spaced d = 0.75A apart. A Taylor design is more stable and has fewer sensitivity problems. For sidelobe where 0o is the desired beam position (measured levels of < -35 dB, the Taylor design gives the from broadside). antenna pattern shown in Figure 3, and all the sidelobes are below -35 dB. However, the cost 3. ARRAY SIZE of lower sidelobes is an increase in the beamwidth of the antenna. For 100 elements, and with this In this section we look at the number of elements particular current excitation, the figure shows that needed to achieve a beamwidth < 1°. As stated the beamwidth is still < 1°. above the beamwidth is directly related to the element spacing and to the number of elements in 4.1 Dependence on phase shifter errors the array. Figure 2 illustrates this effect. This figure shows how as the element spacing increases The low sidelobe design, illustrated in Figure 3, is the beamwidth decreases. Again, if the spacing is for an antenna with perfect phase and amplitude larger than A grating lobes will appear in the vis- distribution across the aperture. In reality, errors ible space. We should note that all of these curves are present in the phase and amplitude and need are based on a 0° scan angle, and if a antenna to be considered in the design. The errors in the is scanned, then grating lobes will appear in the phase and amplitude will remove energy from the visible space for element spacing of d < A. main beam and distribute it into the sidelobes. Figure 2 shows that the greater the number of There are basically two types of error: random elements and the greater the spacing of the ele- and correlated. Pure random errors will distribute ments, the smaller the beamwidth. However, there the energy to create random sidelobes which result is a trade-off, because the more elements in the in increased rms sidelobe level. Correlated errors array the higher the system cost. Because of the (quantization errors) lump the energy in one spe- grating lobe issue, element spacing of d = 0.75A cific location, resulting in large sidelobes at these is chosen. Figure 2 illustrates that for an element far field locations. spacing of d = 0.75A, an array size of 100 x 100 will Phase errors pose the most difficulty in design- give a pencil beam with a beamwidth of < 1.0°. ing very low side lobe antennas. Cost considerations require the minimum number of bits as pos- 4. LOW SIDELOBES DESIGN sible in the phase shifters; therefore, we will concentrate on phase error. Besides meeting the required beamwidth, the other objective for this antenna is to minimize 4.1.1 Random phase errors clutter. This requires an antenna that has very low sidelobes, on the order of -35 dB. Arrays of A phase shifter with p bits has phase steps of: very low side lobe levels can be achieved by tapering the amplitude excitation of each element. 27r A constant amplitude illumination provides the (6) highest gain and narrowest beamwidth with the 2P highest sidelobe. A tapered amplitude can significantly reduce the sidelobes, but the gain and the It can be shown [Morchin, 1993] that the rms side- beamwidth increase. The trade-offs to achieve this lobe level that results from this discrete phase step

394 is given by: For a 15° scan angle the spacing is restricted 3.3 by d < .80. This larger restriction can allow the MSL N2 2 (7) ruN22P7 size of the array to be reduced to approximately 100 x 100 elements, which is a 40 % reduction in where N is the number of elements and ?r is the both the size and cost of the antenna over that of aperture efficiency. For a linear Taylor array r77 the 45° scan. - 0 120 1.37e p (SLL+3 )/ where SLL is the mainlobe to sidelobe ratio expressed in dB. 6. DISCUSSION In this Taylor design the antenna has 100 elements that are all controlled by a phase shifter A preferred rapid scanning doppler radar system with a sidelobe requirement of < -35 dB. The is one that is composed of a four face (or even a aperture efficiency is - .78 and from (7) a 3-bit single face depending on the desired coverage) ac- and 4-bit phased shifter will give rms sidelobe tive array that uses TR-modules at each radiating levels of -32 dB and -38 dB. Therefore, based element. This antenna configuration maybe too on the random phase error, 4-bit phase shifters costly. One can expect to pay an order of mag- are needed to ensure the desired sidelobe level of nitude more for an active array that uses these <-35 dB. TR-modules over what one might pay for a non- active planar array. With this in mind and since 4.1.2 Correlated error a non-active rotating plane array is adequate for weather observation, the most cost effective an- High sidelobes will also occur when periodic phase tenna for the meteorological community would be modulation is present across the aperture. El- a non-active planar array. ements along an array must have a linearly in- Phased array antennas, as described in this pa- creasing phase shift across the aperture to point a per, can be readily used in dual polarization ap- beam at some angle o,. If a phase shifter with p plications. The radiating elements must be ca- bits is used, then the discrete phase shift given in pable of generating the desired polarization, but equation (6) is used to approximate the required the waveform or scanning requirements do not linear increase in phase shift. The result of this prohibit this important remote sensing technique. stairstep approximation is that the linear increase Further the rapid scan architecture can be used in phase shift is the presence of a peak phase error for other research tests, including interferometric of 3 = 2. This phase error results in a so-called wind profiler techniques using partitioned subar- rays, or bistatic radar using distributed receivers. quantization sidelobe (QL). The level of this sidelobe is given by [Morchin, 1993]: 7. ACKNOWLEDGMENT

QL = (2P- 1)-2 (8) This work is partially supported by the Federal Aviation Administration (FAA) TASS (Terminal In order to keep this sidelobe below the Area Surveillance System) program office. The < -35 dB needed for the rapid scan antenna, authors would like to thank Jim Rogers from the a 6-bit phase shifter is needed. If the number of TASS program office and Pat Westfeldt from Ball bits needed in the phase shifter can be reduced, the Aerospace for their valuable discussion and com- cost of the array will be reduced. By introducing a ments. small random phase to each phaser, the the quantization lobes can be significantly reduced. Skolnik 8. REFERENCES [1990] suggests that these small random phases are equivalent to adding 1 bit to the phase shifters in a Balanis, C. A., 1982: "Antenna Theory," Harper 100-element array, 2 bits in a 1000-element array, and Row, Cambridge. and 3 bits in a 5000-element array. Brookner, E., 1991: "Practical Phased Array 5. SCANNING PHILOSOPHY Antenna Systems," Artech House, Boston. Carbone, R. E. and M. J. Carpenter, 1983: "Rapid The next question is how large of an electrical scan doppler radar development considerations Part scanning angle can be tolerated. The first choice I: Sampling requirements in convective storms," 21st might be to set the antenna at 45° and scan the Conference on Radar Meteorology, pp. 278-283, Sept. array to ±45° to cover the hemisphere. This large 19-23. scanning angle has a restriction on the element spacing ased on the appearance of grating lobes Keeler, R. J. and Charles L. Frush, 1983: "Rapid according to equation (4). For a 45° scan angle scan doppler radar development considerations Part the spacing is restricted by - < .58. To achieve a II: Technology Assessment," 21st Conference on Radar Meteorology, pp. 284-290, Sept. 19-23. beamwidth of < 1°, an approximately 140 x 140 element array will be needed. Morchin, W., 1993: "Radar Engineer's We believe the best scanning procedure is il- Sourcebook," Artech House, Boston. lustrated in Figure 1. In this configuration the Skolnik, hemisphere is divided into three sectors or groups M., 1990: "Radar Handbook," corresponding to azimuth angles of: 0° < 8 < 30°, McGraw-Hill, New York. 30° < 0 < 60 and 60° < 8 < 90°. The antenna in this configuration will be mechanically positioned at 15°, 450 and 75°, and electronically scanned to ±15°.

395 Pulse Compression for Phased Array Weather Radar

Appendix G: Keeler, R.J., 1994: "Pulse compression waveform analysis for weather radar", COST-75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium, pp 603-614.

May 11, 1999 Page 47 of 52 COST - 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

Pulse Compression Waveform Analysis for Weather Radar

R. Jeffrey Keeler National Center for Atmospheric Research PO Box 3000 Boulder, Colorado USA 80307 Internet: [email protected] Telephone: 303-497-2031 Fax: 303-497-2044

Abstract. Next century's advanced weather radars can accommodate pulse compression waveforms and phased array electronically scanned antennas to meet potentially higher time and space resolution requirements and specific scanning needs. We have investigated several coded waveforms and compressionfilters for weather radarapplications. Candidate waveforms include Barker and Pseudo-Noise coded bi-phase as well as linear and non-linear FM waveforms. Mini- mum integrated sidelobe (inverse) filters are demonstrated to be superior to matched filters for compression processing of distributedweather echos. We describe the Doppler sensitivity of the waveform and filters and find that special Doppler tolerant processing may be necessary to reduce range sidelobe contamination. We demonstrate these effects using both ground clutter and 50 dB reflectivity gradient weather data taken with the 3 cm ELDORA testbed radar.

1.0 Introduction

Doppler weather radars can accurately depict the reflectivity and velocity structure of convective storms and other weather phenomena. The American WSR-88D (Nexrad) network and the Euro- pean weather radar network require relatively long dwell times (40-100 msec) to acquire enough independent samples for accurately measuring weather parameters. For some operational systems and especially for research systems, the volume scan time and update times are too long to capture essential features of convective evolution with the temporal or spatial resolution desired (Carbone, etal 1985; Wolfson 1993). A more rapidly scanning sensor is required to improve resolution in both space and time.

1.1 High resolution radar system

Figure 1 depicts the two distinct technology efforts required for higher space and time resolution weather radar measurements (Smith 1973): 1) a coded wide bandwidth waveform that Phased allows higher range resolution and subsequent antenr larger number of independent estimates within a A dwell time, and 2) an electronic step scanned (e- Pulse compression I scan) phased array antenna that allows rapid and waveform I agile beam movement. The wideband waveform allows accurate weather measurements in a short data acquisition time for a given beam and the e- Figure 1. Advanced high resolution radarsystem using pulse compression waveform and phased scan antenna allows rapid beam movement using array electronic scanned antenna. a larger number of beams to cover the surveil-

July 29, 1994 Page I COST- 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994 lance volume without inducing scan modulation that degrades the accuracy of the measurements.

As as example from aviation weather, convective activity frequently spawns dangerous winds, such as microbursts, that may rapidly form a lethal aviation hazard in an airport terminal area. Weather volume scan times of 2.5-6 minutes, characteristic of TDWR and Nexrad radars, do not have the time resolution to acquire data by which a microburst hazard forecast can be made. A standard mechanically scanned radar would have extreme difficulty in searching an airport terminal area for precursor signatures in a timely fashion. In this paper we shall discuss only the waveform design aspect of this advanced radar architecture. Other system aspects have been previously discussed by Keeler and Frush (1983a) and Holloway and Keeler (1993).

1.2 FAA/TASS program description

The FAA's Terminal Area Surveillance System (TASS) Program is currently active in the "advanced weather radar" arena. This relatively new research and development program is exploring concepts for a next generation air traffic and weather surveillance radar. The radar is envisioned as a phased array system capable of detecting, tracking and predicting positions of all aircraft and hazardous weather phenomena in the airport terminal area. A solid state transmitter. system using pulse compression is a likely characteristic. Various antenna system configurations are being considered, ranging from a single ID e-scan mechanically rotating phased array to multiple fixed face 2D phase scanned active arrays. Dual polarization measurements are also being studied. The FAA is working closely with American and European industry in developing concepts and relevant system designs.

1.3 Characteristics of weather targets

Weather targets have echo characteristics different from aircraft and other "point" targets and we desire to estimate parameters of this target, such as its backscattered power and radial velocity' (Keeler and Passarelli 1990). Extended targets, such as precipitation, insects, and refractive index: gradients, will scatter from whatever the antenna and transmit pulse illuminate with energy that is scattered back to the receiver. Consequently, sidelobe suppression from both the antenna and the pulse waveform are extremely important in determining precisely where the echo scattering region is located, particularly for weak targets surrounded by nearby strong scattering targets.

Weather targets are typically smaller than the radar wavelength of interrogation. Consequently, Rayleigh scattering theory applies rather than Mie or optical. Radar characterization of precipitation is defined in terms of the "radar reflectivity factor" (Z), a quantity related to the Rayleigh scattering from a dielectric sphere, which, in turn, is related to the radar cross section (a) using the X4 wavelength dependence (Battan 1972; Doviak and Zmic 1993).

1.4 Digital technology

Rapid technology developments in digital signal processing components and associated digital filter methods have led to new capabilities in waveform generation and pulse compression filter techniques. In the past waveforms were designed with the concept of using matched filters to optimize the detectability of targets, or the signal to noise ratio. However, weather radars scatter from targets distributed in range and the integrated range sidelobe response becomes the relevant quan-

July 29, 1994 Page 2 COST - 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994 tity to optimize. Digital sidelobe suppression filters are better suited for weather measurements. Highly precise, real time filters using these techniques are readily implemented using modern digital signal processing (DSP) chips.

2.0 Waveform and compression filter design

Pulse compression is a waveform technique that simultaneously offers higher range resolution and increased average transmit power over that possible with a typical single frequency pulsed radar waveform. Increasing the bandwidth of the waveform increases the range resolution and the number of independent samples of the received echo in a specified range interval. However, the Signal to Noise Ratio (SNR) of each sample is reduced by the same amount. The SNR can be recovered and is independently determined simply by lengthening the transmit pulse, thereby increasing the average transmitted power (Keeler and Frush, 1983b).

2.1 Coded waveform design

The effective range resolution of a waveform is c/2B. For example, a pulse with a 10 MHz waveform has a potential range resolution of 15 m whether it is a 100 nsec single frequency pulse, an N-element phase code changing every 100 nsec, or a chirped pulse linearly sweeping through 10 MHz. The output of an appropriate pulse compression filter gives an estimate of the received signal that can be processed to give independent estimates of reflectivity, velocity, etc every 15 m in range. These "high resolution" measurements can then be averaged in range to provide coarser range resolution. For example, if we average 10 consecutive 15 m measurements, we obtain a processed 150 m final range resolution. For many aviation weather and convective research applications we desire to accelerate volumetric data acquisition by about an order of magnitude over that attainable with present mechanically scanned, simple pulse weather radars. Therefore, we require about 10 times shorter dwell time per beam, or something of order 10 times as many independent range elements over which to obtain base data estimates.

The coded pulse length is somewhat arbitrary and is determined by the desired system sensitivity. To maintain the same SNR for each range sample as existing systems, we require the same increase in average power as was specified for the increase in pulse bandwidth. Consequently, both the time and the bandwidth should increase by the same factor. Typical BT values of 50-100 seem to fit present measurement needs as well as radar and digital processing technology.

The actual coding of the waveform can take many forms. Phase or frequency codes are preferred over amplitude codes to maximize average power and simplify transmitter design. Bi-phase codes reverse the phase according to a specified binary pattern. For example, Barker codes and Pseudo- Noise (PN, or maximal length) codes are common (Cohen 1987). Quadri-phase, or higher order poly-phase codes (Lewis, et al 1986) are also possible but may offer only limited advantages. Fre- quency Modulation (FM) codes have always been popular. Linear FM codes are efficient in obtaining large compression ratios and are easily generated and compressed using both analog July 29, 1994 Pag..3 July 29, 1994 Page 3 COST- 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994 and digital means (Strauch 1988). Non-linear FM waveforms offer spectrum shaping advantages with the accompanying reduced sidelobe response while retaining a rectangular waveform with its the average power advantage (Famett and Stevens 1990).

Complementary codes for dual polarization

Dual polarization radars may accommodate complementary code pairs which completely zero out their sidelobe response (Golay 1961). It is possible to utilize the radar's orthogonal polarization isolation to transmit complementary codes simultaneously, one on each polarization, and obtain extremely low range sidelobes. However, differential scattering effects and Rayleigh fluctuations with the attendant decorrelation of the returns will degrade the sidelobe cancellation as will incomplete polarization isolation between the co-and cross-polarized channels. (Keeler, et al 1993). The unknown Doppler shift further limits the achievable sidelobe cancellation.

2.2 Compression filter design

The joint waveform and compression filter design goal is to determine a waveform having a compression factor of BT=50-100 and low range sidelobes. These range sidelobes occur because of imperfect compression filtering. The most we can hope to achieve is to minimize them in a least squares sense. "Matched filters" (MF) are known to be optimum in the sense of maximizing the output SNR. Common waveforms and matched filters yield peak sidelobe (PSL) values of 20-40 dB below the primary target response, which is not adequate for many weather applications. Weather targets are distributed in range and the important parameter to minimize is the integrated sidelobe (ISL) response, the contribution to the total return from all ranges except for (and relative to) the main response. Typical matched filter ISL values are -10 to -20 dB. For accurately estimating reflectivities and velocities in strong gradients, we need compressed waveforms having ISL values 40 dB or more below the main filter response for all Doppler shifts less than 50 m/s.

Digital sidelobe suppression filters (variously called Wiener filters, inverse filters, deconvolution filters, spiking filters, or whitening filters) are optimal designs that minimize the ISL of the desired filter response in a least squares sense (Wiener 1942, Rice 1961, Treitel and Robinson 1966, Ackroyd and Ghani 1972). For the pulse compression filter design this desired response is an impulse having a time width, tB, equal to the inverse bandwidth of the waveform. Both the PSL and ISL can be suppressed 10's of dB over the MF response at the cost in SNR of a fraction of a dB. Consequently, these optimal ISL compression filters are preferred over the MF in the weather application. The large sidelobe improvement is limited to a relatively small set of velocities so that the Doppler sensitivity of the waveform design is an important ingredient.

2.3 Waveform analysis

Waveform resolution characteristics in the range and Doppler domains may be visualized with the so called "ambiguity function" (Woodward 1953). This two dimensional function shows the joint response of the compression filter to the transmitted waveform and to targets distributed at ranges and velocities about the desired main response. In other words, it is a weighting function in Range/Doppler space for other radar targets. The ambiguity function shows the response for both point and distributed targets so long as the distributed targets are fixed relative to one another, or frozen in space, during the pulse propagation time. This assumption is valid for microwave radars

July 29, 1994 Page 4 COST - 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994 having pulse lengths of 10's of gsec. The primary goal of weather radar waveform design is to maintain low ISL values over the desired set of Doppler velocities. This goal is difficult to achieve even at the relatively low weather Doppler velocities. Longer wavelength radars, eg wind profil- ers, routinely use pulse compression with predictably good results (Keeler and Passarelli 1990).

We shall analyze four coded waveforms that represent potential waveforms for the weather radar measurements as well as point target (aircraft) detection:

1) Barker bi-phase (BT=13) code (B-13) -- known good sidelobe properties, 2) PseudoNoise bi-phase (BT=15 and 63) code (PN) -- larger compression ratio (BT), 3) Linear FM (BT=63) code (LinFM) -- another waveform class with arbitrary BT, 4) Tangent Non-linear FM (BT=63) code (TanFM) - shaped spectrum to reduce sidelobes.

For each waveform we show ambiguity functions and the integrated sidelobes vs Doppler curves for several compression filters and are for the 3.2 cm wavelength (X-band) radar we used to collect test data. Ambiguity functions for 10 cm (S-band) and 5 cm (C-band) radars and the ISL curves would be scaled back to 30% and 60% of the velocities in the curves since the Doppler shift in Hz determines the filter response. Thus, we show the worst case sidelobes for centimeter wavelength weather radars. The waveforms and compression filters are analyzed without any bandlimit filtering so as not to obscure subtle effects using ideal waveforms and filters. In reality, each received waveform must be lowpass filtered by an antialiasing filter to suppress sampling products and limit the transmit bandwidth. : . .

Bi-phase waveform

A bi-phase coded waveform reverses the phase of a single frequency sinusoid at regular "chip" intervals (corresponding to the range resolution c/2B) according to a predetermined sequence. The waveform and filter output are sampled once per chip at the inverse bandwidth sampling interval, tB. Figure 2 shows the ambiguity function of the B-13 waveform and matched filter. The ambiguity function appears to be shaped differently than textbook plots (Rihaczek 1969). We plot only the relatively small weather velocities (<50 mIs) rather than up to Mach speeds typical of military targets. This Barker coded waveform has a time bandwidth product, or compression ratio, of 13. Thus for a given desired range resolution, 13 times more average power (lldB) can be transmitted than a simple single frequency pulse having the same range resolution. In Figure 2 the range, sidelobes are basically constant at -22 dB for all Doppler shifts up to 50 m/s and the ISL is about -11 dB. The Barker codes are known to have unit sidelobe matched filter response. The highlighted curve at Vel=0 is the autocorrelation function of the waveform for the matched compression filter (MF). Figure 3 shows the same B-13 waveform with an inverse compression filter, Inv-5x, five times longer than the waveform itself. The peak sidelobes are down about 60 db and the ISL is approximately -50 dB at zero velocity.

Figure 4 shows the ISL vs Doppler curves for the B-13 waveform and the MF, Inv-lx, Inv-2x, Inv-3x and Inv-5x filters. The MF is clearly inferior to all the inverse filters. The longer inverse filters give exceptionally low. ISL values near Vel=0, but they steeply increase and converge at about -20 dB for larger Doppler. Figure 5 shows the compression filter output response at Vel=0 for each of these.filters. The MF sidelobes are consistently high. The inverse filter sidelobes are much lower and located away from the main response as the filter length is increased. The filter impulse responses (not shown) are instructive to note. The MF impulse response is simply the Jul 29 194Pg July 29, 1994 Page 5 COST - 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

0l 0g

--- Figure 2. Ambiguity function for B-13 and matched Figure 3. Ambiguity function of B-13 and Inv-Sx filter. filter, Sidelobes are uniformly high at -22 dB and main Both ISL and PSL are much lower than the MF response response peak is constant showing negligible Doppler but show extreme Dopplersensitivity near zero velocity. sensitivity. Peak sidelobes at zero velocity are-60 dB. time reversed transmit waveform (as it is defined) and the inverse filter impulse responses are highly tapered'at both ends and approximate the MF response near the central region.

The longest known Barker code is length 13. PN codes have reasonably good autocorrelation sidelobes and occur for lengths 2n-1 and allow larger BT products. Therefore, we consider the PN-15 code for comparison with the B-13 code and the longer PN-63 code. We searched the possible sequences to select the one having the lowest integrated sidelobe autocorrelation sequence. Figure 6 shows the ISL vs Doppler curves for the PN-15 and PN-63 waveforms with the MF and the Inv-1/2/3/5x filters. The lowest ISL is only -22 db for the PN-63 code near zero velocity. Apparently, the PN codes that we have investigated do not have the same low ISL values that are characteristic of the Barker-13 code. Furthermore, the PN-15 code has lower ISL's than the PN-63 code for the high velocities. PN codes seem not to offer a viable technique of obtaining high com-

0 -50o ' \MF -100

0 -50 - Inv lx -100 0 m 'a -so50 Inv 2x -100 0 -50^V,---,J[--m lnv3x -1o00

^ -503.. x^ ~I~~nv~x. ---- v v 0 10 20 30 40 50so -loo_10 .-- . Velocity 0 20 40 60 80 Figure 4. Integrated sidelobes vs Doppler shift up to Figure5. Compressionfilter response to B-13 waveform 50 m/s for B-13 waveform with MF and Inv-1.2/3/5 for MF and Inv-1/2/3/5x filters. Note reduced sidelobes compressionfilters. as filter length is increased. Page 6 July29,July 29, 19941994 Page 6 COST -75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

W - V 1 - i -- -! . pression ratios with-. low ISL ratios. UrKowltz and Bucci (1992) have used a large compression ratio concatonated Barker code and long inverse filters that appear to give better 20 response than these PN codes. Dash-- PN-15 FM waveforms Solid-- PN-63 -40 Frequency modulated (FM or chirp) waveforms represent a different category from the biphase waveforms. The FM waveforms have -6C , , ,,,. ,. , ... ._. . . .|. ._. _._..._. . .. . '' . '. . .. *. a continuous phase change over the duration of 0 ,10 .20 30 40 50 the pulse rather than abrupt phase changes at the "chip" boundaries. This continuous phase Figure 6. Integrated sidelobes vs Dopplerfor Pseudo 63 andfor change representschange representsa dilemma in the compres-compres Noise bi-phase waveforms of length 15 and sion filter design. The filter is designed in a MF ad the Inv-l2/3/5xfiter deterministic manner based on specific samples of the transmit waveform. However, the received samples have a phase determined by the actual range to the target and are different from the filter design samples: Therefore, the compression filter is not optimum. It appears that a larger sampling rate than the waveform bandwidth mitigates this effect. The FM waveforms were oversampled by a factor of 2 to yield 2BT sample points within the pulse. Thus, the matched and inverse filters have twice as many points as the bandwidth would otherwise dictate.

Linear FM waveforms have a well defined compression ratio -- it is simply the frequency sweep B (the bandwidth) times the pulse length T. However, non-linear waveforms have a less well defined BT. Because non-linear FM (NLFM) waveforms control the frequency sweep to tailor the spectrum shape and yield low MF sidelobes (Farnett and Stevens 1990), the 3dB bandwidth is less than the total frequency sweep. Thus, the compression ratio is determined by the particular non- linear frequency sweep selected. For example, a non-linear frequency sweep may cover a 10 MHz interval, but the actual 3 dB bandwidth of the waveform spectrum may be only 6 MHz.

The ambiguity function for the LinFM waveform with BT=63 and a MF (not shown) has sidelobes that are high and slowly tapered in range. However, as shown in Figure 7 an Inv-5x filter significantly reduces both the peak and integrated sidelobes. Figure 8 shows the ISL vs Doppler for the LinFM-63 waveform and the MF and the Inv-l/2/3/5x filters. Inverse filters that are at least 5 times as long as the waveform seem to provide nearly the same sidelobe suppression as Barker waveforms -- about -40 db at Vel-0, rising to about -20 db at 50 m/s.

Shaping the spectrum of the NLFM waveform with a non-linear frequency sweep reduces the 3 dB bandwidth and the compression ratio. But it also allows reduced mismatch loss as the inverse filter better approximates the MF response. Using a frequency sweep that follows the f=tan(t) curve defined in Nevin et al (1994) is one particular waveform, TanFM. If we sample this waveform at 2 times the frequency sweep (not the 3 dB bandwidth), the ambiguity function and ISL vs Doppler curves are virtually identical to the LinFM-63 example. In this case the mainlobe width is over-constrained to be smaller than tB and the sidelobes must rise. However, if the sampling frequency is reduced to 2 times the 3 dB bandwidth so the response has the a fewer number of points and the mainlobe width is constrained to be tB, then the sidelobes can be suppressed further. The TanFM waveform has a compression ratio of about 39. Figure 9 shows the ambiguity July 29. 1994 Page 7 COST - 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

a m

3 VeloclHy Figure 7 Ambiguity function of LinFM-63 waveform Figure 8. ISL vs Doppler for LinFM-63 with the MF and Inv-5x filter. Peak sidelobes are 45db down at and lnv-1/2/3/5x compression filters. Data is oversam- zero velocity. pled byfactor of 2. function for the TanFM and the Inv-5x filter and Figure 10 shows the ISL vs Doppler curves. The sidelobes are significantly lower than for the LinFM cases and show a stronger Doppler sensitivity near zero velocity. The sidelobe levels indicate that the spectrum shaping characteristic of the NLFM contributes significantly to the sidelobe reduction. The mismatch loss is different, but quite small, for both FM waveforms. When these waveforms are low pass filtered, the ISL curves are lowered even more.

3.0 Data acquisition and analysis

To validate the waveform analysis, we modified an existing NCAR radar to acquire pulse compression data which were then compressed and analyzed off-line. Data were collected on strong isolated point clutter targets and high reflectivity gradient weather cases.

is co ·rD

u 10 20 30 40 50 Velocity Figure 9. Ambiguity function of TanFM waveform Figure 10. ISL vs Dopplerfor TanFM (BT=39) with the and nv-5x filter. Peak sidelobes are 70 dB down at MF and lnv-1/2/3/5x compressionfilters.Data are over- zero velocity. Compression ratio is 39. sampled by 2. Page 8~~~~~~~~~~~~~~~~~~~~~~~~~~~ July29, 1994 July 29, 1994 Page 8 COST -75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

3.1 ELDORA test bed radar description

NCAR's 3 cm test radar in Boulder, Colorado has been modified to transmit pulse compression waveforms and record the digitized complex video signal (the inphase and quadrature samples) for each range gate. The radar uses a digital waveform generator, amplified by a 50kw TWT amplifier and fed to a 2.4 m diameter Cassegrain polarization twist antenna with 1 degree beamwidth. The maximum pulse length is 10 isec. The receiver is a conventional low noise coherent system that uses a Digital IF processor (Randall 1991) to suppress low level artifacts that typically exist in analog receivers. The digitizer operates at a maximum rate of 20 MHz and 12 bits. By design the digital IF filtered maximum data rate is 2.5 MHz for bi-phase codes. Consequently, the maximum time bandwidth product available using the Digital IF is BT=25. A new design Digital IF allows complex video digitizing at 10 MHz rate and a maximum BT=100. The data are then processed off-line using NCAR-enhanced PV-WAVE processing and plotting routines.

The system was configured to generate the B-13 bi-phase code for 600 nsec (90 m) range samples. The pulse length was therefore 7.8 psec (702 m). The Digital IF produced a sampled complex data stream at 1.67 MHz rate. Our goal was to point the radar at 1) a strong point ground clutter target and 2) a convective weather having a strong reflectivity gradient at non-zero velocity to evaluate the sidelobe suppression capability of the coded waveforms and inverse filter compression processing. Alternating bursts consisting of 32 simple single frequency 90m rectangular pulses were followed by 32 coded 702 m rectangular pulses. No clutter filtering was performed on any of the data shown here.

3.2 Point clutter target

The data of interest for the evaluation is the relative backscattered power and the radial velocity for the simple and coded pulses. Figure 11 shows the data for the simple pulse plotted for 200 consecutive 90 m range gates from 4 km to 22 km with a strong ground clutter target located on a mountain peak about 16 km to the west. Note the 60 db difference in the clutter signal at range gate 137 and the noise beyond. The clutter has extremely high SNR, zero velocity and is surrounded by noise.

Figure 12 shows the same data for the coded pulse and the Inv-5x filter. Because the average power is 11 dB higher than for the simple pulse and the processing gain is normalized to the same peak power for both coded and simple pulses in our processing, the noise level beyond the point clutter is suppressed 11 dB. Thus, the SNR of the point clutter and the noise beyond is about 71 dB. The velocity values are still zero mean but they are more accurately determined because the SNR has been increased and they show "clutter flooding". The power and velocity estimates clearly show the range sidelobe effects with this extremely strong point target. The non-moving clutter power in the first half of the return is the same for the simple and coded pulses. The sidelobe responses at range gates 107 and 167 are 55 dB down and correspond to those shown 30 samples away from the main response in the lower panel of Figure 5.

The sidelobes close to the main response that are 35-50 db down are not predicted by the filter response. These are likely caused by "distortions" in.the transmitted waveform that are not compensated for in the filter design. A more careful measurement of the actual transmit pulse will be made and the filter redesigned for minimum ISL which we expect to suppress these sidelobes.

P e July 1 .

July 29, 1994 Page 9 COST- 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

so 60

60 60: '0 '- -. . - . .60 dB. 71d.. 40 20 40

1o I 0 50 100S 150 0 I S 100 1SO 20

. &6.------6 , .

- - -~~~~~~~~ .hj he, @1s1l n-0 n t~~~~~~~~~~~~- - 6 . . I 0,O

-0.6-A -04. I --mbr - I . . . . -0.6 I . _ _ - 0 50 100 150 200 0 50 100 150 200 Figure 11. Ground clutter data showing received Figure 12. Ground clutter target using B-13 pulse and power and velocity for simple single frequency 90m Inv-5x filter. Note 11 dB SNR increase and the sidelobe pulse. Nyquist velocity (±0.5)corresponds to ±8m/s. response. Simple and codedpeak powers are equal. 3.3 Convective weather target

Ground clutter has zero velocity and the expected sidelobes are lowest Higher velocities that are sometimes associated with strong reflectivity gradients offer the most severe test of pulse compression waveforms on distributed weather targets. Figure 13 shows a 50 dB weather reflectivity gradient taken with the Eldora test bed radar using the simple 90 m pulse. The echo is from a small thunderstorm cell 15 km to the south of the radar on June 2, 1994. Unless the ISL's are 50 db down, then the strong echoes within the storm will contaminate the weak echo region outside the cell. Figure 14 shows the same storm cell using the B-13 bi-phase coded pulse and the Inv-5x compression filter. The SNR is increased from 49 dB to 60 dB but the tapered echo near the cell edge (formerly below the noise level) shows strong evidence of sidelobe leakage. We expect ISL leakage from half the waveform within the main cell having velocity 5-12 m/s to be 40-45 dB below the main echo (see Figure's 4 and 5), which is approximately the value indicated.

Figure 13. High reflectivity gradient weather using Figure 14. Weather echo using B-13 waveform and the simple 90 m pulse. Gradientis 50 dB over 2 km range Inv-x filter. There is discernible leakage of the sidelobe at front and rear of cell. Nyquist velocity is ±8 m/s. energy from the strong precipitationecho to outside the Velocities within the cell are 5-12 m/s. cell. ~ July29,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~194Pae1 July 29, 1994 Page 10 COST - 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994

Figure 15 shows the 32 point power spectrum of the weak echo in range gate 93 for the simple pulse (solid curve) that is outside the rain cell and for the coded B-13 pulse and Inv-5x filter (dashed curve) that is contaminated by sidelobe leakage. The arrows show how the velocity estimate shifts from near zero velocity for the simple pulse to near the upper Nyquist velocity for the sidelobe leakage of the coded pulse. We may be able to use the spectrum quantitatively to measure the ISL leakage from the strong echo within the cell having one velocity into the weak echo outside the cell having a different velocity.

4.0 Conclusions

Pulse compression is one technique of obtaining the short dwell time necessary to make high space and time resolution weather radar measurements. Range time sidelobes affect weather parameter measurements in exactly the same way as antenna sidelobes. We have shown convincing evidence for both point clutter and moving weather targets that pulse compressed waveforms produce the sidelobe leakage predicted by the ambiguity diagrams. We thus have confidence that additional waveform optimization will accurately predict sidelobe effects from extended weather targets. Doppler sensitivity at low velocity shows the apparent need for Doppler tolerant designs even for 10 cm radars. The cost of Doppler tolerant processing is additional computational power. Urkowitz and Bucci (1992) have suggested a robust processing scheme that will maintain low integrated sidelobes for weather of all velocities.

