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Signal Processing for Atmospheric Radars

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Signal Processing for Atmospheric Radars NCAR/TN-331+STR i NCAR TECHNICAL NOTE I - May 1989 Signal Processing for Atmospheric Radars R. Jeffrey Keeler Richard E. Passarelli ATMOSPHERIC TECHNOLOGY DIVISION NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER, COLORADO TBSIE OF COTENTS TABLE OF CONTENTS ..................... iii LIST OF FIGURES ......................... v LIST OF TABLES ................... .. .vii PREFACE. .. .. i....................... 1. Purpose and scope ................. 1 2. General characteristics of atmospheric radars. 3 2.1 Characteristics of processing .......... 3 2.1.1 Sampling ................... 3 2.1.2 Noise ...... ............... 4 2.1.3 Scattering ............... 5 2.1.4 Signal to noise ratio (SNR) .......... 6 2.2 Types of atmospheric radars .......... 6 2.2.1 Microwave radars . ........... 7 2.2.2 ST/MST radars or wind profilers ....... 8 2.2.3 FM-CW radars .. .............. 8 2.2.4 Mobile radars ............ .. 9 2.2.5 Lidar ............ ....... 10 2.2.6 Acoustic sounders . .......... 11 3. Doppler power spectrum moment estimation . .... 13 3.1 General features of the Doppler power spectrum. 14 3.2 Frequency domain spectral moment estimation . 18 3.2.1 Fast Fourier transform techniques . .... 18 3.2.2 Maximum entropy techniques .......... 20 3.2.3 Maximum likelihood techniques . ....... 23 3.2.4 Classical spectral moment computation ..... 25 3.3 Time domain spectral moment estimation. ..... 27 3.3.1 Geometric interpretations ........... 27 3.3.2 "Pulse pair" estimators ........... 28 3.3.3 Circular spectral moment computation for sampled data. ............. 31 3.3.4 Poly pulse pair techniques ..... 33 3.4 Uncertainties in spectrum moment estimators . 35 3.4.1 Reflectivity. ... ............ 35 3.4.2 Velocity. ..... ...... 36 3.4.3 Velocity spectrum width ........... 37 4. Signal processing to eliminate bias and artifacts. 43 4.1 Doppler techniques for ground clutter suppression 43 4.1.1 Antenna and analog signal considerations. ... 44 4.1.2 Frequency domain filtering. ......... 45 4.1.3 Time domain filtering ............. 46 4.2 Range/velocity ambiguity resolution ....... 50 4.2.1 Resolution of velocity ambiguities ...... 51 iii 4.2.2 Resolution of range ambiguities ....... 55 4.3 Polarization switching consequences ....... 56 5. Exploratory signal processing techniques . .... 57 5.1 Pulse compression .... .......... 57 5.1.1 Advantages of pulse compression . ...... 58 5.1.2 Disadvantages of pulse compression. ...... 59 5.1.3 Ambiguity function. .. 61 5.1.4 Comparison with multiple frequency scheme . 63 5.2 Adaptive filtering algorithms ......... 63 5.2.1 Adaptive filtering applications ....... 64 5.2.2 Adaptive antenna applications .. ..... 68 5.3 Multi-channel processing. ............ 69 5.4 A priori information. ............. 70 6. Signal processor implementation ......... 71 6.1 Signal processing control functions ..... 71 6.2 Signal Z?D conversion and calibration ...... 74 6.3 Reflectivity processing ... .......... 76 6.4 Thresholding for data quality ......... 78 7. Trends in signal processing. ............ 81 7.1 Realization factors ............... 81 7.1.1 Digital signal processor chips ....... 81 7.1.2 Storage media ................. 82 7.1.3 Display technology . .............. 83 7.1.4 Commercial radar processors .......... 83 7.2 Trends in programmability of DSP. ........ 84 7.3 Short term expectations .......... .... 85 7.3.1 Range/velocity ambiguities ......... 85 7.3.2 Ground clutter filtering .......... 86 7.3.3 Waveforms for fast scanning radars ...... 86 7.3.4 Data compression. ............. 87 7.3.5 Artificial intelligence based feature extraction 87 7.3.6 Real time 3D weather image processing .. ... 87 7.4 Long term expectations . ............ 87 7.4.1 Advanced hardware ....... .. 88 7.4.2 Optical interconnects and processing ..... 88 7.4.3 Communications . 88 7.4.4 Electronically scanned array antennas ..... 88 7.4.5 Adaptive systems ............... 89 8. Conclusions. ................... 91 8.1 Assessment of our past. ............. 91 8.2 Recommendations for our future . ........ 92 8.3 Acceptance of new techniques ........... 93 8.4 Acknowledgements. .............. 93 ACRONYM LIST ........................... 95 BIBLIOGRAPHY ....... ........... .... 