On the SNR and Diversity of Quantized Precoded MIMO Systems

A multiple-input multiple-output (MIMO) wireless channel formed by antenna arrays at the transmitter and at the receiver offers high capacity and diversity benefits. Spatial multiplexing (SM) and space-time block coding (STBC) are attractive because they can provide high data-rate and full diversity, respectively, with low receiver complexity. Unitary linear precoding, which generalizes antenna subset selection, may be used to improve the diversity performance of a SM system and provide transmit array gain for a STBC system assuming perfect downlink channel state information (CSI) at the transmitter. This assumption can be relaxed by devising a MIMO system where the precoding matrices are quantized at the receiver and informed to the transmitter using a feedback channel. This leads to a performance degradation due to the mismatch between the quantized precoder and the downlink channel. In this paper, the loss in channel gain (transmit array gain) due to precoder quantization is characterized as a function of the feedback data-rate for precoded SM system with linear receivers and STBC systems. A sufficient condition is derived that will guarantee no loss in diversity due to quantization for such systems. The diversity order of a precoded SM system with perfect CSI is also established in the case when the number of receive antennas is equal to the number of transmitted streams