Robust Multi-Branch Tomlinson-Harashima Source and Relay Precoding Scheme in Nonregenerative MIMO Relay Systems

This paper investigates a robust Tomlinson-Harashima precoding (THP) design for multiple-input multiple-output (MIMO) relay systems based on a multi-branch (MB) strategy. The proposed scheme employs a parallel MB structure at the source according to different pre-stored ordering patterns. For each parallel branch, the robust nonlinear transceiver design consists of a TH precoder at the source along with a linear precoder at the relay and a linear minimum-mean-squared-error (MMSE) receiver at the destination. By taking the channel uncertainties into account, the source and relay precoders are jointly optimised to minimise the MSE. We can finally use an iterative method to obtain the solution for the relay and the source precoders via Karush-Kuhn-Tucker (KKT) conditions. An appropriate selection rule is developed to choose the nonlinear transceiver corresponding to the best branch for data transmission. Simulation results demonstrate that the proposed MB-THP scheme outperforms existing transceiver designs with perfect and imperfect channel state information (CSI).