Decision regions for weak PSK signals with a novel M-ary detection criterion

In this paper, we derive and obtain specific examples of the decision regions of a novel detection criterion for weak M-ary signals. In the sense of minimizing the error probability, the detection criterion is optimum when the signal strength approaches zero. Assuming phase shift keying for convenience, specific decision regions are obtained for the detection of weak signals. It is shown that the proposed detection criterion has almost the same decision regions as the maximum likelihood detection criterion when the strength of signals are small.