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As the number of users connected to communication networks such as cellular networks and Internet of Things (IoT) networks increases, massive multiple-input multiple-output (MIMO) technique has been widely adopted to improve the spectral and energy efficiency. However, the multi-user frequency synchronization problem must be solved before channel estimation and data detection. Concurrent estimation of multiple carrier frequency offsets (CFO) at base station could be very challenging due to the coexisting and intertwined effects of multiple CFOs and uplink channels in the received signal. In this paper, we consider the frequency synchronization and channel estimation for multi-user uplink massive MIMO systems. To solve the complex multi-CFO estimation problem, we first derive the efficient joint multi-user frequency synchronization algorithm based on the maximum likelihood (ML) criterion, whose high computational complexity is reduced by the proposed Gauss-Newton method. Furthermore, we develop a multi-stage iteration update filtering (MIUF) based multi-user CFO and channel estimation method. The least squares (LS) algorithm is adopted to estimate the channels, based on which the filtering matrix is carefully designed to perform multi-user interference (MUI) suppression. Moreover, considering the effect of CFO error on the channel estimation, an iterative procedure is designed to improve MUI suppression and estimation accuracy. We also analyze the CFO estimation performance and obtain the theoretical expression of mean squared error (MSE). Finally, the effect of CFO error on channel estimation is derived. Numerical results are provided to corroborate the effectiveness of the proposed methods and their superiority over the existing ones.
Feng et al. (Wed,) studied this question.
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