In this paper, we address the problem of distributed power allocation in a $K$ user fading multiple access wiretap channel, where global channel state information is limited, i.e., each user has knowledge of their own channel state with respect to Bob and Eve but only knows the distribution of other users' channel states. We model this problem as a Bayesian game, where each user is assumed to selfishly maximize his average \emph{secrecy capacity} with partial channel state information. In this work, we first prove that there is a unique Bayesian equilibrium in the proposed game. Additionally, the price of anarchy is calculated to measure the efficiency of the equilibrium solution. We also propose a fast convergent iterative algorithm for power allocation. Finally, the results are validated using simulation results.

翻译：本文针对K用户衰落多址接入窃听信道中的分布式功率分配问题展开研究，其中全局信道状态信息受限——即每个用户仅知晓自身与合法接收者及窃听者间的信道状态，但对其他用户的信道状态仅知其分布信息。我们将该问题建模为贝叶斯博弈，假设每个用户在部分信道状态信息条件下自私地最大化其平均保密容量。首先证明所提博弈存在唯一的贝叶斯均衡，进而通过计算无政府态价格评估均衡解的效率。此外，提出一种快速收敛的迭代功率分配算法，最终通过仿真结果验证了算法有效性。