This study examines the linear source and relay precoder and destination combiner design for multiple-input multipleoutput full-duplex (FD) relay communication systems. The effect of the residual interference due to the imperfect loop interference cancellation is considered in the design. Two design algorithms are proposed to minimise the mean squared error of the received signal at the destination. The first is a tri-step alternating iterative algorithm while the second is a bi-step iterative

more »

... lgorithm, which has lower complexity and performance comparable to that of the first algorithm. The convergence of these algorithms is evaluated. Results are presented, which show that the proposed FD relay system can provide approximately double the achievable rate of the corresponding half-duplex system if the residual interference is not high.