Coherence-based Subspace Packings for MIMO Noncoherent Communications

In this paper, we propose a new algorithm for designing unstructured Grassmannian constellations for non-coherent MIMO communications over Rayleigh block-fading channels. The algorithm minimizes the maximum coherence between subspaces, which is shown to be equivalent to the diversity product previously proposed in the literature. The coherence criterion is optimized by means of a gradient ascent algorithm on the Grassmann manifold. The method is generalized to optimize a weighted cost function that takes into account several neighboring codewords. Simulation results suggest that the constellations designed with the proposed algorithm achieve better SER performance than existing algorithms for unstructured Grassmannian constellation designs.