Abstract

With the rapid development of light emitting diode (LED), visible light communication (VLC) becomes an important technique for information transmission including underwater applications. However, accurate channel estimation for underwater VLC is still challenging due to the complex environment of the underwater VLC channel. In this paper, by utilizing a proper approximation, where the channel attenuation is linear with the frequency, a new compressive sensing (CS) based channel estimation approach is proposed. Utilizing the sparse property of the reflection path length for the underwater VLC channel, the CS framework is modeled to estimate the reflection path length, which can further recover the underwater VLC channel. Moreover, a Bayesian CS recovery algorithm is investigated to overcome the problem of high coherence for the sensing matrix which outperforms the conventional greedy algorithm such as orthogonal matching pursuit (OMP). Simulation results illustrate that our proposed channel estimation for underwater VLC systems has a superior performance which can significantly reduce the pilot overhead, improve the spectral efficiency, and enhance the estimation accuracy.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
  22. X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
    [Crossref]
  23. X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  32. D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Process. 52(8), 2153–2164 (2004).
    [Crossref]

2017 (5)

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Y. Zhao, J. Xu, A. Wang, W. Lv, L. Zhu, S. Li, and J. Wang, “Demonstration of data-carrying orbital angular momentum-based underwater wireless optical multicasting link,” Opt. Express 25(23), 28743–28751 (2017).
[Crossref]

Y. Zhang, X. Ji, X. Li, and H. Yu, “Thermal blooming effect of laser beams propagating through seawater,” Opt. Express 25(6), 5861–5875 (2017).
[Crossref] [PubMed]

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
[Crossref]

2016 (2)

X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
[Crossref]

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

2015 (4)

2014 (2)

L. Lu, X. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22(22), 27112–27122 (2014).
[Crossref] [PubMed]

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

2013 (3)

2012 (1)

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
[Crossref]

2011 (1)

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

2010 (2)

B. Cochenour, L. Mullen, and J. Muth, “Effect of scattering albedo on attenuation and polarization of light underwater,” Opt. Lett. 35(12), 2088–2090 (2010).
[Crossref] [PubMed]

Z. Ben-Haim, Y. C. Eldar, and M. Elad, “Coherence-based performance guarantees for estimating a sparse vector under random noise,” IEEE Trans. Signal Process. 58(10), 5030–5043 (2010).
[Crossref]

2009 (2)

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26(3), 301–321 (2009).
[Crossref]

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

2008 (1)

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56(6), 2346–2356 (2008).
[Crossref]

2007 (1)

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

2006 (2)

A. Morel, B. Gentili, M. Chami, and J. Ras, “Bio-optical properties of high chlorophyll case 1 waters and of yellow-substance-dominated case 2 waters,” Deep-Sea Research Part I 53(9), 1439–1459 (2006).
[Crossref]

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2005 (1)

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

2004 (1)

D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Process. 52(8), 2153–2164 (2004).
[Crossref]

2000 (1)

Z. Wang and G. B. Giannakis, “Wireless multicarrier communications,” IEEE Trans. Signal Process. 17(3), 29–48 (2000).
[Crossref]

Ahmed, M.

M. Ahmed and L. Lampe, “Power line communications for low-voltage power grid tomography,” IEEE Trans. Commun. 61(12), 5163–5175 (2013).
[Crossref]

Akhoundi, F.

F. Akhoundi, J. A. Salehi, and A. Tashakori, “Cellular underwater wireless optical CDMA network: Performance analysis and implementation concepts,” IEEE Trans. Commun. 63(3), 882–891 (2015).
[Crossref]

Alouini, M.-S.

Baykal, Y.

Ben-Haim, Z.

Z. Ben-Haim, Y. C. Eldar, and M. Elad, “Coherence-based performance guarantees for estimating a sparse vector under random noise,” IEEE Trans. Signal Process. 58(10), 5030–5043 (2010).
[Crossref]

Bourennane, S.

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

Candes, E. J.

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

Cao, T.

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Carin, L.

