  In this paper, we consider the problem of information-theoretic waveform
design for active sensing systems such as radar for extended targets. Contrary
to the popular formulation of the problem in the estimation-theoretic context,
we are rather interested in a Bayes decision theoretic approach where a target
present in the environment belongs to two or more classes whose priors are
known. Optimal information theory based transmit waveforms are designed by
maximizing mutual information (MI) between the received signal and the target
impulse response, resulting in a novel iterative design equation. We also
derive signal to noise ratio (SNR) maximization based waveforms. In an effort
to quantize the benefits of such a design approach, the delay-Doppler ambiguity
function of information-theoretic waveforms are presented and is compared with
Barker codes of similar time-bandwidth product. It is found that the ambiguity
function of information-theoretic waveforms has very sharp main lobe in general
and excellent time autocorrelation properties in particular.