An inverse compression filter design not only minimizes the integrated sidelobes for weather applications but also reduces the peak sidelobes, important for point target detection. An inverse filter five or more times longer than the waveform seems adequate for many expected weather gradients. Based on our limited tests the tangent sweep NLFM waveform with an Inv-5x filter gives the best response for our suite of waveforms. Other NLFM waveforms should perform equally well or better. The best waveforms seem to need low sidelobe autocorrelation functions (matched filter responses) for the compression filter to perform most effectively.

The FM waveforms appear to require oversampling to maintain low sidelobes. Therefore, the processing requirements are higher than with phase codes. The compression sidelobe sensitivity to - ._-1_ _ - r C_.t r-iLA An. w . s.,_tC sampnng pnase iur rmv wavtlous is cuiiiUtcuy being investigated.

For aircraft surveillance and detection the MF may be the optimum processing. Parallel pro-

cc cessing of the same received data using the same pulse waveform may be a good system design that efficiently performs both aircraft and weather surveillance functions simultaneously.

5.0 Acknowledgments Figure 15. Spectra of range gate 93 showing contamination of storm velocity ingressing through the side- We wish to thank Jim Rogers, FAA Terminal lobes of the coded pulse. Arrows show approximate Area Surveillance Systems Program Manager ,,olnri;, aot;matPf far hnth n,.lsps for his support in collecting and analyzing the V4CUJI-Ll GJLL-11""G-3 J(J VVIII&AYVU Page ii JulyJuly29, 29, 1994 Page 11 COST- 75 International Seminar on Advanced Weather Radar Systems, Brussels, Belgium September 1994 data described in this paper, the engineering staff at Martin Marietta Government Electronic Sys- tems in Moorestown, NJ as well as the GE Corporate Research and Development Center in Schenectady, NY for technical discussions, the NCAR Remote Sensing Facility engineering and technician staff for the ELDORA testbed radar modifications, operation, and data acquisition, and to Charles Hwang for his expert assistance performing all the waveform analysis and assisting me with data interpretation.

NCAR is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.

6.0 References

Battan, LJ. (1972) Radar observation of the atmosphere. Chicago Press, Chicago, IL. Carbone, R.E., MJ. Carpenter and C.D. Burghart (1985) Doppler radar sampling limitations in convective storms, J. Atmos. and Ocean. Tech., Vol. 2, pp 357-361. Cohen, M.N. (1987) Pulse Compression in radar systems, Chap. 15, J.L. Eaves and E.K. Reedy, Principles of Modem Radar; VanNostrand Reinhold, NY.. Cook, C.E. and M. Bernfeld (1967) Radar Signals. Academic Press, Orlando, FL. Doviak, R.J. and D.S. Zrnic (1993) Doppler Radar and Weather Observations, Second Ed, Academic, San Diego. Farett, E.C. and G.H. Stevens (1990) Pulse compression radar, Chap.10, M.I. Skolnik, Radar Handbook McGraw- Hil, NY. Golay, MJ.E. (1961) Complementary series, IRE Trans. on Info. Th., IT-17, pp 82-87. Holloway, C.L. and RJ. Keeler (1993) Rapid scan Doppler radar: The antenna issues, 26th Conf. on Radar Meteorol- ogy, AMS, Norman, OK, pp 393-395. Keeler, RJ. and C.L. Frush (1983a) Rapid scan doppler radar development considerations, Part II: Technology Assessment, 21st Conf. on Radar Meteorology, AMS, Edmonton, Canada, pp 284-290. Keeler, R.J. and C.L. Frush (1983b) Coherent wideband processing of distributed radar targets, Int'l Geosc. and Rem. Sens. Symp. (IGARRS-83) San Francisco, CA. Keeler, R.J., C.A. Hwang, V. Chandra, R. Xiao (1993) Polarization pulse compression for weather radar, 26th Conf. on Radar Meteorology, AMS, Norman OK. pp 255-257. Lewis, B.L., F.K. Kretschmer and W.W. Shelton (1986) Aspects of Radar Signal Processing, Artech, Norwood, MA. Nevin, R.L., J.M. Ashe, H. Urkowitz, NJ. Bucci and JD. Nespor (1994) Range sidelobe suppression of expanded/ compressed pulses with droop, Nat'l. Radar Conf., IEEE, Atlanta, GA, pp 116-122. Randall, M. (1991) Digital IF processor for rectangular pulse radar applications, 25th Conf. on Radar Meteorology, AMS, Paris, France, pp 871-874. Rihaczek, A.W. (1969) Principles of High Resolution Radar. McGraw-Hill, N.Y. Smith, P.L. (1973) Weather radar. Achievements, promises, and problems, NCAR Atmos. Tech., Vol. 2, pp 57-65. Strauch, R.G. (1988) A modulation waveform for short dwell time meteorological doppler radars, J. Atmos. and Ocean. Tech., Vol. 5, pp 512-520. Urkowitz, H. and N. Bucci (1992) Doppler tolerant range sidelobe suppression for meteorological radar with pulse compression, Int'l Geosc. and Rem. Sens. Symp. (IGARRS-92) Houston, TX. Wolfson, M. (1993) Characteristics of microbursts, 26th Conf. on Radar Meteorology, AMS, Norman, OK. Woodward, P.M. (1953) Probability and Information Theory with Applications to Radar. Permagon Press.

Page 12 JulyJuly29, 29, 1994 Page 12 Pulse Compression for Phased Array Weather Radar

Appendix H: Keeler, R.J. and C. A. Hwang, 1995: "Pulse compression for weather radar," IEEE Int'l Radar Conf., Washington, DC, pp 529-535.

May 11, 1999 Page 48 of 52 IEEE International Radar Conference / Washington, DC / May 1995

Pulse Compression for Weather Radar R. Jeffrey Keeler and Charles A. Hwang National Center for Atmospheric Research 1 PO Box 3000, Boulder, Colorado USA 80307 Internet: [email protected] Telephone: 303-497-2031 Fax: 303-497-2044

Abstract. Next century's advanced weather radars will microbursts, that may rapidly form a lethal aviation haz- be able to accommodate pulse compression waveforms ard in an airport terminal area. Weather volume scan and phased array electronically scanned antennas to times of 2.5-10 minutes, characteristic of TDWR and meet higher time and space resolution requirements. We NEXRAD radars, do not have adequate time resolution have investigated several coded waveforms and com- to acquire data by which an accurate microburst hazard pression filters for weather radar applications. Candi- can be forecast. A standard mechanically scanned radar date waveforms include Barker bi-phase coded as well would have extreme difficulty in searching an airport as linear and non-linear FM coded waveforms. Mini- terminal area for precursor signatures in a timely fash- mum integrated sidelobe (inverse) filters are demon- ion. By decreasing the beam dwell time, the volume strated to be superior to matchedfiltersfor compression scan time may be decreased dramatically. Alternatively, processing of distributed weather echoes. We describe spatial resolution may be increased for the same volume the Doppler sensitivity of the waveform and filters by scan time by spacing the short dwell time beams more plotting the integrated andpeak sidelobe ratios vs. Dop- closely in azimuth and elevation. pler shift. We demonstrate these effects on both ground clutter and 50 dB reflectivity transition weather data In this paper we discuss waveform design issues of this taken with the 3 cm ELDORA testbed radar. advanced radar architecture. Other system aspects have been discussed by Keeler and Frush (1983a), Holloway 1.0 Introduction and Keeler (1993), and Keeler (1994).

Doppler weather radars can accurately depict the reflec- 1.2 FAA/TASS program description tivity and velocity structure of convective storms and other weather phenomena. The WSR-88D (NEXRAD), The FAA's Terminal Area Surveillance System (TASS) Terminal Doppler Weather Radar (TDWR) and the Program is currently active in the "advanced weather European weather radar networks require relatively long radar" arena. This relatively new research and develop- dwell times (30-100 msec) to acquire enough indepen- ment program is exploring concepts for a next genera- dent samples for accurately measuring weather parame- tion air traffic and weather surveillance radar. The radar ters. Future systems will likely require higher space and is envisioned as a phased array system capable of time resolution measurements. detecting, tracking and predicting positions of all aircraft and hazardous weather phenomena in the airport terminal area. A solid state pulse compression e-scan 1.1 High resolution radar system radar is a promising technology..

Figure 1 depicts the two distinct technologies required for higher space and time resolution weather radar measurements (Smith 1974; Keeler and Frush 1983a): 1) a coded wide bandwidth waveform that allows higher range resolution and subsequent larger number of independent estimates within a dwell time, and 2) an electronic step scanned (e-scan) phased array antenna that Pulse c allows rapid and agile beam movement The wideband wavi waveform allows accurate weather measurements in a short data acquisition time and the e-scan antenna allows rapid beam movement, thereby covering the sur- A, veillance volume without inducing scan modulation that Phased array degrades the accuracy of the measurements. antenna As as example from aviation weather, convective activ- i/// ity frequently spawns dangerous winds, such as Figure 1. Advanced high resolution radarsystem 1. NCAR is operated by the Univeristy Corporation for Atmo- using pulse compression waveform and phased spheric Research under sponsorship of the National Science array electronic scanned antenna. Foundation.

May 26, 1995 Page I IEEE International Radar Conference /Washington, DC / May 1995

1.3 Weather target characteristics 2.2 Compression filter design

Like other extended scatterers, such as insects and The joint waveform and compression filter design goal refractive index gradients, weather is made up of many is to determine a waveform having a compression factor small scatterers, each with its own backscatter cross sec- of BT=50-100 and low range sidelobes. The "matched tion and velocity. Radar characterization of precipitation filter" (MF) receiver is known to be optimum in the is defined in terms of the "radar reflectivity factor" (Z), a sense of maximizing the output SNR but it does not quantity related to the Rayleigh scattering from a dielec- minimize the sidelobe response (Cook and Bernfeld tric sphere, which, in turn, is related to the radar cross 1967). Since weather targets are distributed in range, the 4 section (a) using the ? wavelength dependence (Battan contribution from scatterers at ranges other than that 1973; Doviak and Zmic 1993). Accurately estimating desired enter through the range sidelobes that we desire backscatter power and velocity requires that range side- to minimize. These range sidelobes occur because of lobes in a pulse compression scheme be minimized imperfect compression filtering, but can be minimized (Keeler and Passarelli 1990). in a least squares sense.

In the following three equations, let sj denote sidelobe 2.0 Waveform and filter design samples and mk denote the mainlobe samples of the response. Also let hj be the coefficients of the sidelobe Pulse compression is a waveform technique that simul- suppression filter, gk be the coefficients of the matched taneously offers higher range resolution and increased filter, and ro be the mainlobe peak of the autocorrelation. average transmit power over that possible with a typical Common waveforms and matched filters yield peak single frequency pulsed radar waveform. Increasing the sidelobe (PSL) values of 20-40 dB below the primary bandwidth of the waveform increases the range resolu- target response, which is not adequate for many weather tion and the number of independent samples of the applications. We define the PSL value as received echo in a specified range interval. The Signal to Noise Ratio (SNR) of each sample is reduced by the ( max(s.) } PSL = 201og max( same amount. However, the SNR can be recovered by max(mk) (EQ 1) lengthening the transmit pulse, thereby increasing the average transmitted power (Keeler and Frush 1983b). For accurately estimating reflectivities and velocities of weather, which is always distributed in range, we require compressed waveforms having integrated side- 2.1 Coded waveform design lobe (ISL) values at least 40 dB below the main response for Doppler shifts less than 50 m/s. Typical Any transmitted waveform has a nominal bandwidth B matched filter ISL ratios are only -10 to -20 dB. We and nominal pulse length T. The time-bandwidth prod- define the ISL as uct BT is a measure of the pulse compression factor. That is, given appropriate receiver filtering, the energy of the pulse can be compressed into an effective pulse length BT times shorter than the actual pulse (Cook and ISL = 10log - -- 2 (EQ 2)

Bernfeld 1967). BT values of 100 allow space or time v resolution to be increased an order of magnitude. k 2

The effective range resolution of a waveform is c/2B. Additionally, filtering induces a loss in the SNR from what For example, a pulse with a 10 MHz bandwidth has a a matched filter would yield. We desire to keep this mismatch potential range resolution of 15 m whether it is a 100 loss (Lmm) well below 1 dB to prevent any undesirable nsec single frequency pulse, an N-element phase code loss in detectability. We define Lmm as changing every 100 nsec, or a chirped pulse linearly sweeping 2 through 10 MHz. The output of an appropriate (max (m )/ . )1hj pulse compression filter gives an estimate of the Lmm = 201og (r°/g1 received signal that can be processed to give indepen- I2)(EQ 3) dent estimates of reflectivity, velocity, etc every 15 m in (-./.F 2)~~ range. These "high resolution" measurements can then be averaged in range to provide coarser range resolu- Digital sidelobe suppression filters (variously called tion, but providing more accurate measurements. For inverse filters, Wiener filters, deconvolution filters, spik- example, if we average 10 consecutive 15 m measure- ing filters, or whitening filters) are optimal designs that ments, we obtain a processed 150 m range resolution minimize the ISL of the filter response in a least squares that is about 3 times more accurate than the individual sense (Ackroyd and Ghani 1973).The desired response 15 m short dwell measurements. is an impulse having a time width, tB, equal to the inverse bandwidth of the waveform. Both the PSL and

May 26, 1995 Page 2 IEEE International Radar Conference / Washington, DC / May 1995

ISL can be suppressed 10's of dB over the MF response (1994). Basically, it involves omitting the mainlobe ele- at the cost in SNR of a fraction of a dB. Consequently, ments of Eq. 6 and re-solving for the filter coefficients. optimal ISL compression filters are preferred over the MF in the weather application. Adequate integrated sidelobe suppression is limited to relatively small veloc- 2.3 Waveform analysis ities so that the Doppler sensitivity of the waveform design is an important parameter to be assessed. Waveform resolution characteristics in the range and Doppler domains may be visualized with the "ambiguity The sidelobe suppression filter design algorithm used is function" (Woodward 1953; Rihaczek 1969). This two the deterministic least-squared error method (Roberts dimensional function shows the joint response of the and Mullis 1987). For a given input signal xk, we want compression filter to the transmitted waveform and to to create the inverse filter h such that its output response targets distributed at ranges and velocities about the Yk is as close as possible to the desired response dk. In desired main response. Figure 2 the waveform xk is a 13 bit Barker code and the ideal response dk is a delta function. However the actual We analyze the three waveforms shown in Figure 3 that filter response Yk has finite sidelobes that we desire to represent potential coded waveforms for the weather minimize. We define the length of the inverse filter in radar measurements: 1) the Barker bi-phase (BT=13) terms of the waveform length. Thus, the inverse filter code (B-13) which has known good sidelobe properties, lnv-5x is five times longer than the waveform. 2) the Linear FM (BT=63) code (LinFM) which has a waveform class with arbitrary BT, and 3) the Tangent Non-linear FM (BT=39) code (TanFM) Xk - which has a Yk shaped spectrum to reduce sidelobes.

Xk _Bakcr-13 kd A

- ' - o 5.).1o-0 1.0l-.1 o

Linear FM Figure 2. Graphicaldescription of optimal sidelobe suppressionfilterdesign. The

desired output response, dk, is an impulse. o^2TO10n 41O-LineFM

Tangent-Bosed Non-iUnor FM To design the optimal compression filter h, we desire to minimize the following quantity over the entire filter response: }AfVVkf\I T - n 2x10 , 4x10- 6x1.- second* 2 V(h) = Idk-yk (EQ 4) Figure 3. Waveforms used for compression filter tests: Barker 13 (B-13), Linear FM 63 (LinFM), and Nonlinear FM 39 (TanFM). The bandwidth of [d k - (Xk® hd) 2 (EQ 5) each waveform is 1 MHz and the durations are 13, 63, and 63 microseconds. By using matrix differentiation or Lagrangian multipliers, we can obtain the matrix equation: For each waveform we show the ambiguity function and curves of the integrated sidelobes, peak sidelobe and R-h =q (EQ6) mismatch loss vs. Doppler for the 3.2 cm wavelength (X-band) radar we used to collect test data. Ambiguity where R is an autocorrelation matrix of Xk and q is the functions for 10 cm (S-band) and 5 cm (C-band) radars causal part of the crosscorrelation of dk and xk. One way and the ISL, PSL and Lmm curves would be scaled back to solve for the filter h is by left multiplying by R~, to 30% and 60% of the velocities shown in the curves. which exists because all autocorrelation matrices are The waveforms and compression filters are analyzed positive definite. We used this algorithm to compute the without any bandlimit filtering so as not to obscure sub- bi-phase compression filters. tie effects in analyzing ideal waveforms and filters.

