MIMO spatial multiplexing systems with limited feedback

This paper investigates the problem of transmit beamforming in MIMO spatial multiplexing (SM) systems with a finite-rate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new design criterion for designing the codebook of beamforming matrices that is based on minimizing the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to an optimum codebook. Under the i.i.d, channel and high SNR assumption, the effect on channel capacity of the finite-bit representation of beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multi-mode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits.