New physical-statistical methods and models for clutter and reverberation: the KA-distribution and related probability structures

Effective signal processing in active regimes requires appropriate measurement and statistical modeling of the (usually) dominant scatter returns. Here the critical situation of threshold signal detection is considered, when the clutter (for radar) and reverberation (for sonar) are generally non-Gaussian. The latter is a common condition for operation, particularly at small grazing angles, e.g., with radar off sea and land surfaces, and for sonar in shallow water, where surface and bottom interaction are significant. Two examples of constrained optimization, namely incoherent reception employing instantaneous amplitudes and envelopes, illustrate the statistical role of the non-Gaussian returns in signal processing. The threshold detection algorithms are locally optimum Bayes and locally asymptotically normal. In particular, they are also canonical, i.e., formally independent of the particular physics involved, as are the performance measures, expressed now as probabilities of detection (P/sub D/) and false alarms (/spl alpha//sub F/). The principal emphasis here, however, is on the statistical description of the (signal-dependent) scatter process, including also accompanying ambient and system noise, and (unwanted) "large" reflectors (terrain features and wave surface structure). The derivation of probability distributions (pdf's) is based on the author's earlier counting functional techniques and Decomposition Principle (DP), which here can account for multiple scatter contributions. The resulting non-Gaussian scatter processes include the new KA (i.e., "bunched" Class A) model. This is a generalization of the earlier K-clutter models and one which permits a statistical description of many scatter scenarios not physically covered by the latter. Another significant result is the demonstration of the equivalence of the new approach to the formulations of classical scattering theory. Since, unlike the present method, the latter is not generally capable of providing analytic results for probability densities, this new approach provides a significant advance over previous methods by generating the needed physically derived pdf's for effective signal processing. This paper is in part a work in progress: it includes a discussion of method, a variety of analytical and empirical results and needed next steps, some illustrative comparisons with empirical sonar and radar data, and an Appendix on the physical justification of the gamma pdf for fluctuation scatter intensities.