On the Quantization and Prediction for Precoded MIMO with Delayed Limited Feedback

In closed-loop precoded multiple-input multiple-output (MIMO) systems, the representative quantized channel state information (CSI) usually becomes outdated before its actual use at the transmitter due to the delayed feedback. In this paper, by exploiting the differential geometric properties of the Grassmannian manifold, we invoke the use of Grassmannian subspace predictive coding (GSPC) to compensate for this feedback delay. More specifically, a novel limited feedback strategy is presented which consists of a two-stage optimization process at the receiver. The first-stage optimization is accomplished by the quantization, which is custom designed as a function of the optimally predicted CSI under the framework of GSPC; after the first-stage codeword selection, the second-stage optimization is performed by optimizing the prediction on the Grassmannian manifold. We show by simulations that, the proposed encoding/decoding algorithm exhibits promised system performance over the existing prediction methods, for both spatial multiplexing and transmit beamforming MIMO, under the same amount of feedback bits.