Quantizer-based suboptimal detectors:: noise-enhanced performance and robustness

The goal of the paper is the study of suboptimal quantizer based detectors. We place ourselves in the situation where internal noise is present in the hard implementation of the thresholds. We hence focus on the study of random quantizers, showing that they present the noise-enhanced detection property. The random quantizers studied are of two types: time invariant when sampled once for all the observations, time variant when sampled at each time. They are built by adding fluctuations on the thresholds of a uniform quantizer. If the uniform quantizer is matched to the symmetry of the detection problem, adding fluctuation deteriorates the performance. If the uniform quantizer is mismatched, adding noise can improve the performance. Furthermore, we show that the time varying quantizer is better than the time invariant quantizer, and we show that both are more robust than the optimal quantizer. Finally, we introduce the adapted random quantizer for which the levels are chosen in order to approximate the likelihood ratio.