Non-Coherent Communication in Multiple-Antenna Systems: Receiver Design, Codebook Construction and Capacity Analysis

The thesis addresses the problem of space-time codebook design for communication in multiple-input multiple-output (MIMO) wireless systems. The realistic and challenging non-coherent setup (channel state information is absent at the receiver) is considered. A generalized likelihood ratio test (GLRT)-like detector is assumed at the receiver and contrary to most existing approaches, an arbitrary correlation structure is allowed for the additive Gaussian observation noise. A theoretical analysis of the probability of error is derived, for both the high and low signal-to-noise ratio (SNR) regimes. This leads to a codebook design criterion which shows that optimal codebooks correspond to optimal packings in a Cartesian product of projective spaces. The actual construction of the codebooks involves solving a high-dimensional, nonlinear, nonsmooth optimization problem which is tackled here in two phases: a convex semi-definite programming (SDP) relaxation furnishes an initial point which is then refined by an iterative subgradient-like geodesic descent algorithm exploiting the Riemannian geometry imposed by the power constraints on the space-time codewords. New codebooks are obtained by this method and their performance is shown to outperform previous state-of-art solutions. In fact, for some particular configurations, these new constellations attain the Rankin bound and are therefore provably optimal. The thesis also contains new theoretical results on the capacity (mutual information) of multiple-antenna wireless links in the low SNR regime. The impact of channel and noise correlation on the mutual information is obtained for the on-off and Gaussian signaling. The main conclusion is that mutual information is maximized when both the transmit and receive antennas are fully correlated.