Parametrization Based Limited Feedback Design for Correlated MIMO Channels Using New Statistical Models

Parametrization of unitary matrices using Givens rotations has been used for limited feedback in multiple-input multiple-output (MIMO) systems. Feedback based on these rotations has been adopted in IEEE 802.11n and other upcoming standards. However, the probability distributions of Givens rotations is not known for correlated channels, forcing the use of uniform quantization. In this paper, novel probability density function (PDF) models, based on beta and wrapped Cauchy distributions, are proposed for Givens rotations in correlated MIMO channels. Empirical distributions and goodness-of-fit tests show that the proposed distributions characterize the spatial correlation behavior with good accuracy. Moreover, it is shown that the distributions known in the literature for uncorrelated MIMO channels are only special cases. Distributions of Givens rotations are useful to understand the behavior of singular vectors of correlated channels. In this paper, the PDF models are utilized for bit allocation and optimized codebook design. Simulations show that precoding using the proposed codebooks achieves significant performance improvement, in terms of mean square error and sum rate, as compared to using uniform codebooks. It is also shown that the bit allocations proposed in this paper reduce to that of IEEE 802.11n standard when the MIMO channel is not spatially correlated.