  We study the downlink linear precoder design problem in a multi-cell 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 multi-cell coordinated linear
precoding, full and partial per-cell coordinated multi-point transmission,
zero-forcing precoding and joint BS clustering and beamforming/precoding. The
SUM problem is difficult due to its non-convexity 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 BSUM (Block Successive
Upper-Bound Minimization).} Simulation experiments show that the proposed
framework is effective for solving interference management problems in large
HetNet.
