On Bayesian transmit signal design using information theory

In this paper, we investigate the problem of transmit signal design for extended targets using information theory and possible benefits of such a design approach. An M-ary Bayesian decision theoretic context is considered and a signal design problem is set up to find optimal transmit signals which maximize the mutual information (MI) between the received signal and the target impulse response under total power constraint. Since the exact MI-maximizing signal design problem is analytically intractable because of Bayes context, we formulate an approximate problem instead, and present a fixed point signal design equation which solves the problem. To understand the proposed information theoretic signal design better, and to investigate the effect of different energy scheduling strategies on the detection performance of the radar, it is compared to SNR-maximizing signal design. It is shown that while SNR-maximizing signals are optimal in terms of overall detection performance, MI-maximizing signals perform far better if the target belongs to one of the lesser dominant target classes due to their fundamentally different energy scheduling policy.