Abstract

In this paper, we proposed a system that realized simultaneously visible light positioning (VLP) and visible light communications (VLC) in the same band by using orthogonal frequency division multiple access (OFDMA). This system used the power of data sequence as the metric to estimate the transmission distances and consequently the receiver’s position, without deteriorating the VLC’s throughput. We theoretically analyzed the positioning errors in both overdetermined and determined VLP systems. In overdetermined VLP system, optimal selection of master light-emitting diode (LED) avoided the fluctuation of positioning error. Excluding the LED with longest transmission distance changed the overdetermined VLP system to determined VLP system, and reduced the positioning error. The power allocation scheme reduced further the positioning error in determined VLP system. This method was fast and effective. The well-matched theoretical and Monte-Carlo (MC) simulation results validated our proposed VLP based on VLC system using OFDMA.

© 2017 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]
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    [Crossref]
  3. M. F. Keskin and S. Gezici, “Comparative theoretical analysis of distance estimation in visible light positioning systems,” J. Lightw. Technol. 34, 854–865 (2016).
    [Crossref]
  4. M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor position tracking using multiple optical receivers,” J. Lightw. Technol. 34, 1166–1176 (2016).
    [Crossref]
  5. M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor localization using visible light and accelerometer,” in “IEEE Global Communications Conference (GLOBECOM),” (2013), pp. 3341–3346.
  6. Z. Li, L. Feng, and A. Yang, “Fusion based on visible light positioning and inertial navigation using extended Kalman filters,” Sensors 17, 1093 (2017).
    [Crossref]
  7. S. Y. Jung, S. Hann, and C. S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57, 1592–1597 (2011).
    [Crossref]
  8. T.-H. Do and M. Yoo, “An in-depth survey of visible light communication based positioning systems,” Sensors 16, E678 (2016).
    [Crossref] [PubMed]
  9. T. Q. Wang, Y. A. Sekercioglu, A. Neild, and J. Armstrong, “Position accuracy of time-of-arrival based ranging using visible light with application in indoor localization systems,” J. Lightwave Technol. 31, 3302–3308 (2013).
    [Crossref]
  10. T. Tanaka and S. Haruyama, “New position detection method using image sensor and visible light leds,” in Second International Conference on Machine Vision (2009), pp. 150–153.
  11. W. Gu, M. Aminikashani, P. Deng, and M. Kavehrad, “Impact of multipath reflections on the performance of indoor visible light positioning systems,” J. Lightwave Technol. 34, 2578–2587 (2016).
    [Crossref]
  12. B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  17. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27, 189–204 (2009).
    [Crossref]
  18. M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning with OFDM visible light communications,” in 13th IEEE Annual Consumer Communications Networking Conference (CCNC) (2016), pp. 505–510.
  19. H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
    [Crossref]
  20. A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
    [Crossref]

2017 (2)

Z. Li, L. Feng, and A. Yang, “Fusion based on visible light positioning and inertial navigation using extended Kalman filters,” Sensors 17, 1093 (2017).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

2016 (5)

M. F. Keskin and S. Gezici, “Comparative theoretical analysis of distance estimation in visible light positioning systems,” J. Lightw. Technol. 34, 854–865 (2016).
[Crossref]

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor position tracking using multiple optical receivers,” J. Lightw. Technol. 34, 1166–1176 (2016).
[Crossref]

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
[Crossref]

T.-H. Do and M. Yoo, “An in-depth survey of visible light communication based positioning systems,” Sensors 16, E678 (2016).
[Crossref] [PubMed]

W. Gu, M. Aminikashani, P. Deng, and M. Kavehrad, “Impact of multipath reflections on the performance of indoor visible light positioning systems,” J. Lightwave Technol. 34, 2578–2587 (2016).
[Crossref]

2014 (1)

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

2013 (2)

2012 (1)

2011 (1)

S. Y. Jung, S. Hann, and C. S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57, 1592–1597 (2011).
[Crossref]

2009 (1)

2004 (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

1997 (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Aminikashani, M.

