Sum Capacity of Multiuser MIMO Broadcast Channels with Block Diagonalization

The sum capacity of a Gaussian broadcast MIMO channel can be achieved with dirty paper coding (DPC). Deploying DPC in real-time systems is, however, impractical. Block diagonalization (BD) is an alternative precoding technique for downlink multiuser MIMO systems, which can eliminate interuser interference at each receiver, at the expense of suboptimal sum capacity vs. DPC. In this paper, we study the sum capacity loss of BD for a fixed channel. We show that 1) if the user channels are orthogonal to each other, then BD achieves the complete sum capacity; and 2) if the user channels lie in a common row vector space, then the gain of DPC over BD can be bounded by the minimum of the number of transmit and receive antennas and the number of users. We also compare the ergodic sum capacity of DPC with that of BD in a Rayleigh fading channel. Simulations show that BD can achieve a significant part of the total throughput of DPC. An upper bound on the ergodic sum capacity gain of DPC over BD is derived, which can be evaluated with a few numerical integrations. With this bound, we can easily estimate how far away BD is from being optimal in terms of ergodic sum capacity, which is useful in directing practical system designs