The problem of designing multiple-input-multiple-output (MIMO) relay for multipoint to multipoint communication in wireless networks has been dealt with by considering the fact that only the imperfect channel state information (CSI) is available at the MIMO relay. In particular, assuming that the second-order terms of the uncertainties of the source-relay and relay-destination channels are negligible, we design an amplify-and-forward (AF) MIMO relay that provides robustness against channel uncertainties. In our proposed robust method, the objective is to design the MIMO relay in which the worst-case relay transmit power is minimized by keeping the worst-case signal-to-interference-and-noise ratio (SINR) for all destinations above a certain threshold value. This paper shows that the aforementioned problem is nonconvex but it can be relaxed to a convex problem consisting of second-order cone (SOC) and semidefinite cone constraints using the semidefinite relaxation technique. The optimal solution of the relaxed problem is utilized to generate the best approximate solution of the original nonconvex problem using the well-known randomization technique. Computer simulations verify the robustness of the proposed MIMO relay when compared to the nonrobust MIMO relay.Index Terms-Channel state information, channel uncertainty and convex optimization, Robust MIMO relay, Worst-case performance optimization.

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