Researching | Performance of Satellite-to-Ground Laser Communications Under the Influence of Atmospheric Turbulence and Platform Micro-Vibration

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 3 >Page 301003 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 3, 301003 (2021)

Performance of Satellite-to-Ground Laser Communications Under the Influence of Atmospheric Turbulence and Platform Micro-Vibration

Sun Jing^*, Huang Puming, and Yao Zhoushi

Author Affiliations

Xi''an Institute of Space Radio Technology, Xi''an , Shaanxi 710100, China

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DOI: 10.3788/LOP202158.0301003 Cite this Article Set citation alerts

Sun Jing, Huang Puming, Yao Zhoushi. Performance of Satellite-to-Ground Laser Communications Under the Influence of Atmospheric Turbulence and Platform Micro-Vibration[J]. Laser & Optoelectronics Progress, 2021, 58(3): 301003 Copy Citation Text

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Abstract

The existence of atmospheric turbulence and platform micro-vibration will cause the random channel attenuation of the satellite-to-ground laser communication links， which leads to the unstable communication quality. To further analyzes the performance of satellite-to-ground laser communications with the influence of atmospheric turbulence and platform micro-vibration， a random attenuation model of joint satellite-to-ground laser link is established. Based on binary phase shift keying modulation and heterodyne coherent reception， the closed form expression of system average bit error rate under the model is given. The influence of different satellite-to-ground laser communication system parameters on the bit error rate performance is analyzed by simulation. The research results can provide a theoretical reference for the design of practical satellite-to-ground laser communication system.

Keywords

atmospheric optics atmospheric turbulence bit error rate coherent optical communication satellite-to-ground laser communications

γ (t) = \frac{2 R_{d}^{2} P_{s} (t) P_{L O}}{2 q R_{d} P_{L O} Δ f} = \frac{R_{d} h (t) P_{T}}{q Δ f}

，（1）

\begin{array}{l} f (h_{I}) = \frac{α β}{Γ (α) Γ (β)} \frac{ε^{2}}{A_{0}} \times \\ G_{1,3}^{3,0} (α β \frac{h_{I}}{A_{0}} |\begin{matrix} ε^{2} \\ \begin{matrix} ε^{2} - 1 & α - 1 & β - 1 \end{matrix} \end{matrix}) \end{array}

，（2）

w_{L e q}^{2} = w_{L}^{2} \frac{\sqrt[]{π} e r f (v)}{2 v e x p (- v^{2})}, A_{0} = {[e r f (v)]}^{2}, v = \frac{\sqrt[]{π} D_{R}}{2 \sqrt[]{2} w_{L}},

（3）

w_{L} \approx w_{0} \sqrt[]{1 + ε_{0} {(λ L / π w_{0}^{2})}^{2}}

，（4）

ρ_{c} = {[1.46 k^{2} \frac{1}{c o s ζ} \int_{h_{0}}^{H} C_{n}^{2} (h) d h]}^{- 3 / 5}

，（5）

C_{n}^{2} (h) = 0.00594 {(\frac{w}{27})}^{2} {(10^{- 5} h)}^{10} e x p (- \frac{h}{1000}) + 2.7 \times 10^{- 16} e x p (- \frac{h}{1500}) + B_{0} e x p (- \frac{h}{100})

，（6）

\begin{array}{l} α = {[e x p (\frac{0.49 σ_{R, s p}^{2}}{{(1 + 1.11 σ_{R, s p}^{12 / 5})}^{7 / 6}}) - 1]}^{- 1}, \\ β = {[e x p (\frac{0.49 σ_{R, s p}^{2}}{{(1 + 0.69 σ_{R, s p}^{12 / 5})}^{5 / 6}}) - 1]}^{- 1} \end{array}

，（7）

σ_{R, s p}^{2} = 2.25 k^{7 / 6} s e c^{11 / 6} ζ \int_{h_{0}}^{H} C_{n}^{2} (h) (h - h_{0})^{5 / 6} d h

。（8）

η_{c} = 8 α_{p}^{2} \int_{0}^{1} \int_{0}^{1} e x p [- (x_{1}^{2} + x_{2}^{2}) (α_{p}^{2} + \frac{2 π σ_{β}^{2} A_{R}}{λ^{2}} + \frac{A_{R}}{A_{c}})] I_{0} (\frac{2 A_{R} x_{1} x_{2}}{A_{c}}) x_{1} x_{2} d x_{1} d x_{2}

，（9）

\begin{array}{l} f (h s) = \frac{α β}{Γ (α) Γ (β)} \frac{ε^{2}}{A_{0}} \frac{1}{η_{c}} \times \\ G_{1,3}^{3,0} (α β \frac{h s}{A_{0} η_{c}} |\begin{matrix} ε^{2} \\ \begin{matrix} ε^{2} - 1 & α - 1 & β - 1 \end{matrix} \end{matrix}) \end{array}

