Power minimization of multiaccess MIMO systems with rate constraint and finite-rate feedback

In this paper, power minimization of multi-access multiple-input multiple-output (MIMO) systems with rate constraint is studied where the users only have partial channel state information (CSI) obtained through finite-rate feedback. Although the optimal scheme is difficult to obtain, we propose a sub-optimal beamforming scheme where the beamforming vectors are selected by the feedback. The Base station (BS) broadcasts the optimal index of the code vectors in the codebook to the users. With optimal quatization of CSI and only a small number of feedback bits, the required average sum-power is shown to be close to or even smaller than the sub-optimal maximum eigenmode beamforming (MEB) scheme where perfect CSI is known at the users. To simplify the performance analysis, we use a sub-optimal quantization scheme for the proposed beamforming scheme, where the distance between the code vectors and the strongest eigen-channel vectors of the users is minimized. Although the sub-optimal quantization scheme has a higher sum-power than the optimal one, simulation results show that they achieve similar multi-user gain. By letting the feedback bits approach infinity, this sub-optimal quantization scheme becomes the MEB scheme. A closed-form expression for the sum-power of this sub-optimal quantization scheme is estimated by random matrix theory and quantization bounds on Grassmann manifold. The effect of the finite-rate feedback on multi-user gain is then studied using this closed-form expression.