W. Gu, M. Aminikashani, P. Deng, and M. Kavehrad, “Impact of multipath reflections on the performance of indoor visible light positioning systems,” J. Lightwave Technol. 34, 2578–2587 (2016).
[Crossref]

M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning with OFDM visible light communications,” in 13th IEEE Annual Consumer Communications Networking Conference (CCNC) (2016), pp. 505–510.

Armstrong, J.

Aslam, N.

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Bentley, E.

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

Burton, A.

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

Chen, J.

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

Choudhury, P.

Ciaramella, E.

Corsini, R.

Cossu, G.

Deng, P.

Do, T.-H.

T.-H. Do and M. Yoo, “An in-depth survey of visible light communication based positioning systems,” Sensors 16, E678 (2016).
[Crossref] [PubMed]

Feng, L.

Z. Li, L. Feng, and A. Yang, “Fusion based on visible light positioning and inertial navigation using extended Kalman filters,” Sensors 17, 1093 (2017).
[Crossref]

Gezici, S.

M. F. Keskin and S. Gezici, “Comparative theoretical analysis of distance estimation in visible light positioning systems,” J. Lightw. Technol. 34, 854–865 (2016).
[Crossref]

Ghassemlooy, Z.

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, Y. Li, and S. Zhang, “An indoor VLC positioning system based on OFDMA,” in Asia Communications and Photonics Conference (2016), p. AS1B.5.
[Crossref]

Gu, W.

W. Gu, M. Aminikashani, P. Deng, and M. Kavehrad, “Impact of multipath reflections on the performance of indoor visible light positioning systems,” J. Lightwave Technol. 34, 2578–2587 (2016).
[Crossref]

M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning with OFDM visible light communications,” in 13th IEEE Annual Consumer Communications Networking Conference (CCNC) (2016), pp. 505–510.

Han, S.

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

Hann, S.

S. Y. Jung, S. Hann, and C. S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57, 1592–1597 (2011).
[Crossref]

Haruyama, S.

T. Tanaka and S. Haruyama, “New position detection method using image sensor and visible light leds,” in Second International Conference on Machine Vision (2009), pp. 150–153.

Ho, S. W.

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor position tracking using multiple optical receivers,” J. Lightw. Technol. 34, 1166–1176 (2016).
[Crossref]

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor localization using visible light and accelerometer,” in “IEEE Global Communications Conference (GLOBECOM),” (2013), pp. 3341–3346.

Jung, S. Y.

S. Y. Jung, S. Hann, and C. S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57, 1592–1597 (2011).
[Crossref]

Kahn, J. M.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Kapinas, V. M.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
[Crossref]

Karagiannidis, G. K.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
[Crossref]

Kavehrad, M.

W. Gu, M. Aminikashani, P. Deng, and M. Kavehrad, “Impact of multipath reflections on the performance of indoor visible light positioning systems,” J. Lightwave Technol. 34, 2578–2587 (2016).
[Crossref]

M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning with OFDM visible light communications,” in 13th IEEE Annual Consumer Communications Networking Conference (CCNC) (2016), pp. 505–510.

Keskin, M. F.

M. F. Keskin and S. Gezici, “Comparative theoretical analysis of distance estimation in visible light positioning systems,” J. Lightw. Technol. 34, 854–865 (2016).
[Crossref]

Khalid, A. M.

Komine, T.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

Li, Y.

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, Y. Li, and S. Zhang, “An indoor VLC positioning system based on OFDMA,” in Asia Communications and Photonics Conference (2016), p. AS1B.5.
[Crossref]

Li, Z.

Z. Li, L. Feng, and A. Yang, “Fusion based on visible light positioning and inertial navigation using extended Kalman filters,” Sensors 17, 1093 (2017).
[Crossref]

Liaw, S. K.

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

Lin, B.

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, Y. Li, and S. Zhang, “An indoor VLC positioning system based on OFDMA,” in Asia Communications and Photonics Conference (2016), p. AS1B.5.
[Crossref]

Lin, C.

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

Marshoud, H.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
[Crossref]

Minh, H. L.

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

Muhaidat, S.

