Average Sum-Rate Bound of Multiuser MIMO Beamforming with Direction-Indicating Matrices and Channel Magnitude Feedback

In this paper, we investigate sum-rate bounds for a multiuser beamforming system with feedbacks of direction- indicating (DI) matrices and channel magnitudes. We also adopt a quality-based channel state reporting (QBR) in order to reduce the feedback load in multiuser environments. With QBR, the users with SNR higher than a predefined threshold are allowed to send the feedback information. The feedback consists of only two numbers: a positive real value for the channel magnitude and a positive integer for the index of DI vector. A semi-orthogonal user group and the corresponding beamforming matrix are then constructed by a user selection process using the indices of DI vector. Finding an optimal beamforming matrix is generally known as a difficult nonconvex optimization problem, but using DI matrices may greatly reduce the complexity although there exists some loss on the sum-rate. We obtain upper and lower bounds of the average sum-rate of the proposed scheme and compare the performance with that of an established ZFBF scheme in [1]. Numerical results show that these bounds are valid and the proposed method achieves better performance than the ZFBF scheme when the available feedback bandwidth is small (i.e., the number of mini slots in this paper). And very low feedback-rate also can be obtained especially for a large number of users.