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In this work, we address the problem of a joint robust transmission, reflection and reception strategy design at an active reconfigurable intelligent surface (RIS)-assisted underlay multiple input multiple output (MIMO) cognitive radio networks in which a secondary transmitter serves multiple secondary receivers simultaneously. As such, we study the impact of imperfection in channel state information (CSI) at the secondary transmitter following a norm-bounded error model. A sum mean squared error (MSE) minimization problem is formulated by jointly optimizing the transmit beamforming matrix (BFM) at the secondary transmitter, the linear reception filters (LRF) at the secondary receivers and the reflection coefficient matrix (RCM) at the RIS subject to the constraints of available transmission power at the secondary transmitter, maximum allowed interference power towards the primary receiver and the permissible amplification range at each RIS element. Due to the coupled nature of the BFM, LRF and RCM variables, the formulated problem is non-convex and, thus, cannot be solved using conventional optimization methods. As a result, we propose an alternating optimization (AO) based iterative algorithm that determines the optimal BFM, LRF and RCM using semidefinite programming and inner approximation methods with guaranteed convergence. We also discuss the impact of the limited power budget at active RIS on the performance of the considered network. We present simulation-based numerical results to validate the efficacy and robustness of the proposed algorithm. Moreover, we also highlight the superiority of the use of the active RIS over passive RIS in the considered communication network.
Allu et al. (Tue,) studied this question.