On achievable rates in a multi-antenna broadcast downlink

A Gaussian broadcast channel with r single-antenna receivers where the transmitter is equipped with t antennas and where both the transmitter and the receivers have perfect knowledge of the propagation channel is considered. This provides a very simple model for the downlink of a wireless system, but despite its apparent simplicity it 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". 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 theinterference in each channel harmless without further power penalty. We show that the proposed scheme is throughputwise asymptotically optimal for both low and high SNR. In the special case of 2-antenna and 2- users we propose a modification of the basic strategy achieving optimal throughput for all SNRs. Finally, the infinite-dimensional Rayleigh channel is considered and throughput closed-form expressions are provided in various cases. This analysis shows that a practical and sensible strategy to the downlink of a wireless system consists of hybrid TDMA and space-time multiplexing where only a subset of active users, whose optimal size depends on the available SNR, is served at any given channel use by using our ranked known interference scheme. TDMA is used for time-sharing between different active user subsets to give to all users the same average rate without penalty in the maximum throughput. Also, constant-ower variable-rate coding achieves practically the same throughput of variable-power variable-rate coding (waterolling power allocation).