Error rates of the maximum-likelihood detector for arbitrary constellations: convex/concave behavior and applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multidimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER first and second 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, an implicat...

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Sergey Loyka, Victoria Kostina, François Gagnon
• Keywords: Arbitrary Constellations, Bit Error Rate, Education, Error Rates, TIT 2010