Conic Quadratic Formulations for Wireless Communications Design

As a wide class of resource management problems in wireless communications are nonconvex and even NP-hard in many cases, finding globally optimal solutions to these problems is of little practical interest. Towards more pragmatic approaches, there is a rich literature on iterative methods aiming at finding a solution satisfying necessary optimality conditions to these problems. These approaches have been derived under several similar mathematical frameworks such as inner approximation algorithm, concave-convex procedure, majorization-minimization algorithm, and successive convex approximation (SCA). However, a large portion of existing algorithms arrive at a relatively generic program at each iteration, which is less computationally efficient compared to a more standard convex formulation. The purpose of this paper is to present useful transformations and approximations to deal with nonconvexity in wireless communications design problems. More specifically, the proposed formulations can approximate nonconvex problems by a series of secondorder cone programs (SOCPs) in light of SCA framework. We revisit various design problems in wireless communications to demonstrate the advantages of the proposed idea. Theoretical analysis and numerical results show the superior efficiency in terms of computational cost of our proposed solutions compared to the existing ones.