Stochastic signaling for power constrained communication systems

Abstract

In this thesis, optimal stochastic signaling problem is studied for power constrained communications systems. In the first part, optimal stochastic signaling problem is investigated for binary communications systems under second and fourth moment constraints for any given detector structure and noise probability distribution. It is shown that an optimal signal can be represented by randomization among at most three signal levels for each symbol. Next, stochastic signaling problem is studied in the presence of an average power constraint instead of second and fourth moment constraints. It is shown that an optimal signal can be represented by randomization between at most two signal levels for each symbol in this case. For both scenarios, sufficient conditions are obtained to determine the improvability and nonimprovability of conventional deterministic signaling via stochastic signaling. In the second part of the thesis, the joint design of optimal signals and optimal detector is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. It is shown that the optimal solution involves randomization between at most two signal levels and the use of the corresponding maximum a posteriori probability (MAP) detector. In the last part of the thesis, stochastic signaling is investigated for power-constrained scalar valued binary communications systems in the presence of uncertainties in channel state information (CSI). First, stochastic signaling is performed based on the available imperfect channel coef- ficient at the transmitter to examine the effects of imperfect CSI. The sufficient conditions are derived for improvability and nonimprovability of deterministic signaling via stochastic signaling in the presence of CSI uncertainty. Then, two different stochastic signaling strategies, namely, robust stochastic signaling and stochastic signaling with averaging, are proposed for designing stochastic signals under CSI uncertainty. For the robust stochastic signaling problem, sufficient conditions are derived to obtain an equivalent form which is simpler to solve. In addition, it is shown that optimal signals for each symbol can be written as randomization between at most two signal levels for stochastic signaling using imperfect channel coefficient and stochastic signaling with averaging as well as for robust stochastic signaling under certain conditions. The solutions of the optimal stochastic signaling problems are obtained by using global optimization techniques, specifically, Particle Swarm Optimization (PSO), and by employing convex relaxation approaches. Numerical examples are presented to illustrate the theoretical results at the end of each part.