Channel Estimation for Movable-Antenna MIMO Systems Via Tensor Decomposition

In this letter, we investigate the channel estimation problem for MIMO wireless communication systems with movable antennas (MAs) at both the transmitter (Tx) and receiver (Rx). To achieve high channel estimation accuracy with low pilot training overhead, we propose a tensor decomposition-based method for estimating the parameters of multi-path channel components, including their azimuth and elevation angles, as well as complex gain coefficients, thereby reconstructing the wireless channel between any pair of Tx and Rx MA positions in the Tx and Rx regions. First, we introduce a two-stage Tx-Rx successive antenna movement pattern for pilot training, such that the received pilot signals in both stages can be expressed as a third-order tensor. Then, we obtain the factor matrices of the tensor via the canonical polyadic decomposition, and thereby estimate the angle/gain parameters for enabling the channel reconstruction between arbitrary Tx/Rx MA positions. In addition, we analyze the uniqueness condition of the tensor decomposition, which ensures the complete channel reconstruction between the whole Tx and Rx regions based on the channel measurements at only a finite number of Tx/Rx MA positions. Finally, simulation results are presented to evaluate the proposed tensor decomposition-based method as compared to existing methods, in terms of channel estimation accuracy and pilot overhead.