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如图1所示为具有波长分集的水下无线光通信系统框图,利用复合发射机在同一时刻发出不同工作波长的信号,经过存在传输路径损耗和海洋湍流效应的信道后,接收端的波长检测器接收相应波长信号。
文中采用强度调制/直接检测(IM/DD)与开关键控(OOK)调制的UWOC系统,假设复合发射机使用
$w = 1,2,\cdots,W$ 个不同工作波长同时发出相同数据信号,经过具有加性高斯白噪声(Additive white Gaussian noise,AWGN)的湍流信道模型,由$W$ 个特定波长检测器接收信号。此时,第$w$ 个接收机接收到的信号可表示为[25-26]:$${{y}}_w = {h_w} \gamma x + {n_0}$$ (1) $$h = {h_w}\;\;w = 1,2,\cdots,W$$ (2) 式中:
${y_w}$ 为接收机$w$ 接收到的信号;$h$ 为第$w$ 个信道的联合衰落状态;$\gamma $ 为接收机响应度;$x$ 为二进制传输信号;${n_0}$ 为均值为零且方差为${\sigma _n}^2$ 的独立加性高斯白噪声。考虑UWOC系统具有OOK调制信道衰落特性,接收到的瞬时电信噪比(Signal noise ratio,SNR)受信道状态
$h$ 的影响,表示为:$$SNR(h) = \frac{{2{P_0}^2{\gamma ^2}{h^2}}}{{{\sigma_n }^2}}$$ (3) 式中:
${P_0}$ 为平均发射光功率;$\left\langle {SNR} \right\rangle $ 表示平均电信噪比。因此,可以表示为:$$\left\langle {SNR(h)} \right\rangle = \frac{{2{P_0}^2{\gamma ^2}E^2{{[h]}}}}{{{\sigma _n}^2}}$$ (4) 式中:
$E[.]$ 表示归一化期望。 -
海水中含有复杂的杂质成分,导致光信号与杂质分子相互碰撞作用发生吸收、散射效应,引起接收端光脉冲展宽及延迟效应。通常用比尔-朗伯定律[1]描述海水信道对光信号的传输路径损耗
${h_l}$ ,可表示为:$${h_l} = \exp ( - c(\lambda ) \cdot L)$$ (5) 式中:
$L$ 为光信号在海水信道中的传输距离;$c(\lambda )$ 为总衰减系数。 -
海洋湍流引起的信道衰落被认为是随机过程,由Gamma-gamma分布描述弱、中到强湍流条件。发射端光信号经过湍流后,接收端辐照度分布遵循Gamma-gamma统计分布,其概率密度函数(Probability density function,PDF)表达式[27]为:
$${f_{{h_t}}}({h_t}) = \frac{{2{{(\alpha \;\beta )}^{\frac{{\alpha + \;\beta }}{2}}}}}{{\varGamma (\alpha )\varGamma (\;\beta )}}{h_t}^{\frac{{\alpha + \;\beta }}{2} - 1}{{ K}_{\alpha - \;\beta }}(2\sqrt {\alpha \;\beta {h_t}} )$$ (6) 式中:
${{K}_\nu }(.)$ 为第二类$\nu $ 阶修正贝塞尔函数;$\varGamma (.)$ 为伽马函数。利用Meijer-G函数积分性质[28],公式(6)概率密度函数(PDF)可表示为:$${f_h}_{_t}({h_t}) = \frac{{{{(\alpha \;\beta )}^{\frac{{\alpha + \;\beta }}{2}}}}}{{\varGamma (\alpha )\varGamma (\;\beta )}}{h_t}^{\frac{{\alpha + \;\beta }}{2} - 1}G_{0,2}^{2,0}\left( {\alpha \;\beta {h_t}{\rm{|}}\begin{array}{*{20}{c}} - \\ {\dfrac{{\alpha - \;\beta }}{2},\dfrac{{\;\beta - \alpha }}{2}} \end{array}} \right)$$ (7) 其中,
$\alpha $ 和$\;\beta $ 表示描述海洋湍流引起光束闪烁的尺度大小,$\alpha $ 描述大尺度参量,$\;\beta $ 描述小尺度参量,可表示为[23, 29]:$$\alpha = \dfrac{1}{{\exp \left( {\dfrac{{0.196{\sigma _R}^2}}{{{{(1 + 0.18{d^2} + 0.186{\sigma _R}^{12/5})}^{7/6}}}}} \right) - 1}}$$ (8) $$\;\beta = \dfrac{1}{{\exp \left( {\dfrac{{0.204{\sigma _R}^2{{(1 + 0.23{\sigma _R}^{12/5})}^{ - 5/6}}}}{{1 + 0.9{d^2} + 0.207{d^2}{\sigma _R}^{12/5}}}} \right) - 1}}$$ (9) 式中:
$d = \sqrt {k{D^2}/4L} $ ,$k = 2\pi /\lambda $ 为波矢量,$D$ 为接收孔径大小,$L$ 为链路距离。平面波Rytov方差表示为${\sigma _R}^2 = 1.23C_n^2{k^{7/6}}{L^{11/6}}$ ,其中$C_n^2$ 是海洋湍流参数和各向异性因子表示的等效结构参数,由下式表示[24]:$$\begin{array}{l} C_n^2 = 8\pi {k^{ - 7/6}}{L^{ - 11/6}}\operatorname{Re} \left\{ {\displaystyle\int\limits_0^L {{\rm{d}}{\textit{z}}} \displaystyle\int\limits_{ - \infty }^{ +\infty } {{\rm{d}}{\kappa _x}\displaystyle\int\limits_{ - \infty }^{ + \infty } {{\rm{d}}{\kappa _y}} } } \times\right. \\ \left. {\left[ {P({\textit{z}},{\kappa _x},{\kappa _y})P({\textit{z}}, - {\kappa _x}, - {\kappa _y}) + {{\left| {P({\textit{z}},{\kappa _x},{\kappa _y})} \right|}^2}{\varPhi _n}(\kappa )} \right]} \right\} \\ \end{array} $$ (10) 式中:
