We propose an iterative channel estimation algorithm based on the Least
Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the
Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave
MIMO are approximately modeled as a Bernoulli-Gaussian distribution and the
channel matrix is sparse with only a few non-zero entries. By leveraging the
advantage of sparseness, we propose an algorithm that iteratively detects the
exact locations and values of non-zero entries of the sparse channel matrix. At
each iteration, the locations are detected by the SMP, and values are estimated
with the LSE. We also analyze the Cram\'er-Rao Lower Bound (CLRB), and show
that the proposed algorithm is a minimum variance unbiased estimator under the
assumption that we have the partial priori knowledge of the channel.
Furthermore, we employ the Gaussian approximation for message densities under
density evolution to simplify the analysis of the algorithm, which provides a
simple method to predict the performance of the proposed algorithm. Numerical
experiments show that the proposed algorithm has much better performance than
the existing sparse estimators, especially when the channel is sparse. In
addition, our proposed algorithm converges to the CRLB of the genie-aided
estimation of sparse channels with only five turbo iterations.

本文提出了一种基于迭代通道估计算法的毫米波 MIMO 系统的最小二乘估计（LSE）和稀疏信息传递（SMP）算法，用于检测具有仅少量非零条目的稀疏通道矩阵的位置和值，通过使用高斯近似进行信息密度的密度演化以简化算法的分析，并说明所提出的算法是一种最小方差无偏估计器。