Decision Criterion for Weak M-ary Signals: Part 1. The Criterion and Decison Regions

A novel decision criterion for weak M-ary signals is proposed in this paper. In the sense of minimizing the error probability, the proposed decision criterion is optimum when the signal strength approaches zero. In Part 1, the proposed detection criterion is proposed and investigated in detail, some interesting properties of the proposed decision criterion are described, and examples of decision regions are obtained. Based on the proposed detection criterion, a detection scheme for ultra wideband multiple access systems is investigated in the presence of impulsive interference in Part 2.