$z$ 为光束的传播方向;${\kappa _x}$ 和${\kappa _y}$ 分别表示在$x$ 与$y$ 方向的空间频率分量;$P({\textit{z}},{\kappa _x},{\kappa _y})$ 为$ik\exp ( - 0.5{(kL)^{ - 1}}\times $ $ i{\textit{z}}(L - {\textit{z}})({\kappa _x}^2 + \kappa {{}_y^2}))$ ;${\varPhi _n}(\kappa )$ 表示海洋湍流的折射率空间功率谱,其表达式为[7,30]:$$ \begin{split} {\varPhi _n}(\kappa ) =& 0.388 \times {10^{ - 8}}{u_x}u{}_y{\omega ^{ - 2}}{\varepsilon ^{ - 1/3}}{\chi _T}{u^{ - 11/6}} \times \\ & (1 + 2.35{\nu ^{1/2}}{\varepsilon ^{ - 1/6}}{u^{1/3}}) \times [{\omega ^2}\exp ( - {A_T}\delta ) + \\ & \exp ( - {A_S}\delta ) - 2\omega \exp ( - {A_{TS}}\delta )] \\ \end{split} $$ (11) 式中:
${u_x}$ 和${u_y}$ 分别表示海洋湍流中各向异性因子,$u$ 表示为${({u_x}{\kappa _x})^2} + {({u_y}{\kappa _y})^2}$ ,${u_x}{\rm{ = }}1,{u_y} = 1$ 表示各向同性湍流环境,$ {u}_{x}>1,{u}_{y}>1$ 表示各向异性海洋湍流环境;$\omega $ 表示温度与盐度对海洋湍流贡献的比值大小,取值范围为$[{\rm{ - }}5,0]$ ,当海洋湍流完全由温度梯度贡献时取值为−5,完全由盐度梯度贡献时取值为0;湍流单位动能耗散率$\varepsilon $ 取值范围为$[{10^{ - 10}}{{\rm{m}}^2}/{{\rm{s}}^3},{10^{ - 1}}{{\rm{m}}^2}/{{\rm{s}}^3}]$ ,当处于海洋深海时取值等于${10^{ - 10}}{{\rm{m}}^2}/{{\rm{s}}^3}$ ,处于海洋表层时取值等于${10^{ - 1}}{{\rm{m}}^2}/{{\rm{s}}^3}$ ;${\chi _T}$ 表示均方温度耗散率,取值范围从${10^{ - 10}}$ ~${10^{ - 2}}{{\rm K}^2}/{\rm{s}}$ ;$\nu $ 表示动力粘度系数,取值范围为$[0{{\rm {m}}^2}/{\rm{s}}, {10^{ - 5}}{{\rm{m}}^2}/{\rm{s}}]$ ;${A_T} = 1.863 \times {10^{ - 2}}$ ,${A_S} = 1.9 \times {10^{ - 4}}$ ,${A_{TS}} = 9.41 \times {10^{ - 3}}$ ,$\delta = 8.284\nu {\varepsilon ^{ - 1/3}}{u^{2/3}} + $ $ 12.978{\nu ^{3/2}}{\varepsilon ^{ - 1/2}}u$ 。 -
综合考虑1.2、1.3小节所介绍内容,光信号在海水中传输时,由于受到吸收、散射效应及海洋湍流影响,从而能量发生严重衰减。在波长分集UWOC系统中,信道联合衰减可表示为:
$$h = {h_l}{h_t}$$ (12) 式中:
${h_l}$ 描述海水信道中由于吸收、散射引起的衰减效应;${h_t}$ 描述海洋湍流引起的信号衰落。因此,UWOC系统信道联合衰落状态$h$ 的PDF可表示为:$${f_h}(h) = \left| {\frac{{\rm{d}}}{{{\rm{d}}h}}\left( {\frac{h}{{{h_l}}}} \right)} \right|{f_{{h_t}}}({h_t})$$ (13) 将Gamma-gamma分布海洋湍流引起的衰落PDF代入公式(13),得到以下表达式:
$${f_h}(h) = \frac{{\alpha \;\beta }}{{\varGamma (\alpha )\varGamma (\;\beta ){h_l}}}G_{0,2}^{2,0}\left( {\alpha \;\beta \frac{h}{{{h_l}}}{\rm{|}}\begin{array}{*{20}{c}} - \\ {\alpha - 1,\;\beta - 1} \end{array}} \right)$$ (14) -
中断概率是衡量水下无线光通信系统性能的重要指标之一,其定义为接收端瞬时信噪比小于临界检测阈值
$SN{R_{th}}$ 的概率,由下式表示为:$${P_{out}} = {P_r}(SNR(h) \leqslant SN{R_{th}}) = \int\limits_h {{f_h}(h){\rm{d}}h} $$ (15) 根据1.4小节Gamma-gamma分布的PDF,推导出具有
$W$ 个不同信道的波长分集UWOC系统中断概率表达式。由于每个信道工作波长不同,假定$W$ 个信道彼此独立,得到对应$W$ 个信道的总中断概率表达式为:$${P_{out,W}} = \prod\limits_{w = 1}^W {{P_r}(SNR({h_w}) \leqslant SN{R_{th}})} = \prod\limits_{w = 1}^W {\int\limits_{{h_w}} {{f_{{h_w}}}({h_w}){\rm{d}}{h_w}} } $$ (16) 将公式(14)代入公式(16)得到具有波长分集的UWOC系统总中断概率表达式:
$${P_{out,W}} = \prod\limits_{w = 1}^W {\frac{1}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w})}}} G_{1,3}^{2,1}\left( {{\alpha _w}{\;\beta _w}\sqrt {\frac{{SN{R_{th}}}}{{\left\langle {SN{R_w}} \right\rangle }}} {\rm{|}}\begin{array}{*{20}{c}} 1 \\ {{\alpha _w},{\;\beta _w},0} \end{array}} \right)$$ (17) -