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
[Crossref]

Nakagawa, M.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

Neild, A.

Park, C. S.

S. Y. Jung, S. Hann, and C. S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57, 1592–1597 (2011).
[Crossref]

Sekercioglu, Y. A.

Tanaka, T.

T. Tanaka and S. Haruyama, “New position detection method using image sensor and visible light leds,” in Second International Conference on Machine Vision (2009), pp. 150–153.

Tang, X.

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

B. Lin, X. Tang, Z. Ghassemlooy, Y. Li, and S. Zhang, “An indoor VLC positioning system based on OFDMA,” in Asia Communications and Photonics Conference (2016), p. AS1B.5.
[Crossref]

Vellambi, B. N.

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor position tracking using multiple optical receivers,” J. Lightw. Technol. 34, 1166–1176 (2016).
[Crossref]

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor localization using visible light and accelerometer,” in “IEEE Global Communications Conference (GLOBECOM),” (2013), pp. 3341–3346.

Wang, T. Q.

Wang, Z.

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

Xu, Y.

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

Yang, A.

Z. Li, L. Feng, and A. Yang, “Fusion based on visible light positioning and inertial navigation using extended Kalman filters,” Sensors 17, 1093 (2017).
[Crossref]

Yasir, M.

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor position tracking using multiple optical receivers,” J. Lightw. Technol. 34, 1166–1176 (2016).
[Crossref]

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor localization using visible light and accelerometer,” in “IEEE Global Communications Conference (GLOBECOM),” (2013), pp. 3341–3346.

Yoo, M.

T.-H. Do and M. Yoo, “An in-depth survey of visible light communication based positioning systems,” Sensors 16, E678 (2016).
[Crossref] [PubMed]

Yu, C.

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

Yu, J.

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

Zhang, S.

B. Lin, X. Tang, Z. Ghassemlooy, Y. Li, and S. Zhang, “An indoor VLC positioning system based on OFDMA,” in Asia Communications and Photonics Conference (2016), p. AS1B.5.
[Crossref]

IEEE Commun. Mag. (1)

J. Armstrong, Y. A. Sekercioglu, and A. Neild, “Visible light positioning: a roadmap for international standardization,” IEEE Commun. Mag. 51, 68–73 (2013).
[Crossref]

IEEE Photonics J. (1)

B. Lin, X. Tang, Z. Ghassemlooy, C. Lin, and Y. Li, “Experimental demonstration of an indoor VLC positioning system based on OFDMA,” IEEE Photonics J. 9, 1–9 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. Marshoud, V. M. Kapinas, G. K. Karagiannidis, and S. Muhaidat, “Non-orthogonal multiple access for visible light communications,” IEEE Photonics Technol. Lett. 28, 51–54 (2016).
[Crossref]

IEEE Trans. Consum. Electron. (2)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50, 100–107 (2004).
[Crossref]

S. Y. Jung, S. Hann, and C. S. Park, “TDOA-based optical wireless indoor localization using LED ceiling lamps,” IEEE Trans. Consum. Electron. 57, 1592–1597 (2011).
[Crossref]

IET Circuits, Devices Systems (1)

A. Burton, E. Bentley, H. L. Minh, Z. Ghassemlooy, N. Aslam, and S. K. Liaw, “Experimental demonstration of a 10BASE-T Ethernet visible light communications system using white phosphor light-emitting diodes,” IET Circuits, Devices Systems 8, 322–330 (2014).
[Crossref]

J. Lightw. Technol. (2)

M. F. Keskin and S. Gezici, “Comparative theoretical analysis of distance estimation in visible light positioning systems,” J. Lightw. Technol. 34, 854–865 (2016).
[Crossref]

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor position tracking using multiple optical receivers,” J. Lightw. Technol. 34, 1166–1176 (2016).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (1)

Proc. IEEE (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85, 265–298 (1997).
[Crossref]

Sensors (2)

T.-H. Do and M. Yoo, “An in-depth survey of visible light communication based positioning systems,” Sensors 16, E678 (2016).
[Crossref] [PubMed]

Z. Li, L. Feng, and A. Yang, “Fusion based on visible light positioning and inertial navigation using extended Kalman filters,” Sensors 17, 1093 (2017).
[Crossref]

Other (5)

T. Tanaka and S. Haruyama, “New position detection method using image sensor and visible light leds,” in Second International Conference on Machine Vision (2009), pp. 150–153.

