Channel estimation is essential for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems with hybrid precoding. However, accurate channel estimation is a challenging task as the number of antennas is huge, while the number of RF chains is limited. Traditional methods of compressed sensing for channel estimation lead to serious loss of accuracy due to channel angle quantization. In this paper, we propose a new iterative reweight-based log-sum constraint channel estimation scheme. Specifically, we exploit the structure sparsity of the mmWave channels by formulating the channel estimation problem as an objective optimization problem. We utilize the log-sum as a constraint, via optimizing an objective function through the gradient descent method, the proposed algorithm can iteratively move the channel estimated angle-ofarrivals (AOAs) and angle-of-departures (AODs) towards the optimal solutions, and finally improve the angle estimation performance significantly. In addition, to ensure the accuracy of channel estimation, we introduce a dynamic regularization factor to control the tradeoff between the channel sparsity and the data fitting error. Numerical experiments demonstrate that the proposed algorithm achieves better convergence behavior than conventional sparse signal recovery solutions.

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