Downlink CSI Sensing from Heterogeneous User Feedbacks: A Constrained Phase Retrieval Approach

The paper investigates the downlink channel state information (DL CSI) sensing in 5G heterogeneous networks consisting of user equipment (UE) with different CSI feedback capabilities. The goal is to enhance the DL CSI accuracy at the base station (BS) for the UE that can only afford low-resolution CSI feedback with Type I codebook. The existing works have shown that such a task can be accomplished by solving a phase retrieval (PR) problem at the BS based on the precoding matrix indicator and channel quality indicator feed-backs. However, they require a large number of feedbacks to achieve a high CSI accuracy. In this paper, we propose a new CSI sensing scheme that can significantly reduce the feedback overhead. The key ingredients are exploiting the spatial consistency of wireless channels so that the problem dimension can be considerably reduced by utilizing high-resolution CSI feedbacks of nearby UEs, and the introduction of inequality constraints that characterize the feasible region of the target CSI. An efficient primal-dual algorithm is proposed to solve the formulated constrained PR problem. Simulation results demonstrate that the proposed scheme can achieve promising performance and greatly outperform the existing methods.