ASYMPTOTICALLY OPTIMUM FINITE-MEMORY DETECTORS IN PHI-MIXING DEPENDENT PROCESSES

In this paper, the design of a finite-memory partition system for the detection of a constant signal in psi-mixing noise is investigated. It is found that the new detector converges to the locally optimal finit e-memory practically intractable detector characterized by a multidime nsional Fredholm integral equation of the second kind. The new detecto r 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 class es of detectors even if extremes of dependent noise distributions are considered. The same calculations also suggest that a dependent proces s may be treated as an M-dependent process in finite-memory detectors without causing significant detrimental effects, provided M is suffici ently large. To reduce excessive computational complexity, a priori kn owledge regarding properties of system parameters (such as matrix symm etry) as well as noise distributions (especially Gaussian and its inde pendently nonlinear transformations) are exploited. Generalizations an d extensions of the proposed detectors are also discussed. The operati on of the detector may be easily extended to include adaptability and/ or sequential operation.