An ESPRIT-Based Supervised Channel Estimation Method Using Tensor Train Decomposition for mmWave 3-D MIMO-OFDM Systems

This paper focuses on the downlink supervised channel estimation problem for the millimeter wave three-dimensional multiple-input multiple-output orthogonal frequency division multiplexing (mmWave 3D MIMO-OFDM) systems, where both the transmitter and the receiver are equipped with uniform rectangular arrays (URAs). Based on the sparse scattering nature, the mmWave channel is modeled as a low-rank higher-order tensor. By formulating the channel and the received training signal as tensors, a fast ESPRIT-based Vandermonde-structured tensor decomposition method is proposed to estimate the channel parameters involving angles of arrival and departure (AoAs/AoDs), delays and path gains. In specific, we first establish the relationship of the tensor ranks between the tensor train (TT) model and the higher-order tensor CANDECOMP/PARAFAC (CP) signal model. Then the TT decomposition is used to estimate the signal subspace and derive the shift invariance equation, which exploits the higher-order tensor low-rankness of the signal and the Vandermonde structure in the frequency domain. Based on the derived analytical estimation errors, theoretical justifications are provided to unveil the advantage of using TT decomposition. Moreover, we extend the proposed method in an iterative manner to pursue higher accuracy. According to our simulation results, compared with the state-of-the-art, the proposed method achieves higher estimation accuracy on both the channel parameters and the entire channel. In addition, up to 87% of computing time can be saved in comparison to the current best iterative algorithm in the experiments.