Sum Power Iterative Water-Filling for Multi-Antenna Gaussian Broadcast Channels

TLDR

Obtaining the optimal transmission policy with dirty‑paper coding is a computationally complex nonconvex problem. The paper seeks to maximize the sum rate of a multi‑antenna Gaussian broadcast channel by determining the optimal transmit covariance structure under given channel conditions and power constraints. By exploiting duality, the authors transform the problem into a convex MAC formulation and develop simple, fast iterative algorithms that yield optimal MAC policies, which map directly to optimal BC policies. Dirty‑paper coding has been shown to achieve capacity for the multi‑antenna Gaussian broadcast channel.

Abstract

In this correspondence, we consider the problem of maximizing sum rate of a multiple-antenna Gaussian broadcast channel (BC). It was recently found that dirty-paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e., the optimal transmit covariance structure) given the channel conditions and power constraint must be found. However, obtaining the optimal transmission policy when employing dirty-paper coding is a computationally complex nonconvex problem. We use duality to transform this problem into a well-structured convex multiple-access channel (MAC) problem. We exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the MAC, which can easily be mapped to the optimal BC policies.