Optimal waveform design for cognitive radar

A key component of a cognitive radar system is the method by which the transmitted waveform is adapted in response to information regarding the radar environment. The goal of such adaptation methods is to provide a flexible framework that can synthesize waveforms that provide different tradeoffs between a variety of performance objectives, and can do so efficiently. In this paper, we propose a waveform design method that efficiently synthesizes waveforms that provide a trade-off between estimation performance for a Gaussian ensemble of targets and detection performance for a specific target. In particular, the method synthesizes (finite length) waveforms that achieve an inherent trade-off between the (Gaussian) mutual information and the signal-to-noise ratio (SNR) for a particular target. In addition, the method can accommodate a variety of constraints on the transmitted spectrum. We show that the waveform design problem can be formulated as a convex optimization problem in the autocorrelation of the waveform, and we develop a customized interior point method for efficiently obtaining a globally optimal waveform.