On the achievable throughput of a multi-antenna Gaussian broadcast channel

A Gaussian broadcast channel with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite apparent simplicity, this model is in general a non-degraded broadcast channel, for which the capacity region is not fully known. We propose a novel transmission scheme based on \ranked known interference" (RKI). In brief, the transmitter decomposes the channel into an ordered (or ranked) set of interference channels for which the interference signal in the i-th channel is a linear combination of the signals transmitted in channels j < i. Since all transmitted signals are generated by the transmitter, interference in each channel is known non-causally. Hence, known techniques of coding for non-causally known interference can be applied to make the interference in each channel harmless without further power penalty. We show that the proposed scheme is throughputwise asymptotically optimal for both low and high SNR, and we compare the throughput achievable by RKI with the throughput achievable by more conventional zero-forcing beamforming (space-division multiple access) and with the throughput of a single-user multiple antenna system obtained by allowing the receivers to cooperate. Also, we provide a modi cation of the basic RKI scheme which achieves optimal throughput for all SNRs in the special case of two users. For independent Rayleigh fading, closed-form throughput expressions are obtained for the basic RKI strategy and arbitrary t and r. Numerical results are shown for nite r; t and in the large-system limit of r; t !1 with xed ratio = r=t users per transmit antenna.