Resource allocation in wireless systems under probabilistic outage constraints : fast algorithms and convergence analysis

Abstract

With the explosive growth of Internet-of-Things, the need for high-speed data transmission is exploding. To satisfy the increased demand for higher data rate in diverse wireless networks, optimization has been widely applied to make sure that limited wireless resource is wisely utilized. For resource allocation problems, different constraints may appear under specific quality-of-service (QoS) requirements, including the signal-to-noise ratio greater than a predefined threshold and total transmit power budget, etc.

Due to the appearance of QoS, most resource allocation problems are formulated as nonconvex optimization problems. On the other hand, QoS requirement in its basic form usually assumes channel state information (CSI) is perfectly known. However, in practice, it is impossible to obtain the perfect CSI since channel estimates inevitably contain errors. Therefore, the resource allocation problems under channel uncertainty replace the deterministic QoS requirements with probabilistic ones, leading to a more challenging class of nonconvex stochastic optimization. Although the universal procedure of Monte Carlo simulation can be employed to handle the probabilistic constraint, it brings a heavy computation burden. In contrast, by leveraging the statistical information of the CSI, customized transformations are designed in this thesis to convert the probabilistic constraint into a deterministic one. After obtaining the deterministic problems, the successive convex approximation can be applied to convexify the nonconvex term into convex upper bounds, and then numerical solvers can be used to solve the convex subproblems.

While the convex numerical solvers are convenient to use, they employ the second-order methods such as the interior-point method and Newton's method. However, these methods require the Hessian information of the objective function, leading to at least cubic complexity order with respect to problem size. Considering the modern massive access networks with hundreds of users and antennas, the second-order methods easily overwhelm the most powerful computers today. To tackle this challenge, the class of first-order algorithms with low complexity are adopted for three modern wireless scenarios in this thesis. Based on different properties of the considered communication networks, customized probabilistic constraints transformations and convex approximation methods are incorporated. Due to the nonconvex constraints in the optimization problem, the convergence of the objective function value does not indicate the convergence of the solution sequence. Therefore, this thesis also mathematically proves that the proposed fast algorithms have convergence guaranteed stable solutions.