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Radar Frequencies and Waveforms Radar Frequencies and Waveforms 12th Annual International Symposium on Advanced Radio Technologies Michael Davis Georgia Tech Research Institute Sensors and Electromagnetic Applications Laboratory [email protected] Based on material created by Byron M. Keel, Ph.D., GTRI Waveforms Extract “Target” Information A radar system probes its environment with specially designed waveforms to identify and characterize targets of interest. Detection For a given range, angle, and/or Doppler, decide if a target is or is not present. Example: Moving target indication (MTI) radar Estimation For a given range, angle, and/or Doppler, estimate Example: Synthetic aperture radar (SAR) imaging 2 Overview Radar frequencies Radar waveform taxonomy CW: Measuring Doppler Single Pulse: Measuring range Ambiguity function Pulse compression waveforms (FM and PM) Coherent pulse trains 3 Radar Frequencies 4 Radar Bands Range - Radar Band Frequency Long Poor Angular Resolution Large HF 3 – 30 MHz VHF 30 – 300 MHz UHF 300 – 1000 MHz Range Air Air Range L 1 – 2 GHz - FOPEN Surveillance S 2 -4 GHz Long C 4 – 8 GHz X 8 – 12 GHz Air-to-Air SAR/ Ku 12 – 18 GHz GMTI Fire Fire Control/ Ka 27 – 40 GHz Munitions mm (V & W) 40 – 300 GHz Small Range - Resolution Short Good Good Angular 5 Radar Waveform Taxonomy 6 Continuous Wave (CW) vs. Pulsed CW: Simultaneously transmit and receive Pulsed: Interleave transmit and receive periods 7 Continuous Wave (CW) vs. Pulsed Continuous Wave Pulsed Requires separate Same antenna is used for transmit and receive transmit and receive. antennas. Isolation requirements Time-multiplexing relaxes limit transmit power. isolation requirements to allow high power. Radar has no blind Radar has blind ranges ranges. due to “eclipsing” during transmit events. 8 Modulated vs. Unmodulated Modulation may be applied to each pulse (intrapulse modulation) or from pulse-to-pulse (interpulse modulation) Classes of Modulation Amplitude “ON-OFF” Amplitude Modulation Phase Frequency Modulation Frequency Phase Modulation Polarization 9 Measuring Doppler with CW Waveform 10 Measuring Doppler with a CW Radar Doppler Shift v Target radial velocity fD fc Radar frequency 11 CW Doppler Resolution Df Velocity resolution improves as integration time, TCW, and radar frequency, fc, increases. 12 CW Doppler Processing 0 DFT processing Mainlobe -5 Sample CW returns discretely in time -10 Generate spectrum via Fourier analysis (e.g., FFT) -15 Sidelobes dB -20 Results in sinc shaped response -25 Weighting can be applied to reduce Doppler sidelobes -30 SNR loss -35 Resolution degradation -40 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 normalized frequency Sampling of DFT response a function of 1 0.9 Bin spacing 0.8 Frequency 0.7 0.6 Zero padding reduces bin spacing; does not 0.5 improve resolution Magnitude 0.4 0.3 0.2 0.1 0 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Normalized (cycles/sample) 13 Measuring Range with a Single (Unmodulated) Pulse 14 Unmodulated Pulse PTX Peak transmit power fc Center frequency Tp Pulse width Baseband 15 The Matched Filter Observe a known signal, s(t), in noise Apply matched filter to maximize signal-to-noise ratio (SNR) assuming that signal has unit power, i.e., 16 The Matched Filter Matched Filter 17 Waveform Range Response Matched Filter The range response, h(t), of a waveform is the auto-correlation function of the transmitted signal. 18 Range Resolution: Unmodulated Pulse Tp Range resolution improves as transmitted pulse gets shorter. 19 Ambiguity Function 20 Ambiguity Function Range Response (No Uncompensated Doppler) Ambiguity Function Doppler shift The ambiguity function characterizes the filtered response when the received signal contains an uncompensated Doppler shift 21 Ambiguity Function for a Simple Pulse 1 x t 0 t t Simple Pulse t t sintf 1 d t t A t,1 fd t t t t tfd 1 t Simple Pulse Ambiguity Function Zero Doppler Cut Zero Time-Delay Cut t Zero Doppler Cut A t,0 1 t t t sintfd Zero Time-Delay Cut A0, fd t t tfd 22 Improving Range Resolution with Pulse Compression 23 Limitations of the Unmodulated Pulse Decreasing SNR, Radar Performance Increasing Decreasing Pulse Width Increasing Increasing Range Resolution Capability Decreasing For an unmodulated pulse there exists a coupling between range resolution and waveform energy 24 Pulse Compression Range response is the auto-correlation of the transmitted signal. To have “narrow” in range (time) domain, the waveform must have “wide” bandwidth in frequency domain The bandwidth of an unmodulated pulse of duration Tp is 1/ Tp 2/Tp Pulse Compression Use modulated pulses to get better range resolution. 