描述水下无线光通信系统性能的另一个重要指标是平均误码率。考虑AWGN情况下,采用IM/DD-OOK的UWOC系统平均误码率表达式为:
$${P_e} = P(1)P(e|1) + P(0)P(e|0)$$ (18) 式中:
$P(.)$ 表示发送“0”或“1”的概率;$P(|)$ 表示条件概率。根据对称性得到$P(0) = P(1) = 0.5$ ,$P(e|0) = P(e|1)$ 。 -
对于具有波长分集的UWOC系统,采用复合发射机发射出
$W$ 个波长信号对应多个特定波长检测机接收,假定每个信道链路发送相同的“0”和“1”概率。在最佳组合[18](OC)接收机方案中,根据信号强度对不同信道的信号副本进行同相加权得到具有波长分集的UWOC系统平均BER表达式为:
$${P_{e,OC}} = \int\limits_{{h_w}} {{f_{{h_w}}}({h_w})Q\left( {\frac{{{P_0}}}{{\sqrt W {\sigma _n}}}\sqrt {\sum\limits_{w = 1}^W (\gamma_w {{h_w})^2} } } \right)} {\rm{d}}{h_w}$$ (19) 式中:
${h_w}$ 表示不同信道衰落状态;$Q(.)$ 表示高斯$Q$ 函数,根据其性质近似等于$Q(x) \approx 1/12\exp ( - {x^2}/2) + $ $ 1/4\exp ( - 2{x^2}/3)$ ,因此公式(19)可化简为:$$ \begin{split} {P_{e,OC}} =& \dfrac{1}{{12}}\prod\limits_{w = 1}^W {\displaystyle\int\limits_0^\infty {{f_{{h_w}}}({h_w})} } \exp \left( - \dfrac{{{P_0}^2{\gamma _w}^2{h_w}^2}}{{2W{\sigma _n}^2}}\right){\rm{d}}{h_w} +\\ & \dfrac{1}{4}\prod\limits_{w = 1}^W {\displaystyle\int\limits_0^\infty {{f_{{h_w}}}({h_w})} } \exp \left( - \dfrac{{2{P_0}^2{\gamma _w}^2{h_w}^2}}{{3W{\sigma _n}^2}}\right){\rm{d}}{h_w} \\ \end{split} $$ (20) 将公式(14)代入公式(20),得到:
$$\begin{array}{l} {P_{e,OC}} = \dfrac{1}{{12}}\displaystyle\prod\limits_{w = 1}^W {\displaystyle\int\limits_0^\infty {\dfrac{{{\alpha _w}{\;\beta _w}}}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w}){h_l}}}} } \times \\ G_{0,2}^{2,0}\left( {{\alpha _w}{\;\beta _w}\dfrac{{{h_w}}}{{{h_l}}}{\rm{|}}\begin{array}{*{20}{c}} - \\ {{\alpha _w} - 1,{\;\beta _w} - 1} \end{array}} \right)\exp \left( - \dfrac{{{P_0}^2{\gamma _w}^2{h_w}^2}}{{2W{\sigma _n}^2}}\right){\rm{d}}{h_w} +\\ \dfrac{1}{4}\displaystyle\prod\limits_{w = 1}^W {\displaystyle\int\limits_0^\infty {\dfrac{{{\alpha _w}{\;\beta _w}}}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w}){h_l}}}} } \times \\ G_{0,2}^{2,0}\left( {{\alpha _w}{\;\beta _w}\dfrac{{{h_w}}}{{{h_l}}}{\rm{|}}\begin{array}{*{20}{c}} - \\ {{\alpha _w} - 1,{\;\beta _w} - 1} \end{array}} \right)\exp \left( - \dfrac{{2{P_0}^2{\gamma _w}^2{h_w}^2}}{{3W{\sigma _n}^2}}\right){\rm{d}}{h_w} \\ \end{array} $$ (21) 根据Meijer-G函数指数函数性质,
$\exp (.)$ 可表示为:$$\exp ( - x) = G_{0,1}^{1,0}\left( {x|\begin{array}{*{20}{c}} {\rm{ - }} \\ {\rm{0}} \end{array}} \right)$$ (22) 利用公式(22)代入公式(21)得到波长分集UWOC系统的平均BER简化表达式为:
$$\begin{array}{l} {P_{e,OC}} = \dfrac{1}{{12}}\displaystyle\prod\limits_{w = 1}^W {\dfrac{{{{\rm{2}}^{{\alpha _w}{\rm{ + }}{\;\beta _w}{\rm{ - 2}}}}}}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w})\pi }}} \times \\ G_{{\rm{4}},{\rm{1}}}^{{\rm{1}},{\rm{4}}}\left( {\dfrac{{4\left\langle {SN{R_w}} \right\rangle }}{{W{{({\alpha _w}{\;\beta _w})}^2}}}{\rm{|}}\begin{array}{*{20}{c}} {\dfrac{{1 - {\alpha _w}}}{2},\dfrac{{2 - {\alpha _w}}}{2},\dfrac{{1 - {\;\beta _w}}}{2},\dfrac{{2 - {\;\beta _w}}}{2}} \\ 0 \end{array}} \right) + \\ \dfrac{1}{4}\displaystyle\prod\limits_{w = 1}^W {\dfrac{{{{\rm{2}}^{{\alpha _w}{\rm{ + }}{\;\beta _w}{\rm{ - 2}}}}}}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w})\pi }}} \times \\ G_{{\rm{4}},{\rm{1}}}^{{\rm{1}},{\rm{4}}}\left( {\dfrac{{16\left\langle {SN{R_w}} \right\rangle }}{{3W{{({\alpha _w}{\;\beta _w})}^2}}}{\rm{|}}\begin{array}{*{20}{c}} {\dfrac{{1 - {\alpha _w}}}{2},\dfrac{{2 - {\alpha _w}}}{2},\dfrac{{1 - {\;\beta _w}}}{2},\dfrac{{2 - {\;\beta _w}}}{2}} \\ 0 \end{array}} \right) \\ \end{array} $$ (23) -
在具有波长分集的UWOC系统接收端的不同组合方案中,等增益组合[31](EGC)是将不同信道的接收端处得到的信号副本适当比例合并。与最佳组合(OC)相比,在实际情况中等增益组合(EGC)具有较低的链路复杂度。根据3.1小节OC组合平均BER推导过程,同理得到等增益组合(EGC)的平均BER表达式为:
$${P_{e,EGC}} = \int\limits_{{h_w}} {{f_{{h_w}}}({h_w})Q\left( {\frac{{{P_0}}}{{W{\sigma _n}}} {\sum\limits_{w = 1}^W {\gamma _w}{{h_w}} } } \right)} {\rm{d}}{h_w}$$ (24) 对公式(24)化简得到EGC最终平均BER表达式为:
$$\begin{array}{l} {P_{e,EGC}} = \dfrac{1}{{12}}\displaystyle\prod\limits_{w = 1}^W {\dfrac{{{{\rm{2}}^{{\alpha _w}{\rm{ + }}{\;\beta _w}{\rm{ - 2}}}}}}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w})\pi }}} \times \\ G_{{\rm{4}},{\rm{1}}}^{{\rm{1}},{\rm{4}}}\left( {\dfrac{{4\left\langle {SN{R_w}} \right\rangle }}{{{W^2}{{({\alpha _w}{\;\beta _w})}^2}}}{\rm{|}}\begin{array}{*{20}{c}} {\dfrac{{1 - {\alpha _w}}}{2},\dfrac{{2 - {\alpha _w}}}{2},\dfrac{{1 - {\;\beta _w}}}{2},\dfrac{{2 - {\;\beta _w}}}{2}} \\ 0 \end{array}} \right) + \\ \dfrac{1}{4}\displaystyle\prod\limits_{w = 1}^W {\dfrac{{{{\rm{2}}^{{\alpha _w}{\rm{ + }}{\;\beta _w}{\rm{ - 2}}}}}}{{\varGamma ({\alpha _w})\varGamma ({\;\beta _w})\pi }}} \times \\ G_{{\rm{4}},{\rm{1}}}^{{\rm{1}},{\rm{4}}}\left( {\dfrac{{16\left\langle {SN{R_w}} \right\rangle }}{{3{W^2}{{({\alpha _w}{\;\beta _w})}^2}}}{\rm{|}}\begin{array}{*{20}{c}} {\dfrac{{1 - {\alpha _w}}}{2},\dfrac{{2 - {\alpha _w}}}{2},\dfrac{{1 - {\;\beta _w}}}{2},\dfrac{{2 - {\;\beta _w}}}{2}} \\ 0 \end{array}} \right) \\ \end{array} $$ (25) -
根据第2、3小节得到的中断概率与平均误码率封闭表达式,本小节分析了基于波长分集的水下无线光通信系统受到传输路径损耗和各向异性海洋湍流影响下的性能变化。由水下无线光通信系统信道传输衰减特性可知[4,32],不同海水类型对光的衰减作用有所差异,图2所示为近海水质中不同波长光信号总衰减系数[33-34],在550~590 nm之间的光波衰减系数较小,其中波长为570 nm的光信号在传输过程中受到的吸收、散射效应最小。因此,文中选取受近海水质衰减影响较小的560、570、580 nm光波信号应用于UWOC系统波长分集方案。波长分集可由分集阶
$w{\rm{ = }}1,2,\cdots,W$ 决定,无波长分集$ (W=1)$ 采用570 nm波长工作,2阶分集$ (W\rm{=}2)$ 工作波长为570 nm和560 nm,具有3阶分集$ (W=3)$ 时工作波长为570、560、580 nm。仿真中所用到的参数如表1所示。图 2 近海水质中不同波长光信号总衰减系数
Figure 2. Total attenuation coefficient of optical signals of different wavelengths in coastal ocean
表 1 仿真参数
Table 1. Simulation parameters
Coefficient Value Ratio of temperature and salinity contribution to ocean turbulence, $\omega $ ${\rm{ - }}1$ Kinetic energy dissipation rate, $\varepsilon /{{\rm{m}}^2} \cdot {{\rm{s}}^{{\rm{ - }}3}}$ ${10^{{\rm{ - 4}}}}$ Mean square temperature dissipation rate, ${\chi _T}/{{\rm K}^2} \cdot {{\rm{s}}^{{\rm{ - }}1}}$ ${10^{{\rm{ - 4}}}}$ Dynamic viscosity coefficient, $\nu /{{\rm{m}}^2} \cdot {{\rm{s}}^{{\rm{ - }}1}}$ ${10^{{\rm{ - 5}}}}$ Receiver diameter, $D/{\rm{mm}}$ $1$ Transmission distance, $L/{\rm{m}}$ $10$ 接收机对三种波长光信号的接收响应度不同。仿真中设置560、570、580 nm波长光信号对应的光子检测效率
$\eta $ 分别为32%、30%、29%。由公式$\gamma {\rm{ = }}\dfrac{{M\eta e}}{{hv}}$ 可得到接收机对不同光波长的响应度,其中$e$ 表示电子电量,$h$ 表示普朗克常数,$v$ 表示光频,$M$ 表示雪崩光电二极管倍增系数。结合三种波长光信号在近海水质中的衰减效应以及接收机的响应度,可以计算得到不同工作波长之间的平均信噪比关系。波长为570 nm的光信号在近海水质中传输平均信噪比为$\left\langle {SN{R_1}} \right\rangle $ ,当传输距离为10 m时,560 nm和580 nm的波长信号平均信噪比$\left\langle {SN{R_2}} \right\rangle $ 、$\left\langle {SN{R_3}} \right\rangle $ 分别为$0.95\left\langle {SN{R_1}} \right\rangle $ 、$0.{\rm{78}} $ $ \left\langle {SN{R_1}} \right\rangle $ 。当传输距离等于5 m时,560 nm和580 nm的波长光信号平均信噪比关系分别为${\rm{1}}{\rm{.02}}\left\langle {SN{R_1}} \right\rangle $ 、$0.{\rm{87}}\left\langle {SN{R_1}} \right\rangle $ ;在15 m的传输距离下,560 nm和580 nm的波长光信号平均信噪比关系分别为$0.{\rm{9}}\left\langle {SN{R_1}} \right\rangle $ 、$0.{\rm{7}}\left\langle {SN{R_1}} \right\rangle $ 。在进行波长分集UWOC系统性能仿真时,每个图中平均SNR表示采用570 nm波长光信号在无波长分集系统中传输的平均信噪比$\left\langle {SN{R_1}} \right\rangle $ 。当$W{\rm{ = 2}}$ 时,570 nm和560 nm的光信号在海水信道中传输受到的衰减效应有所差别,此时得到系统中断概率与平均误码率中包含经过两个不同衰减的平均信噪比。同样地,在$W{\rm{ = 3}}$ 的系统中,海水信道对570、560、580 nm波长光信号的衰减效应不同,传输过程中分别对应三个平均信噪比,最终得到3阶波长分集下UWOC系统性能的变化。根据公式(10)获得各向异性海洋湍流等效结构参数,图3(a)~(c)绘制了在不同各向异性因子下波长分集UWOC系统的中断概率变化,表2给出了平均信噪比30 dB时不同各向异性因子下无波长分集与2、3阶波长分集UWOC系统中断概率的具体数值。随着各向异性因子
${u_x}$ 、${u_y}$ 分别在$x$ 和$y$ 方向上同时增加,无波长分集和2、3阶波长分集的UWOC系统中断概率明显降低。比如在$W{\rm{ = }}3$ 的波长分集UWOC系统中,增加各向异性因子${u_x}$ 和${u_y}$ ,系统中断概率从$3.819 \times {10^{{\rm{ - 7}}}}$ 减小至$3.347 \times {10^{{\rm{ - 10}}}}$ 。这是因为各向异性因子增大,海洋湍流内部由于不对称性加剧导致结构密度降低,相邻涡流单元层碰撞减少,使湍流折射率变化起伏降低,海洋湍流强度减小,导致闪烁效应减弱,使UWOC系统具有了较小的中断概率。当各向异性因子相等时,相较于无波长分集UWOC系统,使用波长分集的系统中断概率更低,且$W{\rm{ = }}3$ 的波长分集UWOC系统比$W{\rm{ = 2}}$ 的UWOC系统性能更好。比如在各向异性因子${u_x} = 1,{u_y} = 2$ 时,无波长分集UWOC系统中断概率为$2.798 \times {10^{{\rm{ - 3}}}}$ ,2、3阶波长分集UWOC系统中断概率分别为$1.199 \times {10^{{\rm{ - 5}}}}$ 、$1.{\rm{749}} \times $ $ {10^{{\rm{ - 7}}}}$ 。图 3 不同各向异性因子下波长分集UWOC系统的中断概率性能变化。(a) 无波长分集;(b) 2阶波长分集;(c) 3阶波长分集,L=10 m
Figure 3. Outage probability performance of wavelength diversity UWOC system under different anisotropic factors. (a) No wavelength diversity; (b) Second-order wavelength diversity; (c) Third-order wavelength diversity,
$L{\rm{ = }}10\;{\rm{m}}$ 表 2 不同各向异性因子下波长分集UWOC系统中断概率
Table 2. Outage probability of wavelength diversity UWOC system under different anisotropy factors
Wavelength diversity ${u_x} = 1,{u_y} = 1$ ${u_x} = 1,{u_y} = 2$ ${u_x} = 2,{u_y} = 2$ $W{\rm{ = 1}}$ $3.{\rm{792}} \times {10^{{\rm{ - 3}}}}$ $2.798 \times {10^{{\rm{ - 3}}}}$ $2.{\rm{499}} \times {10^{{\rm{ - 4}}}}$ $W{\rm{ = 2}}$ $2.097 \times {10^{{\rm{ - 5}}}}$ $1.199 \times {10^{{\rm{ - 5}}}}$ $1.{\rm{228}} \times {10^{{\rm{ - 7}}}}$ $W{\rm{ = 3}}$ $3.819 \times {10^{{\rm{ - 7}}}}$ $1.{\rm{749}} \times {10^{{\rm{ - 7}}}}$ $3.347 \times {10^{{\rm{ - 10}}}}$ 图4给出在10 m的传输距离下接收端使用OC和EGC技术的波长分集UWOC系统平均BER变化。当各向异性因子
