Optimal time sharing strategies for parameter estimation and channel switching problems

Ankara : The Department of Electrical and Electronics Engineering and The Graduate School of Engineering and Science of Bilkent Univesity, 2014.Thesis (Ph. D.) -- Bilkent University, 2014.Includes bibliographical references leaves 103-108.Time sharing (randomization) can offer considerable amount of performance improvement in various detection and estimation problems and communication systems. In the first three chapters of this dissertation, time sharing among different signal levels is considered for parametric estimation problems. In the final chapter, time sharing among different channels is investigated for an average power constrained communication system. In the first chapter, the aim is to improve the performance of a single fixed estimator by the optimal stochastic design of signal values corresponding to parameters. It is obtained that the optimal parameter design corresponds to time sharing between at most two different signal values. In the second chapter, the problem in the first chapter is generalized to a scenario where there are multiple parameters and multiple estimators. In this scenario, two different cost functions are considered. The first cost function is the total risk of all the estimators. The optimal solution for this case is time sharing between at most two different signal values. The second cost function is the maximum risk of all the estimators. For this case, it is shown that the optimal parameter design is time sharing among at most three different signal values. In the third chapter, the linear minimum mean squared error (LMMSE) estimator is considered. It is observed that time sharing is not needed for the LMMSE estimator, but still the performance can be improved by modifying the signal level. In the final chapter, the optimal channel switching problem is studied for Gaussian channels, and the optimal channel switching strategy is determined in the presence of average power and average cost constraints. It is shown that the optimal channel switching strategy is to switch among at most three channels.Soğancı, HamzaPh.D

Optimal stochastic design for multi-parameter estimation problems

In this study, we consider performance improvement of an array of fixed estimators by using stochastic design techniques. The optimal design is investigated both in the absence and presence of an average power constraint. Two different performance criteria are considered; the average Bayes risk and the maximum Bayes risk. It is shown that the optimal stochastic parameter design results in a randomization between different numbers of parameter values depending on the type of the performance criterion. © 2014 IEEE