基于Beckmann分布的星间光通信最优输入信号概率分布

Optimum Signal Input Probability Distribution for Inter-Satellite Optical Communications Based on Beckmann Distribution

针对瞄准误差影响下的星间光通信非对称信道,存在最优输入信号概率分布使链路的互信息达到最大,考虑瞄准误差服从Beckmann分布,结合接收天线孔径大小、波束宽度和瞄准误差分布参数,给出了星间光通信的信道矩阵,建立了互信息优化模型,并利用拉格朗日乘数法对模型进行了求解,得出了使互信息最大时的输入信号概率分布的闭合表达式。通过数值仿真,给出了最优输入信号概率分布、信道容量和互信息差值随着归一化判决阈值、光束束腰半径以及瞄准误差分布参数的数值变化关系。仿真分析结果表明:最优输入信号概率分布下输入信号与输出信号之间的互信息值要明显高于等概率分布时。利用数值仿真的结果,可在明确瞄准误差分布规律的基础上,选择最优的信源输入,使星间光通信信道实现最大的信息传输能力。

In the light of the asymmetric channel of inter-satellite optical communication subject to pointing errors, an optimal signal input probability distribution can be found to maximize the mutual information of the link. Considering the aperture size of receiving antenna, beam width and the parameters of pointing errors distribution, the channel matrix of inter-satellite optical communication is given, and the optimization model of mutual information is established, when the pointing errors obey Beckmann distribution. The Lagrange multiplier method is used to solve the model, and the closed expression of the signal input probability distribution is obtained when the mutual information is maximized. Through numerical simulation, the optimal signal input probability distribution, channel capacity and the difference of mutual information vary with the normalized decision threshold, beam width and the parameters of pointing errors distribution are analyzed numerically. The simulation results show that the mutual information between input signal and output signal under the optimal signal input probability distribution is obviously higher than that under the equal probability distribution. Using the results of numerical simulation, the optimal source input can be selected on the basis of known distribution of pointing errors, so that the inter-satellite optical communication channel can achieve the maximum information transmission capacity.