• Infrared and Laser Engineering
  • Vol. 50, Issue 8, 20200382 (2021)
Jinjia Li1、2, Demao Ye3, Linning Wang1, Kang Fu1, and Yongjin Wang1、*
Author Affiliations
  • 1College of Telecommunications & Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
  • 2Harbin University of Science and Technology (Weihai), Weihai 264300, China
  • 3The 713th Research Institute of China Shipbuilding Industry Corporation, Zhengzhou 450015, China
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    DOI: 10.3788/IRLA20200382 Cite this Article
    Jinjia Li, Demao Ye, Linning Wang, Kang Fu, Yongjin Wang. MIMO scheme for underwater wireless optical communication system using PMT array[J]. Infrared and Laser Engineering, 2021, 50(8): 20200382 Copy Citation Text show less

    Abstract

    Underwater wireless optical communication (UWOC) has the characteristics of high bandwidth and low latency, and have become a viable alternative for underwater communication. The transmitter and receiver arrays of this system are composed of six green light emitting diode (LED) and three photomultiplier tube (PMT), respectively, and forming a 6×3 multiple input multiple output (MIMO) transmission mode. This system achieved a 1 Mbps data transmission rate over a distance of 10 m water tank underwater channel. MATLAB was adopted to simulate this underwater channel model and predict the received optical power distribution on the receiving plane and the maximum value is -35.8 dBm. Moreover, the PMT anode output voltage and the cathode current waveform were tested. Derivation and calculation show that the signal-to-noise ratio (SNR) is 19.4 dB, and the bit error rate (BER) is approximately 1.1×10-5. The theoretical minimum received power of the this PMT module can be as low as 1.5×10-9 W, which reflects its extremely high sensitivity. Finally, through Monte Carlo channel simulation, the performance of MIMO is further verified, and the channel capacity of 35 bit·s-1·Hz-1 can be reached at a SNR of 25 dB.
    $ d\geqslant \sqrt{\lambda L}\approx 0.23 \;\rm{cm}$(1)

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    $\rho ={{\left[ 44.2K{{\left( \frac{2\pi }{\lambda } \right)}^{2}}L \right]}^{-{}^{3}\!\!\diagup\!\!{}_{5}\;}}$(2)

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    $ a(\lambda ) = {a_w}(\lambda ) + {a_{CD{\rm{OM}}}}(\lambda ) + {a_{phy}}(\lambda ) + {a_{\det }}(\lambda ) $(3)

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    $ b(\lambda ) = {b_w}(\lambda ) + {b_{CDMA}}(\lambda ) + {b_{phy}}(\lambda ) + {b_{\det }}(\lambda ) $(4)

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    $\tilde \beta (\theta ,\lambda ) = \frac{{\beta (\theta ,\lambda )}}{{b(\lambda )}}$(5)

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    $\tilde{\beta }(\theta ,{\rm{g}})={{P}_{\rm{HG}}{}}(\theta ,{\rm{g}})=\frac{1}{4\pi }\frac{1-{{g}^{2}}}{{{(1+{{g}^{2}}-2g\cos \theta )}^{{}^{3}\!\!\diagup\!\!{}_{2}\;}}}$(6)

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    $\tilde \beta (\theta ,\alpha ,{g_f},{g_b}) = \alpha \tilde \beta (\theta ,{g_f}) + (1 - \alpha )\tilde \beta (\theta , - {g_b})$(7)

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    ${{P}_{R}}(cd)={{P}_{T}}\exp \left[ -\left( 1-\eta {{\omega }_{0}} \right)cd \right],{{\omega }_{0}}={b}/{c}\;$(8)

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    ${H_{los}}{\rm{(0) = }}\frac{{(m + 1){A_{PD}}}}{{2\pi {d^2}}} \cdot \cos (\alpha ) \cdot {\cos ^m}(\beta ) \cdot g(\alpha )$(9)

