On performance limits of optimum reduced rank channel estimation

In a wireless communication link with one transmit and multiple receive antennas we optimally reduce the spatio-temporal channel rank at the receiver based on long-term (average) channel properties. The channel is estimated and symbols are detected using this reduced rank approximation of the received signal. Examples for this receiver architecture are the temporal/spatio-temporal Rake, Space-Time Eigenrake, or beamspace processing. We discuss the fundamental trade-offs in reduced rank channel estimation and detection and propose an appropriate model for describing the spatio-temporal channel structure. Based on these insights and definitions, we derive an analytical expression for the minimum receiver SNR, which is necessary for channel estimation. Furthermore, we state under which conditions reduced rank channel estimation is asymptotically optimum.