Iterative Channel Estimation Using LSE and Sparse Message Passing for MmWave MIMO Systems

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 since there are relatively fewer paths in the mmWave channel, i.e., the channel matrix is sparse and only has a few non-zero entries. By leveraging the advantage of sparseness, we proposed an algorithm that iteratively detects the exact location and value of non-zero entries of the sparse channel matrix. The SMP is used to detect the exact location of non-zero entries of the channel matrix, while the LSE is used for estimating its value at each iteration. We also analyze the Cramer-Rao Lower Bound (CLRB), and show that the proposed algorithm is a minimum variance unbiased estimator. 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 in just 5 turbo iterations. Chau Yuen and Chongwen Huang are with the Singapore Unversity of Technology and Design, Singapore (e-mail: [email protected], Chongwen [email protected]). Lei Liu is with the State Key Lab of Integrated Services Networks, Xidian University, Xian, 710071, China (e-mail: lliu [email protected]). Sumei Sun is with the Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (ASTAR), 138632, Singapore (e-mail: [email protected]). The material in this paper will be presented in part at the conference of IEEE Global Communications Washington, DC USA, Dec. 2016 [1]. ar X iv :1 61 1. 05 65 3v 1 [ cs .I T ] 1 7 N ov 2 01 6