On convexity of MQAM's and MPAM's bit error probability functions

descriptionPublicationkeyboard_double_arrow_right Article 13 Jul 2009 English Publisher:WileyJournal:International Journal of Communication Systems, volume 22, pages 1,465-1,477 (issn: 1074-5351, eissn: 1099-1131,

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Authors: Muhammad Naeem 0001; Daniel Chonghwan Lee;

doi: 10.1002/dac.1035

On convexity of MQAM's and MPAM's bit error probability functions

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Abstract

AbstractFor MQAM and MPAM with practical values of M and Gray mapping, we provide a rigorous proof that the associated bit error probability (BEP) functions are convex of the signal‐to‐noise ratio per symbol. The proof employs Taylor series expansions of the BEP functions' second derivatives and term‐by‐term comparisons between positive and negative terms. Convexity results are useful for optimizing communication systems as in optimizing adaptive transmission policies. Copyright © 2009 John Wiley & Sons, Ltd.

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