Asymptotically optimum finite-memory detectors in φ-mixing dependent processes

The design of a finite-memory partition system for the detection of a constant signal in φ-mixing noise is investigated. It is found that the new detector converges to the locally optimal finite-memory practically intractable detector characterized by a multidimensional Fredholm integral equation of the second kind. The new detector encompasses many classes of known detectors. Numerical calculations demonstrate that the finite-memory detector compares favorably, using asymptotic relative efficiency as a fidelity criterion, to other classes of detectors even if extremes of dependent noise distributions are considered. The same calculations also suggest that a dependent process may be treated as an M-dependent process in finite-memory detectors without causing significant detrimental effects, provided M is sufficiently large. To reduce excessive computational complexity, a priori knowledge regarding properties of system parameters (such as matrix symmetry) as well as noise distributions (especially Gaussian and its independently nonlinear transformations) are exploited. Generalizations and extensions of the proposed detectors are also discussed. The operation of the detector may be easily extended to include adaptability and/or sequential operation