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Optimal stochastic signaling for power-constrained binary communications systems
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. © 2010 IEEE- Article
- additive noise channels
- binary communications
- Detection
- optimization
- probability of error
- randomization
- Average probability of error
- binary communications
- Binary signals
- Communications systems
- Convex relaxation
- Detection
- Error performance
- Moment constraints
- Optimal signals
- Optimization problems
- Power constraints
- probability of error
- randomization
- Signal level
- Statistical characterization
- Stochastic signals
- Sufficient conditions
- Theoretical result
- Additive noise
- Error detection
- Probability
- Relaxation processes
- Signal detection
- Signaling
- Stochastic systems
- Particle swarm optimization (PSO)