Codebook Design for Non-Coherent Communication in Multiple-Antenna Systems

We address the problem of space-time codebook design for non-coherent communications in multiple-antenna wireless systems. The channel matrix is assumed deterministic (no stochastic model assumed) and unknown at both the receiver and the transmitter. In contrast with other approaches, the Gaussian observation noise has an arbitrary correlation structure, known by the transmitter and the receiver. To handle the unknown deterministic space-time channel, a GLRT receiver is implemented. We propose a new methodology for space-time codebook design under this non-coherent setup. This optimizes the probability of error of the receiver´s detector in the high SNR regime, thus solving a high-dimensional nonlinear non-smooth optimization problem in a two-step approach: (i) firstly, a convex SDP relaxation yields a rough estimate of the optimal codebook; (ii) this is then refined through a geodesic descent optimization algorithm that exploits the Riemannian geometry imposed by the power constraints on the space-time codewords. Computer simulations demonstrate that, for the specific case of spatio-temporal white observation noise, our codebooks are marginally better than those provided by state-of-art known solutions. However, the most relevant conclusion is that, for correlated noise environments, our method provides codes that significantly outperform other known codes