Radar Frequencies and Waveforms

1 Radar Frequencies and Waveforms 12th Annual International Symposium on Advanced Radio Technologies Michael Davis Georgia Tech Research Institute Sensors and Electromagnetic Applications Laboratory Based on material created by Byron M. Keel, , 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.

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. Poor Angular Radar Bands Long-Range Resolution Large Radar Band Frequency HF 3 30 MHz Long-Range Air Surveillance VHF 30 300 MHz UHF 300 1000 MHz FOPEN. L 1 2 GHz S 2 -4 GHz C 4 8 GHz X 8 12 GHz Air-to-Air GMTI. SAR/. Munitions Control/. Ku 12 18 GHz Fire Ka 27 40 GHz Short-Range Small Resolution Good Angular mm (V & W) 40 300 GHz 5. Radar Waveform Taxonomy 6. Continuous Wave (CW) vs. Pulsed CW: Simultaneously transmit and receive Pulsed: Interleave transmit and receive periods 7.

3 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.

4 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 -5. Mainlobe Sample CW returns discretely in time -10 Generate spectrum via Fourier analysis -15 Sidelobes ( , FFT). Results in sinc shaped response dB. -20. -25 Weighting can be applied to reduce Doppler sidelobes -30. SNR loss -35. Resolution degradation -40. 0 normalized frequency Sampling of DFT response a function of 1.

5 Bin spacing Frequency Zero padding reduces bin spacing; does not Magnitude improve resolution 0. 0 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, , 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.

6 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 . sin f dt 1 . t t . A t , f d 1 t t t f t 1 t . d . t . Simple pulse Ambiguity Function Zero Doppler Cut Zero Time-Delay Cut t Zero Doppler Cut A t, 0 1 t t t sin f dt . Zero Time-Delay Cut A 0, f d t t f dt 22.

7 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.

8 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 t t the time derivate of the phase x t cos t 2 t . t 2 2 The instantaneous frequency is linear radians t Quadratic Term Linear Term . frequency 4. 2. d 2 . t 2 t t t dt t t time 2 2.

9 T t 1 d . 2 2. time f t 2. 2 dt t 28. Components of LFM Spectrum X X exp j exp j 3 Key Terms 2. 0. Magnitude Quadratic Residual -2. -4. Response Phase Phase t 20. -6. -8. dB. -10. -12. -14. X 1 . -16. For large time-bandwidth products -18. -20. 0 frequency, normalized by . 2. 1 t 2.. 0.. -2. 4 . -4. Quadratic phase term t 50. -6. -8. dB. -10.. -12.. -14. Residual phase term -16. -18. 4 -20. 0 frequency, normalized by . 1 t 2 2. X exp j . 0. 4 . -2. -4. t 100. -6. -8. dB. -10. Reference: Cook, Bernfeld, Radar Signals, An Introduction to Theory and Application , -12. -14. Artech House, 1993, p.

10 49 -16. -18. -20. 0 frequency, normalized by . 29. LFM Match Filtered Response Bandwidth (MHz) Range Resolution (m). 1500. 1 150. 0. 2 75. 5 30. -4. 10 15. 20 -10. 50 3. -13. 100 dB. 200 -20. 500 1000 . sin t t t . -30. t t . -6 -4 -2 -1 0 2 4 6. y t 1 . t t t t . multiples of 1/ . t For t 20, match filtered response approximates a sinc ~ -13 dB peak sidelobes t 1 resolution in time r . c range resolution 2 . Rayleigh resolution: Rayleigh resolution equivalent to 4 dB width 30. LFM Ambiguity Function t . sin t 1 f d t . t t t . y t , f d 1 t t t t 1 t f t . d . t t . t t . sin 1 t f d . t t.