Memoryless discrete-time detection of a constant signal in m-dependent noise

The problem of designing memoryless detectors for known signals in stationary m-dependent noise processes is considered. Applying the criterion of asymptotic relative efficiency, the optimal such detector is shown to be characterized by the solution to a Fredholm integral equation whose kernel depends only on the second-order probability distributions of the noise. General expressions are derived for this solution and for the asymptotic efficiency of the optimal detector relative to other memoryless detectors. To illustrate the analysis, specific results are given for the particular case where the noise process is derived by memoryless nonlinear transformation of a Gaussian process. In addition, an extension of the analytical results to the more general case of -mixing noise processes is discussed.