On the Design of Grassmannian Constellations for Non-Coherent MIMO Communication Systems

We consider the design of the Grassmannian constellations that are required for rate-efficient non-coherent wireless MIMO communication. We begin by providing insight into the way in which these constellations are structured, and we then provide two new techniques for designing them. The first technique enables joint design of all the constellation points by exploiting a new method (proposed herein) for simultaneous optimization of multiple points on the Grassmann manifold. This in contrast to most existing techniques in which the points are designed sequentially. The second technique is a more efficient method for designing large constellations. By expressing large constellations as the disjoint union of rotated versions of a ‘proto-constellation’, one can partition the design problem into the design of a (small) proto-constellation and that of the rotation matrices. It will be shown that, in addition to providing storage and regeneration convenience, the rotation-based design retains two desirable features of the optimal design. Finally, we will provide numerical simulations that illustrate the performance of the constellations designed with the proposed techniques.