Principles of Modern Radar - Volume 2 1891121537

94 CHAPTER 3 Optimal and Adaptive MIMO Waveform DesignFIGURE 3-4Spectra of thecolored noiseinterference alongwith conventionaland optimal pulsemodulations.(a) Short-pulse casewhere total durationfor the LFM andoptimum pulse areset to 11 range bins(fast-time taps).(b) Long-pulse casewhere total durationfor the LFM andoptimum pulse areset to 100 rangebins. Note that inboth cases theoptimum pulseattempts toanti-match to thecolored noisespectrum under thefrequency resolutionconstraint set by thetotal pulse width.Magnitude (dB)Magnitude (dB)1050−5−10−15Noise SpectrumLFM (N = 11)Optimum (N = 11)−20–0.5 0 0.5Frequency(a)1050−5−10−15Noise SpectrumLFM (N = 100)Optimum (N = 100)−200 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Frequency(b)Given R from (3.16), the corresponding whitening filter H w is given byH w = R − 1 2 (3.19)Combining (3.19) with (3.18), the total composite channel transfer matrix H is thus given bySubstituting (3.20) into (3.12) yieldsH = H w H T = H w = R − 1 2 (3.20)R −1 s opt = λs opt (3.21)