  Sparse channel estimation for massive multiple-input multiple-output systems
has drawn much attention in recent years. The required pilots are substantially
reduced when the sparse channel state vectors can be reconstructed from a few
numbers of measurements. A popular approach for sparse reconstruction is to
solve the least-squares problem with a convex regularization. However, the
convex regularizer is either too loose to force sparsity or lead to biased
estimation. In this paper, the sparse channel reconstruction is solved by
minimizing the least-squares objective with a nonconvex regularizer, which can
exactly express the sparsity constraint and avoid introducing serious bias in
the solution. A novel algorithm is proposed for solving the resulting nonconvex
optimization via the difference of convex functions programming and the
gradient projection descent. Simulation results show that the proposed
algorithm is fast and accurate, and it outperforms the existing sparse recovery
algorithms in terms of reconstruction errors.
