User Selection for the MIMO Broadcast Channel with a Fairness Constraint

In this paper, we present a user selection scheme with a fairness constraint when zero-forcing beamforming (ZFBF) transmission is employed in a multiple-input multiple-output (MIMO) broadcast channel. This problem can be reduced to the maximization of a weighted sum rate with a power constraint. In this paper, we first derive a lower bound on the weighted sum rate. Roughly speaking, this bound is inversely proportional to the Frobenius norm of the inverse of the weighted composite channel matrix. We then present a greedy algorithm to select the users that maximize this lower bound, using the same technique in J. Wang et al. Finally, we show that this approach achieves the same scaling law as DPC does as presented in M. Sharif and B. Hassibi. Simulation suggests that this method achieves comparable or better performance than most existing schemes in the moderate to high SNR realm with comparable complexity.