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 <; p 1) minimization and the weighted Ip(0 <; p 1) minimization, and can reduce to the RIP-based analysis results for the I1 minimization and the weighted I1 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 Ip 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 Ip minimization can achieve higher estimation accuracy compared with the Ip minimization, weighted subspace pursuit, weighted I
₁
minimization, general I1 minimization, joint orthogonal matching pursuit, and simultaneous orthogonal matching pursuit in the medium and high signal-to-noise-rate regions.