A Diversity Guarantee and SNR Performance for Unitary Limited Feedback 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 significant diversity. Linear precoding may be used, along with spatial multiplexing (SM) or space-time block coding (STBC), to realize these gains with low-complexity receivers. In the absence of perfect channel knowledge at the transmitter, the precoding matrices may be quantized at the receiver and informed to the transmitter using a feedback channel, constituting a limited feedback system. This can possibly lead to a performance degradation, both in terms of diversity and array gain, due to the mismatch between the quantized precoder and the downlink channel. In this paper, it is proven that if the feedback per channel realization is greater than a threshold, then there is no loss of diversity due to quantization. The threshold is completely determined by the number of transmit antennas and the number of transmitted symbol streams. This result applies to both SM and STBC with unitary precoding and confirms some conjectures made about antenna subset selection with linear receivers. A closed form characterization of the loss in SNR (transmit array gain) due to precoder quantization is presented that applies to a precoded orthogonal STBC system and generalizes earlier results for single-stream beamforming.