Decomposition by Successive Convex Approximation: A Unifying Approach for Linear Transceiver Design in Heterogeneous Networks

We study the downlink linear precoder design problem in a multicell dense heterogeneous network (HetNet). The problem is formulated as a general sum-utility maximization (SUM) problem, which includes as special cases many practical precoder design problems such as multicell coordinated linear precoding, full and partial per-cell coordinated multipoint transmission, zero-forcing precoding, and joint BS clustering and beamforming/precoding. The SUM problem is difficult due to its nonconvexity and the tight coupling of the users' precoders. In this paper, we propose a novel convex approximation technique to approximate the original problem by a series of convex subproblems, each of which decomposes across all the cells. The convexity of the subproblems allows for efficient computation, while their decomposability leads to distributed implementation. Our approach hinges upon the identification of certain key convexity properties of the sum-utility objective, which allows us to transform the problem into a form that can be solved using a popular algorithmic framework called block successive upper-bound minimization (BSUM). Simulation experiments show that the proposed framework is effective for solving interference management problems in large HetNet.