Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 93-97.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.Göken, ÇağrıM.S
