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Asymptotic Comparison of ML and MAP Detectors for Multidimensional Constellations

Alvarado, A; Agrell, E; Brannstrom, F; (2017) Asymptotic Comparison of ML and MAP Detectors for Multidimensional Constellations. IEEE Transactions on Information Theory 10.1109/TIT.2017.2727521. (In press). Green open access

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Abstract

A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit this problem for nonequally likely symbols and study the behavior of the optimal maximum a posteriori (MAP) detector at asymptotically high signal-to-noise ratios. Exact closed-form asymptotic expressions for SEP and BEP for arbitrary constellations and input distributions are presented. The well-known union bound is proven to be asymptotically tight under general conditions. The performance of the practically relevant maximum likelihood (ML) detector is also analyzed. Although the decision regions with MAP detection converge to the ML regions at high signal-to-noise ratios, the ratio between the MAP and ML detector in terms of both SEP and BEP approach a constant, which depends on the constellation and a priori probabilities. Necessary and sufficient conditions for asymptotic equivalence between the MAP and ML detectors are also presented.

Type: Article
Title: Asymptotic Comparison of ML and MAP Detectors for Multidimensional Constellations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TIT.2017.2727521
Publisher version: http://doi.org/10.1109/TIT.2017.2727521
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/.
Keywords: Error probability, Detectors, Signal to noise ratio, Maximum likelihood detection, AWGN channels, Digital communication, Constellation diagram, Additive white Gaussian noise channel, bit error probability, error probability, high-SNR asymptotics, maximum a posteriori, maximum likelihood, multidimensional constellations, symbol error probability
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/10038626
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