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On convexity of MQAM's and MPAM's bit error probability functions
Author(s) -
Naeem M.,
Lee Daniel C.
Publication year - 2009
Publication title -
international journal of communication systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.344
H-Index - 49
eISSN - 1099-1131
pISSN - 1074-5351
DOI - 10.1002/dac.1035
Subject(s) - convexity , computer science , probability of error , term (time) , taylor series , algorithm , series (stratigraphy) , regular polygon , mathematics , financial economics , economics , mathematical analysis , paleontology , physics , geometry , quantum mechanics , biology
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.