EMF-Constrained Artificial Noise for Secrecy Rates with Stochastic Eavesdropper Channels

An information-theoretic confidential communication is achievable if the eavesdropper has a degraded channel compared to the legitimate receiver. In wireless channels, beamforming and artificial noise can enable such confidentiality. However, only distribution knowledge of the eavesdropper channels can be assumed. Moreover, the transmission of artificial noise can lead to an increased electromagnetic field (EMF) exposure, which depends on the considered location and can thus also be seen as a random variable. Hence, we optimize the $\varepsilon$-outage secrecy rate under a $\delta$-outage exposure constraint in a setup, where the base station (BS) is communicating to a user equipment (UE), while a single-antenna eavesdropper with Rayleigh distributed channels is present. Therefore, we calculate the secrecy outage probability (SOP) in closed-form. Based on this, we convexify the optimization problem and optimize the $\varepsilon$-outage secrecy rate iteratively. Numerical results show that for a moderate exposure constraint, artificial noise from the BS has a relatively large impact due to beamforming, while for a strict exposure constraint artificial noise from the UE is more important.