。（10）

P_{B P S K} (γ) = e r f c (\sqrt[]{γ / 2}) / 2

，（11）

P_{e} = \int_{0}^{\infty} P_{B P S K} (γ) f (γ) d γ

。（12）

\begin{matrix} f (γ) = \frac{α β}{Γ (α) Γ (β)} \frac{ε^{2}}{A_{0}} \frac{1}{η_{c}} \frac{q Δ f}{R_{d} P_{T}} \times \\ G_{1,3}^{3,0} (α β \frac{q Δ f}{A_{0} η_{c} R_{d} P_{T}} γ |\begin{matrix} ε^{2} \\ \begin{matrix} ε^{2} - 1 & α - 1 & β - 1 \end{matrix} \end{matrix}) \end{matrix}

。（13）

G_{1,3}^{3,0} (z |\begin{matrix} a_{1} \\ b_{1}, b_{2}, b_{3} \end{matrix}) = \sum_{k = 1}^{3} \frac{\prod_{j = 1, j \neq k}^{3} Γ (b_{j} - b_{k})}{Γ (a_{1} - b_{k})} \times z^{b_{k}} {}_{1}F F_{2} \{1 - a_{1} + b_{k}; [1 + b_{k} {- b]}^{+}; z\}

，（14）

{}_{1} F_{2} (a_{1}; b_{1}, b_{2}; z) = \sum_{n = 0}^{\infty} \frac{{(a_{1})}_{n}}{{(b_{1})}_{n} {(b_{2})}_{n} n!} z^{n}

，（15）

f (γ) = X_{0, γ} γ^{ε^{2} - 1} + \sum_{n = 0}^{\infty} Y_{n, γ} γ^{n + α - 1} + \sum_{n = 0}^{\infty} Z_{n, γ} γ^{n + β - 1}

，（16）

X_{0, γ} = \frac{ε^{2}}{Γ (α) Γ (β)} Γ (α - ε^{2}) Γ (β - ε^{2}) {(\frac{α β q Δ f}{A_{0} η_{c} R_{d} P_{T}})}^{ε^{2}},

（17）

Y_{n, γ} = \frac{ε^{2}}{Γ (α) Γ (β)} \frac{Γ (ε^{2} - α) Γ (β - α)}{Γ (1 + ε^{2} - α)} \frac{{(α - ε^{2})}_{n}}{{(1 + α - ε^{2})}_{n} {(1 + α - β)}_{n} n!} {(\frac{α β q Δ f}{A_{0} η_{c} R_{d} P_{T}})}^{n + α}

，（18）

Z_{n, γ} = \frac{ε^{2}}{Γ (α) Γ (β)} \frac{Γ (ε^{2} - β) Γ (α - β)}{Γ (1 + ε^{2} - β)} \frac{{(β - ε^{2})}_{n}}{{(1 + β - ε^{2})}_{n} {(1 + β - α)}_{n} n!} {(\frac{α β q Δ f}{A_{0} η_{c} R_{d} P_{T}})}^{n + β}

。（19）

\frac{1}{2} \int_{0}^{\infty} e r f c (\sqrt[]{x / 2}) x^{b} d x = \frac{Γ (b + \frac{3}{2}) 2^{b}}{(b + 1) \sqrt[]{π}}

。（20）

\begin{array}{l} P_{e} = \frac{1}{2 \sqrt[]{π} Γ (α) Γ (β)} \{\begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} C_{P}^{ε^{2}} Γ (α - ε^{2}) Γ (b - ε^{2}) Γ (\frac{1}{2} + ε^{2}) + \\ C_{1} [\frac{{}_{2} F_{2} (α, \frac{1}{2} + α; 1 + α, 1 + α - β; C_{P})}{α} - \frac{{}_{2} F_{2} (α - ε^{2}, \frac{1}{2} + α; 1 + α - ε^{2}, 1 + α - β; C_{P})}{a - ε^{2}}] + \\ C_{2} [\frac{{}_{2} F_{2} (β, \frac{1}{2} + β; 1 + β, 1 + β - α; C_{P})}{β} - \frac{{}_{2} F_{2} (β - ε^{2}, \frac{1}{2} + β; 1 + β - ε^{2}, 1 + β - α; C_{P})}{β - ε^{2}}]\} \end{array}

，（21）

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Sun Jing, Huang Puming, Yao Zhoushi. Performance of Satellite-to-Ground Laser Communications Under the Influence of Atmospheric Turbulence and Platform Micro-Vibration[J]. Laser & Optoelectronics Progress, 2021, 58(3): 301003

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