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/sub T/-transmit antennas per user and if the single-user space-time constellation employed requires only the minimum dimension N/sub T/, no more than N/sub T/+1 dimensions are required for the common signal space of all users, i.e., each user's spreading matrix is of size (N/sub T/+1)/spl times/N/sub 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.