光电工程  2020, Vol. 47 Issue (3): 190619      DOI: 10.12086/oee.2020.190619

Research on the key technology of turbulence suppression for atmospheric optical laser communication based on OFDM
Guo Qian, Song Peng, Zhang Zhouqiang, Zhou Awei, Qu Pingge
School of Mechanical and Electrical Engineering, Xi'an Polytechnic University, Xi'an, Shaanxi 710048, China
Abstract: Based on the analysis of the two main problems of atmospheric channel in free space optics (FSO), aiming at the problem of laser atmospheric channel especially the problems of frequency selective fading and multipath effect in complex turbulent environment, the suppression method is proposed based on OFDM turbulence effect, the FSO-OFDM system is built, the baseband model of this system and the signal of multi-carrier modulation and demodulation method are studied. First of all, this article systematically analyzes the mechanism of turbulence effect of atmospheric channel, and discusses the model of plane wave laser communication system under the influence of atmospheric turbulence, the space optical communication system model of Gaussian beam of a logarithmic normal turbulent channel is established under the influence of atmospheric turbulence, the probability density function of light intensity is deduced, the methods for analyzing the effects of various atmospheric turbulence effects on system performance using the signal-to-noise ratio probability density function; the OFDM multi-carrier modulation scheme of FSO-OFDM system is designed, the baseband mode model of FSO-OFDM system is constructed, and the modulation and demodulation principle of its signal is studied using this model. Finally, FSO-OFDM system is realized by using MATLAB, and the FSO communication system under the multipath interference is simulated, experiments on bit error rate characteristics under different guard intervals are performed. It is confirmed that the FSO-OFDM system has a strong ability to resist multipath interference and frequency selective fading, as well as good bit error rate (BER) performance. It can effectively solve the problem of intersymbol interference and the reliable link, and has a very broad application prospect and using value.
Keywords: free space optics    turbulence effect    orthogonal frequency division multiplexing    multipath fading    bit error rate

1 引言

2 激光大气传输理论分析 2.1 湍流效应

 图 1 大气环境与无线光学系统性能之间的关系 Fig. 1 Relationship between atmospheric environment and wireless optical system performance

 ${R_{\rm{e}}} = \frac{{pvL}}{\mu } = \frac{{vL}}{v},$ (1)

2.2 湍流效应的级串特性

 图 2 大气信道湍流涡旋 Fig. 2 Turbulent vortices in atmospheric channels

 图 3 Richardson湍流级串图 Fig. 3 Richardson turbulence cascade
3 激光大气传输数值计算

3.1 Kolmogorov折射率起伏功率谱

 $n = 1 + 77.6(1 + 7.52 \times {10^{ - 3}}{\lambda ^{ - 2}})\frac{P}{T} \times {10^{ - 6}},$ (2)

 ${D_n}(r) = \left\langle {{{\left[ {n(r + {r_1}) - n(r)} \right]}^2}} \right\rangle = C_n^2{r^{{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.} \!\lower0.7ex\hbox{$3$}}}},$ (3)

 ${\mathit{\Phi} _n}(k) = 0.033C_n^2{k^{{\raise0.7ex\hbox{${ - 11}$} \!\mathord{\left/ {\vphantom {{ - 11} 3}}\right.} \!\lower0.7ex\hbox{$3$}}}},$ (4)

3.2 激光大气传输平面波模型

 $\sigma _x^2 = 0.307{k^{{\raise0.7ex\hbox{$7$} \!\mathord{\left/ {\vphantom {7 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{L^{{\raise0.7ex\hbox{${11}$} \!\mathord{\left/ {\vphantom {{11} 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}C_n^2;$ (5)

 $\sigma _x^2 = 0.56{k^{{\raise0.7ex\hbox{$7$} \!\mathord{\left/ {\vphantom {7 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{\left[ {\sec \varphi } \right]^{{\raise0.7ex\hbox{${11}$} \!\mathord{\left/ {\vphantom {{11} 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}\int\limits_0^L {C_n^2(} x){(L - x)^{{\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{\rm{d}}x,$ (6)

 $\sigma _x^2 = 0.124{k^{{\raise0.7ex\hbox{$7$} \!\mathord{\left/ {\vphantom {7 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{L^{{\raise0.7ex\hbox{${11}$} \!\mathord{\left/ {\vphantom {{11} 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}C_n^2。$ (7)

 $\sigma _x^2 = 0.56{k^{{\raise0.7ex\hbox{$7$} \!\mathord{\left/ {\vphantom {7 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{\left[ {\sec \varphi } \right]^{{\raise0.7ex\hbox{${11}$} \!\mathord{\left/ {\vphantom {{11} 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}\int\limits_0^L {C_n^2(} x){\left( {\frac{x}{L}} \right)^{{\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{(L - x)^{{\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{\rm{d}}x。$ (8)
3.3 光波强度的概率密度分布

 $\sigma _l^2 = < {(\ln I - < \ln I > )^2} > 。$ (9)

 $\sigma _l^2 = 1.23{k^{{\raise0.7ex\hbox{$7$} \!\mathord{\left/ {\vphantom {7 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}{L^{{\raise0.7ex\hbox{${11}$} \!\mathord{\left/ {\vphantom {{11} 6}}\right.} \!\lower0.7ex\hbox{$6$}}}}C_n^2，$ (10)

 $I = \ln {\left( {\frac{A}{{{A_0}}}} \right)^2} = 2x，$ (11)

 $I = {I_0}\exp (l)。$ (12)

 $P(I) = P(x)\left| {\frac{{{\rm{d}}x}}{{{\rm{d}}I}}} \right|。$ (13)

 $P(x) = \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} {\sigma _x}}}\exp \left\{ { - \frac{{{{\left( {x - E(x)} \right)}^2}}}{{2\sigma _x^2}}} \right\},$ (14)

 $P(I) = \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} {\sigma _I}I}}\exp \left\{ { - \frac{{{{\left( {\ln (I/{I_0}) - E[l]} \right)}^2}}}{{2\sigma _l^2}}} \right\}, I \geqslant 0。$ (15)

4 激光大气传输模型建立 4.1 OFDM

 图 4 OFDM调制原理 Fig. 4 Modulation principle of OFDM

 图 5 OFDM多载波并行传输原理图 Fig. 5 Principle diagram of OFDM multi-carrier parallel transmission
4.2 系统建模

 图 6 FSO-OFDM系统基带模型图 Fig. 6 Baseband model of the FSO-OFDM system
4.3 系统光信号调制与解调

FSO-OFDM系统的信号调制与解调过程如图 7所示。

 图 7 FSO-OFDM系统信号的调制与解调 Fig. 7 Signal modulation and demodulation of FSO-OFDM system

5 激光大气传输实验与仿真 5.1 FSO通信系统的不同载波下的平均误码率特性实验

 图 8 不同载波数下的误码率特性曲线 Fig. 8 Bit error rate characteristics under different carrier numbers

5.2 FSO通信系统不同保护间隔下的误码率特性实验

 图 9 不同保护间隔下的误码率特性曲线 Fig. 9 Bit error rate characteristic curves under different protection intervals
6 结论

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