On convexity of MQAM's and MPAM's bit error probability functions |
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Authors: | M Naeem Daniel C Lee |
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Affiliation: | School of Engineering Science at Simon Fraser University, Burnaby, BC, Canada V5A 1S6 |
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Abstract: | For 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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Keywords: | convexity bit error probability Taylor series |
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