One-Step Memory Nonlinearities for Signal Detection and Discrimination from Correlated Observations

Abstract

New detectors employing test statistics which are formed by passing pairs of consecutive observations through one-step memory nonlinearities g(x, y) and summing the resulting terms are introduced. Problems of discrimination between two arbitrary stationary m-dependent or mixing noise are considered in this context. For each problem, the nonlinearity g is optimized for performance criteria, such as the generalized signal-to-noise ratio and the efficacy and is obtained as the solution to an appropriate linear integral equation. Moreover, the schemes considered can be robustified to statistical uncertainties determined by 2-alternating capacity classes, for the second- order joint pdfs 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 new schemes via simulation reveals significant gains over that of detectors employing memoryless nonlinearities or the i.i.d. nonlinearity.