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Two new precoding schemes based on the minimum mean-square error (MMSE) criterion for amplify-and-forward MIMO relay networks with quality-of-service (QoS) requirements are proposed. In the optimal joint source and relay precoding (OJSRP) scheme, primal decomposition technique is employed to decompose the non-convex optimization problem into a sub-problem and a master problem, which are convex and solvable. To relax the computation complexity of the OJSRP scheme, the suboptimal relay only precoding (SROP) scheme, which assumes equal power distribution over source antennas and has closed form solution, is also studied. Our numerical results show that both the minimum mean-square (MSE) performance and the capacity achieved by the two proposed schemes improve with the increase in signal-to-noise- ratio (SNR). Furthermore, OJSRP scheme has better MSE performance and capacity than SROP scheme. Finally, given a total transmission power, it is found that there exists an optimal power distribution over the source and the relay to achieve the best MSE performance and capacity. This indicates that transmission power should be distributed delicately over the source and the relay to optimize the resource utilization.