Principles of Modern Radar - Volume 2 1891121537

56 CHAPTER 2 Advanced Pulse Compression Waveform ModulationsFIGURE 2-19 TheNLFM waveformexhibits a shapedspectrumresembling a Taylorweighting. Theamplitude ripple isassociated with thefinite time andfrequency extentconstraints placedon the waveform.amplitude10.90.80.70.60.50.40.30.20.10−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1frequency (normalized by β)contains the first 30 coefficients. No attempt is made to determine the number of coefficientsor the numerical precision needed to achieve a specified level of performance.The time-domain phase function is obtained by integrating the expression in equation(2.102)φ(t) = πβτ t 2 −M∑m=1βτ2d kmThe resultant baseband, complex NLFM waveform is( ) 2πmtcos τ(2.107)x(t) = exp ( jφ(t)) (2.108)The waveform’s spectrum is plotted in Figure 2-19. The envelope of squared spectrumresembles a Taylor weighting. The ripples in the spectrum are a result of the waveform’sfinite extent imposed in both domains.Consider an LFM waveform with a 500 MHz swept bandwidth and a 1 μsec pulselength. Applying the matched filter in either the time or frequency domain generatesthe compressed response shown in Figure 2-20. The peak sidelobes are approximatelyFIGURE 2-20 TheNLFM waveformachieves a rangecompressedresponse with peaksidelobes slightlyabove −40 dB.dB0−10−20−30−40−50−60−0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.02time (μsec)