In this paper, we investigate the impact of channel estimation errors on the physical layer security of an overlaying device-to-device (D2D) wireless network with an amplify-and-forward untrusted relay. An untrusted relay assists D2D communication while may capture the confidential data. Under the practical assumption of imperfect channel state information (ICSI) for the relay-to-receiver D2D link, we take into account optimal power allocation (OPA) problem to maximize the achievable secrecy rate of two different scenarios which are without jamming and with friendly jamming. Based on these OPA solutions, we study the secrecy performance of the two scenarios by driving closed-form expressions for the ergodic secrecy rate (ESR) in Rayleigh fading channel. We also calculate the high signal-to-noise ratio (SNR) slope and high SNR power offset of the optimized scenarios by finding the asymptotic ESR. Numerical results confirm the accuracy of our proposed theoretical analysis. The results also demonstrate that our proposed OPAs enhance the ESR performance compared with other power allocation techniques. Moreover, they show the effect of ICSI on the ESR such that as channel estimation error grows, the ESR performance reduction is occurred.

在本文中，我们研究了信道估计错误对具有放大转发不信任中继的覆盖设备到设备（D2D）无线网络的物理层安全性的影响。不信任的中继可以在捕获机密数据的同时协助D2D通信。在实际的中继到接收器D2D链路信道状态信息（ICSI）不完美的假设下，我们考虑了最佳功率分配（OPA）问题，以最大程度地提高两种不同场景的可实现的保密率，这两种场景均不会造成干扰且友好干扰 基于这些OPA解决方案，我们通过在Rayleigh衰落信道中驱动遍历保密率（ESR）的闭式表达式来研究这两种情况的保密性能。通过找到渐近ESR，我们还计算了优化方案的高信噪比（SNR）斜率和高SNR功率偏移。数值结果证实了我们提出的理论分析的准确性。结果还表明，与其他功率分配技术相比，我们提出的OPA增强了ESR性能。而且，它们显示了ICSI对ESR的影响，从而随着信道估计误差的增加，ESR性能会降低。