A limited feedback scheme for massive MIMO systems based on principal component analysis

Massive multiple-input multiple-output (MIMO) is becoming a key technology for future 5G cellular networks. Channel feedback for massive MIMO is challenging due to the substantially increased dimension of the channel matrix. This motivates us to explore a novel feedback reduction scheme based on the theory of principal component analysis (PCA). The proposed PCA-based feedback scheme exploits the spatial correlation characteristics of the massive MIMO channel models, since the transmit antennas are deployed compactly at the base station (BS). In the proposed scheme, the mobile station (MS) generates a compression matrix by operating PCA on the channel state information (CSI) over a long-term period, and utilizes the compression matrix to compress the spatially correlated high-dimensional CSI into a low-dimensional representation. Then, the compressed low-dimensional CSI is fed back to the BS in a short-term period. In order to recover the high-dimensional CSI at the BS, the compression matrix is refreshed and fed back from MS to BS at every long-term period. The information distortion of the proposed scheme is also investigated and a closed-form expression for an upper bound to the normalized information distortion is derived. The overhead analysis and numerical results show that the proposed scheme can offer a worthwhile tradeoff between the system capacity performance and implementation complexity including the feedback overhead and codebook search complexity.