M. Yasir, S. W. Ho, and B. N. Vellambi, “Indoor localization using visible light and accelerometer,” in “IEEE Global Communications Conference (GLOBECOM),” (2013), pp. 3341–3346.

M. Aminikashani, W. Gu, and M. Kavehrad, “Indoor positioning with OFDM visible light communications,” in 13th IEEE Annual Consumer Communications Networking Conference (CCNC) (2016), pp. 505–510.

B. Lin, X. Tang, Z. Ghassemlooy, Y. Li, and S. Zhang, “An indoor VLC positioning system based on OFDMA,” in Asia Communications and Photonics Conference (2016), p. AS1B.5.
[Crossref]

Y. Xu, Z. Wang, J. Chen, S. Han, C. Yu, and J. Yu, “Incorporate visible light communication into visible light positioning using orthogonal frequency division multiple access,” in Asia Communications and Photonics Conference (2017), pp. M3F.4.

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Figures (13)

Fig. 1
Fig. 1 Simultaneous realization of VLP and VLC using OFDMA.
Fig. 2
Fig. 2 The system that realizes VLC and VLP simultaneously in the same band.
Fig. 3
Fig. 3 Spectrum allocation of VLP system using OFDMA. †: Hermitian symmetry.
Fig. 4
Fig. 4 Frame structure for VLP system using OFDMA. †: Hermitian symmetry. Dark: subcarriers allocated by data.
Fig. 5
Fig. 5 Locations of LEDs and receivers. Red: LEDs, blue: receivers, inner frame: receiver region.
Fig. 6
Fig. 6 (a) Δ D i 2, i = 1, 2, 3, 4, (b) Δ D M 2 Δ D S j 2 and ‖Δp2, blue: slave LED 1, green: slave LED 2, pink: slave LED 3, black: slave LED 4, red: ‖Δp2.
Fig. 7
Fig. 7 Positioning error in overdetermined VLP system using OFDMA, when the receiver locates at the diagonal of the room.
Fig. 8
Fig. 8 Estimated position for the receiver at [−4m, −3m, 1m]T in overdetermined (filled) and determined (hollow) VLP systems using OFDMA.
Fig. 9
Fig. 9 Positioning error in determined VLP system using OFDMA for the receivers at the diagonal of the room.
Fig. 10
Fig. 10 VLP system using OFDMA and power allocation.
Fig. 11
Fig. 11 Δ D PA , i , k 2 (k ≥ 1) using power allocation scheme for the receiver at [−4m, −3m, 1m]T. k = 0: without using power allocation scheme. Blue: theory, green: LED 2, pink: LED 3, black: LED 4.
Fig. 12
Fig. 12 Δ D PA , i , k 2 (a) without using and (b) using power allocation scheme.
Fig. 13
Fig. 13 Positioning error of determined VLP system using OFDMA in the whole room: (a) without using power allocation scheme, (b) using power allocation scheme.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

