One-step memory nonlinearities for signal detection and discrimination from correlated observations

Detectors based on one-step memory nonlinearities are introduced. Problems of discrimination between two arbitrary stationary m-dependent or mixing sequences of observations and problems of detecting a weak signal in additive stationary m-dependent or mixing noise are considered in this context. For each problem, the nonlinearity is optimized for performance criteria such as the generalized signal-to-noise ratio (SNR) and the efficacy, and is obtained as the solution to an appropriate linear integral equation. The schemes considered can be made robust to statistical uncertainties determined by two-alternating capacity classes, for the second-order joint PDFs (probability distribution functions) of the observations, and by bounds on the correlation coefficients of time shifts of the observation sequence for the third- and fourth-order joint PDFs. Evaluation of the performance of the schemes via simulation reveals significant gains over that of detectors employing memoryless nonlinearities or the independent and identically distributed nonlinearity