Information-Theoretic Optimal Radar Waveform Design

In this letter, we address the problem of designing the optimal radar waveform for the detection of an extended target in a colored noise environment. The locally most powerful detector and the corresponding optimal waveform based on maximizing the detector's performance under a small-signal assumption are derived. The performance is evaluated analytically, and numerically compared with that of the mutual information based method. The locally most powerful detection metric is shown to be the Kullback-Leibler divergence. The use of the latter measure leads to a substantial performance improvement. Moreover, a useful relationship among the three existing waveform design metrics, namely the output signal-to-noise ratio, the Kullback-Leibler divergence, and the mutual information, is provided. It explains the tradeoffs of the various metrics currently used for radar waveform design.