Tensor-Based Channel Estimation and Iterative Refinements for Two-Way Relaying With Multiple Antennas and Spatial Reuse

Relaying is one of the key technologies to satisfy the demands of future mobile communication systems. In particular, two-way relaying is known to exploit the radio resources in a very efficient manner. In this contribution, we consider two-way relaying with amplify-and-forward (AF) MIMO relays. Since AF relays do not decode the signals, the separation of the data streams has to be performed by the terminals themselves. For this task both nodes require reliable channel knowledge of all relevant channel parameters. Therefore, we examine channel estimation schemes for two-way relaying with AF MIMO relays. We investigate a simple Least Squares (LS) based scheme for the estimation of the compound channels as well as a tensor-based channel estimation (TENCE) scheme which takes advantage of the special structure in the compound channel matrices to further improve the estimation accuracy. Note that TENCE is purely algebraic (i.e., it does not require any iterative procedures) and applicable to arbitrary antenna configurations. Then we demonstrate that the solution obtained by TENCE can be improved by an iterative refinement which is based on the structured least squares (SLS) technique. In this application, between one and four iterations are sufficient and consequently the increase in computational complexity is moderate. The iterative refinement is optional and targeted for cases where the channel estimation accuracy is critical. Moreover, we propose design rules for the training symbols as well as the relay amplification matrices during the training phase to facilitate the estimation procedures. Finally, we evaluate the achievable channel estimation accuracy of the LS-based compound channel estimation scheme as well as the tensor-based approach and its iterative refinement via numerical computer simulations.