On The Construction of Non-coherent Space Time Codes from High-dimensional Spherical Codes

This paper analyzes the performance of noncoherent space time codes obtained from a new class of spherical codes by mapping the surface of a higher-dimensional half-sphere to the Grassmann manifold. The deployed spherical code contains a structure which can be exploited by the receiver, leading to a reasonable decoding complexity. Therefore, high-dimensional coding spaces (Grassmann manifolds) can be used as a basis for the construction. This corresponds to codes with larger block lengths, as opposite to the usual construction of space time codes from small-dimensional spaces, such as the unitary group U(n_T), where n_T is the number of transmit antennas. The construction is flexible, meaning that codes of various dimensions and rates (spectral efficiency) may be constructed. Additionally, because of the properties of the deployed mapping, the structure of the spherical codes applies to the Grassmannian constellations as well