Linear Transceiver Design for a MIMO Interfering Broadcast Channel Achieving Max-Min Fairness

TL;DR

This paper addresses the challenge of designing linear transceivers for MIMO interfering broadcast channels to maximize the minimum user rate, proving NP-hardness and proposing an efficient iterative algorithm with proven convergence.

Contribution

The paper demonstrates NP-hardness of the max-min fairness problem in MIMO IBCs and introduces a low-complexity, convergent algorithm for practical transceiver design.

Findings

The problem is NP-hard when each node has at least two antennas.

The proposed algorithm converges globally to a stationary point.

Numerical results show the algorithm effectively achieves fairness.

Abstract

We consider the problem of linear transceiver design to achieve max-min fairness in a downlink MIMO multicell network. This problem can be formulated as maximizing the minimum rate among all the users in an interfering broadcast channel (IBC). In this paper we show that when the number of antennas is at least two at each of the transmitters and the receivers, the min rate maximization problem is NP-hard in the number of users. Moreover, we develop a low-complexity algorithm for this problem by iteratively solving a sequence of convex subproblems, and establish its global convergence to a stationary point of the original minimum rate maximization problem. Numerical simulations show that this algorithm is efficient in achieving fairness among all the users.