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Maximizing the minimum rate for a full-duplex multiple-input multiple-output (MIMO) wireless network encompassing two sources and a two-way (TW) relay operating in a two-hop manner is investigated. To improve the overall performance, using a zero-forcing approach at the relay to suppress the residual self-interference arising from full-duplex (FD) operation, the underlying max-min problem is cast as an optimization problem which is non-convex. To circumvent this issue, semidefinite relaxation technique is employed, leading to upper and lower bound solutions for the optimization problem. Numerical results verify that the upper and lower bound solutions closely follow each other, showing that the proposed approach results in a close-to-optimal solution. In addition, the impact of residual self-interference upon the overall performance of the network in terms of the minimum rate is illustrated by numerical results …