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This paper investigates the downlink channel state information (CSI) sensingin 5G heterogeneous networks composed of user equipments (UEs) with differentfeedback capabilities. We aim to enhance the CSI accuracy of UEs only affordingthe low-resolution Type-I codebook. While existing works have demonstrated thatthe task can be accomplished by solving a phase retrieval (PR) formulationbased on the feedback of precoding matrix indicator (PMI) and channel qualityindicator (CQI), they need many feedback rounds. In this paper, we propose anovel CSI sensing scheme that can significantly reduce the feedback overhead.Our scheme involves a novel parameter dimension reduction design by exploitingthe spatial consistency of wireless channels among nearby UEs, and aconstrained PR (CPR) formulation that characterizes the feasible region of CSIby the PMI information. To address the computational challenge due to thenon-convexity and the large number of constraints of CPR, we develop atwo-stage algorithm that firstly identifies and removes inactive constraints,followed by a fast first-order algorithm. The study is further extended tomulti-carrier systems. Extensive tests over DeepMIMO and QuaDriGa datasetsshowcase that our designs greatly outperform existing methods and achieve thehigh-resolution Type-II codebook performance with a few rounds of feedback.

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