Abstract

We propose a vsible light communication scheme utilizing red, green and blue light-emitting diodes (LEDs) and three color-tuned photodiodes. Amplitude shift keying modulation is considered, and its effect on light emission in terms of flickering, dimming, and color rendering is discussed. The presence of interference at each photodiode generated by the other two colors is used to improve detection since interference is symbol-dependent. Moreover, the capability of the photodiodes to follow the LEDs speed is considered by analyzing the possibility of equalizing the received signal, and also self-interference mitigation is proposed. The system performance is evaluated both with computer simulations and tests on an Arduino board implementation.

© 2017 Optical Society of America

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References

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2016 (1)

2015 (4)

G. Cossu, W. Ali, R. Corsini, and E. Ciaramella, “Gigabit-class optical wireless communication system at indoor distances (1.5 − 4 m),” Opt. Express 23(12), 15700–15705 (2015).
[Crossref] [PubMed]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

S. Pergoloni, M. Biagi, S. Rinauro, S. Colonnese, R. Cusani, and G. Scarano, “Merging color shift keying and complementary pulse position modulation for visible light illumination and communication,” J. Lightwave Technol. 33(1), 192–200 (2015).
[Crossref]

2014 (1)

2013 (1)

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications”, J. Lightwave Technol. 31(13), 37715–3779 (2013).
[Crossref]

2012 (4)

2011 (1)

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

2010 (1)

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22(19), 1455–1457 (2010).
[Crossref]

2003 (1)

S. R. Perez, R. P. Jimenez, O. B. G. Hernandez, R. Borges, and R. Mendoza, “Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithm,” Microw. Opt. Technol. Lett. 36(4), 262–267 (2003).
[Crossref]

1993 (1)

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

Ahn, K. I.

Ali, W.

Bamiedakis, N.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Barry, J. R.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

Biagi, M.

Borges, R.

S. R. Perez, R. P. Jimenez, O. B. G. Hernandez, R. Borges, and R. Mendoza, “Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithm,” Microw. Opt. Technol. Lett. 36(4), 262–267 (2003).
[Crossref]

Borogovac, T.

M. Rahaim, T. Borogovac, and J. B. Carruthers, “CandLES: Communications and Lighting Emulation Software,” in Proceedings of the fifth ACM international workshop on Wireless network testbeds, experimental evaluation and characterization (ACM, 2010), pp. 9–14.
[Crossref]

Carruthers, J. B.

M. Rahaim, T. Borogovac, and J. B. Carruthers, “CandLES: Communications and Lighting Emulation Software,” in Proceedings of the fifth ACM international workshop on Wireless network testbeds, experimental evaluation and characterization (ACM, 2010), pp. 9–14.
[Crossref]

Chen, C. W.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, and K. Huang, “3.22-Gb/s WDM visible light communication of a single RGB LED employing carrier-less amplitude and phase modulation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh1G.4.

Chen, J.

Chen, M.

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications”, J. Lightwave Technol. 31(13), 37715–3779 (2013).
[Crossref]

Chen, W.

Chen, Z. Y.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, and K. Huang, “3.22-Gb/s WDM visible light communication of a single RGB LED employing carrier-less amplitude and phase modulation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh1G.4.

Chi, N.

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Y. Wang, X. Huang, J. Zhang, Y. Wang, and N. Chi, “Enhanced performance of visible light communication employing 512-QAM N-SC-FDE and DD-LMS,” Opt. Express 22(13), 15328–15334 (2014).
[Crossref] [PubMed]

Choudhury, P.

Chow, C. W.

Ciaramella, E.

Colonnese, S.

Corsini, R.

Cossu, G.

Cui, L.

Cusani, R.

Dawson, M. D.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Dimitrov, S.

S. Dimitrov and H. Haas, “Principles of LED Light Communications: Towards Networked Li-Fi,” (Cambdrige University Ppress, 2015).
[Crossref]

Elgala, H.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

Ferreira, R.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Francois, S.

Gnade, B.

Gu, E.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Haas, H.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

S. Dimitrov and H. Haas, “Principles of LED Light Communications: Towards Networked Li-Fi,” (Cambdrige University Ppress, 2015).
[Crossref]

Hernandez, O. B. G.

S. R. Perez, R. P. Jimenez, O. B. G. Hernandez, R. Borges, and R. Mendoza, “Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithm,” Microw. Opt. Technol. Lett. 36(4), 262–267 (2003).
[Crossref]

Hu, Q.-S.

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications”, J. Lightwave Technol. 31(13), 37715–3779 (2013).
[Crossref]

Huang, K.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, and K. Huang, “3.22-Gb/s WDM visible light communication of a single RGB LED employing carrier-less amplitude and phase modulation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh1G.4.

Huang, P. Y.

Huang, X.

