On the Minimum Differential Feedback for Time-Correlated MIMO Rayleigh Block-Fading Channels

Abstract

In this paper, we consider a general multiple input multiple output (MIMO) system with channel state information (CSI) feedback over time-correlated Rayleigh block-fading channels. Specifically, we first derive the closed-form expression of the minimum differential feedback rate to achieve the maximum erdodic capacity in the presence of channel estimation errors and quantization distortion at the receiver. With the feedback-channel transmission rate constraint, in the periodic feedback system, we further investigate the relationship of the ergodic capacity and the differential feedback interval, and we find by theoretical analysis that there exists an optimal differential feedback interval to maximize ergodic capacity. Finally, analytical results are verified through simulations in a practical periodic differential feedback system using Lloyd's quantization algorithm.

On Optimizing Feedback Interval for Temporally Correlated MIMO Channels With Transmit Beamforming and Finite-Rate Feedback

“…The recursive function φ is defined in (15). The integral in (28) can be evaluated by any numerical method.…”

“…2 m+n+1 . (63) Adding the last two terms in (63) gives (15). The initial conditions are obtained by evaluating the double integral in (60).…”

“…The optimal feedback period for coordinated multi-point (COMP) systems was considered in [14] where channels are also modeled as a first-order Gauss-Markov process. In [15], the minimum feedback rate of a differential feedback scheme was analyzed. The authors in [16] have proposed a differential codebook, which is rotated according to channel correlation, feedback rate, and the previous transmit beamforming.…”