Nonconvex Regularized Gradient Projection Sparse Reconstruction for Massive MIMO Channel Estimation

Novel sparse reconstruction algorithms are proposed for beamspace channel estimations in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective with a nonconvex regularizer. This regularizer removes the penalties on a few large-magnitude elements from the conventional l1-norm regularizer, and thus it only forces penalties on the remaining elements that are expected to be zeros. Accurate and fast reconstructions can be achieved by performing gradient projection updates in a difference of convex functions (DC) programming framework. A double-loop algorithm and a single-loop algorithm are derived by different DC decompositions, and they have distinct computation complexities and convergence rates. An extension algorithm is further proposed to generalize the step size of the single-loop algorithm. This extension algorithm has a faster convergence rate and can achieve the same level of accuracy as the proposed double-loop algorithm. Numerical results show significant advantages of the proposed algorithms over the existing reconstruction algorithms in terms of reconstruction accuracies and runtimes.