Secure Integrated Sensing and Communication Downlink Beamforming: A Semidefinite Relaxation Approach With Tightness Guaranteed

Integrated sensing and communication (ISAC) is considered as a key solution toward spectrum congestion in future generations of wireless system. On the other hand, physical-layer security has recently regained attentions as network-layer encryption is becoming more challenging in 5G and beyond. This paper studies a multiuser MIMO beamforming design for ISAC with physical-layer security. Specifically, we consider a power minimization problem with signal-to-interference-plus-noise ratio constraints and with a Cramér-Rao-based sensing performance constraint. The problem is non-convex, but can in principle be approximated by semidefinite relaxation (SDR) which is a convex optimization-based scheme. The main contribution of this paper lies in showing that, with a nearly harmless modification, the problem can be exactly solved by SDR. Prior works showed that the same ISAC problem without physical-layer security can be solved by SDR, but the proof method therein appears to be inapplicable to our secure ISAC problem. Numerical results are presented to illustrate the efficiency of our SDR for solving the secure ISAC problem.