${u_x} = 1,{u_y} = 2$ ,平均信噪比为30 dB时,2阶波长分集UWOC系统接收端使用OC和EGC的平均BER分别为$7.634 \times {10^{{\rm{ - 5}}}}$ 、$1.355 \times $ $ {10^{{\rm{ - 4}}}}$ ,3阶波长分集UWOC系统接收端使用OC和EGC的平均BER分别等于$7.375 \times {10^{{\rm{ - 6}}}}$ 、$2.707 \times {10^{{\rm{ - 5}}}}$ 。根据数值结果表明,相同阶数的波长分集UWOC系统接收端使用OC技术比EGC技术得到的平均误码率更低。图 4 使用OC与EGC技术的波长分集UWOC系统在不同各向异性因子下的平均BER性能比较,
$L{\rm{ = }}10\;{\rm{m}}$ Figure 4. Comparison of the average BER performance of the UWOC system without wavelength diversity using OC and EGC technology under different anisotropic factors,
$L{\rm{ = }}10\;{\rm{m}}$ 图5和图6更加详细地表明了使用波长分集的UWOC系统在不同海洋湍流参数下的性能变化。选取各向异性因子
${u_x} = 1,{u_y} = 2$ 时,不同的动能耗散率$\varepsilon $ 、均方温度耗散率${\chi _T}$ 、温度与盐度对海洋湍流贡献比值$\omega $ 对波长分集UWOC系统中断概率和平均误码率的影响。改变每个图所示变量,给定其余海洋湍流参数。由图5(a)和图6(a)可知,随着湍流中动能耗散率的增加,波长分集UWOC系统的中断概率和平均误码率逐渐降低。这是因为动能耗散率决定湍流中的能量转化,单位流体质量的动能耗散率越大,湍流中转化为分子热能的能量越快,海洋湍流强度越弱,此时系统性能受到的影响减小。从图5(b)和图6(b)中可以看出,当均方温度耗散率减小时,波长分集UWOC系统中断概率与平均误码率降低。这是因为均方温度耗散率描述湍流对流体温度场的影响,当均方温度耗散率减小时,分子热传导作用对温度的波动影响变小,系统性能受湍流影响减弱。从图5(c)和图6(c)中可以发现,波长分集UWOC系统的中断概率与平均误码率随着温度与盐度对海洋湍流贡献比值$\omega $ 的增大而增加。$\omega $ 越大,表明盐度引起的海洋湍流的贡献越大,湍流强度变大,系统的通信系统性能恶化。图 5 波长分集UWOC系统在不同海洋湍流参数,(a)动能耗散率
$\varepsilon $ ,(b)均方温度耗散率${\chi _T}$ , (c)温度与盐度对海洋湍流贡献比值$\omega $ 下的中断概率性能变化,$L{\rm{ = }}10\;{\rm{m}}$ Figure 5. Outage probability performance of wavelength diversity UWOC system under different ocean turbulence parameters, (a) kinetic energy dissipation rate
$\varepsilon $ , (b) mean square temperature dissipation rate${\chi _T}$ , (c) the ratio of temperature and salinity contribution to ocean turbulence$\omega $ ,$L{\rm{ = }}10\;{\rm{m}}$ 图 6 波长分集UWOC系统在不同海洋湍流参数,(a)动能耗散率
$\varepsilon $ ,(b)均方温度耗散率${\chi _T}$ ,(c)温度与盐度对海洋湍流贡献比值$\omega $ 下的平均BER性能变化,$L{\rm{ = }}10\;{\rm{m}}$ Figure 6. Average BER performance of wavelength diversity UWOC system under different ocean turbulence parameters, (a) kinetic energy dissipation rate
$\varepsilon $ , (b) mean square temperature dissipation rate${\chi _T}$ , (c) the ratio of temperature and salinity contribution to ocean turbulence$\omega $ ,$L{\rm{ = }}10\;{\rm{m}}$ 图7给出在近海水质和各向异性因子
${u_x} = 1, $ $ {u_y} = 2$ 的海洋湍流条件下,波长分集UWOC系统经过不同传输距离时的平均BER变化曲线,表3给出了平均信噪比30 dB时不同传输距离下无波长分集与2、3阶波长分集UWOC系统平均BER的具体数值。当传输距离从5 m增加到15 m时,无波长分集UWOC系统平均BER从$3.{\rm{42}} \times {10^{{\rm{ - 5}}}}$ 变为$4.308 \times {10^{{\rm{ - 3}}}}$ ;2阶波长分集UWOC系统平均BER从$1.481 \times {10^{{\rm{ - 8}}}}$ 变为$2.198 \times $ $ {10^{{\rm{ - 4}}}}$ ;同样地,3阶波长分集UWOC系统平均BER从$8.761 \times {10^{{\rm{ - 11}}}}$ 变为$3.604 \times {10^{{\rm{ - 5}}}}$ 。随着传输距离的增加,波长分集UWOC系统平均误码率变大。这是因为增加传输距离,不同波长光信号传输时受到的海水衰减和海洋湍流效应影响逐渐加剧,导致UWOC系统性能下降。当处于同一传输距离时,使用波长分集的UWOC系统比无波长分集系统性能更好,并且3阶波长分集比2阶波长分集的UWOC系统平均误码率明显改善。比如当传输距离等于5 m时,无波长分集UWOC系统平均BER为$3.{\rm{42}} \times {10^{{\rm{ - 5}}}}$ ,而$W{\rm{ = 2}}$ 和$W{\rm{ = 3}}$ 的波长分集UWOC系统平均BER分别为$1.481 \times $ $ {10^{{\rm{ - 8}}}}$ 、$8.761 \times {10^{{\rm{ - 11}}}}$ 。图 7 使用OC技术的波长分集UWOC系统在不同传输距离下的平均BER性能变化