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Y. Wang, X. Huang, J. Zhang, Y. Wang, and N. Chi, “Enhanced performance of visible light communication employing 512-QAM N-SC-FDE and DD-LMS,” Opt. Express 22(13), 15328–15334 (2014).
[Crossref] [PubMed]

Jain, A. K

A. K Jain, “Fundamentals of Digital Image Processing,” (Prentice-Hall, Inc., 1989), Chap. 3.

Jia, H.

Jimenez, R. P.

S. R. Perez, R. P. Jimenez, O. B. G. Hernandez, R. Borges, and R. Mendoza, “Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithm,” Microw. Opt. Technol. Lett. 36(4), 262–267 (2003).
[Crossref]

Kahn, J. M.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

Khalid, A. M.

Krause, W. J.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

Kwon, J. K.

K. I. Ahn and J. K. Kwon, “Capacity analysis of M-PAM inverse source coding in visible light communications,” J. Lightwave Technol. 30(10), 1399–1404 (2012).
[Crossref]

J. K. Kwon, “Inverse source coding for dimming in visible light communications using NRZ-OOK on reliable links,” IEEE Photon. Technol. Lett. 22(19), 1455–1457 (2010).
[Crossref]

Lee, E. A.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

Li, X.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Lin, C. T.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, and K. Huang, “3.22-Gb/s WDM visible light communication of a single RGB LED employing carrier-less amplitude and phase modulation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh1G.4.

Liu, Y.

Liu, Y. F.

Luo, J.

McKendry, J. J. D.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Mendoza, R.

S. R. Perez, R. P. Jimenez, O. B. G. Hernandez, R. Borges, and R. Mendoza, “Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithm,” Microw. Opt. Technol. Lett. 36(4), 262–267 (2003).
[Crossref]

Mesleh, R.

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

Messerschmitt, D. G.

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

Panazio, C. M.

C. M. Panazio and J. M. T. Romano, “On the convergence of a new joint DFE & decoding procedure for blind decision directed LMS equalization,” in Proceedings of IEEE International Conference on Communications (IEEE, 2002), pp. 129–133.
[Crossref]

Penty, R. V.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Perez, S. R.

S. R. Perez, R. P. Jimenez, O. B. G. Hernandez, R. Borges, and R. Mendoza, “Concentrator and lens models for calculating the impulse response on IR-wireless indoor channels using a ray-tracing algorithm,” Microw. Opt. Technol. Lett. 36(4), 262–267 (2003).
[Crossref]

Pergoloni, S.

Rahaim, M.

M. Rahaim, T. Borogovac, and J. B. Carruthers, “CandLES: Communications and Lighting Emulation Software,” in Proceedings of the fifth ACM international workshop on Wireless network testbeds, experimental evaluation and characterization (ACM, 2010), pp. 9–14.
[Crossref]

Rinauro, S.

Romano, J. M. T.

C. M. Panazio and J. M. T. Romano, “On the convergence of a new joint DFE & decoding procedure for blind decision directed LMS equalization,” in Proceedings of IEEE International Conference on Communications (IEEE, 2002), pp. 129–133.
[Crossref]

Scarano, G.

Shi, J.

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

Tang, Y.

Tao, L.

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Tsang, H. K.

Wang, J.

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications”, J. Lightwave Technol. 31(13), 37715–3779 (2013).
[Crossref]

Wang, J.-B.

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications”, J. Lightwave Technol. 31(13), 37715–3779 (2013).
[Crossref]

Wang, J.-Y.

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications”, J. Lightwave Technol. 31(13), 37715–3779 (2013).
[Crossref]

Wang, Y.

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Y. Wang, X. Huang, J. Zhang, Y. Wang, and N. Chi, “Enhanced performance of visible light communication employing 512-QAM N-SC-FDE and DD-LMS,” Opt. Express 22(13), 15328–15334 (2014).
[Crossref] [PubMed]

Y. Wang, X. Huang, J. Zhang, Y. Wang, and N. Chi, “Enhanced performance of visible light communication employing 512-QAM N-SC-FDE and DD-LMS,” Opt. Express 22(13), 15328–15334 (2014).
[Crossref] [PubMed]

Wang, Z.

Wei, C. C.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, and K. Huang, “3.22-Gb/s WDM visible light communication of a single RGB LED employing carrier-less amplitude and phase modulation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh1G.4.

White, I. H.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Wu, F. M.

F. M. Wu, C. T. Lin, C. C. Wei, C. W. Chen, Z. Y. Chen, and K. Huang, “3.22-Gb/s WDM visible light communication of a single RGB LED employing carrier-less amplitude and phase modulation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2013), paper OTh1G.4.

Xie, E.

N. Bamiedakis, X. Li, J. J. D. McKendry, E. Xie, R. Ferreira, E. Gu, M. D. Dawson, R. V. Penty, and I. H. White, “Micro-LED-based guided-wave optical links for visible light communications”, in Proceedings of IEEE Conference on Transparent Optical Networks (IEEE, 2015), pp. 1–4.

Yeh, C. H.

Yu, C.

Zhang, J.

Zhong, W. D.

