Quantization based on statistical moments for signal detection: design and analysis

This paper addresses a signal detection problem based on a class of quantizers. The known moments of the underlying noise distribution are used to index a set of quantization points that have been predetermined under an assumed noise model. The fact that lower order moments are easy to obtain and that they are required in the implementation and analysis of most threshold detectors makes this approach quite appealing. The performance of the resulting quantizers is shown to be relatively insensitive to variations in the underlying noise distribution and to small deviations of the presumed moments. The detector's performance in the finite-sample-size case is investigated, and the distribution resulting in the highest false alarm rate is described for both symmetric and asymmetric noise cases. By setting the test threshold according to the worst distribution, a lower bound on the detector's performance is guaranteed