Sequentially operating finite memory detectors

The Bayesian approach in signal detection theory generally yields detectors with memory which contains appropriate statistics used in producing a detection output. This memory summarizes each available observation in terms of precisely representable continuous variables. Precise representation of any real number requires an infinity of digits which in turn means an infinite soft or changeable memory requirement. This presentation provides a procedure for design of sequentially operating finite memory detectors applicable to the open-ended type detection problem. The approach is applied to a general class of problems including the Signal-Known-Exactly (SKE), Signal-Known-Except-Amplitude (SKEA), and the M-ary signaling problems. Results presented compare the detection performance of the finite and optimum infinite memory detector designs using the Receiver Operating Characteristic (ROC).