Low-dimensional spreading matrices for multiuser space-time modulation

In a previous paper we proposed a multiuser space-time modulation scheme that leverages single-user space-time constellations and guarantees both, a full diversity order, as well as an asymptotic (high SNR) single-user like performance for every user. This is achieved by multiplying each user\´s space-time information matrix symbol by a low-dimensional "spreading matrix." For instance, for N_T-transmit antennas per user and if the single-user space-time constellation employed requires only the minimum dimension N _T, no more than N_T+1 dimensions are required for the common signal space of all users, i.e., each user\´s spreading matrix is of size (N_T+1)×N_T, independent of the number of users. In this paper, we present a simplified design criterion to obtain these spreading matrices by numerical optimization. Since the columns of each user\´s spreading matrix are constrained to be orthonormal, we propose to perform the optimization using a parameterization of the Grassmann manifold. A special feature of the simplified criterion, and thus of the resulting spreading matrices, is that they are independent of the particular single-user space-time constellations (of a given dimension), so that different spectral efficiencies can be attained without changing or redesigning the spreading matrices