Principles of Modern Radar - Volume 2 1891121537

4.5 Waveforms for MIMO Radar 137Power (dB)0−20−40−60Auto−CorrelationCross−CorrelationFIGURE 4-9 Thecorrelationproperties and rangeresponse of the upanddown-chirpwaveforms.−80−100−5 0 5Time (µs)0Range Response−20Power (dB)−40−60−80−100−5 0 5Time (µs)As shown in Figure 4-9, each waveform has a desirable auto-correlation, and the peakof the cross-correlation is well below that of the auto-correlation. However, the crosscorrelationdoes not decay as the delay offset increases. This is apparent in the rangeresponse, which for a broadside target is the sum of the auto- and cross-correlations, asstated in (4.34).The resulting range response when using an up- and a down-chirp as MIMO waveformshas the same range sidelobe structure near the peak as a single LFM, where theauto-correlation function dominates the MIMO range response. Instead of decaying tovery low levels the contribution of the cross-correlation of the waveforms is apparent,even for relatively large delays.From this analysis, we see that the simple case of an up- and down-chirp may provideacceptable peak sidelobe performance. Another figure of merit in waveform design isthe integrated sidelobe level, which characterizes not simply the largest sidelobe but alsoincludes the effect of all of the sidelobe energy. Clearly, the integrated sidelobe level iscompromised by transmitting the second quasi-orthogonal LFM waveform.This example of two waveforms was presented not as a recommendation for use in aMIMO radar but instead to present an example of the analysis that is required in choosingwaveforms. We have seen previously that the zero-lag of the correlation matrix in (4.33),