25 Pulse Compression Waveforms Permit a de-coupling between range resolution and waveform energy. Apply modulation to increase bandwidth. Range resolution, DR, improves as bandwidth, W, increases. SNR is unchanged if pulse width remains the same. 26 Linear Frequency Modulated (LFM) Waveforms 27 LFM Phase and Frequency Characteristics Linear Frequency Modulated Waveforms • LFM phase is quadratic • Instantaneous frequency is defined as the time derivate of the phase 2 t t x t cos t t t 22 • The instantaneous frequency is linear t Quadratic Term Linear Term 4 radians 2 d 2 frequency tt 2 dt tt time t t 1 d time ft 2 2 2 2tdt 28 Components of LFM Spectrum X X exp j exp j 3 Key Terms 2 0 -2 Magnitude Quadratic Residual -4 -6 Response Phase Phase -8 dB t 20 -10 -12 -14 -16 X 1 For large time-bandwidth products -18 -20 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 frequency, normalized by 2 0 1 t 2 -2 -4 4 Quadratic phase term -6 -8 dB t 50 -10 -12 -14 Residual phase term -16 -18 -20 4 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 frequency, normalized by 2 1 t 2 0 Xj exp -2 4 -4 -6 -8 dB t 100 -10 Reference: Cook, Bernfeld, “Radar Signals, An Introduction to Theory and Application”, -12 -14 Artech House, 1993, p. 49 -16 -18 -20 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 frequency, normalized by 29 LFM Match Filtered Response Bandwidth (MHz) Range Resolution (m) 0.1 1500 1 150 0 2 75 5 30 -4 10 15 20 7.5 -10 50 3 -13 100 1.5 dB 200 0.75 -20 500 0.3 1000 0.15 -30 sin ttt t t -6 -4 -2 -1 0 0.5 2 4 6 yt 1 multiples of 1/ t ttt t For t ≥ 20, match filtered response approximates a sinc 1 c ~ -13 dB peak sidelobes t resolution in time r range resolution 2 Rayleigh resolution: Rayleigh resolution equivalent to 4 dB width 30 LFM Ambiguity Function t sint 1ft d t tt y t,1 fd t t t t t 1ftd tt t t sin 1 tf d t t y t, fd 1 t t t t t 1 t fd t Sinc functions are time shifted versions of one another t f sin 1 t d td t t t y t,0 1 t t t t 1 t t The triangle shaped response does not shift with the sinc response 31 Amplitude Weighting 5 Amplitude weighting reduces peak sidelobe levels 0 reduces straddle loss -4 Price paid -10 increased mainlobe width (degraded -15 resolution) -20 loss in SNR (loss computable from dB weighting coefficients) -25 -30 -35 N 1 2 -40 wn -45 n0 SNRLoss N 1 -50 2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 N w n normalized delay n0 Weighting as a part of X() “Fast Convolution” FFT FFT-1 X*() X W() 32 Taylor Weighting Function Peak Sidelobe Level (dB) -20 -25 -30 -35 -40 -45 -50 -55 -60 nbar SNR Loss (dB) 2 -0.21 -0.38 -0.51 3 -0.21 -0.45 -0.67 -0.85 4 -0.18 -0.43 -0.69 -0.91 -1.11 -1.27 5 -0.16 -0.41 -0.68 -0.93 -1.14 -1.33 -1.49 6 -0.15 -0.39 -0.66 -0.92 -1.15 -1.35 -1.53 -1.68 7 -0.15 -0.37 -0.65 -0.91 -1.15 -1.36 -1.54 -1.71 -1.85 8 -0.16 -0.36 -0.63 -0.90 -1.14 -1.36 -1.55 -1.72 -1.87 9 -0.16 -0.36 -0.63 -0.90 -1.14 -1.36 -1.55 -1.72 -1.87 Peak Sidelobe Level (dB) -20 -25 -30 -35 -40 -45 -50 -55 -60 nbar 4 dB Resolution Normalized by c/2 2 1.15 1.19 1.21 3 1.14 1.22 1.28 1.33 4 1.12 1.22 1.29 1.36 1.42 1.46 5 1.11 1.20 1.29 1.36 1.43 1.49 1.54 6 1.10 1.19 1.28 1.36 1.43 1.50 1.56 1.61 7 1.09 1.19 1.28 1.36 1.43 1.50 1.56 1.62 1.67 8 1.08 1.18 1.27 1.35 1.43 1.50 1.57 1.63 1.68 33 Exciter / LO Stretch Processing Stretch Processing: a technique for converting Frequency fb time-delay into frequency ftbd t beat frequency 2DR Time td BB t c A/D DFT BB Filter limits range of frequencies t t+td d Filter defines A/D requirements Target Exciter / LO Filter defines range window extent Return Commonly referred to as a de-ramp operation Frequency Example Calculation Parameter Value Units Time Pulse Length 50 usec Waveform Bandwidth 500 MHz Caputi, “Stretch: A Time-Transformation Technique”, March 1971 Filter Bandwidth 40 MHz A/D Sampling Rate 40 MHz Range Window Extent 600 m ct BB Nominal Range Resolution 0.3 m DR Range Window Extent 2 34 Range Resolution and SAR Imagery 1 m resolution (> 150 MHz bandwidth) Ku band 10 cm resolution (> 1.5 GHz bandwidth) Source: Sandia National Labs (www.sandia.gov) 35 Phase Coded Waveforms 36 Phase Code Waveforms Composed of concatenated sub-pulses (or chips) Chip-to-chip phase modulation applied to achieve desired compressed response (e.g., mainlobe, sidelobes, & Doppler tolerance) Phase modulation Bi-phase codes (only 2 phase states) Poly-phase codes (exhibit more than 2 phase states) 7 6 5 4 t chip Chip width 3 amplitude 2 + + + - - + - ct chip r 2 1 0 -6 -4 -2 0 2 4 6 Nt correlation delay (normazlied by t) • Consists of N chips each with duration, tchip • For appropriately chosen codes, the Rayleigh range resolution is equal to the chip width • Energy in the waveform is proportional to the number of chips • In general, sidelobe levels are inversely proportional to the number of chips 37 Barker Codes Perfect bi-phase aperiodic codes Correlation Belief that no Barker code exists + + + - - + -
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