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56(6), 2346–2356 (2008).
[Crossref]

Chami, M.

A. Morel, B. Gentili, M. Chami, and J. Ras, “Bio-optical properties of high chlorophyll case 1 waters and of yellow-substance-dominated case 2 waters,” Deep-Sea Research Part I 53(9), 1439–1459 (2006).
[Crossref]

Chi, Y.-C.

Chow, C. W.

Cochenour, B.

Dai, L.

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

Dai, W.

W. Ding, F. Yang, W. Dai, and J. Song, “Time-frequency joint sparse channel estimation for MIMO-OFDM systems,” IEEE Commun. Lett. 19(1), 58–61 (2015).
[Crossref]

Ding, W.

X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
[Crossref]

W. Ding, F. Yang, W. Dai, and J. Song, “Time-frequency joint sparse channel estimation for MIMO-OFDM systems,” IEEE Commun. Lett. 19(1), 58–61 (2015).
[Crossref]

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Duarte, M. F.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

Duran, J. R.

Elad, M.

Z. Ben-Haim, Y. C. Eldar, and M. Elad, “Coherence-based performance guarantees for estimating a sparse vector under random noise,” IEEE Trans. Signal Process. 58(10), 5030–5043 (2010).
[Crossref]

Eldar, Y. C.

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

Z. Ben-Haim, Y. C. Eldar, and M. Elad, “Coherence-based performance guarantees for estimating a sparse vector under random noise,” IEEE Trans. Signal Process. 58(10), 5030–5043 (2010).
[Crossref]

Faulkner, G.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Gentili, B.

A. Morel, B. Gentili, M. Chami, and J. Ras, “Bio-optical properties of high chlorophyll case 1 waters and of yellow-substance-dominated case 2 waters,” Deep-Sea Research Part I 53(9), 1439–1459 (2006).
[Crossref]

Giannakis, G. B.

Z. Wang and G. B. Giannakis, “Wireless multicarrier communications,” IEEE Trans. Signal Process. 17(3), 29–48 (2000).
[Crossref]

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

Goode, W.

Grubor, J.

J. Grubor, O. Jamett, J. Walewski, S. Randel, and K.-D. Langer, “High-speed wireless indoor communication via visible light,” ITG Fachbericht (2007).

Guo, L.

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Hamza, T.

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

Han, Z.

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
[Crossref]

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
[Crossref]

Z. Han, H. Li, and W. Yin, Compressive Sensing for Wireless Networks, Cambridge University Press, UK, (2013).

He, J.-H.

Hou, W.

Jamett, O.

J. Grubor, O. Jamett, J. Walewski, S. Randel, and K.-D. Langer, “High-speed wireless indoor communication via visible light,” ITG Fachbericht (2007).

Janjua, B.

Jarosz, E.

Ji, S.

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56(6), 2346–2356 (2008).
[Crossref]

Ji, X.

Jung, D.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Kaddoum, G.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

Kaushal, H.

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

Khalighi, M. A.

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

Kuo, H.-C.

Lampe, L.

M. Ahmed and L. Lampe, “Power line communications for low-voltage power grid tomography,” IEEE Trans. Commun. 61(12), 5163–5175 (2013).
[Crossref]

Langer, K.-D.

J. Grubor, O. Jamett, J. Walewski, S. Randel, and K.-D. Langer, “High-speed wireless indoor communication via visible light,” ITG Fachbericht (2007).

Lee, K.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Léon, P.

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

Li, C.

Li, H.

Z. Han, H. Li, and W. Yin, Compressive Sensing for Wireless Networks, Cambridge University Press, UK, (2013).

Li, S.

Li, X.

Li, Y.

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
[Crossref]

Lin, G.-R.

Liu, S.

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
[Crossref]

Liu, Y. L.

Lu, L.

Lv, W.

Ma, X.

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
[Crossref]

X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
[Crossref]

Meng, J.

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
[Crossref]

Minh, H.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Morel, A.

