Compressive Downlink Channel Estimation for FDD Massive MIMO using Weighted lp Minimization

We propose a weighted $l_{p}$ 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 $l_{p}$ 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 $l_{p}$ 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 $l_{p} (0 minimization and the weighted $l_{p} (0 minimization, and can reduce to the RIP-based analysis results for the $l_{1}$ minimization and the weighted $l_{1}$ minimization which have been discussed in the previous literature. The discussion on the weight selection is also presented which is based on the derived upper bound. Simulations show that the weighted $l_{p}$ minimization is preferred when the correct percentage of the estimated support is more than 0.5. For the channel estimation, the proposed method with support diagnosis and the weighted $l_{p}$ minimization can achieve higher estimation accuracy compared with the $l_{p}$ minimization, weighted subspace pursuit, weighted $l_{1}$ minimization, general $l_{1}$ minimization, joint orthogonal matching pursuit, and simultaneous orthogonal matching pursuit in the medium and high signal-to-noise-rate regions.