Locally optimum Bayes detection in ergodic Markov noise

The locally optimum Bayes theory of signal detection in non-Gaussian noise/interference environments is extended to include ergodic Markov noise models under mild regularity assumptions on the conditional probability density functions. The proposed method expresses the log-likelihood ratio under the null hypothesis, via martingale limit theory, as a locally asymptotically normal likelihood ratio, which yields under the implied condition of contiguity the statistics of the detection algorithm under the alternative hypothesis. Thus, optimum detection algorithms in both coherent and incoherent cases are obtained, which are canonical in signal waveform and noise statistics and which have the desired property of asymptotic optimality (acceptably small error probabilities as sample size becomes necessarily large, while the terms in the Taylor expansion of the log-likelihood ratio about the null signal remain fixed). Furthermore, locally optimum detection structures in Gauss-Markov noise are given together with a specific example in the coherent mode of reception in order to demonstrate the significant improvement in performance obtained over independent sampling.>