Millimeter wave (mmWave) frequency spectrum offers orders of magnitude greater spectrum to mitigate the severe spectrum shortage in conventional cellular bands. To overcome the high propagation loss in the mmWave band, massive multiple-input and multiple-output (MIMO) can be adopted at both transmitter and receiver to provide large beamforming gains. At the same time, hybrid architecture is applied to reduce the huge power consumption caused by devices operating at radio frequency (RF). However, because of the hybrid architecture and large number of antennas, it is hard to obtain the channel state information (CSI) which is crucial for obtaining desirable beamforming gains. Off-grid error and sparsity pattern (SP) estimation error are two main limiting factors of the performance of most existing compressive sensing (CS) based channel estimation (CE) algorithms. Off-grid error presents when the true angle does not lie on the discretized angle grid of mmWave channel in the spatial domain. In this paper, we first propose a fast Bayesian matching pursuit method with ‘virtual sparsity’ to improve the accuracy of SP estimation and name it as the improved Bayesian matching pursuit (IBMP). Then an enhanced algorithm, named off-grid IBMP (OG-IBMP), is developed to mitigate the off-grid problem, followed by a theoretical analysis of OG-IBMP. This method iteratively updates the selected grid points and updates the corresponding parameters based on the maximum a posteriori (MAP) criterion. Numerical simulations are performed to validate our theoretical analysis and evaluate the performance of the proposed method. Compared to other existing methods, the results show that our proposed OG-IBMP algorithm greatly reduces the off-grid error and significantly enhances the accuracy of the SP estimation with low computational complexity.
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