Principles of Modern Radar - Volume 2 1891121537

2.4 Nonlinear Frequency Modulated Waveforms 57−37 dB; the goal was −40 dB. The peak sidelobe levels are close to the designed-tolevel. The waveform’s time–bandwidth product does have a direct bearing on sidelobeperformance. In general, the higher the time-bandwidth product the closer one gets to thedesign-to level. Time–bandwidth products greater than 100 are generally required.For an LFM waveform with 500 MHz swept bandwidth, the time resolution, measuredat the –4 dB width, is 0.002 μsec. A close examination of the response in Figure 2-20reveals a −4 dB width of 0.0029 μsec. The modulation has degraded the resolution by afactor of 1.45 over that achieved by an LFM swept over the same bandwidth. Of course,a similar degradation in resolution occurs when an amplitude taper is applied to an LFMwaveform.2.4.4 Doppler AnalysisNLFM waveforms are less Doppler tolerant [24–26] than their LFM counterparts. NLFMwaveforms exhibit high near-in sidelobes in the presence of small, uncompensated, fractionalDoppler shifts (i.e., f d /β). Doppler shifts on the order of a 1/4 cycle across theuncompressed pulse width are sufficient to significantly elevate the near-in sidelobes. Figure2-21 and 22 contain plots of the compressed response with a 1/4 and full cycle ofDoppler, respectively. The Doppler shifts used in this example (0.25 MHz and 1 MHz,respectively) are not commonly realized, but several cycles of Doppler may be observedwhen employing longer pulses (e.g., 1 msec) operating against fast moving targets. Inthis example, the peak sidelobes have increased from −40 dB to approximately −28 dBand –15 dB, respectively. As with the LFM waveform, a loss in the peak amplitude andresolution are experienced with increasing Doppler shift. Johnston [24, 25] provides anexcellent discussion on Doppler sensitivity.2.4.5 SummaryNFLM waveforms achieve low range sidelobes without the SNR loss associated with anamplitude taper. Frequency modulation is used to shape the waveform’s spectrum, andthe square of the spectrum magnitude determines the shape of the time-domain response.dB100−10−20−30FIGURE 2-21 Aquarter cycle ofDoppler shift acrossthe uncompressedpulse starts toelevate the near-insidelobes of theNLFM waveform.−40−50−60−70−2 −1.5 −1 −0.5 0 0.5 1 1.5 2time delay (x10 −8 sec)