Joint Beamforming and Scheduling for SDMA Systems with Limited Feedback

On a multi-antenna broadcast channel, exploiting spatial degrees of freedom supports simultaneous transmission to multiple users in the same time and frequency slot. Unfortunately, the optimal approach for such multi-user transmission, namely dirty paper coding, requires non-causal channel state information (CSI) and is hence not directly realizable. Therefore, this paper proposes a practical joint beamforming and scheduling algorithm, which supports multi-user simultaneous transmission, relies on quantized CSI feedback, and furthermore is capable of exploiting multi-user diversity. Using this algorithm, each user quantizes CSI using a codebook comprised of multiple orthonormal vector sets and sends back quantized CSI to the base station. Next, using feedback CSI, the base station jointly performs beamforming and scheduling. For a large number of users, the proposed algorithm is shown to achieve the optimal sum capacity scaling, which scales double logarithmically with the number of users and linearly with the number of antennas at the base station. To constrain the capacity loss due to CSI quantization, the required quantizer codebook size is derived as a polynomial function of the signal-to-noise ratio (SNR). Moreover, fixing the codebook size is found to prevent the sum capacity from growing continuously with the SNR. Numerical results show that the proposed algorithm achieves higher throughput than the conventional algorithms for the same amount of CSI feedback.