On the Sum Capacity Achieving Precoders and Their CSI Requirements for MIMO-BC

Abstract

Dirty paper coding (DPC) precoders achieve the sum capacity of Gaussian MIMO broadcast channels. However, most systems employ zero-forcing (ZF) and MMSE precoders that are near-optimal at high SNR if the base station (BS) has a large number of antennas, but achievable sum rates with ZF and MMSE precoders are significantly below sum capacity otherwise. We show that capacity achieving DPC precoding requires CSI that scales only as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(M^{2})$ </tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -antenna user (not full CSI as is generally assumed) irrespective of the number of BS antennas. Moreover, easily computable generalized decision feedback equalizers significantly outperform MMSE and ZF precoders.