Precoder design for MIMO relay networks with direct link and decision feedback equalisation

In this letter we derive the source and relay precoders for a multiple-input multiple-output (MIMO) relay system with zero-forcing (ZF) decision feedback equalisation (DFE) when a direct link exists between the source and destination. Assuming full channel state information (CSI) is available at each node in the network, the processors are optimised for a large class of objective functions subject to the ZF condition and average power constraints at both the source and relay terminals. Simulation results show that the proposed design outperforms existing techniques in terms of bit error ratio (BER).