To compute filter coefficients for FM waveforms, we Bi-phase waveforms first sampled the waveform into an array (since FM signals are continuous) and unconstrained the main lobe to A bi-phase coded waveform reverses the phase of a sin- a. specified width using the same method as Nevin et al gle frequency sinusoid at regular "chip" intervals (corre-. sponding to the range resolution c/2B) according to a

May 26, 1995 Page 3 IEEE International Radar Conference / Washington, DC / May 1995 predetermined sequence. The waveform and filter output are sampled once per chip at the inverse bandwidth sampling interval, tB. The Barker coded waveform shown in Figure 3 has a time bandwidth product, or compression ratio, of 13. Thus for a given desired range resolution, 13 times more average power (11dB) can be transmitted than a simple single frequency pulse having the same range resolution. The Barker codes are known to have unit sidelobe matched filter response. The range sidelobes are basically constant at -22 dB for all velocities up to 50 m/s and the ISL is about -11 dB. Figure 4 shows compression filter output response at Vel=O for the MF and several inverse filters of increasing length. The MF sidelobes are consistently high. The inverse filter peak sidelobes become increasingly lower and located farther from the main response as the compression filter length Figure 5. Ambiguityfunction of B-13 and Inv-5xfil- is increased. ter. Both ISL and PSL are much lower than the MF 00~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~response but show extreme Doppler sensitivity. Peak sidelobes at zero velocity are -60 dB. -50 MF -100

-50 Invlx -lo0 ,

-50 ,1- Inv2x _s -100 a 'a a,

.J E -50 l r Inv3x mn 0 S

0 -50 InvSx -100 0 20 40 60 80 0 10 20 30 40 . 50 Figure 4. Compression filter response to B-13 Velocity (m/s) . waveform for MF and Inv-1/2/3/5x filters. Note Figure 6. Integrated sidelobe level, peak sidelohe reduced sidelobes asfilter length is increased. level and mismatch loss for Barker-13 waveform. Longerfilters suppress sidelobes, increase loss and show greaterDoppler sensitivity. Figure 5 shows the ambiguity function for the B-13 waveform with an inverse compression filter, Inv-5x, five times longer than the waveform itself. The peak FM waveforms sidelobes are down about 60 dB and the ISL is approximately -50 dB at zero velocity. The ambiguity function Frequency modulated (FM or chirp) waveforms repre- appears different from textbook plots (eg, Rihaczek sent a different category from the bi-phase waveforms. 1969) because we plot only the relatively small weather The FM waveforms have a continuous phase change velocities rather than Mach speeds typical of aviation over the duration of the pulse rather than abrupt phase and military targets. changes at the "chip" boundaries. This continuous phase change represents Figure 6 shows the ISL, PSL and Lmm vs. Doppler a dilemma in the compression filter design. The filter is designed in a curves for the B-13 waveform and the MF, Inv-lx and deterministic manner based on specific samples of Inv-5x filters. The MF is inferior to all the inverse fil- the transmit waveform. However, the received samples have a ters. Longer inverse filters give exceptionally low ISL phase determined by the actual range to the target and values near Vel=0, but they increase and converge to are generally different from about -20 dB for larger Doppler. the filter design samples. Therefore, the compression filter is not optimum. It appears that a larger

May 26, 1995 Page 4 IEEE International Radar Conference / Washington, DC / May 1995 sampling rate than the waveform bandwidth mitigates However, if the sampling frequency is reduced to twice this effect. The FM waveforms were oversampled by a the bandwidth so the response has the a fewer number of factor of 2 to yield 2BT sample points within the pulse. points and the mainlobe width is constrained to be tB, Thus, the matched and inverse filters have twice as then the sidelobes can be further suppressed. The many points as the bandwidth would otherwise dictate. TanFM waveform has a compression ratio of about BT=39. Figure 8 shows the ISL, PSL and Lmm vs. Dop- Linear FM waveforms have a well defined compression ratio -- it is simply the frequency sweep B (the bandwidth) times the pulse length T. However, non-linear waveforms have a less well defined BT. Because non- linear FM (NLFM) waveforms control the frequency sweep to tailor the spectrum shape and yield low MF sidelobes (Farnett and Stevens 1990), the 3dB band- m width is less than the total frequency sweep. I) 1-5(A

J The ambiguity function for the LinFM waveform with (nl BT=63 and a MF (not shown) has sidelobes that are high and slowly tapered in range. However, an Inv-5x filter significantly reduces the peak and integrated sidelobes. Figure 7 shows the ISL, PSL and Lmm vs. Dop- pler for the LinFM waveform. Inverse'filters that are at least 5 times as long as the waveform seem to provide nearly the same sidelobe suppression characteristics as Velocity (m/s) Barker waveforms. However, Lmm values are much Figure 8. ISL, PSL and Lmm vs. Doppler for larger than for the B-13 code. TanFM (BT=39) with the MF, Inv-lx and Inv-5x

0 * --*--~~~~~~~~-i-**---*-'*' ....-...... 0 compression filters. Data are oversampled by twice the bandwidth, not twice the sweep. MF MT MF -2 pier curves. The sidelobes are significantly lower than Ix for the LinFM cases and show a stronger Doppler sensi- -20 tivity near zero velocity. The sidelobe levels indicate m -4 m ....._ . .... that the NLFM spectrum shaping contributes signifi- -l ------_- -- cantly to the sidelobe reduction. The mismatch ix loss is UL also significantly reduced over the LinFM case. {/) 5x -6 .- -40

SISL-, - - -8 3.0 Data acquisition / analysis --- PSL-..PISL---- ....-.-..... Lmm To validate the waveform analysis, we modified an v,., ...... I ...... - . J-luL_1in existing NCAR radar to acquire Barker 0 10 20 30 40 50 13 pulse com- Velocity (m/s) pression data which were then compressed and analyzed off-line. Both a ground clutter spike case and a high Figure 7. ISL, PSL and Lmm vs. Doppler for reflectivity weather gradient were chosen for analysis. LinFM (BT=63) with MEF Inv-lx and Inv-5x compressionfilters. Data are oversampled by 2B. 3.1 Point clutter target Shaping the spectrum of the FM waveform by using a non-linear frequency sweep reduces the 3 dB bandwidth The data of interest for the evaluation is the relative and the compression ratio. But it also allows reduced backscattered power and the radial velocity for the sim- mismatch loss over the LinFM waveform as the inverse ple and coded pulses. Figure 9 shows the data for the filter better approximates the MF response. Using a fre- simple pulse plotted for 200 consecutive 90 m range quency sweep that follows the f=tan(t) curve defined in gates from 4 km to 22 km with a strong ground clutter Nevin et al (1994) is one particular waveform, TanFM. target located on a mountain peak about 16 km to the If we sample this waveform at twice the frequency west. Note the 60 dB difference in the clutter spike at sweep (not the 3 dB bandwidth), the ambiguity function range gate 137 and the noise beyond. is virtually identical to the LinFM example. In this case the mainlobe width is over-constrained to be smaller Figure 10 shows the same data for the B-13 coded pulse than tB and the sidelobes are large. and the Inv-5x filter. Because the average power is 11 dB higher than for the simple pulse and the processing

May 26, 1995 Page 5 IEEE International Radar Conference / Washington, DC / May 1995

not - - ·

60Z

60 dB -

UI - . * . . 0 50 100 IU0 20o RangeCat

E· i.b c '5

mafq OO RogataC Figure 11. High reflectivity gradient weather using Figure 9. Ground clutter data showing received simple 90 m pulse. Gradient is 50 dB over 2 km power and velocity for simple frequency 90m pulse. range at front and rear of cell. Nyquist velocity is Nyquist velocity (±0.5) corresponds to ±8 m/S. ±8s. Radial velocities within the cell are aliased Ranges greater than 150 are noise only. ad between 5-12 m/s.

'2: 0.2

:I - A .

-04 -

0o o0oI ot* 150 200 RonogCot Figure 12. Weather echo using B-13 waveform and Figure 10. Ground clutter target using B-13 pulse the Inv-5xfilter. There is discernible leakage of the and Inv-Sx filter. Note 11 dB SNR increase and the sidelobe energy from the strong precipitation echo sidelobe response. Simple and coded peak powers to outside the cell in both reflectivity and velocity. are equal. 35-50 dB down are not predicted by the filter response. gain is normalized to the same peak power for both These are likely caused by "distortions" in the transmit coded and simple pulses in our processing, the noise waveform not compensated in the filter design. level beyond the point clutter is suppressed 11 dB. Thus, the SNR of the point clutter is about 71 dB. The velocity values are still zero mean but are more accurately deter- 3.2 Convective weather target mined because the SNR has been increased. The power and velocity estimates clearly show the range sidelobe Ground clutter has zero velocity and the expected com- effects with this extremely strong point cluster "flood- pression filter sidelobes are designed to be minimum ing" into adjacent range gates. over + 50 m/s. Higher velocities that are sometimes associated with strong reflectivity gradients offer a more The non-moving clutter power in the first half of the severe test of pulse compression waveforms on distrib- return is the same for the simple and coded pulses. But uted weather targets. Using the simple 90 m pulse wave- the sidelobe responses at range gates 107 and 167 are 55 form Figure 11 shows a 49 dB reflectivity transition dB down and correspond to those shown 30 samples from a small thunderstorm cell 15 km to the south of the away from the main response in the lower panel of Fig- radar on June 2, 1994. Unless the ISL's are 50 db down, ure 4. The sidelobes close to the main response that are then the strong echoes within the storm will contaminate

May 26, 1995 Page 6 IEEE International Radar Conference / Washington, DC / May 1995 the weak echo region outside the cell. Figure 12 shows Facility technical staff (Eric Loew, Chuck Frush, Mitch the same storm cell using the B-13 bi-phase coded pulse Randall, Joe VanAndel, Craig Walther, Joe Vinson, and and the Inv-5x compression filter. The SNR is increased Jack Good) for the ELDORA testbed radar modifica- from 49 dB to 60 dB but the tapered echo near the cell tions, operation, and data acquisition. edge (formerly below the noise level) shows strong evidence of sidelobe leakage. The velocities in the "shoulders" of the cell are similar to the velocities on the 6.0 References nearer portion of the cell. Ackroyd, M.H. and F. Ghani (1973) Optimum mismatched filters for sidelobe suppression, IEEE Trans. Aerospace Elec- 4.0 Conclusions tronics, Vol. AES-2, pp 214-218. Battan, L.J. Pulse compression (1973) Radar Observation of the Atmosphere, is one technique of obtaining the Chicago Press, Chicago, IL. short dwell time necessary to make high space and time resolution weather radar measurements. Range time Cook, C.E. and M. Bernfeld (1967) Radar Signals -- Introduc- sidelobes affect weather parameter measurements in tion to Theory and Application, Artech House, Boston, MA. exactly the same way as antenna sidelobes and we Doviak, RJ. and D.S. Zmic (1993) Doppler Radar and desire to minimize both. We have shown convincing Weather Observations, Second Ed., Academic, San Diego. evidence for both point clutter and moving weather tar- Farnett, E.C. and G.H. Stevens (1990) Pulse compression gets that pulse compressed waveforms produce the side- radar, Chap.10, in M.I. Skolnik, Radar Handbook, McGraw- lobe leakage predicted by the ambiguity diagrams. Hill, NY Holloway, C.L. and R.J. Keeler (1993) Extreme Doppler sensitivity even at low weather veloci- Rapid scan Doppler radar: The antenna issues, 26th Conf. on Radar Meteorology, ties and even for 10 cm radars shows the apparent need AMS, Norman, OK, pp 393-395. for Doppler tolerant designs. The principal cost of Dop- pler tolerant processing is additional computational Keeler, R.J. and C.L. Frush (1983a) Rapid scan doppler radar development considerations, Part I: Technology power. Urkowitz and Bucci (1992) have suggested a Assessment, 21st Conf. on Radar Meteorology, AMS, Edmonton, Canada, robust processing scheme that will maintain low inte- pp 284-290. grated sidelobes for weather of all velocities. Keeler, RJ. and C.L. Frush (1983b) Coherent wideband pro- An inverse filter five or more times longer than the cessing of distributed radar targets, Int'l Geosc. and Rem. Sens. Symp. (IGARRS-83) waveform seems adequate for many expected weather San Francisco, CA, pp 3.1-3.5. gradients. Based on.our limited tests the tangent NLFM Keeler, R.J. and R.E. Passarelli (1990), Signal processing for waveform with an Inv-5x filter gives the best response atmospheric radars, Chap 20 in Atlas, Radar in Meteorology. from our suite of waveforms. Other NLFM waveforms AMS, Boston, pp 199-229. should perform equally well or better. The extended Keeler, R.J. (1994) Pulse compression waveform analysis for range response of long waveforms and compression fil- weather radar, COST-75 Int'l Seminar on Advanced Weather ters requires alternative techniques for short range cov- Radar Systems, Brussels, Belgium. erage that we have not addressed here. Nevin, R.L., J.M. Ashe, H. Urkowitz, N.J. Bucci and J.D. Nespor (1994) Range sidelobe suppression of expanded/com- An inverse compression filter design not only minimizes pressed pulses with droop, Nat'l. Radar Conf., IEEE, Atlanta, the integrated sidelobes for weather applications but GA, pp 116-122. also reduces the peak sidelobes, important for point tar- Rihaczek, A.W. (1969) Principles of High Resolution Radar, get detection. Thus the same waveform should be McGraw-Hill, N.Y. acceptable for both distributed weather targets as well as Roberts, R.A. and C.T. Mullis (1987) Digital Signal Process- aircraft point targets. ing, Addison-Wesley, Reading, MA. Smith, P.L. (1974) Applications of radar to meteorological 5.0 Acknowledgments operations and research, IEEE Proc., Vol. 62, pp 724-745. Urkowitz, H. and N. Bucci (1992) Doppler tolerant range sidelobe suppression for meteorological radar with pulse compres- We wish to thank Jim Rogers, FAA Terminal Area Sur- sion, Int'l Geosc. and Rem. Sens. Symp. (IGARRS-92) veillance Systems Program Manager, and his program Houston, TX. office staff for their support in collecting and analyzing Woodward, P.M. (1953) Probability and Information Theory the data described in this paper, the engineering staff at with Applications to Radar. Permagon Press. Martin Marietta Government Electronic Systems in Moorestown, NJ (Harry Urkowitz, Nick Bucci, and Jerry Nespor) as well as the GE Corporate Research and Development Center in Schenectady, NY (Jeff Ashe) for technical discussions, and the NCAR Remote Sensing

May 26, 1995 Page 7 Pulse Compression for Phased Array Weather Radar

Appendix I: Hwang, C.A. and R.J. Keeler, 1995: "Sample phase aspects of FM pulse compression waveforms," Int'l Geoscience and Remote Sensing Symposium (IGARSS 95), Florence, Italy, pp 2126-2128.

May 11, 1999 Page 49 of 52 IEEE International Geoscience and Remote Sensing Symposium '95/ Florence, Italy / July 1995

Sample Phase Aspects of FM Pulse Compression Waveforms Charles A. Hwang and R. Jeffrey Keeler National Center for Atmospheric Research1 / Atmospheric Technology Division / Remote Sensing Facility P.O. Box 3000, Boulder, CO 80307 Tel: (303) 497-2031 Fax: (303) 497-2044 Email: [email protected]

Abstract adjacent range gates. SideLobe Suppression (SLS) filters By utilizing a long, low-power pulse, pulse compression are designed to minimize sidelobe response. These filters waveforms allow systems to improve sensitivity without always have better integrated sidelobe (ISL) and peak sacrificing range resolution. Matched filters are sidelobe (PSL) levels than MF levels, but by definition have traditionallyusedfor pulse compression, but range sidelobe suboptimal signal-to-noise ratio. One generates these filters responses are too high to adequately measure weak weather by solving equations that minimize the integrated sidelobes echoes near strong targets such as aircraft, ground clutter [2][3]. In this paper we will address only sampled and heavy weather. Least-squares sidelobe suppression Frequency Modulated (FM) waveforms. filters have superior characteristics for hard targets, but The sidelobe suppression filter design algorithm used is have not been well tested for weather radars. When these the deterministic least-squared error method [4]. For a given filters are applied to FM waveforms, the sampled phase of input signal xk, we want to create the inverse filter h such the target rarely matches the sampled phase from which the that its output response yk is as close as possible to the filter was defined. This causes the sidelobes to rise steeply. desired response dk. In Fig. 1 the waveform xk is an FM In this paper, we propose a technique to minimize sidelobes chirp and the ideal response dk is a delta function. However over arbitrary sampling phase by integrating the effects of the actual filter response yk has finite sidelobes that we all sample phase shifts into the minimizing equations. desire to minimize. Comparing this technique with simply oversampling shows To design the optimal compression filter h, we that oversampling generally yields lower expected minimize the following quantity over the entire filter integratedsidelobes. response

