Does frequent low resolution feedback outperform infrequent high resolution feedback for multiple antenna beamforming systems?

Multiple antenna systems that adapt to the channel conditions are known to provide numerous rate and reliability benefits. In frequency division duplexing, the transmitter typically learns about the channel conditions using a small amount of feedback (called limited feedback) sent on the reverse link. While feedback is well studied, there has been only limited work addressing how feedback techniques should be modified depending on the amount of mobility. This paper concerns a signaling scheme for limited feedback multiple antenna wireless communications taking the temporal correlation into account during feedback design. We refer to this as using an adaptive feedback period (AFP) scheme. In the AFP scheme, the transmitter and receiver reuse the past channel state information (CSI) as side information. Feedback to be used for several channel uses is sent from the receiver to the transmitter using a predetermined feedback update period. The feedback update period is determined by characterizing the temporal correlation statistic, so that the proposed AFP scheme outperforms the traditional limited feedback approach, which we refer to as the minimal feedback period (MFP) scheme. To measure the performance, the average effective SNR is considered. Bounds on the feedback update period, correlation coefficient, and feedback rate needed for the AFP scheme to outperform the MFP scheme are derived. Moreover, criteria to initiate the control of the feedback update period are obtained. Results on the average effective SNR are used to develop bounds on the feedback update period using the capacity loss. It is also shown that in the large system limit the feedback update periods required for both the average effective SNR and capacity loss converge to the same bound. These results verify that infrequent high resolution feedback is sometimes preferable to frequent low resolution feedback.