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The problem of channel estimation, in largescale multiple input single output orthogonal frequency division multiplexing (MISO-OFDM) systems, is studied in this paper. In order to take full advantage of the sparse property, an intermediate random vector is introduced to control the sparsity of the estimation of the channel state information (CSI) based on the maximum a posteriori estimator. After carefully designing the prior probability density function (PDF) of the intermediate random vector and the unknown CSI conditioned on it, the sparse optimization problem over the CSI is constructed. The Bayesian inference theory is applied to relax the optimization problem by calculating an approximated PDF with simpler form. After that, variational message-passing (VMP) is used to obtain the solution in iterative analytical form. Furthermore, block sparse structure is implemented to improve the performance. Simulation results demonstrate the merit of proposed algorithm over the traditional ones.

Sparse Channel Estimation for Large-Scale MISO-OFDM System - a Bayesian VMP Approach