Space—time threshold detection in non-additive non-Gaussian noise fields

Recent work on optimum threshold signal detection in non-additive non-Gaussian noise is extended here to include in addition to the non-Gaussian field the often important situation where the fields received by an antenna array are not uniform over the array elements. Non-uniformity of the noise fields introduces spatial sampling (in addition to the usual temporal sampling), which can noticeably improve detection. Space—time detector structures are derived from a stochastic expansion of the log-likelihood ratio in both coherent and incoherent modes and are shown to be locally optimum Bayes (LOB), i.e., the minimization criterion is the average cost of decisions with very small but non-zero signals and large but finite sample sizes, and also asymptotically optimum (AO) meaning that acceptably small error probabilities are achieved, while the terms in the expansion of the log-likelihood ratio about the null signal remain fixed. The optimum detection algorithms obtained are non-linear adaptive including the associated processes of beamforming and beamsteering as well as fading and Doppler “smear”, the latter two being highly realistic phenomena in electromagnetic and acoustic interference environments. Moreover, their locally asymptotically normal character is shown to provide their statistics under both null (“no signal present”) and alternative (“signal present”) hypotheses. Thus, performance measures, i.e., error probabilities, are obtained together with the concepts of minimum detectable signal and processing gain which are useful for systems comparison.