A. Morel, B. Gentili, M. Chami, and J. Ras, “Bio-optical properties of high chlorophyll case 1 waters and of yellow-substance-dominated case 2 waters,” Deep-Sea Research Part I 53(9), 1439–1459 (2006).
[Crossref]

Mullen, L.

Muth, J.

Needell, D.

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26(3), 301–321 (2009).
[Crossref]

Ng, T. K.

Nguyen, N. T.

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
[Crossref]

O’brien, D.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Oh, Y.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Ooi, B. S.

Opderbecke, J.

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

Oubei, H. M.

Pan, C.

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

Park, K.-H.

Randel, S.

J. Grubor, O. Jamett, J. Walewski, S. Randel, and K.-D. Langer, “High-speed wireless indoor communication via visible light,” ITG Fachbericht (2007).

Rao, B.

D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Process. 52(8), 2153–2164 (2004).
[Crossref]

Ras, J.

A. Morel, B. Gentili, M. Chami, and J. Ras, “Bio-optical properties of high chlorophyll case 1 waters and of yellow-substance-dominated case 2 waters,” Deep-Sea Research Part I 53(9), 1439–1459 (2006).
[Crossref]

Salehi, J. A.

F. Akhoundi, J. A. Salehi, and A. Tashakori, “Cellular underwater wireless optical CDMA network: Performance analysis and implementation concepts,” IEEE Trans. Commun. 63(3), 882–891 (2015).
[Crossref]

Song, J.

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
[Crossref]

X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
[Crossref]

W. Ding, F. Yang, W. Dai, and J. Song, “Time-frequency joint sparse channel estimation for MIMO-OFDM systems,” IEEE Commun. Lett. 19(1), 58–61 (2015).
[Crossref]

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

Tao, T.

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

Tashakori, A.

F. Akhoundi, J. A. Salehi, and A. Tashakori, “Cellular underwater wireless optical CDMA network: Performance analysis and implementation concepts,” IEEE Trans. Commun. 63(3), 882–891 (2015).
[Crossref]

Tian, H.

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Tropp, J. A.

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26(3), 301–321 (2009).
[Crossref]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

Tsai, C.-T.

Walewski, J.

J. Grubor, O. Jamett, J. Walewski, S. Randel, and K.-D. Langer, “High-speed wireless indoor communication via visible light,” ITG Fachbericht (2007).

Wang, A.

Wang, H.-Y.

Wang, J.

Wang, P.

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Wang, W.

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Wang, Z.

Z. Wang and G. B. Giannakis, “Wireless multicarrier communications,” IEEE Trans. Signal Process. 17(3), 29–48 (2000).
[Crossref]

Weidemann, A.

Wipf, D.

D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Process. 52(8), 2153–2164 (2004).
[Crossref]

Won, E. T.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

Woods, S.

Xu, J.

Xue, Y.

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56(6), 2346–2356 (2008).
[Crossref]

Yang, F.

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
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X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
[Crossref]

W. Ding, F. Yang, W. Dai, and J. Song, “Time-frequency joint sparse channel estimation for MIMO-OFDM systems,” IEEE Commun. Lett. 19(1), 58–61 (2015).
[Crossref]

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

Yeh, C. H.

Yin, W.

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
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Z. Han, H. Li, and W. Yin, Compressive Sensing for Wireless Networks, Cambridge University Press, UK, (2013).

Yu, H.

Zeng, L.

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
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Zhang, Y.

Y. Zhang, X. Ji, X. Li, and H. Yu, “Thermal blooming effect of laser beams propagating through seawater,” Opt. Express 25(6), 5861–5875 (2017).
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W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

Zhao, Y.

Zhu, L.

