Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications

TL;DR

This paper investigates the convexity and concavity properties of symbol error rates in maximum likelihood detection over AWGN channels, providing bounds and applications for power allocation and jamming strategies.

Contribution

It identifies conditions for convexity/concavity of SER, derives universal bounds, and discusses practical applications in communication systems.

Findings

SER convexity/concavity depends on SNR and constellation

Universal bounds for SER derivatives are established

Applications include optimal power allocation and jamming strategies

Abstract

Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied. Generic conditions are identified under which the SER is a convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, and implication for fading channels.