Adaptive Signal Detection with Finite Memory

Abstract

In the Bayesian approach to signal-detection theory, infinite soft or changeable memory is tacitly assumed. Since an infinite memory is physically unrealizable, this study is concerned with formulating and optimizing a finite memory applicable to a large class of signal-detection problems. An optimum finite memory design is presented, assuming a priori that neither the eventual length nor the maximum length of the observation is known. The open-ended design is obtained and evaluated for the signal-known-exactly (SKE), the signal-known-except-amplitude (SKEA), and the M-ary signal-detection problems. Detection performance as a function of memory size is presented using the receiver operating characteristic (ROC) and plots of probability of decision error versus time. These results show the trade-off between memory size and processing time for the same detection performance. An important result is that a small finite memory detector with a memory size on the order of seven states, i.e., a three-bit computer word, yields detection performance very near that of the optimum infinite memory detector. [Research supported by Office of Naval Research, Acoustics Branch.]