Determining the false-alarm performance of HOS-based quadratic phase coupling detectors

Quadratic Phase Coupling (QPC) can be detected using Higher Order Statistics (HOS) measures. Previously, the bispectrum, biphase and bicoherence have been used as components in two QPC-detection algorithms. In this paper it is shown that the expressions which describe these detectors reduce to the same form for the white Gaussian noise case. The performance of these detectors is discussed, and particular attention is given to false alarms, which occur when QPC is detected in signals which do not exhibit QPC. A simple expression is derived which gives the probability of false alarm (P
fa
) for QPC detectors. This expression shows how the P
fa
increases as the Signal to Noise Ratio decreases, a relationship which is also observed in a simulation example.