Optimum receivers and low-dimensional spreaded modulation for multiuser space-time communications

The jointly optimum receiver is obtained for multi- user communications in a frequency nonselective Rayleigh-fading channel with N_T transmit antennas per user and N_R receive antennas. Based on a general analysis of quadratic receivers in zero-mean complex Gaussian vectors, asymptotically tight expressions (for high signal-to-noise ratio (SNR)) for the pairwise error probabilities are derived. Subsequently, it is shown that N_T-dimensional single-user signaling suffices to provide full diversity order N=N_TN_R for all the users. In other words, the presence of other users does not increase the minimum dimension required beyond what is needed for the single-user space-time channel. For the special case of low-rank "code-division multiple-access (CDMA)" signaling with N_T=1 and provided the signatures of any two users are linearly independent, it is shown that the error probability of a K-user system asymptotically approaches single-user-like performance for every user. Remarkably, therefore, an increase in the number of users, and hence an increase in the aggregate spectral efficiency, does not require the users to transmit with more power to achieve single-user-like performance asymptotically. A signal design algorithm is proposed to illustrate this point and examples are given. These results are then generalized to the multiple transmit antenna case. A new (N_T+1)-dimensional signaling strategy is proposed for the multiuser channel that leverages existing single-user space-time signal designs while ensuring full diversity order and single-user-like performance asymptotically for every user.