The downlink channel covariance matrix (CCM) acquisition is the key step for
the practical performance of massive multiple-input and multiple-output (MIMO)
systems, including beamforming, channel tracking, and user scheduling. However,
this task is challenging in the popular frequency division duplex massive MIMO
systems with Type I codebook due to the limited channel information feedback.
In this paper, we propose a novel formulation that leverages the structure of
the codebook and feedback values for an accurate estimation of the downlink
CCM. Then, we design a cutting plane algorithm to consecutively shrink the
feasible set containing the downlink CCM, enabled by the careful design of
pilot weighting matrices. Theoretical analysis shows that as the number of
communication rounds increases, the proposed cutting plane algorithm can
recover the ground-truth CCM. Numerical results are presented to demonstrate
the superior performance of the proposed algorithm over the existing benchmark
in CCM reconstruction