Applied and Computational Harmonic Analysis (1)

D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis 26(3), 301–321 (2009).
[Crossref]

Deep-Sea Research Part I (1)

A. Morel, B. Gentili, M. Chami, and J. Ras, “Bio-optical properties of high chlorophyll case 1 waters and of yellow-substance-dominated case 2 waters,” Deep-Sea Research Part I 53(9), 1439–1459 (2006).
[Crossref]

IEEE Access (1)

H. Kaushal and G. Kaddoum, “Underwater optical wireless communication,” IEEE Access 4(1), 1518–1547 (2016).
[Crossref]

IEEE Commun. Lett. (1)

W. Ding, F. Yang, W. Dai, and J. Song, “Time-frequency joint sparse channel estimation for MIMO-OFDM systems,” IEEE Commun. Lett. 19(1), 58–61 (2015).
[Crossref]

IEEE J. Sel. Areas Commun. (2)

X. Ma, F. Yang, S. Liu, J. Song, and Z. Han, “Design and optimization on training sequence for mmwave communications: A new approach for sparse channel estimation in massive MIMO,” IEEE J. Sel. Areas Commun. 35(7), 1486–1497 (2017).
[Crossref]

L. Zeng, D. O’brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white LED lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
[Crossref]

IEEE J. Sel. Topics Signal Process. (1)

J. Meng, W. Yin, Y. Li, N. T. Nguyen, and Z. Han, “Compressive sensing based high-resolution channel estimation for OFDM system,” IEEE J. Sel. Topics Signal Process. 6(1), 15–25 (2012).
[Crossref]

IEEE Photon. J. (2)

M. A. Khalighi, T. Hamza, S. Bourennane, P. Léon, and J. Opderbecke, “Underwater wireless optical communications using silicon photo-multipliers,” IEEE Photon. J. 9(4), 1–10 (2017).
[Crossref]

W. Wang, P. Wang, T. Cao, H. Tian, Y. Zhang, and L. Guo, “Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence,” IEEE Photon. J. 9(5), 1–15 (2017).

IEEE Trans. Broadcast. (2)

X. Ma, F. Yang, W. Ding, and J. Song, “Novel approach to design time-domain training sequence for accurate sparse channel estimation,” IEEE Trans. Broadcast. 62(3), 512–520 (2016).
[Crossref]

W. Ding, F. Yang, C. Pan, L. Dai, and J. Song, “Compressive sensing based channel estimation for OFDM systems under long delay channels,” IEEE Trans. Broadcast. 60(2), 313–321 (2014).
[Crossref]

IEEE Trans. Commun. (2)

M. Ahmed and L. Lampe, “Power line communications for low-voltage power grid tomography,” IEEE Trans. Commun. 61(12), 5163–5175 (2013).
[Crossref]

F. Akhoundi, J. A. Salehi, and A. Tashakori, “Cellular underwater wireless optical CDMA network: Performance analysis and implementation concepts,” IEEE Trans. Commun. 63(3), 882–891 (2015).
[Crossref]

IEEE Trans. Inf. Theory (3)

D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007).
[Crossref]

E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

IEEE Trans. Signal Process. (5)

Z. Ben-Haim, Y. C. Eldar, and M. Elad, “Coherence-based performance guarantees for estimating a sparse vector under random noise,” IEEE Trans. Signal Process. 58(10), 5030–5043 (2010).
[Crossref]

D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Process. 52(8), 2153–2164 (2004).
[Crossref]

M. F. Duarte and Y. C. Eldar, “Structured compressed sensing: From theory to applications,” IEEE Trans. Signal Process. 59(9), 4053–4085 (2011).
[Crossref]

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56(6), 2346–2356 (2008).
[Crossref]

Z. Wang and G. B. Giannakis, “Wireless multicarrier communications,” IEEE Trans. Signal Process. 17(3), 29–48 (2000).
[Crossref]

Opt. Express (7)

W. Hou, E. Jarosz, S. Woods, W. Goode, and A. Weidemann, “Impacts of underwater turbulence on acoustical and optical signals and their linkage,” Opt. Express 21(4), 4367–4375 (2013).
[Crossref] [PubMed]

L. Lu, X. Ji, and Y. Baykal, “Wave structure function and spatial coherence radius of plane and spherical waves propagating through oceanic turbulence,” Opt. Express 22(22), 27112–27122 (2014).
[Crossref] [PubMed]

