On achievable rates in 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 its 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 of the i-th channel is generated as a linear combination of the signals transmitted in channels j<i. In this way, 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. We provide a modification of the basic RKI scheme which achieves optimal throughput for all SNRs in the special case of 2 antenna and 2 users. For independent Rayleigh fading closed-form throughput expressions are obtained in various cases of interest and numerical examples are provided for the infinite-dimensional Rayleigh channel.