20 1.0 Need for pulse-compression V(h) -d-yh= - E [d,-(xk

May 25, 1995 Page 1 IEEE International Geoscience and Remote Sensing Symposium '95/ Florence, Italy / July 1995 unconstrained the main lobe to a specified width using the filter responses over multiple phases. same method as Nevin, et al [5]. Basically, it involves omitting the mainlobe elements of (1) and (2) and then re- 3.0 Optimization over unknown phase solving for the filter coefficients. 3.1 Filter Design 2.0 Phase mismatch with FM waveforms We propose a technique to minimize sidelobes over any SLS filters can be designed only for sequences, not arbitrary sampling phase of FM waveforms using a method continuous waveforms. Therefore, we can generate a SLS originally proposed by Baden [7] for Doppler tolerant filter only for a sampled continuous waveform. However, design. We integrate the effects of all sample phase shifts any of an infinite set of different sequences can result from into the minimizing matrix equations sampling at arbitrary time delays. The problem with SLS filtering is similar to Doppler sensitivity. SLS filters are designed for a specific received R'(O)dO· = Jq'(O)dO . (3) waveform. When a Doppler shift occurs, the received -IT -it waveform varies from the template waveform and degrades R'(8) is an autocorrelation matrix assuming that the the optimization. The same effect occurs from a shift in the template waveform has sample shift of 0. q'(O) is similarly sample-phase. With a zero-phase, the filter will operate assumed to be a sampled waveform having phase of 0. All optimally. Weather targets can have sample-phase shifts phase shifts are uniformly weighted in the design of the between -180 to 180 degrees with uniform probability. This filter. However, an SLS filter's strength comes from being phase randomness degrades the response by bringing the "inverse" for some input waveform. This new filter is sidelobes up. now not an inverse of any one waveform, but an inverse Part of this effect is due to having N-1 points in the over the set of all phase shifts and we call it the All-Phase interpolation rather than N points [6]. The interpolation SLS (APSLS) filter. Another variation of this approach points do not correlate well with the zero-shift sequence and ·would be to weight the integral with some positive thus end up being suboptimal. weighting function w(0) Although the techniques for developing filters has had significant attention, robust modelling of them has not. Fig. 2 shows the response of an SLS filter to a Linear FM chirp R'(O)w(O)dO . h = qj(l)w(o)do . (4) waveform. The inverse filter used is 5 times (Inv-5x) the -;IC -xtC length of the linear chirp sequence. The upper response shows only the zero phase shift response. The bottom half 3.2 Performance Measure figure shows a composite phase response when oversampled Several performance measures are available for by 8 times. The sidelobes of the zero-shifted response cast measuring probabilistic distributions: PSL and ISL an overly optimistic view of what is actually happening. maximum values, root mean squared (rms) values, expected The lower figure, in essence, shows the range of possible values, etc. We use the expected logarithmic ISL value over all phase shifts. The expected value should give us a more general idea of how well the filter performs, since filter responses (and hence ISL's) will vary depending on the phase 0 (assumed to be uniformly distributed). o . . - . . .100, 1 3.3 Analysis 20 4 2 0 20 40 6o 8o 100 120 Fig. 3 illustrates ISL responses of two filters generated from a 1 MHz, 20 psec complex linear FM chirp sampled at a Nyquist (IN) rate (defined as one complex bandwidth: 1 MHz in this example). The Zero-Phase Sidelobe Suppression (ZPSLS) filter achieves a much lower minimum than the APSLS filter, but the APSLS filter maximum is lower than the ZPSLS filter maximum. When the uniform sample-phase distribution of scatterers is Figure 2. Inv-5x SLS filter response to a linear chirp applied to ISL distributions over phase shifts, we obtain the waveform under optimum sampling conditions (top) probability distributions for ISL values shown in Fig. 4. The and the same filter response to all phase shifts three pairs of responses in Fig. 4 were generated from the simulated by 8 times oversampling (bottom). same template FM chirp waveform, but with a Nyquist (IN), twice Nyquist (2N) and quintuple Nyquist (5N)

May 25, 1995 Page 2 IEEE International Geoscience and Remote Sensing Symposium '95/ Florence, Italy / July 1995

and different filter lengths. However, filter length had very 5 1I1 - little effect on the results so they are not presented. For IN

0 - sampling, the APSLS filters exhibited about 0.1 dB improvement in expected ISL over the ZPSLS filters. However, oversampling twice as fast (2N) improved the expected 0al ISL of APSLS and ZPSLS filters by about 14 and

.£--10 15 dB, respectively. Basically, ZPSLS filters have better cn expected ISL values when any oversampling (2N and -15 greater) is used. APSLS filtering does not always yield better expected an ISL values but.it appears to always lower the maximum ISL. If the measure of performance is lowest maximum ISL -25 I I -200 0 over all phases, then APSLS method works very well. It Sample-Phase offset in degrees also has a narrower range of possible values. Fig. 4 Figure 3. ISL response to sample-phase offset (shift) illustrates this difference in range of possible ISL values. for zero-phase SLS filters and all-phase SLS filters at Systems that cannot tolerate high ISL's can benefit from the a Nyquist (IN) sampling rate. The expected ISL for APSLS technique. the APSLS filter is -5.9 dB andfor the ZPSLS filter is -5.8dB. 4.0 Conclusions This analysis shows how SLS filtering reacts under a sampling rates. The average or expected ISL value for the more robust form of modelling. It is generally not best to APSLS filter in Fig. 3 (and the rightmost pair of curves in measure performance only in the zero-phase, especially if Fig. 4) is slightly lower than the expected ISL of the this best case has a very slim probability of occurring. ZPSLS filter. APSLS filtering addresses this problem, but SLS.filtering Most previous research has considered only the ISL with oversampling suppresses more effectively over all value under perfect zero-phase conditions. The zero-phase phases. This, however, is also dependent on the measure of ISL is really the best case and is insufficient to compare performance used. We have looked only at uniform performance of different filters under unknown received weighting schemes in the phase integration. Other phase. Our algorithm is an attempt to lower the expected weighting schemes could yield better results. ISL rather than to lower only the zero-phase ISL. This work was sponsored by the FAA Terminal Area Frequently, it turns out that minimizing at the zero-shift Surveillance System Program Office. results in a lower expected ISL. We compared responses of ZPSLS and APSLS filters 5.0 References by using different sampling rates (IN, 2N, 3N, 4N, and 5N) [1] R. J. Keeler and C. A. Hwang, "Pulse Compression Waveform Analysis for Weather Radar", COST-75 Int'l 0.08 . . . Seminar on Advanced Weather Radar Systems, Brussels. Belgium, September, 1994. [2] R. J. Keeler, C. A. Hwang and E. Loew, "Pulse 0.06 Compression for Weather Radar," IEEE Int'l Radar Conf., Washington, DC, May, 1995, in press.

tn [3] R. J. Keeler, C. A. Hwang and E. Loew, "A Pulse To 0.04 0.04 ll Compression Phased Array Weather Radar," J. of Atmos. and Oceanic Tech., unpublished. 6 5N 12N- N [4] R. A. Roberts and C. T. Mullis, 2 Digital Signal Processing, °"° ' A " Addison-Wesley, 1987, pp 229-242. [5] R. L. Nevin, J. M. Ashe, H. Urkowitz, N.J. Bucci and J.D. Nespor, "Range Sidelobe Suppression of Expanded/ Compressed Pulses with Droop," IEEE Nat'l Radar Conf., -60 -40 -20 0 20 ISL (dB) Atlanta, Ga, March, 1994, pp. 116-122. Figure 4. Probability distribution of ISL's for [6] M. Labbitt, "Obtaining Low Sidelobes Using Non-Linear FM Pulse Compression," Lincoln Laboratory Technical both APSLS and ZPSLS filters with IN, 2N, and 5N Report ATC-223, NTIS, Springfield, Va, November, 1994. sampling rates. Expected AP/ZP ISL's are (-5.9/-5.8) [7] J. M. Baden, "Pulse Compression Doppler Sensitivity for IN, (-20.6/-21.9)for 2N, and (-32.5/-33.3) dB. Reduction Study," Georgia Institute of Technology, Masters Thesis, August, 1989.

May 25, 1995 Page 3 Pulse Compression for Phased Array Weather Radar

Appendix J: Keeler, R.J., C.A. Hwang and E. Loew, 1995: "Pulse compression weather radar waveforms", 2 7 th Conf. on Radar Meteorology, AMS, Vail, CO, pp 767-769.

May 11, 1999 Page 50 of 52 AMS 27th Conference on Radar Meteorology / Vail, CO / October 1995

PULSE COMPRESSION WEATHER RADAR WAVEFORMS R. Jeffrey Keeler, Charles A. Hwang and Eric Loew National Center for Atmospheric Research* / Atmospheric Technology Division / Remote Sensing Facility P.O. Box 3000, Boulder, CO 80307 Tel: (303) 497-2031 Fax: (303) 497-2044 Email: [email protected]

1.0 INTRODUCTION (TanFM) has a shaped spectrum to reduce sidelobes. To better understand and to better predict rapidly The "ambiguity function" provides a two dimensional evolving atmospheric events, meteorologists and airport visual tool to compare the response of the compression filter controllers need radars with higher time and space resolution. to a set of doppler shifted input sequences. We show The FAA's Terminal Area Surveillance System (TASS) ambiguity functions and Doppler curves of the integrated Program has been active in the "advanced weather radar' sidelobes, peak sidelobes and mismatch.loss (over the MF) arena. The radar system envisioned is a phased array radar vs. Doppler shift for the 3.2 cm wavelength (X-band) radar capable of detecting, tracking. and predicting positions of all we used to collect test data. The velocity scales on ambiguity aircraft and hazardous weather phenomena in the airport functions for 10 cm (S-band) and 5 cm (C-band) radars and terminal area. Solid-state active array systems can fulfill this the ISL, PSL and Lmm curves would be scaled up according need by electronically steering their beams, but with current to the wavelength ratios. technology the peak power is so low that these radar systems Figure 3 shows the ambiguity function for the Tan-FM have poor sensitivity. Pulse compression allows these radar waveform with an inverse compression filter, Inv-5x, five systems to increase the sensitivity while maintaining high times longer than the waveform itself. The peak sidelobes are range resolution by transmitting larger average power in a down about -70 dB and the ISL is approximately -60 dB at longer coded pulse (Smith 1974, Keeler and Frush 1983). zero velocity. The ambiguity function appears different from Compression is typically done with matched filters textbook plots (e.g., Rihaczek 1969) because we plot only the (MF). However, sidelobe responses of matched filters are too relatively small weather velocities. high for most modem applications and cause range smearing. SideLobe Suppression (SLS) filters, (Ackroyd and Ghani 3.1 BI-PHASE WAVEFORMS 1973) are designed to minimize the sidelobe response. These Bi-phase coded waveforms reverse the phase of a single filters always have better integrated sidelobe (ISL) and peak frequency sinusoid at regular "chip" intervals corresponding sidelobe (PSL) levels than MF levels, but by definition have to the range resolution c/2B. The waveform and filter output suboptimal signal-to-noise ratio. We discuss the waveform are sampled at the inverse bandwidth sampling interval, tB. design issues of this advanced radar architecture.

2.0 FILTER DESIGN Figure 1 illustrates the filter design strategy. For a given Xk h input signal xi, we want to create a filter h such that its output Ak- - response yk approximates, in the least squares sense, the desired response dk. The response Yk will vary from the delta function dk, as little as possible when minimizing the _._ A-- following quantity over the entire filter response:

2 2 V(h) = lIdk-ye| = [d k,-( k h)l . (1) Figure 1. Graphical description of optimal sidelobe k= suppressionfilter design. The desired output response dk is an By using matrix differentiation or Lagrange multipliers, we impulse, i.e. zero sidelobes. can obtain the matrix equation ~~r------BorhEr-t R-h=q (2) where R is an autocorrelation matrix of xk and q is the causal part of the crosscorrelation of dk and xk Left multiplying by R , we solve for the inverse compression filter h (Roberts LI- F

and Mullis 1987). 0

3.0 WAVEFORM ANALYSIS T.-a-t-13-d No-U..., F&A The three waveforms shown in Figure 2 represent potential coded waveforms for the weather radar 6 *O~; ~ r measurements: 1) the Barker bi-phase (BT=13) code (B-13) has known good sidelobe properties, 2) the Linear FM Figure 2. Waveforms used for compression filter tests: (BT=63) code (LinFM) is a waveform class with arbitrary Barker 13 (B-13), Linear FM 63 (LinFM), and Nonlinear BT, and 3) the Tangent Non-linear FM (BT=39) code FM 39 (TanFM). The bandwidths of the waveforms are 1, 1 * NCAR is sponsored by the National Science Foundation. and 0.7 MHz with durationsof 13, 63, and 63 microseconds.

May 26, 1995 Page 3 AMS 27th Conference on Radar Meteorology / Vail,.CO / October 1995

0 _.._..C_ ...... Mr " 0

MF -2

-20 .Ix ma> .'...-.r c..-...... :::::::::::::::::::::::::::....-...... 7.. -4 m 'o 0 11 () ~ x------' *"" 'o a. -Sx -- E U) -6 .8 :2 -40

-- ISL -8 Figure 3. Ambiguity function of TanFM waveform and --- ~5~x - PSL---- Inv-5xfilter Note sidelobe sensitivity to Doppler Lmm ......

The Barker coded waveform shown in Figure 2 has a time -60 I . I...... I--1n . 0 10 bandwidth product, or compression ratio, of 13. Thus for a 20 30 40 50 Velocity (m/s) given desired range resolution, 13 times more average power Figure 5. ISL, PSL and Lmm vs. Doppler for LinFM (11dB) can be transmitted than a simple single frequency (BT=63) with MF Inv-lx and Inv-5x compression filters. pulse having the same range resolution. The Barker codes are Data are oversampled by 2B. known to have unit sidelobe matched filter response. The peak sidelobes are basically constant at -22 dB for all is defined to be outside +/- 2.5 tB of the peak and the velocities up to 50 m/s and the ISL is about -11 dB. mainlobe region contains all points within 6 dB of the peak. Figure 4 shows the ISL, PSL and Lmm vs. Doppler The ambiguity function for the LinFM waveform with curves for the B-13 waveform and the MF, Inv-lx and Inv-5x BT=63 and a MF (not shown) has sidelobes that are high and filters. The MF is inferior to all the inverse filters. Longer slowly tapered in range. However, an Inv-5x filter inverse filters give exceptionally low ISL values near Vel=0, significantly reduces both the peak and integrated sidelobes. but these increase for larger Doppler. Figure 5 shows the ISL, PSL and Lmm vs. Doppler for the LinFM waveform. 3.2 FM WAVEFORMS Shaping the spectrum of the FM waveform by using a Frequency modulated (FM) waveforms represent a non-linear frequency sweep reduces the 3 dB bandwidth and different category from the bi-phase waveforms. The FM the compression ratio. But it also allows reduced mismatch waveforms have a continuous phase change over the duration loss over the LinFM waveform as the inverse filter better of the pulse rather than abrupt phase changes at the "chip" approximates the MF response. Using a frequency sweep that boundaries. The FM waveforms were oversampled by a follows the f=tan(t) curve defined in Nevin, et al (1994) is factor of 2 to yield 2BT sample points within the pulse. Thus, one particular waveform, Tan-FM. the matched and inverse filters have twice as many points as If the sampling frequency is twice the bandwidth so the the bandwidth would otherwise dictate. The sidelobe region response has the a fewer number of points than the LinFM

I 03m I -c II 0.-v II 1-1 V)

-j En a. EL i V)

0 10 20 30 40 50 0 10 20 30 40 50 Velocity (m/s) Velocity (m/s) Figure 4. Integrated sidelobe level, peak sidelobe level and Figure 6. ISL, PSL and Lmm vs. Doppler for TanFM mismatch loss for Barker-13 waveform. Longer filters (BT=39) with the MF, Inv-lx and lnv-5x compression suppress sidelobes, increase loss and show greater Doppler filters. Data oversampled by twice the bandwidth, not sensitivity. Dataare sampled once per chip. twice the sweep.

