Outage analysis of multi-antenna rate adaptive systems with outdated feedback

The effect of imperfect channel state information (CSI) on rate adaptation in time-varying multi-antenna fading channels is studied. In the presence of feedback delay and channel estimation error, we analyze the outage probability (OP), defined as the average probability that the achievable rate in the current channel state is lower than data rate scheduled based on outdated feedback, for maximum ratio combining receivers in single-input multiple-output channels and zero-forcing (ZF) receivers in multiple-input multiple-output (MIMO) channels. In particular, for temporally correlated MIMO channels, the conditional distribution of SNR at the output of ZF detection in the current channel state is unknown; hence we apply a Gaussian approximation to obtain a closed-form expression for the average OP of the MIMO-ZF receiver. Simulation results show that our derivations are well-matched to the actual OP and throughput of multi-antenna rate adaptive systems. Also, based on our analysis results, we propose a simple rate adaptation scheme that maximizes the average throughput under a target OP constraint. The proposed schemes optimize the scheduled rate according to a given CSI condition, and effectively maximize the average outage-constrained throughput.