Predictive Feedback for Transmit Beamforming with Delayed Feedback and Channel Estimation Errors

The effect of limited-rate feedback on the transmit beamforming (TB) channel capacity has been well studied in the literature, but the negative effects of outdated feedback and imperfect channel estimation (ICE) have not been adequately addressed yet. In this paper, we study the joint effects of receiver ICE and delayed and limited feedback on the capacity of transmit beamforming over Rayleigh fading channels. Our results show that with perfect receiver channel state information (CSI) the TB capacity may not monotonically decrease even as the delay increases. However, if the delay is not properly considered in the channel estimation, the TB channel capacity may quickly degrade to zero as the feedback delay increases. As countermeasures, we propose a predictive channel feedback scheme to improve the feedback quality and a pilot symbol assisted channel estimation (PSA-CE) scheme to improve channel estimation quality. Analytical and numerical results show that the proposed scheme is much more robust against feedback delay than the traditional one, and can provide a capacity performance close to the case with perfect receiver CSI and without feedback delay. Our results provide new insight into the achievable performance of transmit beamforming impaired by limited and delayed feedback and receive ICE.