Figure 7. Average BER performance of wavelength diversity UWOC system using OC technology under different transmission distances
表 3 使用OC技术的波长分集UWOC系统在不同传输距离下的平均BER
Table 3. Average BER of wavelength diversity UWOC system using OC technology under different transmission distances
Wavelength diversity $L{\rm{ = }}5\;{\rm{m}}$ $L{\rm{ = 10\;m}}$ $L{\rm{ = 1}}5\;{\rm{m}}$ $W{\rm{ = 1}}$ $3.{\rm{42}} \times {10^{{\rm{ - 5}}}}$ $2.7 \times {10^{{\rm{ - 3}}}}$ $4.308 \times {10^{{\rm{ - 3}}}}$ $W{\rm{ = 2}}$ $1.481 \times {10^{{\rm{ - 8}}}}$ $7.634 \times {10^{{\rm{ - 5}}}}$ $2.198 \times {10^{{\rm{ - 4}}}}$ $W{\rm{ = 3}}$ $8.761 \times {10^{{\rm{ - 11}}}}$ $7.{\rm{375}} \times {10^{{\rm{ - 6}}}}$ $3.604 \times {10^{{\rm{ - 5}}}}$
Performance analysis of wavelength diversity wireless optical communication system in ocean turbulence
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摘要: 由于海水的吸收、散射衰减以及海洋湍流效应会引起水下无线光通信(Underwater wireless optical communication,UWOC)系统接收端光信号的闪烁,导致UWOC系统传输性能下降。基于Gamma-gamma分布的海洋湍流信道模型,根据海洋湍流参数和各向异性因子表示的等效结构参数,推导出波长分集UWOC系统中断概率(Outage probability,OP)与平均误码率(Bit error rate,BER)封闭表达式。研究分析随着各向异性因子的增加,具有不同波长分集阶的水下无线光通信系统中断概率与平均误码率的变化,比较接收端使用最佳组合(Optimal combining,OC)与等增益组合(Equal gain combining,EGC)技术的水下无线光通信系统平均误码率,并仿真不同海洋湍流参数、传输距离对波长分集UWOC系统性能的影响。数值结果表明,随着各向异性因子的增加,海洋湍流对水下无线光通信系统产生的影响逐渐减弱,使用波长分集技术的UWOC系统比无波长分集技术的UWOC系统中断概率与平均误码率明显改善。Abstract: Due to seawater absorption, scattering attenuation and ocean turbulence effects, the optical signal at the receiving end of the underwater wireless optical communication (UWOC) system will flicker. The flickering signal will result in a decrease in the transmission performance of the UWOC system. Based on the Gamma-gamma distribution of the ocean turbulence channel model, according to the equivalent structural parameters represented by ocean turbulence parameters and anisotropy factors, the closed expressions of the outage probability (OP) and the average bit error rate (BER) of the wavelength diversity UWOC system were derived. With the increase of the anisotropy factor, the changes in the outage probability and the average bit error rate of UWOC system with different wavelength diversity orders were analyzed. The average bit error rate difference of the UWOC system between the optimal combining (OC) and the equal gain combining (EGC) used at the receiving end technology were compared, and the influence of different ocean turbulence parameters and transmission distances on the performance of the wavelength diversity UWOC system was simulated. The numerical results show that the ocean turbulence effect on the UWOC system gradually weakens with the increase of the anisotropy factor. The UWOC system with wavelength diversity technology has significantly improved the outage probability and the average bit error rate than the UWOC system without wavelength diversity technology.
