Cooperative Multi-Cell Block Diagonalization with Per-Base-Station Power Constraints

TL;DR

This paper develops an optimal cooperative multi-cell block diagonalization precoding method under per-base-station power constraints, enhancing sum-rate performance in multi-user MIMO systems with practical power limitations.

Contribution

It introduces a convex optimization-based algorithm for optimal BD precoding with per-BS power constraints and derives a closed-form solution, revealing non-orthogonal precoding vectors.

Findings

Optimal BD precoding vectors are generally non-orthogonal under per-BS power constraints.

The proposed solution reduces to the known ZF-BF in the single-antenna case.

Suboptimal low-complexity schemes achieve rates close to the optimal precoding.

Abstract

Block diagonalization (BD) is a practical linear precoding technique that eliminates the inter-user interference in downlink multiuser multiple-input multiple-output (MIMO) systems. In this paper, we apply BD to the downlink transmission in a cooperative multi-cell MIMO system, where the signals from different base stations (BSs) to all the mobile stations (MSs) are jointly designed with the perfect knowledge of the downlink channels and transmit messages. Specifically, we study the optimal BD precoder design to maximize the weighted sum-rate of all the MSs subject to a set of per-BS power constraints. This design problem is formulated in an auxiliary MIMO broadcast channel (BC) with a set of transmit power constraints corresponding to those for individual BSs in the multi-cell system. By applying convex optimization techniques, this paper develops an efficient algorithm to solve this problem, and derives the closed-form expression for the optimal BD precoding matrix. It is revealed that the optimal BD precoding vectors for each MS in the per-BS power constraint case are in general non-orthogonal, which differs from the conventional orthogonal BD precoder design for the MIMO-BC under one single sum-power constraint. Moreover, for the special case of single-antenna BSs and MSs, the proposed solution reduces to the optimal zero-forcing beamforming (ZF-BF) precoder design for the weighted sum-rate maximization in the multiple-input single-output (MISO) BC with per-antenna power constraints. Suboptimal and low-complexity BD/ZF-BF precoding schemes are also presented, and their achievable rates are compared against those with the optimal schemes.