Compressive Downlink Channel Estimation for FDD Massive MIMO Using Weighted $l_{p}$ Minimization

We propose a weighted Ip minimization method for downlink channel estimation in frequency division duplexing massive multiple-input multiple-output (MIMO) systems. The proposed algorithm involves two stages, in which it first diagnoses the downlink supports by utilizing the channel sparsity in angular domain and angular reciprocity for uplink and downlink channels. In stage two, a weighted Ip minimization algorithm based on the diagnosed supports is used for downlink channel estimation. The diagnosed supports are used for generating the weighting matrix in the weighted Ip minimization. The restricted isometry property (RIP)-based guarantees and upper bound of the recovery error are derived. Our analytical results have the universal forms for the Ip(0 1 minimization, general I1 minimization, joint orthogonal matching pursuit, and simultaneous orthogonal matching pursuit in the medium and high signal-to-noise-rate regions.