Reduced-complexity Krylov subspace methods for large-scale MIMO channel estimation

Large-scale multiple-input multiple-output (MIMO) system has been intensively studied for wireless communications. Channel estimation is one of the challenges in large-scale MIMO. Direct implementation of the minimum mean squared error (MMSE) channel estimator has a cubic computational complexity due to the operation of matrix inverse. Iterative Krylov subspace methods can be applied to reduce the complexity to quadratic, which is dominated by the matrix-vector products involved. In this paper, we apply conjugate gradient (CG) method and preconditioning to improve the convergence rate and reduce complexity. The computational complexities are analyzed, showing that the preconditioned CG (PCG) schemes have significantly lower complexities compared to several alternative Krylov subspace schemes.