Y. Zhang, X. Ji, X. Li, and H. Yu, “Thermal blooming effect of laser beams propagating through seawater,” Opt. Express 25(6), 5861–5875 (2017).
[Crossref] [PubMed]

H. M. Oubei, C. Li, K.-H. Park, T. K. Ng, M.-S. Alouini, and B. S. Ooi, “2.3 gbit/s underwater wireless optical communications using directly modulated 520 nm laser diode,” Opt. Express 23(16), 20743–20748 (2015).
[Crossref] [PubMed]

H. M. Oubei, J. R. Duran, B. Janjua, H.-Y. Wang, C.-T. Tsai, Y.-C. Chi, T. K. Ng, H.-C. Kuo, J.-H. He, M.-S. Alouini, G.-R. Lin, and B. S. Ooi, “4.8 gbit/s 16-QAM-OFDM transmission based on compact 450-nm laser for underwater wireless optical communication,” Opt. Express 23(18), 23302–23309 (2015).
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Y. Zhao, J. Xu, A. Wang, W. Lv, L. Zhu, S. Li, and J. Wang, “Demonstration of data-carrying orbital angular momentum-based underwater wireless optical multicasting link,” Opt. Express 25(23), 28743–28751 (2017).
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C. H. Yeh, Y. L. Liu, and C. W. Chow, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
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Opt. Lett. (1)

Other (3)

“IEEE standard for local and metropolitan area networks-part 15.7: short-range wireless optical communication using visible light,” (2011).

J. Grubor, O. Jamett, J. Walewski, S. Randel, and K.-D. Langer, “High-speed wireless indoor communication via visible light,” ITG Fachbericht (2007).

Z. Han, H. Li, and W. Yin, Compressive Sensing for Wireless Networks, Cambridge University Press, UK, (2013).

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Figures (4)

Fig. 1
Fig. 1 A typical attenuation trend in sea water [25].
Fig. 2
Fig. 2 The snapshot of the typical 3-path underwater VLC equivalent baseband channel in frequency domain (a) and time domain (b).
Fig. 3
Fig. 3 Simulation for accurate recovery probabilities when SNR = 20 dB.
Fig. 4
Fig. 4 The MSE performance of CIR simulations.

Tables (2)

Tables Icon

Algorithm 1 Bayesian CS for underwater VLC channel estimation.

Tables Icon

Table 1 Coefficients in the Simulations

Equations (23)

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t = [ c T , u T ] T ,
H ( f ) = α e β ( f ) s ,
H ( f ) = l = 0 L 1 α e β ( f ) s l ,
β ( f ) = β 1 f + β 2 ,
H ( f ) = l = 0 L 1 α e ( β 1 f + β 2 ) s l .
Δ f = f max f min P 1 ,
f i = f min + i Δ f ,
H ( f i ) = l = 0 L 1 α e ( β 1 f i + β 2 ) s l = l = 0 L 1 α e [ β 1 ( f min + i Δ f ) + β 2 ] s l = l = 0 L 1 λ l ω l i ,
λ l = α e ( β 1 f min + β 2 ) s l ,
ω l = e β 1 Δ f s l ,
y = [ H ( f 0 ) , H ( f 1 ) , , H ( f P 1 ) ] T .
s l = n l Δ s ,
y = Φ x ,
x = [ x 0 , x 1 , , x N 1 ] T ,
Φ = [ ν 0 ν 1 ν N 1 ν 0 2 ν 1 2 ν N 1 2 ν 0 P ν 1 P ν N 1 P ] ,
ν k = e β 1 Δ f Δ s k .
S = { s l Δ s } l = 0 L 1 .
s l = S l Δ s ,
μ = max 0 j , k N 1 , j k | φ j , φ k | φ j 2 φ k 2 ,
H ^ ( f i ) = Y i / X i ,
y = Φ D x D .
x est = Φ D   + y = ( Φ D   H Φ D ) 1 Φ D y .
CRLB = E { x est x 2 } = L σ 2 / P .

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