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In this paper, we investigate the energy efficiency (EE) problem underreconfigurable intelligent surface (RIS)-aided secure cell-free networks, wheremultiple legitimate users and eavesdroppers (Eves) exist. We formulate amax-min secure EE optimization problem by jointly designing the distributedactive beamforming and artificial noise at base stations as well as the passivebeamforming at RISs under practical constraints. To deal with it, we firstdivide the original optimization problem into two sub-ones, and then propose aniterative optimization algorithm to solve each sub-problem based on thefractional programming, constrained convex-convex procedure (CCCP) andsemi-definite programming (SDP) techniques. After that, these two sub-problemsare alternatively solved until convergence, and the final solutions areobtained. Next, we extend to the imperfect channel state information of theEves' links, and investigate the robust SEE beamforming optimization problem bybringing the outage probability constraints. Based on this, we first transformthe uncertain outage probability constraints into the certain ones by thebernstein-type inequality and sphere boundary techniques, and then propose analternatively iterative algorithm to obtain the solutions of the originalproblem based on the S-procedure, successive convex approximation, CCCP and SDPtechniques. Finally, the simulation results are conducted to show theeffectiveness of the proposed schemes.

Robust Security Energy Efficiency Optimization for RIS-Aided Cell-Free Networks with Multiple Eavesdroppers