Nonconvex Power Control in Multiuser Communication Systems

Interference control is a major and fundamental issue in the design of a multiuser communication system such as a CDMA cellular network, an ad hoc wireless network or a DSL cable binder, where interference is a central phenomenon. The goal of an interference-limited system is to develop a resource allocation scheme that jointly optimizes the performance of all users in the presence of mutual interference. In this dissertation, we study how dynamic power control solves several nonconvex resource allocation problems motivated by engineering system design. We first present a systematic study of the weighted sum rate maximization problem in a Gaussian interference-limited channel, where users have individual power constraints. We focus on three theoretical aspects: optimality, algorithms and performance guarantees. Our analysis exploits the intriguing relationship between irreducible nonnegative matrix theory and nonconvex optimization by transforming the original nonconvex problems into eigenvalue optimization problems. The key steps are exploiting the eigenspace of specially crafted interference matrices and the application of irreducible nonnegative matrix theory, in particular the Perron-Frobenius Theorem, quasi-invertibility and the Friedland-Karlin inequalities. Performance guarantees are then established for a wide range of fast power control algorithms, including the weighted max-min SIR allocation under low to moderate interference regimes. Through connections with the nonlinear Perron-Frobenius theory, the weighted max-min SIR can be solved efficiently and distributedly by reusing existing CDMA power control. In addition, we present two global optimization techniques that use successive geometric programming and an outer approximation based on the Friedland-Karlin inequalities and its extensions to maximize sum rates. We demonstrate that the outer approximation technique can compute the global optimal solution efficiently for a small to medium sized network. Our general theory and fast algorithms have several applications. In combination with congestion control at the transport layer, we propose a joint scheduling and power control scheme to stabilize packet queue lengths by first using the IEEE 802.11 RTS/CTS protocol to construct favorable transmission schedules and then use power control to maximize sum rates. Another application is establishing the optimality of DSL dynamic spectrum management algorithms. We next extend our analysis to solve the nonconvex weighted sum mean-squared error minimization problem in a downlink setting, where users have a total power constraint. By connecting it to the sum rate maximization through the arithmetic-geometric mean inequality, fast power control algorithms are developed to solve the weighted mean-squared error minimization and sum rate maximization problems optimally under low to moderate interference regimes that are modulated by beamforming control. We also solve distributedly the joint power control and beamforming optimization of the max-min SIR problem. We then study the tradeoff between energy and robustness of uplink power control. An optimization problem is formulated where robustness is captured in the constraint and the price of robustness penalized in the objective function, which models a large class of robust power control. A primal-dual algorithm is developed based on the uplink-downlink duality to modulate the tradeoff between energy and robustness, and between energy and speed of admission control.