This study evaluates the performance of a secure ground-to-satellite free-space optical (FSO) system using a bipolar pulse amplitude modulation over modulated gamma fading channel. A closed-form expression is derived for the joint probability of a satellite-based continuous-variable quantum key distribution (CV-QKD) protocol that uses dual-threshold detection. Furthermore, to study the system behaviour, closed-form expressions for quantum bit-error-rate (QBER) and quantum bit-discard rate (QBDR) are given. The accuracy of the proposed derivations is validated using Monte-Carlo simulations and numerical analysis. The dual-threshold range is optimised to satisfy design criteria in terms of QBER and QBDR. Finally, a sufficient selection of transmitter and receiver parameters ensures a guarantee of system security. Additionally, the information capacity is maximised by a scaling coefficient of .

中文翻译：

---

CV-QKD协议的地对地FSO系统性能评估和安全性分析

这项研究评估了在调制伽玛衰落信道上使用双极性脉冲幅度调制的安全地对卫星自由空间光学（FSO）系统的性能。对于使用双阈值检测的基于卫星的连续变量量子密钥分配（CV-QKD）协议的联合概率，得出了一种封闭形式的表达式。此外，为了研究系统性能，给出了量子误码率（QBER）和量子丢包率（QBDR）的闭式表达式。使用蒙特卡洛模拟和数值分析验证了所提出的推导的准确性。优化了双阈值范围，以满足QBER和QBDR的设计标准。最后，充分选择发送器和接收器参数可确保系统安全性。另外， 。