Optimum and Sub-optimum Detection of Digital Sequences Corrupted by White Noise

Abstract

This paper presents an optimum and a sub-optimum, but easily recognizable, method for the detection of K binary symbols corrupted by white Gaussian noise with unknown mean. Basically the optimum procedure requires picking the sequence from a set of 2ᴷ sequences which minimizes a certain functional. However this procedure requires a great deal of computation. This computational problem is considerably reduced by the use of an efficient searching procedure developed in this paper. However a sub-optimum procedure exists and is very simple to instrument with the advantage that decisions are made in a bit-by-bit fashion. This procedure is analyzed and the average error probability is obtained.