Non-parametric identification of QAM constellations in noise

The objective of the proposed classifier is the correct identification of a signal which belongs to a set of equally likely QAM constellations and is received in additive noise. The parametric solution for this task which maximizes the average probability of correct decision is a maximum-likelihood (ML) classifier. However, this classifier needs the exact density function of the noise, which is often unknown. The alternative undertaken here is to develop a non-parametric classifier. Its decision statistic is the location of the first zero-crossing (FZC) in the characteristic function of the received symbols. The FZC-based classifier is inferior to the ML classifier in terms of the nominal performance. However, it puts only mild technical conditions on the probability density function of the noise (mainly that the density be even) and does not require additional information. Analytical expressions for the performance of the FZC-based classifier are derived, and performance is compared to that of the fully-informed ML classifier. The comparison is performed by evaluating the signal-to-noise ratio and the number of symbols that are needed in order for the two classifiers to have the same average correct classification rate. Overall the FZC-based decision-maker provides a robust and practical alternative to the optimal, but often impractical, ML classifier.