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Abstract—In this paper, we generalize the iterative algorithms proposed by Khandaker to amplify-and-forward multiuser Multiple-Input Multiple-Output (MIMO) relay communication systems with the source-destination links. Compared with the conventional algorithms, where the source-destination links are ignored, the evolved Tri-Step method and Bi-Step method are derived for the new system model with the source-destination links for more spatial diversity gain. From the theoretical derivation of the Minimum Mean-Squared Error (MMSE) of the signal waveform estimation at the destination node, we show that the existence of the source-destination links bring benefits no matter how weak they are. Numerical examples demonstrate that the evolved algorithms perform much better than the original algorithms and other existing ones in terms of both MSE and Bit-Error-Rate (BER). Index Terms—MIMO relay, MMSE, multiuser, direct links Cite: Weipeng Jiang, Zhiqiang He, Xiaonan Zhang, Yunqiang Bi, and Yue Rong, "Joint Transceiver Design for Amplify-and-Forward Multiuser MIMO Relay Communication Systems with Source-Destination Links," Journal of Communications, vol. 10, no. 7, pp. 457-465, 2015. Doi: 10.12720/jcm.10.7.457-465