On the Asymptotic Optimality of Block-diagonalization for Themimo Bc under Linear Filtering

In this paper, we address the high SNR regime of the MIMO broadcast channel under linear filtering. For systems where the base station is equipped with more antennas than the user terminals have in sum, we prove that block-diagonalization is the asymptotically optimum transmission strategy for maximizing the sum rate. For this type of transmission strategy, the asymptotically optimum transmit covariance matrix in the broadcast channel is derived in closed form. In addition, we present an expression for the asymptotic sum capacity for an instantaneous channel realization which only depends on this particular channel realization. No precoders or singularvalue-decompositions arise as they used to do in hitherto existing sum rate expressions in the multi-antenna terminal case. All results are deduced from the dual multiple access channel in which the optimum transmit covariancematrices can easily be computed. Our recent rate duality for multi-antenna systems where the individual streams of a user are not treated as self-interference allows us then to convert the solution of the dual uplink back to the downlink and to find the optimum transmit and receive filters in the broadcast channel.