Channel estimation for MIMO multi-relay systems using a tensor approach

In this paper, we address the channel estimation problem for multiple-input multiple-output (MIMO) multi-relay systems exploiting measurements collected at the destination only. Assuming that the source, relays, and destination are multiple-antenna devices and considering a three-hop amplify-and-forward (AF)-based training scheme, new channel estimation algorithms capitalizing on a tensor modeling of the end-to-end communication channel are proposed. Our approach provides the destination with the instantaneous knowledge of all the channel matrices involved in the communication. Instead of using separate estimations for each matrix, we are interested in a joint estimation approach. Two receiver algorithms are formulated to solve the joint channel estimation problem. The first one is an iterative method based on a trilinear alternating least squares (TALS) algorithm, while the second one is a closed-form solution based on a Kronecker least squares (KRLS) factorization. A useful lower-bound on the channel training length is derived from an identifiability study. We also show the proposed tensor-based approach is applicable to two-way MIMO relaying systems. Simulation results corroborate the effectiveness of the proposed estimators and provide a comparison with existing methods in terms of channel estimation accuracy and bit error rate (BER).