  In this paper, we investigate the beam domain statistical channel state
information (CSI) estimation for the two dimensional (2D) beam based
statistical channel model (BSCM) in massive MIMO systems.The problem is to
estimate the beam domain channel power matrices (BDCPMs) based on multiple
receive pilot signals. A receive model shows the relation between the
statistical property of the receive pilot signals and the BDCPMs is derived
from the 2D-BSCM. On the basis of the receive model,we formulate an
optimization problem with the Kullback-Leibler (KL) divergence. By solving the
optimization problem, a novel method to estimate the statistical CSI without
involving instantaneous CSI is proposed. The proposed method has much lower
complexity than the MMV focal underdetermined system solver (M-FOCUSS)
algorithm. We further reduce the complexity of the proposed method by utilizing
the circulant structures of particular matrices in the algorithm. We also
showed the generality of the proposed method by introducing another
application. Simulations results show that the proposed method works well and
bring significant performance gain when used in channel estimation.
