Matched-filter detection of the presence of MPSK signals

The matched-filter detector is used to detect the presence of an MPSK signal in white Gaussian noise. The probabilities of detection and false alarm of the matched-filter detector are evaluated using Craig's method in terms of a simple one-fold integral. The matched-filter detector is compared to the optimal Bayesian detector whose performance is an upper bound for the detection performance. It is shown that although the detection rules of the matched-filter detector and the optimal detector are not the same, their performances coincide. It is also shown that the conventional energy detector is considerably suboptimal for activity detection of MPSK signals. A modified energy detector is proposed based on the behaviors of the decision regions of the matched-filter and the Bayesian detectors. It is shown that the performance of the proposed detector is very close to the performances of the matched-filter and the optimal detector, for M ≥ 8, while its implementation requires a much lower computational complexity.