Intelligent reconfigurable surfaces (IRSs) have gained much attention due to their passive behavior that can be a successor to relays in many applications. However, traditional relay systems might still be a perfect choice when reliability and throughput are the main concerns in a communication system. In this work, we use an IRS along with a decode-and-forward relay to provide a possible solution to address one of the main challenges of future wireless networks which is providing reliability. We investigate a robust transceiver design against the residual self-interference (RSI), which maximizes the throughput rate under self-interference channel uncertainty-bound constraints. The yielded problem turns out to be a non-convex optimization problem, where the non-convex objective is optimized over the cone of semidefinite matrices. We propose a novel mathematical method to find a lower bound on the performance of the IRS that can be used as a benchmark. Eventually, we show an important result in which, for the worst-case scenario, IRS can be helpful only if the number of IRS elements are at least as large as the size of the interference channel. Moreover, a novel method based on majorization theory and singular value decomposition (SVD) is proposed to find the best response of the transmitters and relay against worst-case RSI. Furthermore, we propose a multi-level water-filling algorithm to obtain a locally optimal solution iteratively. We show that our algorithm performs better that the state of the art in terms of time complexity as well as robustness. For instance, our numerical results show that the acheivable rate can be increased twofold and almost sixfold, respectively, for the case of small and large antenna array at transceivers.
Keywords: IRS; MIMO; decode-and-forward; robust design; worst case.