A secrecy rate maximization problem for active reconfigurable intelligent surface (RIS) aided non-orthogonal multiple access networks has been studied in this paper. Assuming that the perfect channel state information is available, we aim to maximize the secrecy rate while satisfying the quality of service of the legitimate users and power budget at the base station and active RIS. Additionally, artificial noise (AN) weakens the performance gain that the wireless channel's characteristics would otherwise bring to the eavesdropper. We propose an iterative algorithm to address the non-convex nature of the objective function. Based on the penalty functions and successive convex approximation, we obtain a local-optimal solution. Simulation results show that: 1) active RIS with AN can bring higher performance gains as compared to the one with passive RIS; 2) the amplitude parameter in the reflection coefficient of active RIS is another parameter to enhance the secrecy rate.
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