Capacity of Differential versus Non-Differential Unitary Space-Time Modulation for MIMO Channels

Differential Unitary Space-Time Modulation (DUSTM) and its earlier nondifferential counterpart, USTM, permit high-throughput MIMO communication entirely without the possession of channel state information (CSI) by either the transmitter or the receiver. For an isotropically random unitary input we obtain the exact closed-form expression for the probability density of the DUSTM received signal, which permits the straightforward Monte Carlo evaluation of its mutual information. We compare the performance of DUSTM and USTM through both numerical computations of mutual information and through the analysis of low- and high-SNR symptotic expressions. In our comparisons the symbol durations of the equivalent unitary space-time signals are both equal to T, as are the number of receive antennas N. For DUSTM the number of transmit antennas is constrained by the scheme to be M = T/2, while USTM has no such constraint. If DUSTM and USTM utilize the "same number of transmit antennas" at high SNR's the normalized mutual information of the differential and the nondifferential schemes xpressed in bits/sec/Hz are asymptotically equal, with the differential scheme performing somewhat better, while at low NR's the normalized mutual information of DUSTM is symptotically twice the normalized mutual information of USTM. If, instead, USTM utilizes the optimum number of transmit antennas then USTM can outperform DUSTM as sufficiently low SNR's.