May 26, 1995 Page 3 AMS 27th Conference on Radar Meteorology / Vail, CO / October 1995

,-·. -- I----

!---i~o 10i------, ------,To ------

- .M wrm r r -! _ - _

Figure8. High reflectivity gradientweather using simple 90 Figure 7. TanFM waveform response from Inv-St m pulse (dotted) and B-13/Inv-5x (solid) compression compression filter with waveform sampled at optimum filtering. Gradient is 50 dB over 2 km range at front and phase (top). Response of 8x oversampled waveform rear of cell. There is discernible sidelobe leakage from the (bottom) shows severe increases in sidelobes at non-optimal precipitationecho to just outside the storm cell. samplephases. case, then the sidelobes are further suppressed. The TanFM 5.0 CONCLUSIONS waveform has a compression ratio of about BT=39. Figure 6 Pulse compression is one technique of obtaining the shows the ISL, PSL and Lmm vs. Doppler curves. The short dwell times necessary to make high space and time sidelobes are significantly lower than for the LinFM cases resolution weather radar measurements. Range time sidelobes and show a stronger Doppler sensitivity near zero velocity. affect weather parameter measurements in exactly the same The sidelobe levels indicate that the TanFM spectrum way as antenna sidelobes and we desire to minimize both. We shaping significantly reduces the sidelobes and the mismatch. have collected and analyzed pulse compression weather radar data showing that moving weather targets produce the 33 PHASE MISMATCH WITH FM WAVEFORMS sidelobe leakage expected from the ambiguity diagrams. FM waveforms show phase mismatch degradation similar to Doppler degradation. SLS compression filters are 6.0 ACKNOWLEDGEMENTS optimized for a sampled template waveform (a sequence). We thank Jim Rogers, FAA Terminal Area Surveillance When a Doppler shift occurs, the received waveform varies Systems Program Manager and his program office staff for from the template waveform and degrades the sidelobe their support, and the NCAR Remote Sensing Facility response. The same effect occurs from a shift in the sampling technical staff for data acquisition assistance. phase. This phase shift of the waveform input to the compression filter causes the sidelobes to rise, sometimes 7.0 REFERENCES dramatically. In practice this time shift is inevitable since the Ackroyd, M. H. and F. Ghani, 1973: Optimum mismatched range to the target is unknown. Weather targets have filters for sidelobe suppression, IEEE Trans. Aerospace uniformly distributed sample-phase shifts. This increase in Electronics, AES-2, 214-218. PSL and ISL is shown in Figure 7 for the TanFM waveform Hwang, C. A. and R. J. Keeler, 1995: Sample phase aspects and may be related to frequency aliasing. One can increase of fm pulse compression waveforms, Int'l Geosc. and phase shift tolerance with an optimization that integrates the Rem. Sens. Symp. (IGARRS-95), Florence, Italy. effects of all possible shifts (Hwang and Keeler 1995). Keeler, R. J. and C. L. Frush, 1983: Rapid scan doppler radar development considerations, Part II: Technology 4.0 DATA ACQUISITION/ANALYSIS Assessment, 21st Conf. on Radar Met., AMS, To validate the waveform analysis, we modified an Edmonton, Canada, 284-290. existing NCAR X-band radar to acquire B-13 data which Keeler, R. J., C. A. Hwang, and E. Loew, 1995: Pulse were then compressed and analyzed off-line. Higher compression for weather radar, IEEE Int'l Radar Conf., velocities that are sometimes associated with strong Washington, DC, 529-535. reflectivity gradients offer a difficult test of pulse Nevin, R. L., J. M. Ashe, H. Urkowitz, N. J. Bucci, and J. D. compression waveforms on distributed weather targets. Using Nespor, 1994: Range sidelobe suppression of expanded/ the simple 90 m pulse waveform Figure 8 shows a 49 dB compressed pulses with droop, IEEE Nat'l. Radar Conf., reflectivity transition from a small thunderstorm cell 15 km to Atlanta, GA, 116-122. the south of the radar on June 2, 1994. Unless the ISL's are Rihaczek, A. W., 1969: Principles of High Resolution Radar, 50 db down, then the strong echoes within the storm will McGraw-Hill, N.Y. contaminate the weak echo region outside the cell. The same Roberts, R. A. and C. T. Mullis, 1987: Digital Signal storm cell using the B-13 bi-phase coded pulse and the Inv- Processing, Addison-Wesley, Reading, MA. 5x compression filter show the SNR increasing to 60 dB. Smith, P. L. 1974: Applications of radar to meteorological However, the tapered echo near the cell edge (formerly below operations and research, IEEE Proc., 62, 724-745. the noise level) shows evidence of sidelobe leakage representative of the 5-10 m/s velocities within the cell (not shown here).

May 26, 1995 Page 3 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 1, JANUARY 1998 125 Pulse Compression for Weather Radars

Ashok S. Mudukutore, V. Chandrasekar, Member, IEEE, and R. Jeffrey Keeler, Member, IEEE

Abstract-Wideband waveform techniques, such as pulse com- the long pulse to a duration 1/B, where B is the bandwidth pression, allow for accurate weather radar measurements in of the transmit waveform. a short data acquisition time. However, for extended targets The driving force behind exploring such as precipitation systems, range sidelobes mask and corrupt pulse compression for observations of weak phenomena occurring near areas of strong military applications is the necessity for greater pulse energy echoes. Therefore, sidelobe suppression is extremely important and increased range resolution. The same reason makes it in precisely determining the echo scattering region. A simulation suitable for a number of meteorological applications where procedure has been developed to accurately describe the signal high peak powers are difficult or expensive to obtain (e.g., returns from distributed weather targets, with pulse compression for millimeter-wave systems). Weather waveform coding. This procedure is unique and improves on radars with high peak earlier work by taking into account the effect of target reshuffling power transmitters, however, have adequate sensitivity and during the pulse propagation time which is especially important range resolution required for many applications. Using pulse for long duration pulses. The simulation procedure is capable of compression with weather radars allows them to rapidly scan generating time series from various input range profiles of re- three-dimensional (3-D) precipitation patterns and trace their flectivity, mean velocity, spectrum width, and SNR. Results from evolution with time. This is accomplished the simulation are used to evaluate the performance of phase- as follows. Antenna coded pulse compression in conjunction with matched and inverse beams for weather radars are typically circular in cross- compression filters. The evaluation is based on comparative section with half-power beamwidths of 0.25 to 3.0° and pulse analysis of the integrated sidelobe level and Doppler sensitivity lengths on the order of 100 m. Therefore. the pulse volume after the compression process. Pulse compression data from the is "pancake" shaped for ranges beyond 10-20 km, with the CSU-CHILL radar is analyzed. The results from simulation and cross-range width larger compared the data analysis show that pulse-compression techniques indeed to the down-range depth. provide a viable option for faster scanning rates while still retain- Thus, it appears that using pulse compression to improve the ing good accuracy in the estimates of various parameters that can down-range resolution would have little to offer. However, be measured using a pulsed-Doppler radar. Also, it is established averaging the fine-scale down-range measurements allows the that with suitable sidelobe suppression filters, the range-time dwell time to be reduced and provides the same or larger sidelobes can be suppressed to levels that are acceptable for number operational and research applications. of independent samples, thereby improving accuracy in measurements of the radar received signals. Index Terms-Pulse compression, weather radar. A. Background I. INTRODUCTION Pulse compression techniques have been well established PULSE compression techniques allow for the transmission for applications in military and aviation systems where the of a low peak-power, long-duration coded pulse and attain backscattering medium consists of hard targets. Several tech- the fine range resolution and improved detection performance niques have been proposed and studied since the early 1950's of a short duration, high peak-power pulse system. This is and are reviewed in a number of textbooks [1], [2]. Use of accomplished by widening the bandwidth of the transmitted pulse compression for extended precipitation targets was not pulse by coding it in either phase or frequency, which yields investigated until the early 1970's. Fetter [3] demonstrated a finer range resolution (AR = c/(2B)) than can be achieved the use of a 7-bit Barker phase-coded transmit pulse and a with a conventional radar system using an uncoded pulse. The matched-filter receiver, implemented on the coherent FPS-18 received echo waveform is processed using some variant of a radar at McGill University. Gray and Farley [4] investigated filter matched to the transmit coding scheme which compresses the use of binary phase-coded pulse compression for incoherent scatter observations. Keeler and Passarelli [5] have traced the evolution of pulse compression techniques in the weather Manuscript received July 21, 1996; revised January 29, 1997. This work was radar community. supported by the U.S. Air Force Office of Scientific Research Grant F49620- 95-1-0133 and National Science Foundation Grant ATM-9413453. The work of R. J. Keeler was supported by the FAA Terminal Area Suiveillance Systems B. Description program. Fig. 1 illustrates the basic concept of pulse A. S. Mudukutore is with the Research Triangle Institute, Hampton, VA compression 23666 USA (e-mail: [email protected]). processing in a weather radar system. The signal from the V. Chandrasekar is with the Department of Electrical Engineering, Colorado waveform modulator is used to code the radio frequency (RF) State University, Fort Collins, CO 80523 USA. signal. Fig. 1 shows a transmit waveform R. J. Keeler is with the Remote Sensing Facility, National Center for modulated by a 5- Atmospheric Research, Boulder, CO 80307 USA. bit phase code. The received signal is fed through a pulse Publisher Item Identifier S 0196-2892(98)00035-7. compression filter, which frequently'consists of a matched 0196-2892/98$10.00 © 1998 IEEE 126 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 36, NO. 1. JANUARY 1998

T= /B

T Phase coded transmit waveformn ANTENNA

DISTRIBUTED TARGET

range sidelobes range sidelobes

Received waveform after compression

Fig. 1. Block diagram of pulse compression radar.

filter section followed by a sidelobe suppression filter. The *Integrated sidelobe level (ISL), a measure of the energy peak power of the compressed pulse is increased by the distributed in the sidelobes, is defined as compression ratio (CR) defined as ISL = 10 log power integrated over sidelobes ILtotalloobe main power (3) T total mainlobe power CR = B.T - - (1) r *Loss in processing gain (LPG), a measure of loss in SNR due to mismatched as opposed to matched filtering, is where T is the transmitted pulse length, B is the bandwidth of defined as the transmitted waveform, and T is the effective (compressed) pulse length (r = 1/B) of the system. This ratio, alternatively B.T LPG = 10 log BT (4) known as time-bandlsidth product, is a measure of the degree total mainlobe power to which the pulse is compressed. For pulse compression waveforms, the compression ratio is greater than 1. Typical D. Inplementation 5 values range from 5 to as large as 10 . The choice of a pulse compression system is dependent on the type of waveform selected and the method of generation C. Range Sidelobes and Weighting and processing. Frequency-modulated pulse compression techniques involve sweeping the carrier frequency of the transmit A major drawback to the application of pulse compression is waveform in a linear or nonlinear fashion. These techniques the presence of range sidelobes which tend to smear the returns have been investigated [6], [7] and are known to yield good in range. Suppression of range sidelobes is critical, especially sidelobe performance. In this paper, however, we consider only in applications for weather radars where the observed targets phase-coded waveforms because of the ease in implementation are distributed in nature and often have strong and steep for a high-powered, ground-based weather radar system. gradients in reflectivity. Sidelobe suppression, in general, is Phase-coded pulse compression involves transmitting a long achieved by tapering the matched filter response by weighting pulse of duration T consisting of N subpulses, each of the transmitted waveform, the matched filter, or both in either width T = T/N. The phase of each subpulse is chosen frequency or amplitude. The weighting is usually applied to to be one of two possible values (0 or 7r rad) for biphase the matched filter which causes a loss of SNR due to the coding or one of several values for polyphase coding. Various mismatched section. The following measures are often used codes with known sidelobe properties have been studied [8]. to quantify the performance of range sidelobe suppression Important among them are Barker codes, combined Barker techniques. codes, pseudorandom codes, etc. Barker codes are the biphase Peak sidelobe level (PSL) is defined as codes having the property that after passage through a matched peak sidelobe power filter, the resulting sequence has sidelobes of unit magnitude PSLtotal mainlobe power (2) total mainlobe power (PSL = 1/N). Barker codes have the attractive property that MUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 127

REFERENCE WAVEFORM

COMPRESSED PULSE

RECEIVED WAVEFORM

(a)

REFERENCE WAVEFORM

PULSE

RECEIVED WAVEFORM

(b) Fig. 2. Matched filter implementation: (a) correlation processor and (b) FFT processor. their sidelobe structures contain the minimum energy that is The radar ambiguity function proposed by Woodward [10] theoretically possible and this energy is uniformly distributed quantitatively describes the interference to a reference target among the sidelobes. caused by targets which are range- and Doppler-shifted with respect to the reference target. For a range delay TR and E. Related Issues Doppler frequency fd, the cross ambiguirtyfunction is defined This section outlines the concepts of matched filtering and as ambiguity functions which are of fundamental importance to the understanding of pulse compression. 'Ju,(TR, fd) = u(t)v*(t +TR) exp (j2rfdt)dt 1) Matched Filter: For a received waveform s(t), it can (7) be shown that the frequency-response function of a linear, time-invariant filter which maximizes the output peak-signal where u(t) is the transmit waveform and v(t) is the impulse to mean-noise ratio for a fixed input SNR is [9] response of the filter. H(f)= S*(f) (5) II. SIMULATION OF DISPERSED RADAR PULSE WEATHER ECHO where S(f) is the Fourier transform of s(t) and * superscript This section addresses the problem of accurately simulating denotes the complex conjugation. The filter whose frequency radar echoes from coded wideband waveforms in the context response is given by (5) is called the matched filter. In of distributed, time-varying targets. If the scatterers in the obtaining (5), it is assumed that the noise accompanying the radar resolution volume were stationary or move with identical signal is stationary and has a uniform spectrum (white noise). velocities, the dispersed pulse echo could be achieved by The impulse response of the matched filter, therefore, is given passing the complex signal from the simple pulse echo through by a filter whose impulse response is the desired dispersed pulse h(t) = s*(-t). (6) transmission. This simple model cannot be applied to a distributed weather medium consisting of scatterers moving with Fig. 2 shows the time- and frequency-domain implementations different velocities. The Doppler shifts resulting from phase of the matched filter. Both implementations are widely used fluctuations during the course of passage of the dispersed pulse and the choice between them depends on the waveform and are responsible for the Doppler sensitivin' of various sidelobe the domain (time or Doppler) over which the receiver must suppression techniques. In addition, echoes from distributed process signals. weather targets have pulse-to-pulse fluctuation controlled by 2) Radar Ambiguity Function: The study of radar wave- the velocity distribution of the scatterers. In order to be able forms would be quite straightforward if the scatterers in the to see the fluctuation that takes place during the passage of the radar resolution volume were stationary. However, when there dispersed pulse, one needs to simulate the signal characteristics is a significant Doppler shift, the reflections from even a at a time-scale corresponding to the propagation time over a point target are no longer replicas of the transmit waveform. resolvable range bin, rather than observations separated by the 128 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. 1, JANUARY' 1998

pulse repetition period. A new simulation technique is deivel- to accurately describe the joint-distribution characteristics of oped here to accurately describe the statistical characteris tics the radar returns as the dispersed pulse propagates through (the joint-distribution) of radar returns of a coded wavefcDrm the medium. This procedure yields a two-dimensional (2-D) from distributed targets, for both single and dual polarizattion complex array S[m, n], (m = 1. ,* nbins; n = 1, *., nrot), operation. The simulation procedure accounts for the eftfect where ntot represents the number of samples at each range bin of reshuffling of scatterers during the pulse propagation tihme. separated by Ts, and nbins is the number of range bins. This is especially important while considering long durat:ion 2) Evolution of the Dispersed Pulse Echo: The effect of pulses (>l10s). the modulation waveform (p[n], n = 1, -,rp) on the simple pulse time series S[m, n] is incorporated in the new A. Radar Signals firom Weather Targets representation of the echo-signal shown below

The inphase (I) and quadrature (Q) components of the xi[m, n] = S[m, (i - l)nd + n]p[n] (11) complex echo signal from a weather target have a Gaussa'// distribution with zero mean [11]. Therefore, their probabi lity where i is the sample-time index (i.e., samples separated by density functions are given by TPRT) and rnd = TRT/T,. The evolution of the dispersed echo from xi[m. n] is shown in Fig. 3 for a 5-bit phase code 1 _[=/2a2 p -( i e-I2/2= -x < I < +.x (8) and explained below. Given that T, = 1/B = r (r is the subpulse duration), each subpulse in the transmit pulse defines a range bin. As the pulse at any sample-index i propagates, at p(Q) = e 2/a- -x < Q < +x (9) H~a the first range-sampling instant, the first subpulse encounters the first range bin (1,1) contributing to the first echo y[i. 1]. where o' is the variance of the I and Q samples (also the mean As the pulse moves on, at the next range-sampling instant. square value because I and Q are zero-mean). In addition to the first subpulse now encounters the second range-bin (2.1) being Gaussian random variables, the I and Q components and the second subpulse encounters the first range bin (1,2) are independent of each other [12]. The power spectrum of and the combination of these two gives yields echo sample weather signals, also referred to as the Doppler spectrum y[i. 21. Echoes at other ranges are similarly obtained. The echo in velocity space, is a power-weighted distribution of radial construction procedure explained here is similar to that used velocities of all scatterers that lie in a resolution volume. by Bucci and Urkowitz [14], and is mathematically described as The first three moments of the power spectrum are directly related to the reflectivity, mean radial velocity, and velocity y[i. j = E xi[m, 7n] (12I spectrum width, respectively. The Doppler spectrum can be V m+tn-1=-= approximated to be of Gaussian shape sitting on a white noise pedestal. i.e., III. RANGE SIDELOBE SUPPRESSION

S() =S __ 2NTs Due to the distributed nature of weather targets. the in- S(u)= e (+ (10) tegrated v27e-(7u A sidelobe level (ISL) provides a good measure of range sidelobe contamination. While evaluating the perfor- where S is the mean signal power, ! is the mean velocity. aL. mance of pulse compression systems, generally speaking. is the spectrum-width. N is the mean white noise power, A is any waveform-filter combination is considered suitable if it the wavelength, and Ts is the time spacing between samples. yields an ISL comparable to the sidelobe contribution from". typical two-way antenna pattern. In this section. based on thL B. Simulation Technique Description simulation procedure described in Section II. the performance The simulation procedure to obtain a dispersed radar echo of matched and inverse range sidelobe suppression filter is a two-step process. are evaluated. The criteria used in evaluation are integratet 1) Simple Pulse Echo Simulation: The time series from a sidelobe level (ISL). Doppler sensitivity after the compression simple pulse can be simulated using the simulation algorithm process, and how well the estimates of various parameters afte for multivariate signals described by Chandrasekar et al. [13]. pulse compression match up with those obtained from simpl This procedure constructs the Doppler spectrum at each range pulses. bin based on the distribution properties of the signal and range profiles of radar reflectivity (Z), mean velocity (U), velocity A. Inverse Filter spectrum width (cr), and SNR. The complex time series is Ackroyd and Ghani [15] discuss an optimal filtering tec! then obtained via an inverse DFT. For dual-polarization opera- nique for minimizing the ISL of the code response in tion. in addition to the parameters listed above, the differential least squares sense. This filter, called inverse filter, can L reflectivity (ZDR) and correlation between horizontally (H) implemented to act directly on the dispersed echo or on tl and vertically (V) polarized returns (PHv) are also specified. output of the matched filter. By implementing this optimal IS Separate time series are then generated at H and V polariza- technique, the PSL and ISL levels can be driven to very lo tions. The time spacing between adjacent samples is chosen values. For example, for a 13-bit Barker code, a modest fill to be Ts = 1/B (B = transmit waveform bandwidth). This is length of 39 (code-length x 3) yields a PSL of -38 dB and. in contrast to the procedure used by [13] where T, = TpRT. ISL of-30 dB. Application of optimal ISL filtering techniq' the pulse repetition time. The finer time-scale is necessary to combined Barker codes also yields good results [16]. MUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 129

Output Range cell

6,5 7,4 8,3 9,2 10,1 [ , -- y(i,10)

5,5 6,4 7,3 8,2 9,1 --_--- -I y(i, 9)

4,5 5,4 6,3 7,2 8,1 ---- > -- -' y(i,8)

3,5 4,4 5,3 6,2 7,1 --_------y(i,7)

2,5 3,4 4,3 5,2 6,1 ------y(i,6)

1,5 2,4 3,3 4,2 5,1 - -)------> --- - y,5)

1,4 2.3 3,2 4,1 ------> -- y(i4)

1,3 2.2 3,1 _------y(i,3)

1,2 2,1 =------_ _ _------~------y(i,( > y I ) 2.1 y~~~i,2) 1,1 - ---I f- .

