Abstract
This paper investigates uplink channel estimation for massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with uniform planar array (UPA) antennas at the base station (BS). We first establish a triple beam-based channel model using sampled steering vectors. Based on the presented channel model, we further develop a three-dimensional (3D) Markov random field (MRF) probability model to capture the structured channel sparsity. Then constrained Bethe free energy (BFE) minimization is introduced to provide a systematic theoretical framework for message passing. Under this framework, we derive a structured hybrid message passing (SHMP) algorithm to address the channel estimation problem. The proposed algorithm can significantly improve the estimation accuracy by exploiting the clustered sparse structure of channels with low complexity. Moreover, aiming at the fine factors of the triple beam-based channel model and the coupling parameter of the 3D-MRF sparsity model, we analyze the effect of their different settings in the numerical simulation. Finally, extensive simulation results verify the superiority of the proposed SHMP algorithm.
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