IEEE Commun. Mag. (1)

H. Elgala, R. Mesleh, and H. Haas, “Indoor optical wireless communication: potential and state-of-the-art,” IEEE Commun. Mag. 49(9), 56–62 (2011).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

J. R. Barry, J. M. Kahn, W. J. Krause, E. A. Lee, and D. G. Messerschmitt, “Simulation of multipath impulse response for indoor wireless optical channels,” IEEE J. Sel. Areas Commun. 11(3), 367–379 (1993).
[Crossref]

IEEE Photo. J. (2)

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “Enhanced performance of a high-speed WDM CAP64 VLC system employing volterra series-based nonlinear equalizer,” IEEE Photo. J. 7(3), 1–7 (2015).
[Crossref]

Y. Wang, L. Tao, X. Huang, J. Shi, and N. Chi, “8-Gb/s RGBY LED-based WDM VLC system employing high-order CAP modulation and hybrid post equalizer,” IEEE Photo. J. 7(6), 1–7 (2015).
[Crossref]

IEEE Photon. Technol. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1 Scheme of the transmitter, channel and receiver.
Fig. 2
Fig. 2 CIE 1931 diagram with primaries and an example of symbol (4,4,4) and (4,2,1).
Fig. 3
Fig. 3 BER comparison between the proposed scheme with Vishay BPW34 and Telstore C7718 photodiodes and MIMO white LEDs [6].
Fig. 4
Fig. 4 BER for different values of symbol rates on each transmitting branch and modulation order.
Fig. 5
Fig. 5 Picture of the implementation of the system. On right hand side transmitter, on left side receiver with AOFs.
Fig. 6
Fig. 6 BER evaluation as a function of distance.
Fig. 7
Fig. 7 BER evaluation as a function of training sequence frequency when the receier is moving.

Tables (3)

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Table 1 Model Parameters

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Table 2 Mean Opinion Score on color rendering on 50 candidates

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Table 3 Mean Opinion Score on light intensity on 50 candidates

Equations (24)

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s ( t ) = c 𝒞 A c s c ( t )
𝒫 = 1 T retina T retina p = 1 N s c 𝒞 A c ( p ) s c ( t p T 𝒫 ) d t .
𝒫 ( ill ) = 1 T retina T retina c 𝒞 A c ( ill ) d t
Δ 𝒫 = 𝒫 ( ill ) 𝒫 = 1 T retina T retina c 𝒞 ( A c ( ill ) p = 1 N s A c ( p ) s c ( t p T p ) ) d t
X ( f ) = 1 T retina T retina p = 1 N s c 𝒞 A c ( p ) s c ( t p T 𝒫 ) e i 2 π f t d t
H ( t ) = [ h R R ( t ) h R G ( t ) h R B ( t ) h G R ( t ) h G G ( t ) h G B ( t ) h B R ( t ) h B G ( t ) h B B ( t ) ]
y j ( t ) = c 𝒞 A c s c ( t ) * h c j ( t ) + w j ( t )
h c j ( t ) = f L ( t ) * f c j ( t ) * f PD ( t ) * F FSP c j ( t )
F FSP c j ( t ) m + 1 2 π cos m ( ϕ ) d Ω rect ( θ / FOV ) δ ( t d c , j / v ) ,
d Ω = cos ( θ ) A e / d c , j 2 ,
a ( d ) = m + 1 2 π cos m ( ϕ ) d Ω rect ( θ / FOV ) .
y j ( t ) = A R s R ( t ) * h R j ( t ) + w j ( t )
H ˜ c j ( k ) = Y j ( k ) S c ( k )
Z j = [ z j ( A c m = 1 , A c l = 1 ) z j ( A c m = M , A c l = M ) ]
Z j [ n , v ] = y j ( n T s ) = c v 𝒞 / { j } A c v s c v ( n T s ) * h ˜ c v j ( n T s ) .
X j = [ x j ( A c m = 1 , A c l = 1 ) x j ( A c m = M , A c l = M ) ]
x j ( A c m = m , A c l = l ) = z j ( A c m = m , A c l = l ) * g i j ( n T s ) .
q j = n = 0 N L 1 X j [ n , v ]
q j [ v ] = n = 0 N L 1 x j ( A c k = k , A c l = l ) .
q j [ v ] = n = 0 N L 1 [ c 𝒞 A c s c ( n T s ) * h c j ( n T s ) * g j j ( n T s ) ] n = 0 N L 1 [ c v 𝒞 / { j } A v s c v ( n T s ) * h ˜ c v j ( n T s ) * g j j ( n T s ) ] + n = 0 N L 1 w j ( n T s ) * g j j ( n T s ) .
u j [ p ] = n = 0 N L 1 A j [ p ] s j ( n T s ) * h j j ( n T s ) * g j j ( n T s ) .
δ j , p , v = ( q j [ v ] u j [ p ] ) 2 .
Δ p , v = j = 1 3 δ j , p , v .
[ A ^ R , A ^ G , A ^ B ] = argmin A R , A B , A G Δ p , v ,

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