基于Beckmann分布的星间光通信最优输入信号概率分布
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摘要
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.
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.
引文
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[18] SONG T,WANG Q,WU M W,et al.Impact of Pointing Errors on the Error Performance of Inter-Satellite Laser Communications[J].Journal of Lightwave Technology,2017,35(14):3082-3091.
[2] 韩立强,游雅晖.大气湍流及瞄准误差联合效应下自由空间通信的性能[J].光学学报,2014,34(11):1106005.HAN L Q,YOU Y H.Performance of Free Space Optical Communication with Combined Effects from Atmospheris Turbulence and Pointing Erros[J].Acta Optica Sinica,2014,34(11):1106005.(in Chinese)
[3] SANDALIDIS H G.Optimization Models for Misalignment Fading Mitigation in Optical Wireless Links[J].IEEE Communications Letters,2008,12(5):395-397.
[4] FARID A A,HRANILOVIC S.Outage Capacity Optimization for Free-Space Optical Links with Pointing Errosrs[J].Journal of Lightwave Technology,2007,25(7):1702-1710.
[5] TOYOSHIMA M,JONO T,NAKAGAWA K,et al.Optimum Divergence Angle of a Gaussian Beam Wave in the Presence of Random Jitter in Free-Space Laser Communication Systems[J].Journal of the Optical Society of America A Optics Image Science & Vision,2002,19(3):567.
[6] 丁涛,许国良,张旭苹,等.空间光通信中平台振动对误码率影响的抑制[J].中国激光,2007,34(4):499-502.DING T,XU G L,ZHANG X P,et al.Control of Bit Error Rate Introduced by Platform Vibration for Free Space Optical Communication[J].Chinese Journal of Lasers,2007,34(4):499-502.(in Chinese)
[7] SONG T,WANG Q,WU M W,et al.Performance of Laser Inter-Satellite Links with Dynamic Beam Waist Adjustment[J].Optics Express,2016,24(11):11950.
[8] 吴继礼,赵尚弘,胥杰,等.相干光脉冲位置调制信道容量及传信率最大化研究[J].光学学报,2008,28(4):643-647.WU J L,ZHAO S H,XU J,et al.Study of Capacity of Coherent Pulse-Position Modulation Channel and Maximization of Information Transmitting Rate[J].Acta Optica Sinica,2008,28(4):643-647.(in Chinese)
[9] HOO K P.Exact Evaluation of the Capacity for Intensity-Modulated Direct-Detection Channels with Optical Amplifier Noises[J].IEEE Photonics Technology Letters,2005,17(4):858-860.
[10] ANGUITA J,DJORDJEVIC I,NEIFELD M,et al.Shannon Capacities and Error-Correction Codes for Optical Atmospheric Turbulent Channels[J].Journal of Optical Networking,2005,24(9):586-601.
[11] BOLUDA-RUIZ R,GARCIA-ZAMBRANA A,CASTILLO-VAZQUEZ C,et al.Novel Approximation of Misalignment Fading Modeled by Beckmann Distribution on Free-Space Optical Links[J].Optics Express,2016,24(20):22635.
[12] 南航,张鹏,佟首峰,等.大气湍流下带有跟踪误差的空间相干光通信性能分析[J].光子学报,2015,44(8):50-55.NAN H,ZHANG P,TONG S F,et al.Performance Analysis of Free Space Coherent Optical Communication in Atmosphere Turbulence with Tracking Error[J].Acta Photonica Sinica,2015,44(8):50-55.(in Chinese)
[13] YANG F,CHENG J,TSIFTSIS T A.Free-Space Optical Communication with Nonzero Boresight Pointing Errors[J].IEEE Transactions on Communications,2014,62(2):713-725.
[14] 王惠琴,曹明华,陈海燕,等.无背景噪声时光多输入多输出系统的信道容量[J].光学学报,2012,32(3):28-33.WANG H Q,CAO M H,CHEN H Y,et al.Channel Capacity of Optical Multiple Input Multiple Output System Without Background Noise[J].Acta Optica Sinica,2012,32(3):28-33.(in Chinese)
[15] 姜义君.星地激光通信链路中大气湍流影响的理论和实验研究[D].哈尔滨:哈尔滨工业大学,2010:2-15.JIANG Y J.Theoretica and Experimental Researches on Influences of Atmosphere Turbulence in the Satellite-to- Ground Laser Communication Link[D].Harbin:Harbin Institute of Technology,2010:2-15.(in Chinese)
[16] PROAKIS J G.Digital communication[M].[S.l.]:McGraw-Hill Book Co,1989.
[17] 刘剑锋,李宏伟,刘智慧.拉格朗日乘数法求解极值点的讨论[J].高等数学研究,2017,20(2):13-14.LIU J F,LI H W,LIU Z H.Discussion on Lagrange Multiplier Method in Solving Extreme Value Point Problems[J].Studies in College Mathematics,2017,20(2):13-14.(in Chinese)
[18] SONG T,WANG Q,WU M W,et al.Impact of Pointing Errors on the Error Performance of Inter-Satellite Laser Communications[J].Journal of Lightwave Technology,2017,35(14):3082-3091.