Energy Detection for M-QAM Signals

Abstract

In this paper, we address energy detection for M-ary quadrature amplitude modulation (QAM) signals. In the literature deterministic signal model is widely used and detection probability is a function of signal energy. Unlike constant amplitude signals, the QAM signal is not deterministic since the energy in each QAM symbol can randomly vary. For random signals, model where both signal and noise are Gaussian has been widely used. However, this approximation may not provide accurate detection probability for QAM signals. Instead the detection probability should be averaged over the distribution of the energy. Previous work has considered calculating exact detection probability for given M analytically. However, the method presented previously has complexity that increases as a function of M and the number of samples.In this paper, we show that the distribution of observed energy for any M can be accurately approximated by one distribution which is derived analytically. Multiple numerical results showing probability density function, Kolmogorov-Smirnov distance, and detection probability are shown. Based on these results, a range where the proposed approximation is applicable is obtained.