research-article

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

Authors:

Victoria Kostina,

François GagnonAuthors Info & Claims

IEEE Transactions on Information Theory, Volume 56, Issue 4

Pages 1948 - 1960

https://doi.org/10.1109/TIT.2010.2040965

Published: 01 April 2010 Publication History

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 multi-dimensional 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.

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Cited By

Bendecheche HSadoudi STeguig DMessaadi M(2022)Efficient jamming attack against MIMO transceiverDigital Signal Processing10.1016/j.dsp.2022.103593127:COnline publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1016/j.dsp.2022.103593
Keskin MKurt MTutay MGezici SArikan O(2016)Maximization of average number of correctly received symbols over multiple channels in the presence of idle periodsDigital Signal Processing10.1016/j.dsp.2016.03.00954:C(95-118)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1016/j.dsp.2016.03.009
Keskin MKurt MTutay MGezici SArikan O(undefined)Maximization of correct decision probability via channel switching over Rayleigh fading channels2016 IEEE Wireless Communications and Networking Conference10.1109/WCNC.2016.7564995(1-6)
https://dl.acm.org/doi/10.1109/WCNC.2016.7564995

Error rates of the maximum-likelihood detector for arbitrary constellations: convex/concave behavior and applications
1. Mathematics of computing
  1. Information theory
2. Security and privacy
  1. Cryptography

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cover image IEEE Transactions on Information Theory

IEEE Transactions on Information Theory Volume 56, Issue 4

April 2010

574 pages

ISSN:0018-9448

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Copyright © 2010.

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IEEE Press

Publication History

Published: 01 April 2010

Revised: 06 November 2009

Received: 07 December 2007

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Cited By

Bendecheche HSadoudi STeguig DMessaadi M(2022)Efficient jamming attack against MIMO transceiverDigital Signal Processing10.1016/j.dsp.2022.103593127:COnline publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1016/j.dsp.2022.103593
Keskin MKurt MTutay MGezici SArikan O(2016)Maximization of average number of correctly received symbols over multiple channels in the presence of idle periodsDigital Signal Processing10.1016/j.dsp.2016.03.00954:C(95-118)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1016/j.dsp.2016.03.009
Keskin MKurt MTutay MGezici SArikan O(undefined)Maximization of correct decision probability via channel switching over Rayleigh fading channels2016 IEEE Wireless Communications and Networking Conference10.1109/WCNC.2016.7564995(1-6)
https://dl.acm.org/doi/10.1109/WCNC.2016.7564995

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