Locally optimum Bayes detection in nonadditive first-order Markov noise

The purpose of this paper is to extend the recent formulation of locally optimum Bayes (LOB) detection in nonadditive non-Gaussian noise with independent sampling to the case where dependence between the noise samples is modeled via an ergodic first-order Markov discrete-time process. Moreover, unlike previous related work, numerical results are provided which are based on an empirically derived second-order transition density, the marginal PDF of which is Middleton´s (1993) Class A noise, an experimentally verifiable and widely applicable non-Gaussian model. Canonical, in signal waveform and noise statistics, asymptotically and LOB detectors in both coherent and incoherent modes are derived and their statistics are computed under both “signal present” and “signal absent” hypotheses. Performance measures are thus obtained together with the correlation gain G^(M.P.), which is used for systems comparison. Explicit forms for the transition density and and the nonlinearities involved, as well as numerical values of the noise indices, are calculated from a generalized observation model containing multiplicative and additive Markov noise components. It is shown that significant performance gains over the case with independent sampling can be achieved, depending upon the degree of correlation between the noise samples