MIMO performance under covariance matrix feedback

We study the finite-rate feedback of optimal input covariance matrices from the channel-aware receiver to the transmitter in a multi-antenna single-user setup. Under a block fading model for the channel matrix, the receiver computes the covariance matrix corresponding to the current channel realization and feeds back information about it using a finite, say N_f, number of bits per block. Our finite-rate feedback analysis is based on a novel geometric paradigm whereby the feedback information is modeled as a source distributed over a new Riemannian surface called the Pn manifold. For a given system strategy, the gap between the achievable rates in the infinite and finite-rate feedback cases is shown to be O(2 ^{- N}_f^/N), where N is the dimension of the Pn manifold used for quantization.