Fig. 3. Evolution of dispersed echo at sample-time index i. Each square labeled (nm n) represents sample .rIt(m. n) (in = 1. . . nbins.: n = 1. * . n,) and the resulting output is shown on the right. In figure, nbins = 10 and np = 5.

1) Filter Design: We will restrict ourselves to the design Each Doppler filter output is then multiplied with a complex of an optimal ISL filter to act directly on the dispersed echo- exponential phase term, corresponding to the Doppler phase signal in contrast with other schemes which could operate on obtained from the center frequency of that filter but of opposite the signal at the output of the matched filter. Let (zk, k = polarity, to remove the residual Doppler phase along the 1. -.*, N) represent the input signal, (wk. k = 1. *-, M) range samples. The resulting waveform is then passed through represent the weighting sequence of the filter, and (k,. k = standard sidelobe suppression filters. 1, ** , A+ N - 1) represent the sequence at the output of the filter. Let (dk, k = 1. ., M+ N-l1) be the desired response, B. Evaluation Based On a Point Tlrget defined here to be an impulse function. The filtering criterion The evaluation presented here are based on using the is the minimization of the mean-squared-error. defined as following model. V = E[(dk - k)2]. (13) * Modulation waveform: Barker biphase code of length 13 (B-13). The optimum weight-vector Wo, satisfying (13), is obtained * Wavelength A = 0.1 m. by solving the vector-matrix equation * Bandwidth B = 1.024 MHz. * Transmit pulse-length T - 12.7L Rwo =p (14) s. Fig. 4 shows the ambiguity function of the B-13 waveform where R is the auto correlation matrix of :k and p is the using (a) matched filter (MF), (b) inverse filter of length discrete cross-correlation of Xk and dk [17]. Equation (14) is 65 (IF x5), and (c) IF x5 - DT, the Doppler tolerant the discrete form of the Wiener-Hopf equation. implementation of IF x5. The range of the Doppler velocities 2) Doppler Tolerant nIplementation: The performance of shown in the Fig. 4 is [0, 50] m/s which is typical for weather the matched filter as well as the inverse filter degrades in targets. Note that this corresponds tot wice the Nyquist velocity the presence of a Doppler shifted radar return. This is due to (l'lyq = A/(4TPRT) = 25 m/s) for a coherent S-band radar the fact that both the matched filter and the inverse sidelobe system operating at a pulse repetition time TPRT of 1 ms. Due suppression filter are designed for optimal performance under to symmetry about the zero Doppler velocity axis (vel = 0), the zero Doppler velocity conditions. A measure of the Doppler ambiguity function over the Doppler velocity interval [0,-50] sensitivity can be obtained from the Doppler phase shift m/s would be identical. For the matched filter output, the PSL over the pulse duration given by 0q = 27rfdT, where fd is constant at -22.27 dB and the ISL is -11.48 dB over the is the Doppler frequency shift and T is the duration of entire Doppler velocity range shown in the figure. the uncompressed pulse. Urkowitz and Bucci [18] outline The output of the inverse filter shows a much lowered a Doppler tolerant sidelobe suppression technique which al- sidelobe level (PSL 0 -60 dB, ISL ' -50 dB at zero leviates the sensitivity of the ISL on the target Doppler velocity). However, note the increased sensitivity of the output velocity. The technique suggests passing the received complex of the inverse filter with Doppler velocity. This sensitivity is signal through a filter-bank to separate out the signal into reduced using the Doppler tolerant processing scheme shown several Doppler-bins. The signal still contains the Doppler in panel (c). The Doppler tolerant scheme uses time series phase shift across the pulse (i.e., along the range samples). samples spaced TPRT apart as input to a Doppler filter bank. IIC== 'ro %l% A· fT~nmq t r.;r:;TTN1C1F AND RF.N-MTF SFECNSNG V(L 36 NO. 1. JANUARY I oQ 7U 130 irtzr I ¶.rniN3AL I-..IU£J13 ) Ul.* .ANN-.- -

. a

(a)

-2

-4

-6

-8

-1C 5 40

(b)

0 -40

-6C

-8C

-10C 5C 40

(c) Fig. 4. Ambiguity function based on point target analysis for the B-13 waveform. The compression filters used are (a) MF (range index from -12 to (b) IFx5 (range index from -38 to 38), and (c) IFx5-DT (range index from -38 to 38. MUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 131

0 10 20 30 40 50 60 70 80

-50 ...... | | ...... ,N=65 -100I 0 10 20 30 40 50 60 70 80

Fig. 5. Compression filter response to B-13 waveform for matched filter (MF>) and inverse filters of length 13 (IF xl), 25 (IFx2), 39 (IFx3), and 65 (IFx5) at zero Doppler velocity.

Therefore, the frequency domain representation of the time due to incorrect phase compensation at the Doppler filter-bank signal at the output of the filter bank lies in the fundamental output. Fig. 6(b) plots the ISL versus filter length for the B-13 Nyquist interval (-1/2TpRT, 1/2TpRT) corresponding to the waveform using inverse compression filters at zero Doppler. velocity interval (-V/nyq, Vnyq). Thus, for radial velocities Note that the higher order filters (lengths >90) yield ISL levels outside the Nyquist interval, the multiplication of the complex of less than -70 dB. exponential phase term at the output of each filter bank corresponding to the center frequency results in incorrect compensation of the Doppler phase along the range samples. C. Evaluation Based On Time-Varying, Distributed Targets This effect is evident in Fig. 4(c) for velocities greater than We demonstrate the application of the matched and inverse 25 m/s, where we see that the output of the Doppler tolerant filters by analyzing four profiles generated by the new sim- scheme yields higher range sidelobes than the inverse filter ulation procedure described in Section II. A more detailed without Doppler tolerance. discussion on the results from the first three profiles described Fig. 5 shows the output of the matched filter and inverse below can be found in Mudukutore et al. [19], [20]. filters of different lengths for a stationary point target. The I) Evaluation of ISL Using a Reflectivint Notch: Consider MF consistently yields higher sidelobes. The inverse filter an input profile consisting of a constant reflectivity level at sidelobes are much lower and located away from the main all ranges except for a deep reflectivity notch at one of the response with increasing filter length. For the B-13 waveform range bins. For time-varying distributed targets, a measure under consideration, the loss in processing gain due to mis- of the ISL can be obtained by computing the ratio of power match (LPG) is less than 0.5 dB for all the inverse filters under of the compressed signal at the notch to the power at any consideration (i.e., IFxl through IFx 7). Fig. 6(a) shows the other range. However, this procedure does not yield the ISL ISL versus Doppler velocity curves for the B-13 waveform for hard targets due to the fact that for a fluctuating target, in the Doppler velocity interval [0, 50] m/s. The different the contributions to the total power at a given range bin curves correspond to outputs of matched filter (labeled MF), from adjacent range bins add up incoherently as opposed to inverse filters of length 13, 65, and 91 (labeled IFxl, IFx5 coherent addition for a hard target. The ratio Pnotch/Pother and IFx7), and the Doppler tolerant implementation of IFx5 then reduces to (3) for the fluctuating target. Fig. 7 shows the and IFx7 (labeled IFx5-DT and IFx7-DT, respectively). range profile of the returned power at the output of various The MF yields the highest ISL. The ISL for the inverse filters compression filters for a input profile with a 100 dB notch improve with increasing filter length. Also, the sensitivity of at the center range bin from (a) hard target and (b) random the ISL with Doppler shifts increases with filter length (see distributed target with v = 0, c, = 2.5 m/s and SNR = curves for IFxl, IFx5 and IFx7). The Doppler tolerant 80 dB, for all ranges. The ISL values for the time-varying implementation does a good job of maintaining low ISL's for distributed targets computed in this fashion are consistent with all Doppler shifts within the Nyquist interval (see IFx5-DT those shown in Section III-B. Fig. 7 specifically brings out and IFx7-DT). Note the sudden increase in ISL at 25 m/s the power of our simulation algorithm showing the distinction 132 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. I. JANUARY

Sm -j.

0 Velocity (m/s)

(a)

1 n IU I I i i i I I I I I

-20 _.

-30 _.

-40 .a -J ul - -50 _.

-60 _ ., ... I ... : ......

-70

- Hl] II -- - I I I I I-~ I - - I I 10 20 30 40 50 60 70 80 90 100 Filter length

(b) Fig. 6. (a) ISL versus Doppler velocity for a point target using the B-13 waveform. (b) ISL versus filter length for the B-13 waveform using inverse compression filters for zero Doppler velocity.

between hard target responses and' time-varying, distributed bins. Integrating the power levels in the sidelobes yields a target responses. measure of the ISL, which is plotted in Fig. 8 as a function of 2) Evaluation of ISL Using a Reflectivity Spike: The input mean Doppler velocity for a time-varying, distributed target reflectivity profile consists of a 100 dB spike at the center with (a) Doppler spectrum width av = 1 m/s, SNR = 50 range bin. The range sidelobes due to the echo spill-over from dB; (b) cr = 1 m/s, SNR = 80 dB. It can be seen from the spike dominate the power levels in the adjacent range Fig. 8 that the responses of the various filters to the fluctuating MUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 133

(a)

0 2 4 6 8 10 12 14 16 18 20 Range Index

(b) Fig. 7. Range profiles of returned power at output of various compression filters for input notch profile (100 dB notch) using (a) hard target and (b) time-varying distributed target. targets is similar to the hard target response shown in Fig. 6(a). tolerant implementations degrades as the velocities approach However, there are a couple of interesting differences from the the extremities of the unambiguous Nyquist interval. This hard target response, especially at longer filter lengths. is due to the fact that at these higher velocities, the aliased a) Effect of spectrum width: As explained before, the portions of the Doppler spectrum wrap around the Nyquist- ISL for IFxS-DT and IFx7-DT increases steeply at the interval, resulting in incorrect Doppler phase compensation at Nyquist interval, for hard target responses. However, for the output of the Doppler filter-bank. The situation gets worse fluctuating responses, the performance of these Doppler with larger spectrum widths as can be seen from Fig. 9. 134 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. 1, JANUARY 1998

11 ...... -.-.

1 MF 10

-20 ...... ; ...... F...... x 1 ......

-30

cn '-.' - . : :-- ...... - 40 : -50

-50

:.tFx-Dx : IFx7 D:T-- -60 ...... I.F x ?.--D T ......

-70 I. ... I......

I I I -- - I~~~~~~~~~~~~~~~ -Ou-or) t - I I --- L I l 0 5 10 15 20 25 30 35 40 45 50 Velocity (m/s)

(a)

m ..-0 C3

-au 0 5 10 15 20 25 30 35 40 45 50 Velocity (m/s)

(b) Fig. 8. ISL versus Doppler velocity from a time-varying, reflectivity spike with (a) ao = I m/s, SNR = 50 dB and (b) a,. = 1 mis. SNR = 80 dB.

b) Effect of SNR: The outputs IF x 7 and IF x 7-DT in through the distributed medium, the fluctuations of the signal Fig. 8(a) (SNR = 50 dB) do not match with those for the occurring at a time-scale corresponding to the range sampling hard target. However, the same outputs match up well with time (inverse bandwidth) are small and do not decorrelate the the hard target response in Fig. 8(b) (SNR = 80 dB). This signal significantly from one range sampling instant to the suggests that the minimum ISL that can be obtained for any next. However, the effect of the fluctuatinc noise is to add a inverse filter is limited by the SNR. This can be explained random phase component to the underlying phase modulation by the fact that as the coded dispersed waveform propagates of the transmit waveform, thereby degrading the performance MUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 135

I I I~~~~~

-35-3 5 - ...... : ...... -4035.... i...... 4_ .::' ./ ...... :

-4 0 ...... -...... ·...../ ;'... ,......

-- SW:--1 -455 /*'/*/' / ...... ·-:.. 7.$W.-2,5. mf- ,"- .IFx5-DT : . i : : -··: : I: : ' 'SW=5 o0 . _: ...... -J e) -'* ......

-60 ...... ' . ....1 ..- .I ...... '' . i ! ..' I .

IFx7-DT I : :

I I I m · , 0 5 10 15 20 25 30 35 40 45 50 Velocity (m/s)

Fig. 9. ISL versus Doppler velocity for IF x5-DT and IFx7-DT at various spectrum widths.

A n II I I I

-10 : .. . . .i......

-20 ......

-30 ......

m -40 -J cn ; IFx5 ."~ ~ .;~ : : -50 ...... : ~ : :~IFx5-DT

-60 .~ ~: : i ~~ ~~~~ "F x 7 '

-70 ...... Fx - D T .. ..

-As) I _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I I I .I -I-'t 0 10 20 30 40 50 60 70 80 90 100 SNR (dB)

Fig. 10. ISL versus SNR for the B-13 waveform using inverse and matched filters for compression.

Of the compression filter on the received signal. The SNR dB, the ISL - -30 dB, and so on until SNR >50 dB where the imposed limitation on the ISL is evident in Fig. 10 where the ISL levels off at its minimum value of -50 dB. We therefore ISL is plotted as a function of SNR for a 100 dB fluctuating must be wary about arbitrarily extending filter lengths to get Spike target with zero mean velocity and spectrum-width of 1 improved sidelobe suppression performance and recognize the m/s. The solid lines in Fig. 10 represent the outputs of various role played by the SNR as a limiting factor in the sidelobe filters and the dashed lines correspond to their Doppler tolerant suppression performance of any filter. Counterparts. Examining the output of say the IF x 5 filter, we 3) Reflectivity and Velocity Step-Function Profiles: To eval- See that at SNR = 20 dB, the ISL - -20 dB and at SNR = 30 uate the effects of gradients, an input profile consisting of 136 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. 1. JANUARY 1998

Rn - IITI -I I

v .

70 ...... I ......

1......

60 ......

,...... :...... a...... · 50 .. --.:......

a.0 * '''':'` '' Id :'''''

40 ......

:......

* I~t~~'":~" ...... :...... 30 ...... I ...... ''·:.1. · · ·. ·

- V : :v I I. _ _ . I . ... .I zir3rn 0 10 20 30 40 50 60 0 Range Index

(a)

15 _ I

5 *~ ~~~~~~~~~I'~'''''

I-E 0 ...... Q)> :1

-5 :1

1 / -10 V ~~ ~ ~ ~ ~ ~ ..~~~~~~~......

