Optimal stochastic signaling for power-constrained binary communications systems

Date
2010
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Source Title
IEEE Transactions on Wireless Communications
Print ISSN
1536-1276
Electronic ISSN
Publisher
IEEE
Volume
9
Issue
12
Pages
3650 - 3661
Language
English
Type
Article
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Abstract

Optimal stochastic signaling is studied under second and fourth moment constraints for the detection of scalar-valued binary signals in additive noise channels. Sufficient conditions are obtained to specify when the use of stochastic signals instead of deterministic ones can or cannot improve the error performance of a given binary communications system. Also, statistical characterization of optimal signals is presented, and it is shown that an optimal stochastic signal can be represented by a randomization of at most three different signal levels. In addition, the power constraints achieved by optimal stochastic signals are specified under various conditions. Furthermore, two approaches for solving the optimal stochastic signaling problem are proposed; one based on particle swarm optimization (PSO) and the other based on convex relaxation of the original optimization problem. Finally, simulations are performed to investigate the theoretical results, and extensions of the results to M-ary communications systems and to other criteria than the average probability of error are discussed.

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Keywords
Additive noise channels, Binary communications, Detection, Optimization, Probability of error, Randomization, Particle swarm optimization (PSO)
Citation