Adaptive time invariant finite memory detection

Finite memory detector formulations have provided some insight into the role of receiver memory in signal detection problems[1]-[5]. One design uses a finite set of integers to characterize a ?? state memory such that a sequentially operating transition rule involving observation thresholding can offer performance comparable to the optimal infinite memory detector. This generally suboptimal algorithm generates time varying observation thresholds offering a convergent probability of decision error for a rather large class of problems, including SKE, SKEA, and M-ary detection problems[5]. Conversely, it has been shown that time invariant transition rules generally offer a non-convergent decision error probability[1]. The essential contribution here is an analytical analysis of a simple time invariant finite memory detector. These results are compared to the time varying finite memory detector, and the optimal infinite memory detector.