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    ${P_R}(d) = {P_T}\exp \left[ { - \left( {1 - \eta {\omega _0}} \right)cd} \right]{H_{los}}(0)$(10)

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    $C = \mathop {\max }\limits_{{{\boldsymbol{R}}_x}:Tr({{\boldsymbol{R}}_x}) = \rho } E\left[ {W{{\log }_2}\det [{{\boldsymbol{I}}_{{M_r}}} + {\boldsymbol{H}}{{\boldsymbol{R}}_x}{{\boldsymbol{H}}^{\rm{T}}}]} \right]$(11)

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    ${I_k} = \frac{{\eta eP\lambda }}{{hc}}$(12)

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    $\eta = \frac{{hc}}{{\lambda e}}{S_K} = \frac{{1240}}{\lambda }{S_K} \approx 20.8{\rm{\% }}$(13)

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    $P = \frac{{hc{I_k}}}{{\lambda e\eta }} = \frac{{0.0237{I_k}}}{\eta } \approx 0.114{I_k}$(14)

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    $F = \left( {{1 / \alpha }} \right) \cdot \left( {{1 / {{\delta _1} + {1 / {{\delta _1}{\delta _2} + \cdots {1 / {{\delta _1}{\delta _2} \cdots {\delta _n}}}}}}}} \right)$(15)

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    $F \approx \delta /(\delta - 1)$(16)

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    ${I_n} = \mu {\left( {2e{I_k}\alpha BF} \right)^{{1 / 2}}}$(17)

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    ${I_s} = {I_k}\alpha \mu $(18)

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    $SNR \!\approx\! \frac{{{I_s}}}{{{I_n}}} \!=\! {\left. {\left( {\frac{{{I_k}\alpha }}{{2eB}} \cdot \frac{1}{{1 + {1 / {{\delta _1} \!+\! {1 / {{\delta _1}{\delta _2} + \cdots {1 / {{\delta _1}{\delta _2} \cdots {\delta _n}}}}}}}}}} \right.} \right)^{{1 /2}}}$(19)

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    $SNR \approx \frac{{{I_s}}}{{{I_n}}} = \sqrt {\frac{{{I_k}}}{{2eB}} \cdot \frac{1}{{\delta /\left( {\delta - 1} \right)}}} $(20)

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    $SNR \approx {\left( {{I_k}/2eB} \right)^{{1 / 2}}} \approx 1.75 \times {10^3}\sqrt {\frac{{{I_k}({ \text{μ}{\rm{A}}})}}{{B(\rm{MHz})}}} \approx 19.4\;\rm{dB}$(21)

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    ${P_e} = \frac{1}{2}erfc\left( {\sqrt {\frac{{SNR}}{2}} } \right) \approx 1.1 \times {10^{ - 5}}$(22)

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    ${P_i} \!=\! \frac{{e \cdot \mu \cdot F \cdot B}}{{{S_k}}} \!+\! \frac{{\sqrt {{{\left( {e \cdot \mu \cdot F \cdot B} \right)}^2} \!+\! 4e \cdot {I_k} \cdot \mu \cdot F} }}{{{S_k}}} \approx 1.5 \times {10^{ - 9}}\;\rm{W}$(23)

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    ${f_\alpha }(\alpha ) = \frac{1}{{\alpha \sqrt {2\pi \sigma _X^2} }}\exp \left\{ { - \frac{{{{(\ln \alpha - {\mu _X})}^2}}}{{2\sigma _X^2}}} \right\},\alpha > 0$(24)

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    ${P_R}(d) = {P_T}\exp \left[ { - \left( {1 - \eta {\omega _0}} \right)cd} \right]{H_{los}}(0){\alpha ^2}$(25)

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    Jinjia Li, Demao Ye, Linning Wang, Kang Fu, Yongjin Wang. MIMO scheme for underwater wireless optical communication system using PMT array[J]. Infrared and Laser Engineering, 2021, 50(8): 20200382
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