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 meas
urements. 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.
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This regularizer remove
s 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 within the framework of difference of convex functions (DC) programming. A double-loop algorithm and a single-loop algorithm are proposed via different DC decompositions, and these two algorithms have distinct computation complexities and convergence rates. Then, an extension algorithm is further proposed by designing the step sizes of the single-loop algorithm. The extension algorithm has a faster convergence rate and can achieve approximately the same level of accuracy as the proposed double-loop algorithm. Numerical results show significant advantages of the proposed algorithms over existing reconstruction algorithms in terms of reconstruction accuracies and runtimes. Compared to the benchmark channel estimation techniques, the proposed algorithms also achieve smaller mean squared error and higher achievable spectral efficiency.
A major challenge to implement the compressed sensing method for channel state information (CSI) acquisition lies in the design of a well-performed measurement matrix to reduce the dimension of sparse channel vectors. The widely adopted randomized me
asurement matrices drawn from Gaussian or Bernoulli distribution are not optimal. To tackle this problem, we propose a fully data-driven approach to optimize the measurement matrix for beamspace channel compression, and this method trains a mathematically interpretable autoencoder constructed according to the iterative solution of sparse recovery. The obtained measurement matrix can achieve near perfect CSI recovery with fewer measurements, thus the feedback overhead can be substantially reduced.
