Information Theoretic Criterion for Waveform Selection

A novel criterion for waveform selection in adaptive radar and other sensing applications is presented that is based on the information theoretic concept of mutual information. In addition, its application to the area of waveform diversity for synthetic aperture radar (SAR) systems is examined. Mutual information is a measure of the information (in the sense of Shannon) in a random variable or vector about another random variable or vector. It is shown herein that such a framework provides the basis for a conceptually simple and powerful criterion for context-dependent evaluation of candidate waveforms, as well as context-dependent design of waveforms. Furthermore, in the special case of zero-mean Gaussian-distributed clutter, interference, and noise, the criterion attains an analytically simple form - a scalar function of the singular values of a specific cross-covariance matrix. The criterion can be used in distinct optimization contexts (minimization or maximization) as a function of the problem to be addressed. In addition, the criterion inherently includes the statistical information of the sensed parameters. More specifically, in the context of a SAR system the criterion includes the covariance matrix of the set of illuminated ground scatterers. The formulation and simulation-based results are presented in the context of a first-order radar system model for simplicity, but the approach can be extended in a straightforward manner to cover more complex models. Results presented show that the criterion is an effective means for waveform selection in an adaptive SAR system