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Jointly optimized linear transmit beamforming and receive combining is a low complexity approach for communication in the multiuser MIMO (multiple input multiple output) broadcast channel. This paper proposes an iterative algorithm for jointly designing the beamforming and combining vectors, which enforces a zero interference requirement after combining. Since the optimization is performed at the base station with channel state information for all the users, the receive beamformers are quantized at the basestation and sent to the users via a lowrate feedforward control channel. Rate bounds are provided to estimate the impact of quantization loss on the achievable rate in Rayleigh channels is performed. Simulations show that the proposed approach using Grassmannian codebooks approaches the sum capacity of the MIMO broadcast channel.

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The capacity-achieving coding scheme for the multiple-input multiple-output (MIMO) broadcast channel is dirty-paper coding. With this type of transmission scheme the optimal number of active users that receive data and the optimal power allocation strategy are highly dependent on the structure of the channel matrix and on the total transmit power available. In the context of packet-data access with adaptive transmission where mobile users are equipped with a single receive antenna and the base station has multiple transmit antennas, we study the optimal number of active users and the optimal power allocation. In the particular case of two transmit antennas, we prove that the optimal number of active users can be a non-monotonic function of the total transmit power. Thus not only the number of users that should optimally be served simultaneously depends on the user channel vectors but also on the power available at the base station transmitter. The expected complexity of optimal scheduling algorithms is thus very high. Yet we then prove that at most as many users as the number of transmit antennas are allocated a large amount of power asymptotically in the high-power region in order to achieve the sum-capacity. Simulations confirm that constraining the number of active users to be no more than the number of transmit antennas incurs only a marginal loss in spectral efficiency. Based on these observations, we propose low-complexity scheduling algorithms with sub-optimal transmission schemes that can approach the sum-capacity of the MIMO broadcast channel by taking advantage of multiuser diversity. The suitability of known antenna selection algorithms is also demonstrated. We consider the cases of complete and partial channel knowledge at the transmitter. We provide simulation results to illustrate our conclusions.