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Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Loyka, Sergey and Kostina, Victoria and Gagnon, François (2010) Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications. IEEE Transactions on Information Theory, 56 (4). pp. 1948-1960. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20140910-093556659

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Abstract

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 implication for fading channels (¿fading is never good in low dimensions¿) and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates, and to coded systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5437418PublisherArticle
http://dx.doi.org/10.1109/TIT.2010.2040965DOIArticle
http://arxiv.org/abs/0911.3921UNSPECIFIEDDiscussion Paper
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2010 IEEE. Manuscript received December 07, 2007; revised November 06, 2009. Current version published March 17, 2010. This paper was presented in part at the IEEE International Symposium on Information Theory (ISIT 2007), Nice, France, June 2007. The first author would like to thank F. Kschischang and M. Dohler for fruitful discussions, and D. Palomar for his interest in this work.
Subject Keywords:Convexity/concavity, error rate, jamming, maximum-likelihood detection, OFDM, optimum transmission
Issue or Number:4
Record Number:CaltechAUTHORS:20140910-093556659
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140910-093556659
Official Citation:Loyka, S.; Kostina, V.; Gagnon, F., "Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications," Information Theory, IEEE Transactions on , vol.56, no.4, pp.1948,1960, April 2010 doi: 10.1109/TIT.2010.2040965
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49526
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Sep 2014 16:54
Last Modified:03 Oct 2019 07:14

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