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Log-concavity property of the error probability with application to local bounds for wireless communications

Author(s)
Tralli, V.; Sidenko, S.; Panchenko, Dmitry A.; Conti, Andrea
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Abstract
clear understanding of the behavior of error probability (EP) as a function of signal-to-noise ratio (SNR) and other system parameters is fundamental for assessing the design of digital wireless communication systems. We propose an analytical framework based on the log-concavity property of the EP which we prove for a wide family of multidimensional modulation formats in the presence of Gaussian disturbances and fading. Based on this property, we construct a class of local bounds for the EP that improve known generic bounds in a given region of the SNR and are invertible, as well as easily tractable for further analysis. This concept is motivated by the fact that communication systems often operate with performance in a certain region of interest (ROI) and, thus, it may be advantageous to have tighter bounds within this region instead of generic bounds valid for all SNRs. We present a possible application of these local bounds, but their relevance is beyond the example made in this paper.
Date issued
2009-05
URI
http://hdl.handle.net/1721.1/52395
Department
Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Conti, A. et al. “Log-Concavity Property of the Error Probability With Application to Local Bounds for Wireless Communications.” Information Theory, IEEE Transactions on 55.6 (2009): 2766-2775. © 2009 IEEE
Version: Final published version
ISSN
0018-9448

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