On the effective spatio-temporal rank of wireless communication channels

We consider the following receiver architecture for a wireless communication link with one transmit and multiple receive antennas: spatial and temporal rank reduction based on long-term (average) spatio-temporal channel properties followed by space-time processing using maximum-likelihood estimates of the channel coefficients. Receivers based on this architecture use e.g. a temporal or spatio-temporal Rake, beamspace processing, or eigenvalue decomposition. Their performance critically depends on a good choice of the spatio-temporal rank. We define the effective spatio-temporal rank based on the mean square error (MSE) of the receiver´s reduced rank channel estimate. Thus, we can determine the optimum rank and get an analytical insight in the fundamental trade-offs involved, when designing such systems. Using this criterion we discuss under which conditions beamforming is optimal compared to diversity combining.