97 iv TIST OF FJIGRES Fig 3.1 Doppler power spectrum (128 point periodogram) of 15 typical weather echo in white noise. Estimated parameters are velocity ~ 0.4 Vax velocity spectrum width ~ .04 Vmax, and SNR 10 dB. Fig 3.2 Three dimensional representation of the complex 29 autocorrelation function as a helix. Radius of helix Rs(0) is proportional to total signal power, Ps; rotation rate of helix is proportional to velocity, V; width of envelope is inversely proportional to velocity spectrum width, W. Delta function Rn(0) represents noise power. Fig 3.3 Periodogram power spectrum plotted on unit circle in the 32 z-plane. Note velocity aliasing point, the Nyquist velocity, at z=-l. Fig 3.4 Comparison of classical and circular (pulse pair) first 34 moment estimators. Classical estimate is determined by linear weighting of spectrum estimate and circular estimate, by sinusoidal weighting. Fig 3.5 Velocity error as function of spectrum width and SNR. 39 Spectrum width is normalized to Nyquist interval, vn=W/2Vmx=2WTs/X. M is number of sample pairs and error is normalized to Nyquist velocity interval, 2va = 2Vmax. Small circles represent simulation values (Doviak and Zrnic, 1984). Fig 3.6 Width error as a function of spectrum width and SNR. 42 Spectrum width is normalized to Nyquist interval, vn=W/2Vmax=2Wrs/X. M is number of sample pairs and error is normalized to Nyquist interval, 2Vmax. Small circles represent simulation values (Doviak and Zrnic, 1984). Fig 4.la Clutter filter frequency response for a 3 pole infinite 47 impulse response (IIR) high pass elliptic filter. For ground clutter width of 0.6 ms- 1 and scan rate of 5 rpm this filter gives about 40 dB suppression. V = stop - band. Vp = pass band cutoff, Vmax = 16 ms (Hamidi and Zrnic, 1981). Fig 4.lb Implementation of 3rd order IIR clutter suppression 48 -1 filter; z is 1 PRT delay. K1 - K4 are filter coeffi- cients (Hamidi and Zrnic, 1981). v Fig 5.1 Ambiguity diagram for single FM chirped pulse waveform 62 with TB=10. T is range dimension. 0 is velocity dimension. Targets distributed in (r,q) space contribute to the filter output proportional to the ambiguity function. For atmospheric targets, Doppler shift frequencies are typically very small relative to pulse bandwidth (Rihaczek, 1969). Fig 5.2 Prediction error surface for 2 weight adaptive filter. 65 The LMS algorithm estimates the negative gradient of the quadratic error and steps toward the minimum mean square error (mse). The optimum weight vector is W* = (0.65, -2.10). If the input statistics change so that the error surface varies with time, the adaptive weights will track this change (Widrow and Stearns, 1985). Fig 5.3 Adaptive filter structure. The desired response (dk) is 66 determined by the application. The adaptive filter. coefficients (Wk) and/or the output signal (Yk) are the parameters used for spectrum moment estimation (Widrow and Stearns, 1985). Fig 6.1 Block diagram of a typical signal processor. 26 vi LSTr OF TAHBI Table 1 Comparison of remote sensor sampling schemes and rates. 7 Table 2 Characteristics of several popular windows when applied 20 to time series data analysis (Marple, 1987). Table 3 Expressions for variance of velocity estimators at high 38 SNR. Assumes Gaussian spectra in white noise, low normalized velocity width (Wn=W/2Vmx) and large M. Expressions apply to both pulse pair and Fourier transform estimators. Table 4 Expressions for variance of width estimators at high 41 SNR. Assumes Gaussian spectra in white noise, low normalized velocity width (Wn=W/2Vmax) and large M. Expressions apply to both pulse pair and Fourier transform estimators. vii PiRFACE This review of signal processing for atmospheric radars was originally written as Chapter 20 of the book Radar in Meteorology, edited by Dave Atlas (1989) for the Proceedings of the 40th Anniversary and Louis Battan Memorial Radar Meteorology Conference. We have attempted to give the reader an overview of signal processing techniques and the technology that are applicable to the atmospheric remote sensing tools of weather radar, lidar, ST/MST radars and wind profilers. This NCAR Technical Note includes the signal processing chapter and the relevant references in a single document. The text has had minor editing and the references have been slightly expanded over the version published in Radar in Meteorology. We hope that this Technical Note will assist the many individuals who want a better understanding of signal processing to achieve that goal. R. Jeffrey Keeler Richard E. Passarelli March 1989 ix 1. PURPOSE AND SODFE Signal processing is perhaps the area of atmospheric remote sensing where science and engineering make their point of closest contact. Signal processing offers challenges to engineers who enjoy developing state-of-the- art systems and to scientists who enjoy being at the crest of the wave in observing atmospheric phenomena in unique ways. The primary function of radar signal processing is the accurate, efficient extraction of information from radar echoes. A typical pulsed Doppler radar system samples data at 1000 range bins at 1 kilohertz pulse repetition frequency (PRF), generating approximately 3 million samples per second (typically in-phase (I) and quadrature phase (Q) components from a linear channel and often a log receiver). These "time series", in their
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