Cooperative Double-IRS Aided Proactive Eavesdropping

Proactive eavesdropping was used recently to efficiently intercept a suspicious wireless communication link, by jamming the suspicious destination node. However, While jamming helps weaken the suspicious link, it does not improve the eavesdropping channel from the source node to the legitimate eavesdropper. This work proposes to use intelligent reflecting surfaces (IRS) to enhance proactive eavesdropping, by jointly affecting both the suspicious and eavesdropping channels, and is the first to employ the cooperative passive beamforming in the double-IRS aided monitoring system. By considering the cooperative two single-reflection links and especially the double-reflection link, we jointly design the passive phase shift matrices of double IRSs to optimize the eavesdropping capability. Due to the coupled variables caused by double-IRS cooperation and the intractable unit modulus constraints of IRS elements, the non-convex optimization problem is difficult to solve. We first divide the problem into two subproblems, and apply the idea of minimization majorization to make each subproblem convex. We obtain the solution of reflective coefficient matrix in closed form, and then propose an alternating algorithm with low complexity to obtain the Karush-Kuhn-Tucker (KKT) solution. Finally, simulation results are presented to demonstrate the effectiveness of cooperative passive beamforming design over the traditional single-IRS and jamming assisted eavesdropping schemes.