Design and Performance Analysis of Wireless Legitimate Surveillance Systems with Radar Function

Integrated sensing and communication (ISAC) has recently been considered as a promising approach to save spectrum resources and reduce hardware cost. Meanwhile, as information security becomes increasingly more critical issue, government agencies urgently need to legitimately monitor suspicious communications via proactive eavesdropping. Thus, in this paper, we investigate a wireless legitimate surveillance system with radar function. We seek to jointly optimize the receive and transmit beamforming vectors to maximize the eavesdropping success probability which is transformed into the difference of signal-to-interference-plus-noise ratios (SINRs) subject to the performance requirements of radar and surveillance. The formulated problem is challenging to solve. By employing the Rayleigh quotient and fully exploiting the structure of the problem, we apply the divide-and-conquer principle to divide the formulated problem into two subproblems for two different cases. For the first case, we aim at minimizing the total transmit power, and for the second case we focus on maximizing the jamming power. For both subproblems, with the aid of orthogonal decomposition, we obtain the optimal solution of the receive and transmit beamforming vectors in closed-form. Performance analysis and discussion of some insightful results are also carried out. Finally, extensive simulation results demonstrate the effectiveness of our proposed algorithm in terms of eavesdropping success probability.