_l -I I i I I I 0 10 20 30 40 50 60 70 80 Range Index

(b) Fig. 11. Range profiles of (a) reflected power and (b) Doppler velocity. The input profile to the simulation has a 50-dB reflectivity step and a 20-m/s velocity step. gradients in both reflectivity and velocity was used. Fig. 11 both reflectivity and velocity is inferior to the inverse filters. shows the range profiles of (a) the reflected power and (b) The IFx 5 (best ISL ,-48 dB) estimates of reflectivity at Doppler velocity at the outputs of the simple pulse MF, IFx 5, range bins just before the gradient are biased toward the and IF x 7. The reflectivity values on either side of the gradient higher reflectivity values past the gradient (-2-3 dB difference differ by 50 dB and the velocity jumps from -10 m/s to +10 compared to simple pulse output) which is responsible for m/s. The SNR at all ranges was set at 60 dB with a, at 2.5 biasing the Doppler velocity estimates at these bins towar m/s. It can be seen that the performance of MF in estimating the velocities of the higher reflectivity targets. The IFX MUDUKUTORE er al.: PULSE COMPRESSION FOR WEATHER RADARS 137

(best ISL -70 dB) does a good job of estimating both the TABLE I reflected power and Doppler velocity. The best performance MEAN DEVIATION OF VARIOUS PARAMETERS ATTHE OUTPUT was obtained from the IFx7-DT and the reflectivity and OF MATCHED AND INVERSE FILTERS FOR B-13 PHASE CODE velocity profiles at the filter output very closely followed the ___ MFIFxl IFx5 IFx5-DT IFx7 IFx7-DT simple pulse profiles (not shown in figure for clarity). Z(dB) 2.6268 1.9658 4) Input Profilesfrom Weather Data: The analysis of the 0.1621 0.1606 0.0731 0.0706 performance of matched and inverse filters thus far was done v (m/s) 1.1586 0.9729 0.2803 0.2779 0.1060 0.1034 using synthetic profiles for reflectivity, velocity, SNR, etc. a, (m/s) 0.3684 0.3429 0.1632 0.1640 0.0369 0.0372 These profiles illustrate the behavior of matched and inverse ZDR (dB) 0.4128 0.3165 0.1102 0.1105 0.0867 0.0856 filters in extreme conditions and provide a worst-case analysis. PHv(O) 0.0442 0.0405 0.0120 0.0119 0.0084 0.0084 When observing distributed weather targets, however, we say jDP (deg) 4.2325 3.6347 1.7767 that any waveform-filter combination is suitable if it yields 1.7749 1.3812 1.3655 an ISL comparable to the nonmainlobe power from the two- way antenna pattern. In order to test this requirement, real weather data collected using the CSU-CHILL multiparameter rr/s and the degradation in ISL of inverse filters at these weather radar were used to generate input range profiles for velocities is not significant for the reflectivity gradients under reflectivity Z, mean velocity v, SNR, differential reflectivity consideration. ZDR, copolar correlation coefficient at lag 0 PHV(O), and differential phase-shift OqDP (see review article by Bringi et IV. DATA EVALUATION FOR FAST-SCAN APPLICATIONS al. [21] for a description of these parameters). The spectrum width a, was set at 2.5 m/s at all ranges to better observe The CSU-CHILL radar transmits 1 mW peak power and the degradation in sidelobe suppression performance due to it is not easy to implement large bandwidth waveforms with factors other than the spectrum width. The data was collected such high-power transmitters. However, a phase-coded pulse )n June 7, 1995, while observing an intense thunderstorm compression scheme has been implemented through the use producing both rain and hail. The two main cores of precip- of a phase modulator interfaced with the RF synthesis circuit itation, located at approximately 41 and 47 km, show high in the transmitter. Operating at a frequency of 60 MHz, the reflectivities (50-65 dB). The ZDR values at both cores are modulator is capable of shifting the phase in 90° increments close to zero and the corresponding KDP values are fairly every 200 ns. This phase shifted 60 MHz signal is mixed with large (-4°/km corresponding to rain-rate of about 130 mm/h) the 2.785 GHz signal and the difference signal is sent to an indicating possible rain-hail mixture. The input reflectivity amplifier and fast pulse modulator to produce a 1 pls pulse. profile exhibits steep reflectivity gradients (15-25 dB/km) There are two such units in order to facilitate complementary and is a good candidate for sidelobe suppression evaluation. coding. A wideband intermediate power amplifier has been 1ig. 12(a)-(f) shows range profiles of Z, v, a,, ZDR, PHV(O), acquired to accommodate the higher bandwidth of the signal. and qDP. The solid line shows the values obtained from simple Both biphase and quadriphase codes of length 5 were used pulse simulation. The different dashed patterns represent the to modulate the phase of the l-Ls-long transmit pulse. On outputs of MF, IFxl, and IFx5 for the coded pulse. It is reception, the received signal was sampled at the inverse evident from the figure that MF and IF x 1 estimates of various bandwidth rate (T, = 1/5 MHz = 200 ns) corresponding parameters have unacceptable errors near the gradient regions. to 30-m range spacing. The received I/Q time series data The IFx5 filter, however, matches the simple pulse response was processed off line to test the various pulse compression and performs well in these regions. Other filter outputs are not algorithms. sI-own in figure for the sake of clarity. In order to quantify the performance of various filters, A. Data Analysis we define the mean deviation of variable x as MD(x) = On August 30, 1995. time-series data was collected over a E[abs(xpc - Xs)], where the expectation is carried out over storm to the Northwest of the CSU-CHILL radar. The antenna all range bins. xs and xpc refer to estimates of x obtained from position was fixed pointing at the core of the storm. As before, the output of simple pulse simulation and pulse compression the transmit polarization was set at horizontal (H), and the simulation, respectively. Table I shows the mean deviation of received signal was sampled every 200 ns (corresponding various parameters at the output of the matched and inverse to 30 m in range). Time series data was collected with filters. It can be seen from Table I that with increasing filter the transmit pulse-width (r) set at 1Is, with and without lernth, the accuracy of the estimates gets better. Depending phase coding. Various 5-bit phase codes, including Barker and or the required accuracy of the multiparameter estimates, it complementary codes, were used. Fig. 13 shows the standard appears that for reflectivity gradients encountered in typical deviation in estimates of reflectivity factor 10 log P as a Weather situations, the IFx5 or the IFx7 (ISL < -45 dB) function of number of samples used to form the mean estimate, Provide sidelobe suppression adequate to represent the actual at a fixed resolution cell. The power values from five adjacent reflectivity structure. Also, the improvement obtained from the range bins, i.e., reference bin and the two bins on either side of Doppler-tolerant implementation is not very significant in this the reference bin, were averaged and therefore, the net range :ase. This could be due to the fact that the input velocity sampling interval was increased to 150 m (corresponding to the 3rofile to the simulation is confined to the interval (-6, 10) range resolution of the uncoded pulse). Note that the lowered 138 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. 1. JANUARY 1998

80 I I ~ J

..-I V v

CL) 0

I .. -1 1 . 30 35 40 45 50 Range (km) (a)

', E

0o 0

__ 5 Range (km) (b) Fig. 12. Range profiles of (a) Z (dB) and (b) v (mis). The different curves show the profile from the simple pulse and the outputs of MF, IFxl, and IFx5 for the B-13 coded pulse.

values for standard deviation (by approximately the expected dard deviation followed by the complementary coding scheme v/5) for the pulse compression data is due to the fact that more and the Barker code, MF processed outputs, respectively. independent samples in range are available for averaging than for the uncoded pulse. V. SUMMARY AND CONCLUSIONS Also, note that the various pulse compression schemes, the A new simulation procedure has been developed which ac- Barker coded. IFx5 processed output yields the lowest stan- curately models the joint distribution properties of fluctuating LUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 139

c- c.

C , 03 (n

Range (km)

(c)

0) 0) Q 0) as

(1)

Range (km)

(d) Fig. 12. (Conrinued.) Range profiles of (c) ar, (m/s) and (d) ZDR (dB) The different curves show the profile from the simple pulse and the outputs Of lM, IFxl, and IFx5 for the B-13 coded pulse.

Weather radar echoes with pulse compression. This procedure pression filters were evaluated using simulation output and accOUnts for the reshuffling of scatterers within the resolution pulse compression data for both point targets and time-varying Volume during the pulse propagation time which is important, distributed targets. The criteria used in evaluation were ePecially for longer pulse lengths. The procedure generates * integrated sidelobe level (ISL); ie-records for both single and dual polarization operations. * Doppler sensitivity over the velocity interval commonly he Performance of various compression and sidelobe sup- encountered with meteorological targets, i.e., [0, 50] m/s; 140 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. 1. JANUARY 1998

(e)

Q ._

.- en

CLC, CD c- CO.

- 2 ?£=.0) Q, 0

5 Range (km) (0' Fig. 12. (Continued.) Range profiles of (e) IpHv(0)l and (f) ODp (O). The different curves show the profile from the simple pulse and the out: of MF, IFxl. and IFx5 for the B-13 coded pulse.

*comparison with output from simple pulse waveform of at longer filter lengths (five or more times longer than wa equal bandwidth. form). The same performance carries over to dual polarizat Our analysis shows that the level of suppression offered implementations, i.e., good estimates of polarimetric varial by the matched filter is not sufficient in cases with strong can be obtained. gradients in reflectivity. Inverse filters, designed to minimize It is shown that the sidelobe suppression performanCL the integrated sidelobe level, seem to perform more than ade- inverse filters degrades considerably with increasing n quately for commonly expected weather gradients. especially Doppler velocities of the weather targets. Evaluation b: MUDUKUTORE et al.: PULSE COMPRESSION FOR WEATHER RADARS 141

%3 la%d I

- No PC * BC-MFB 2.5 ...... \ - BC-IFx5 IL :: i '\ :*-- -CC-MF oC 2 t*-

.° 1.5 h ...... : ., -oIf. Cr : : "\:·. *\'^x : :

A\,: > -X 0.5 '-~~~~:~-~.. :.:...... '...... ;.. .. ~

i. . II II I vO 50 100 150 200 250 300 # of samples

Fig. 13. Standard deviation of 10 logto P versus number of samples used in estimate. Various curves represent output from uncoded pulse (solid). 5-bit Barker coded pulse with MF> processing (dotted). 5-bit Barker coded pulse with IF x5 processing (h, andn 5-bi-it complementamplmntr codingi (dashed),(dash-dot). on simulation using steep reflectivity gradients show that the multiparameter radars, accuracies equal to or better than those Doppler tolerant implementation helps maintain low sidelobe currently available can be achieved at NEXRAD-like scan- levels even at higher Doppler velocities. This scheme, how- rates. ever, is effective only when the full Doppler spectrum of the radar returns are confined to the unambiguous Nyquist interval. ACKNOWLEDGMENT With increasing spectrum width, the range of velocities that The authors acknowledge very helpful discussions with Dr. can be processed effectively narrows down significantly. V. N. Bringi at Colorado State University and the CSU-CHILL For low SNR, the performance of all range sidelobe sup- radar staff with their assistance in obtaining pulse compression pression filters were shown to be limited by the SNR. In these data. cases, arbitrarily increasing filter length does not necessarily yield lower sidelobe levels. Thus, the SNR imposed limit REFERENCES on the ISL can cause significant sidelobe contamination in [1] C. E. Cook and M. Bernfeld. Radar Signals: An Introdulcrion to Tleory measurements made while observing weak echo regions using ami Application. New York: Academic. 1967. pulse compression weather radars. This analysis also shows [2] A. W. Rihaczek, Principles of High Resolution Radar. New York: that for high SNR cases where noise does not limit the ISL. McGraw-Hill. 1969. [3] R. W. Fetter, "Radar weather performance enhanced by pulse compres- the longer filters do generally reduce the ISL. sion." in Preprints, 14th A.MS Conf. RadarMereorol., Tucson, AZ. Nov. One of the main applications of high-resolution measure- 1970, pp. 413-418. ments is to improve accuracy in estimates of radar [4] R. W. Gray and D. T. Farley, "Theory of incoherent-scatter measure- parameters ments using compressed pulses," Radio Sci., vol. 8, no. 2, pp. 123-13 1 such as Z, ZDR, etc., through range averaging. For example, Feb. 1973. using a 5-bit Barker code and averaging over five adjacent [5] R. J. Keeler and R. E. Passarelli. "Signal processing for atmospheric radars." in Proc. Radar Meteorol., pp. 199-229, 1990. range bins, the standard deviation in reflectivity estimates [6] R. J. Keeler and C. A. Hwang. "Pulse compression for weather radar," was reduced by a factor of about N/'. With longer codes, in Proc. IEEE Int. Radar Cotf., May 1995. pp. 529-535. better improvement can be achieved. These improvements in [7] J. G. Weiler and F. Ohora. "Stormfinder 2000: A solid-state S-band weather radar system characteristics," in Preprints, 27th AMS Cotlf accuracy of radar measurements are not at the expense of Radar Meteorol., Vail, CO, Oct. 1995, pp. 720-722. increased dwell time. Currently, weather radars operated by the [8] M. N. Cohen and F. E. Nathanson, "Phase-coding techniques." Radar Design Principles. New York: McGraw-Hill. 1990, ch. 12. National Weather Service (NEXRAD) use scan-rates of about [9] M. I. Skolnik, Introduction to Radar Systems. New York: McGraw- 18-20°/s in precipitation mode corresponding to integration Hill. 1980, pp. 371-373. of 50 samples. However for multiparameter radars, due to [10] P. N. Woodward, Probabilint and Information Theory, With Applications to Radar. New York: McGraw-Hill, , 1953. accuracy requirements in estimates polarimetric variables, [ I] J. S. Marshall and W. Hitschfeld, "The interpretation of the fluctuating integration over 64 sample-pairs (i.e., 128 samples) is usu- echo from randomly distributed scatterers. Part 1." Cant. J P/hrs., vol. ally considered acceptable. This necessitates slower antenna 31. pp. 962-994, 1953. [121 R. J. Doviak and D. S. Zrni&. Dtoppler Radarand Weather Obser'ations. Scan rates (6-8°/s). Using pulse compression techniques with San Diego. CA: Academic. 1984. 142 . IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING. VOL. 36. NO. I. JANUARY 1998

[13] V. Chandrasekar, V. N. Bringi. and P. J. Brockwell, "Statistical prop- V. Chandrasekar (S'83-M'87), photograph and biography not available at erties of dual-polarized radar signals," in Proc. 23rd AMS Conf Radar the time of publication. Meteorol., Snowmass, CO, Sept. 1986, pp. 193-196. [14] N. J. Bucci and H. Urkowitz, "Testing of doppler tolerant range sidelobe suppression in pulse compression meteorological radar." in Proc. IEEE Nar. Radar Conf., Boston, MA, Apr. 1993, pp. 206-211. [15] M. H. Ackroyd and F. Ghani, "Optimum mismatched filters for sidelobe R. Jeffrey Keeler (S'63-M'66) received the suppression," IEEE Trans. Aerosp. Electron. Svst., vol. AES-9, pp. B.S.E.E. degree from the Rose-Hulman Institute 214-218, Mar. 1973. \ of Technology, Terre Haute. IN, the M.S.E.E. from [16] N. J. Bucci, "Doppler tolerant range sidelobe suppression for pulse Stanford University, Stanford. CA. and the Ph.D. compression radars. Tech. Rep. MTMR-91-TR-001, GE Aerospace, degree. in 1979, in electrical engineering from the Moorestown, NJ, 1991. ;'' University of Colorado. Boulder [17] S. Trietel and E. A. Robinson. "The design of high resolution digital He has previously worked at the NOAA/ERL filters." IEEE Trans. Geosci. Electron.. vol. GE-4, pp. 25-38, June 1966. Wave Propagation Laboratory, Boulder, and Bell [18] H. Urkowitz and N. J. Bucci, "Doppler tolerant range sidelobe suppres- Laboratories, Holmdel. NJ. He is presently a sion for meteorological radar with pulse compression." in Proc. IGARSS, Research Engineer and Manager of the Remote Houston, TX, May 1992, vol. 1, pp. 206-208. Sensing Facility, National Center for Atmospheric [19] A. Mudukutore, V. Chandrasekar, and R. J. Keeler. "Range sidelobe Research, Boulder. where he coordinates remote sensor development and suppression for weather radars with pulse compression: Simulation and deployment activities including UHF. microwave. and optical remote sensors. evaluation." in Preprints, 27th AMS Conf Radar Meteorol. Vail, CO, He is an Adjunct Professor at Colorado State University, Fort Collins, where Oct. 1995, AMS, pp. 763-766. he teaches courses on meteorological radar technology and applications. His [20] A. Mudukutore. V. Chandrasekar, and R. J. Keeler, "Simulation and current research interest center on advanced weather radar system design, analysis of pulse compression for weather radars," in Proc. IGARSS. which rely on phased array antennas and pulse compression waveform desian Firenze. Italy, July 1995. and processing techniques. as well as optical remote sensing techniques. [21] N. N. Bringi. V. Chandrasekar, P. Meischner, J. Hubbert and Y. Golestani. "Polarimetric radar signatures of precipitation at S- and C- bands" Proc. Inst. Elect. Eng.. pt. F. vol. 138. no. 2. pp. 109-119, 1991.

Ashok S. Mudukutore received the B.E. decree in electronics and communications from the University of Mysore. Mysore, India in 1988 and the M.S. and Ph.D. degrees in electrical engineering from Colorado State University (CSU), Fort Collins. in 1992 and 1996, respectively. He was a Research Assistant at CSU while pur- suing the Ph.D. degree. He is presently a Research Engineer at the Center for Aerospace Technology. Research Triangle Institute. Hampton. VA. Pulse Compression for Phased Array Weather Radar

Appendix K: Mudukutore, A.S., V. Chandrasekar and R.J. Keeler, 1998: "Pulse compression for weather radars", IEEE Trans. Geoscience and Remote Sensing, Vol. GE-36, pp 125-142.

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