To fully attain array gains of massive multiple-input multiple-output (MIMO) and its energy and spectral efficiency, deriving channel state information (CSI) at the base station (BS) side is essential. However, CSI estimation of frequency-division duplex (FDD) based massive MIMO is a challenging task owning to the required pilots, which are proportional to the number of antennas at the BS side. Therefore, the pilot overhead should be inevitably mitigated in the process of downlink channel estimation of FDD technique. In this paper, we propose a novel compressed sensing (CS) algorithm which takes advantage of correlation between the received and transmitted signals to estimate the channel with high precision, and moreover, to reduce the computational complexity imposed on the BS side. The main idea behind the proposed algorithm is to sort the specific number of maximum correlations as a common support in each iteration of the algorithm. Simulation results indicate that the proposed algorithm is capable of estimating downlink channel better than the counterpart algorithms in terms of mean square error (MSE) and the computational complexity. Meanwhile, the complexity of the proposed method linearly grows up when the number of BS antennas increases.