P T ( t ) = K [ I 0 + i ( t ) ] = P 0 + K i ( t ) ,
G = ( m + 1 ) A 2 π D 2 cos m ( ϕ ) cos ( ψ ) ,
G = ( m + 1 ) A h m + 1 2 π 1 D m + 3 .
y ( t ) = s ( t ) + n ( t ) = R G δ ( t τ ) * K i ( t ) + n ( t ) .
Y ( f ) = S ( f ) + N ( f ) = R G K I ( f ) exp ( j 2 π f τ ) + N ( f ) .
G ˜ = { 𝔼 [ | Y ( f ) | 2 ] R 2 K 2 𝔼 [ | I ( f ) | 2 ] } 1 2 = { R 2 G 2 K 2 𝔼 [ | I ( f ) | 2 ] + 𝔼 [ | N ( f ) | 2 ] R 2 K 2 𝔼 [ | I ( f ) | 2 ] } 1 2 ,
[ X ˜ , Y ˜ , Z ˜ ] [ X i , Y i , Z i ] 2 2 = D ˜ i 2 , i 𝕃 ,
A p ˜ = b ˜ .
A = 2 [ X S 1 X M Y S 1 Y M X S 2 X M Y S 2 Y M X S N 1 X M Y S N 1 Y M ] ,
p ˜ = [ X ˜ Y ˜ ] = [ X Y ] + [ Δ X Δ Y ] ,
b ˜ = [ X S 1 2 Y M 2 + Y S 1 2 Y M 2 + D ˜ M 2 D ˜ S 1 2 X S 2 2 X M 2 + Y S 2 2 Y M 2 + D ˜ M 2 D ˜ S 2 2 X S N 1 2 X M 2 + Y S N 1 2 Y M 2 + D ˜ M 2 D ˜ S N 1 2 ] .
A ( p + Δ p ) = b + Δ b ,
b = [ X S 1 2 Y M 2 + Y S 1 2 Y M 2 + D M 2 D S 1 2 X S 2 2 X M 2 + Y S 2 2 Y M 2 + D M 2 D S 2 2 X S N 1 2 X M 2 + Y S N 1 2 Y M 2 + D M 2 D S N 1 2 ] , Δ b = [ Δ D M 2 Δ D S 1 2 Δ D M 2 Δ D S 2 2 Δ D M 2 Δ D S N 1 2 ] .
Δ p = [ Δ X Δ Y ] = ( A T A ) 1 A T Δ b .
D ˜ i 2 = { 1 D i 2 ( m + 3 ) + σ N 2 [ R K ( m + 1 ) A h m + 1 2 π ] 2 𝔼 [ | I ( f ) | 2 ] } 1 m + 3 ,
Δ D i 2 = D ˜ i 2 D i 2 = { 1 D i 2 ( m + 3 ) + σ N 2 [ R K ( m + 1 ) A h m + 1 2 π ] 2 𝔼 [ | I ( f ) | ] } 1 m + 3 D i 2 .
Δ p = [ Δ X Δ Y ] = ( A T A ) A T Δ b ,
i = 2 4 α PA , i , k 2 = 3
α PA , 2 , k 2 G ˜ PA , 2 , k 2 = α PA , 3 , k 2 G ˜ PA , 3 , k 2 = α PA , 4 , k 2 G ˜ PA , 4 , k 2 .
α PA , i , k 2 = 3 G ˜ PA , i , k 2 i = 2 4 1 G ˜ PA , i , k 2 , i = 2 , 3 , 4 .
Y PA , i , k ( f ) = S PA , i , k ( f ) + N ( f ) = R G i K α PA , i , k 1 I ( f ) exp ( j 2 π f τ ) + N ( f ) .
G ˜ PA , i , k = { 𝔼 [ | Y PA , i , k ( f ) | 2 ] R 2 K 2 α PA , i , k 1 2 𝔼 [ | I ( f ) | 2 ] } 1 2 = { R 2 G i 2 K 2 α PA , i , k 1 2 𝔼 [ | I ( f ) | 2 ] + 𝔼 [ | N ( f ) | 2 ] R 2 K 2 α PA , i , k 1 2 𝔼 [ | I ( f ) | 2 ] } 1 2 = { G i 2 + σ N 2 R 2 K 2 𝔼 [ | I ( f ) | 2 ] G ˜ PA , i , k 1 2 3 i = 2 4 1 G ˜ PA , i , k 1 2 } 1 2 .
Δ D PA , i , k 2 = D ˜ PA , i , k 2 D i 2 = { 1 D i 2 ( m + 3 ) + σ N 2 [ R K ( m + 1 ) A h m + 1 2 π ] 2 𝔼 [ | I ( f ) | 2 ] i = 2 4 D ˜ PA , i , k 1 2 ( m + 3 ) 3 D ˜ PA , i , k 1 2 ( m + 3 ) } 1 m + 3 D i 2 .

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