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图 3 不同各向异性因子下波长分集UWOC系统的中断概率性能变化。(a) 无波长分集;(b) 2阶波长分集;(c) 3阶波长分集,L=10 m
Figure 3. Outage probability performance of wavelength diversity UWOC system under different anisotropic factors. (a) No wavelength diversity; (b) Second-order wavelength diversity; (c) Third-order wavelength diversity,
$L{\rm{ = }}10\;{\rm{m}}$ 图 5 波长分集UWOC系统在不同海洋湍流参数,(a)动能耗散率
$\varepsilon $ ,(b)均方温度耗散率${\chi _T}$ , (c)温度与盐度对海洋湍流贡献比值$\omega $ 下的中断概率性能变化,$L{\rm{ = }}10\;{\rm{m}}$ Figure 5. Outage probability performance of wavelength diversity UWOC system under different ocean turbulence parameters, (a) kinetic energy dissipation rate
$\varepsilon $ , (b) mean square temperature dissipation rate${\chi _T}$ , (c) the ratio of temperature and salinity contribution to ocean turbulence$\omega $ ,$L{\rm{ = }}10\;{\rm{m}}$ 图 6 波长分集UWOC系统在不同海洋湍流参数,(a)动能耗散率
$\varepsilon $ ,(b)均方温度耗散率${\chi _T}$ ,(c)温度与盐度对海洋湍流贡献比值$\omega $ 下的平均BER性能变化,$L{\rm{ = }}10\;{\rm{m}}$ Figure 6. Average BER performance of wavelength diversity UWOC system under different ocean turbulence parameters, (a) kinetic energy dissipation rate
$\varepsilon $ , (b) mean square temperature dissipation rate${\chi _T}$ , (c) the ratio of temperature and salinity contribution to ocean turbulence$\omega $ ,$L{\rm{ = }}10\;{\rm{m}}$ 表 1 仿真参数
Table 1. Simulation parameters
Coefficient Value Ratio of temperature and salinity contribution to ocean turbulence, $\omega $ ${\rm{ - }}1$ Kinetic energy dissipation rate, $\varepsilon /{{\rm{m}}^2} \cdot {{\rm{s}}^{{\rm{ - }}3}}$ ${10^{{\rm{ - 4}}}}$ Mean square temperature dissipation rate, ${\chi _T}/{{\rm K}^2} \cdot {{\rm{s}}^{{\rm{ - }}1}}$ ${10^{{\rm{ - 4}}}}$ Dynamic viscosity coefficient, $\nu /{{\rm{m}}^2} \cdot {{\rm{s}}^{{\rm{ - }}1}}$ ${10^{{\rm{ - 5}}}}$ Receiver diameter, $D/{\rm{mm}}$ $1$ Transmission distance, $L/{\rm{m}}$ $10$ 表 2 不同各向异性因子下波长分集UWOC系统中断概率
Table 2. Outage probability of wavelength diversity UWOC system under different anisotropy factors
Wavelength diversity ${u_x} = 1,{u_y} = 1$ ${u_x} = 1,{u_y} = 2$ ${u_x} = 2,{u_y} = 2$ $W{\rm{ = 1}}$ $3.{\rm{792}} \times {10^{{\rm{ - 3}}}}$ $2.798 \times {10^{{\rm{ - 3}}}}$ $2.{\rm{499}} \times {10^{{\rm{ - 4}}}}$ $W{\rm{ = 2}}$ $2.097 \times {10^{{\rm{ - 5}}}}$ $1.199 \times {10^{{\rm{ - 5}}}}$ $1.{\rm{228}} \times {10^{{\rm{ - 7}}}}$ $W{\rm{ = 3}}$ $3.819 \times {10^{{\rm{ - 7}}}}$ $1.{\rm{749}} \times {10^{{\rm{ - 7}}}}$ $3.347 \times {10^{{\rm{ - 10}}}}$ 表 3 使用OC技术的波长分集UWOC系统在不同传输距离下的平均BER
Table 3. Average BER of wavelength diversity UWOC system using OC technology under different transmission distances
Wavelength diversity $L{\rm{ = }}5\;{\rm{m}}$ $L{\rm{ = 10\;m}}$ $L{\rm{ = 1}}5\;{\rm{m}}$ $W{\rm{ = 1}}$ $3.{\rm{42}} \times {10^{{\rm{ - 5}}}}$ $2.7 \times {10^{{\rm{ - 3}}}}$ $4.308 \times {10^{{\rm{ - 3}}}}$ $W{\rm{ = 2}}$ $1.481 \times {10^{{\rm{ - 8}}}}$ $7.634 \times {10^{{\rm{ - 5}}}}$ $2.198 \times {10^{{\rm{ - 4}}}}$ $W{\rm{ = 3}}$ $8.761 \times {10^{{\rm{ - 11}}}}$ $7.{\rm{375}} \times {10^{{\rm{ - 6}}}}$ $3.604 \times {10^{{\rm{ - 5}}}}$ -
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