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Accurate channel state information (CSI) is extremely crucial to realize high-accurate hybrid precoding, in millimeter wave communication systems. In order to improve the CSI estimation performance, several traditional channel estimators have been developed by exploiting the sparse or low-rank property, whilst they bring huge channel training overhead and computational complexity. In this work, based on jointly sparse and low-rank property of massive multiple input multiple output (MIMO) channel, one non-convex mmWave channel estimation problem is formulated and a novel scheme to acquire one accurate CSI estimation result with greatly reduced training overhead is proposed. Specifically, the non-convex problem is reformulated as two simple sub-problems, by exploiting the alternating direction method of multipliers (ADMM) technique. Based on the low-rank characteristic, one fast gradient descent matrix completion algorithm is developed to accurately solve the first sub-problem. On this basis, the compressed sensing (CS) technique to acquire the accurate CSI estimation matrix is further utilized. Numerical simulation validates that the method could achieve the much higher channel estimation accuracy, yet only incurs the lower overhead compared with the traditional scheme.

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