On the Optimality of Linear Multiuser MIMO Beamforming for a Two-User Two-Input Multiple-Output Broadcast System

The asymptotic optimality of a jointly optimized linear multiuser beamforming system with two transmit and many receive antennas for the fading multiple-input multiple-output (MIMO) Gaussian broadcast channel is investigated. We derive the asymptotic sum capacity of the independent and identically-distributed (i.i.d.) MIMO broadcast channel and the asymptotic sum rate of a linear multiuser beamforming system with respect to the number of receive antennas per user, where two users are served with a zero inter-user interference constraint. Based on this result, we show that linear multiuser beamforming with many receive antennas can asymptotically achieve the sum capacity of the two-user i.i.d. MIMO broadcast channel even without opportunistic scheduling gain. Numerical results confirm that as the number of receive antennas increases the sum rate of linear multiuser beamforming system converges to the sum capacity.