Tensor-Based Channel Estimation for 3D mmWave Massive MIMO Systems

In this paper, we investigate the channel estimation problem for three-dimensional (3D) massive multiple-input multiple-output (MIMO) system, where the base station (BS) employs a uniform cuboid array (UCA) and the mobile station (MS) is equipped with a uniform linear array (ULA). The channel between MS and BS can be formulated as a fourth-order tensor. By exploring the geometric parameter channel model, we simplify the problem to a third-order tensor decomposition problem. We further exploit the vandermonde structure of the factor matrices and introduce the Multi-mode Vandermonde Constrains Canonical Polyadic Decomposition (MVC-CPD) based channel estimation algorithm. The sufficient condition of uniqueness is analyzed. Under the uniqueness condition, the angle information can be recovered from the columns of the factor matrices. Since all the factor matrices share the same permutation ambiguity, the operation of angle pairing is not required. Then the complex gains can be obtained by Least Square (LS) method. Simulation results show that the proposed method outperforms the compressed sensing (CS) based method and the iteration based method in terms of accuracy, robustness, and stability.