A Fast Algorithm for Designing Grassmannian Constellations

In this paper, we propose an algorithm for designing Grassmannian constellations for noncoherent MIMO communications over Rayleigh block fading channels. The new algorithm, named ManOpt, is based on a gradient ascent approach that operates directly on the Grassmann manifold to maximize the minimum pairwise chordal distance of the constellation. We analyze the performance of the algorithm in terms of convergence speed, minimum chordal distance achieved, and symbol error rate (SER), and we compare it with some other Grassmannian constellation designs. Our simulation results suggest that ManOpt constellations have a higher packing efficiency (represented by the minimum chordal distance), which translates into better SER performance, with lower computational complexity than existing algorithms for unstructured constellation designs.