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.