Robust optimization and its applications in cognitive radio networks.

An optimal design of the cognitive radio may not operate properly due to unexpected fluctuations of system parameters in non-ideal working environment. Among various uncertain factors, the most notorious factor is the fluctuation of channel gain due to the stochastic nature of wireless channels. In our research, we try to propose a new framework that brings uncertainty into the analysis and design of a practical system. As a demonstration, we apply this framework to study two major aspects of the cognitive radio networks, i.e., spectrum identification and exploitation. Our first challenge is the characterization of channel uncertainty, which usually results in unreliable sensing performance. Though a lot of existing works focus on improving the detection probability, few works consider the reliability or robustness of the detector. The design objective of a robust detector is to provide a sensing performance that is not changing significantly with respect to the fluctuations of wireless channel. In this work, we propose a new model to describe the channel uncertainty, namely, the distribution uncertainty, that combines two well-known approaches, i.e., the stochastic and the worst-case robust approaches. This model allows the uncertain parameter to draw from a distribution function, but the type of distribution is not deterministic and can be arbitrarily selected from a pool of distributions, i.e., uncertainty set. To the best of our knowledge, we are the first to introduce distribution uncertainty into robust sensing of cognitive radio networks. Based on the characterization of channel uncertainty, we study the robust performance of spectrum sensing, and aim at providing analytical results for the lower bound of detection probability, which gives the secondary users (SUs) a guaranteed performance even under worst-case channel fluctuation. Specifically, we propose two types of uncertainties. For the moment-based uncertainty, the lower bound of detection probability can be found in a convex semi-definite program. While for the other reference-based uncertainty, though we cannot find closed-from result, we propose an iterative procedure that will converge to the lower detection bound. Another challenge is to design the system parameters and improve the robust detection performance. We consider the robust design of decision thresholds in multi-user cooperative spectrum sensing. It is shown to be a non-convex problem, however, we can approximate the design problem by a series of tractable semi-definite programs and propose an iterative algorithm to search the optimal decision threshold for each SU while maintaining the desired false alarm probability. We also demonstrate, through simulations, that the robust design can provide more stable sensing performance no matter how the channel gain fluctuates. Besides, we also face a challenge in designing efficient spectrum utilization mechanism. Considering a power control problem, if SUs' estimations of the interference power at primary user (PU) side are subject to channel uncertainty, their transmissions will easily violate PUs' interference power constraints thus degrade PUs' throughput performance. Based on our work in robust spectrum sensing, we present a robust formulation of the power control problem for SUs, and propose several iterative algorithms to determine the robust transmit power of SUs. Simulation results show that our robust design provides better PU protection than the existing works which fail to take account of channel uncertainty. In summary, our works investigate two important aspects in cognitive radio networks, i.e., spectrum identification by spectrum sensing, and efficient exploitation by power control. We find that channel uncertainty is a common challenge for both of these two aspects. Our main contribution lies in the introduction of distribution uncertainty into channel modeling, based on which we propose a novel framework to design the robust versions of spectrum sensing and power control algorithms.DOCTOR OF PHILOSOPHY (SCE