Abstract

A new dimming control scheme termed spatial dimming orthogonal frequency division multiplexing (SD-OFDM) is proposed for multiple-input and multiple output OFDM based visible light communication. The basic idea of SD-OFDM is that the illumination can be represented by the number of glared light emitting diodes (LEDs) in an LED lamp. As the biasing level of LEDs does not adjust to represent the required illumination level, the proposed scheme can significantly mitigate the clipping noise compared to analogue dimming schemes. Furthermore, unlike digital dimming schemes that control illumination levels by setting different duty cycles of pulse width modulation, the proposed scheme is always in the “on-state” for varied illumination levels. Both analytical and simulation results indicate that the proposed scheme is an efficient and feasible dimmable scheme.

© 2016 Optical Society of America

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References

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  1. J. Armstrong, “OFDM for optical communications,” J. Lightw. Technol. 27(3), 189–204 (2009).
    [Crossref]
  2. H. Elgala and T. D. C. Little, “Reverse polarity optical RPO-OFDM-OFDM: dimming compatible OFDM for gigabit VLC links,” Opt. Exp. 21(20), 24288–24299 (2013).
    [Crossref]
  3. Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM for visible light communications with dimming control,” IEEE Photon. Technol. Lett. 27(9), 974–977 (2015).
    [Crossref]
  4. Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
    [Crossref]
  5. J. Armstrong and A. J. Lowery, “Power effcient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
    [Crossref]
  6. Y. T. Hsieh and Y. Z. Juang, “Analysis and suppression of overcurrent in boost LED drivers,” J. Display Technol. 9(5), 388–395 (2013).
    [Crossref]
  7. H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
    [Crossref]
  8. Z. Wang, W.-D. Zhong, C. Yu, J. Chen, C. P. S. Francois, and W. Chen, “Performance of dimming control scheme in visible light communication system,” Opt. Express 20(17), 18861–18868 (2012).
    [Crossref] [PubMed]
  9. G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
    [Crossref]
  10. J. Ding, Z. Xu, and L. Hanzo, “Accuracy of the point-source model of a multi-led array in high-speed visible light communication channel characterization,” IEEE Photon. J. 7(4), 1600714 (2015).
    [Crossref]
  11. T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. on Commun. 61(2), 733–742 (2013).
    [Crossref]
  12. M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communications using OFDM and multiple LEDs,” IEEE Trans. on Commun. 63(11), 4304–4313 (2015).
    [Crossref]
  13. S. Dimitrov and H. Haas, “Information rate of OFDM-based optical wireless communication systems with nonlinear distortion,” J. Lightw. Technol. 31(6), 918–929 (2013).
    [Crossref]
  14. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consumer Electron. 50(1), 100–107 (2004).
    [Crossref]
  15. R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
    [Crossref]
  16. J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.
  17. H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proceedings of IEEE International Conf. Telecommun. (IEEE2009), pp. 25–29.

2016 (2)

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
[Crossref]

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

2015 (4)

Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM for visible light communications with dimming control,” IEEE Photon. Technol. Lett. 27(9), 974–977 (2015).
[Crossref]

J. Ding, Z. Xu, and L. Hanzo, “Accuracy of the point-source model of a multi-led array in high-speed visible light communication channel characterization,” IEEE Photon. J. 7(4), 1600714 (2015).
[Crossref]

M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communications using OFDM and multiple LEDs,” IEEE Trans. on Commun. 63(11), 4304–4313 (2015).
[Crossref]

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

2013 (4)

S. Dimitrov and H. Haas, “Information rate of OFDM-based optical wireless communication systems with nonlinear distortion,” J. Lightw. Technol. 31(6), 918–929 (2013).
[Crossref]

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. on Commun. 61(2), 733–742 (2013).
[Crossref]

Y. T. Hsieh and Y. Z. Juang, “Analysis and suppression of overcurrent in boost LED drivers,” J. Display Technol. 9(5), 388–395 (2013).
[Crossref]

H. Elgala and T. D. C. Little, “Reverse polarity optical RPO-OFDM-OFDM: dimming compatible OFDM for gigabit VLC links,” Opt. Exp. 21(20), 24288–24299 (2013).
[Crossref]

2012 (1)

2011 (1)

G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
[Crossref]

2009 (1)

J. Armstrong, “OFDM for optical communications,” J. Lightw. Technol. 27(3), 189–204 (2009).
[Crossref]

2006 (1)

J. Armstrong and A. J. Lowery, “Power effcient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

2004 (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

Armstrong, J.

J. Armstrong, “OFDM for optical communications,” J. Lightw. Technol. 27(3), 189–204 (2009).
[Crossref]

J. Armstrong and A. J. Lowery, “Power effcient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

Chang, C. H.

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

Chang, Y. N.

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

Chen, J.

Chen, W.

Cheng, C. A.

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

Cheng, H. L.

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

Cheng, J.

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
[Crossref]

Dai, L.

Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM for visible light communications with dimming control,” IEEE Photon. Technol. Lett. 27(9), 974–977 (2015).
[Crossref]

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

Dimitrov, S.

S. Dimitrov and H. Haas, “Information rate of OFDM-based optical wireless communication systems with nonlinear distortion,” J. Lightw. Technol. 31(6), 918–929 (2013).
[Crossref]

Ding, J.

J. Ding, Z. Xu, and L. Hanzo, “Accuracy of the point-source model of a multi-led array in high-speed visible light communication channel characterization,” IEEE Photon. J. 7(4), 1600714 (2015).
[Crossref]

Elgala, H.

H. Elgala and T. D. C. Little, “Reverse polarity optical RPO-OFDM-OFDM: dimming compatible OFDM for gigabit VLC links,” Opt. Exp. 21(20), 24288–24299 (2013).
[Crossref]

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proceedings of IEEE International Conf. Telecommun. (IEEE2009), pp. 25–29.

Fath, T.

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. on Commun. 61(2), 733–742 (2013).
[Crossref]

Francois, C. P. S.

Gao, Q.

J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.

Gu, D.

J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.

Guo, C.

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
[Crossref]

Haas, H.

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. on Commun. 61(2), 733–742 (2013).
[Crossref]

S. Dimitrov and H. Haas, “Information rate of OFDM-based optical wireless communication systems with nonlinear distortion,” J. Lightw. Technol. 31(6), 918–929 (2013).
[Crossref]

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proceedings of IEEE International Conf. Telecommun. (IEEE2009), pp. 25–29.

Hanzo, L.

J. Ding, Z. Xu, and L. Hanzo, “Accuracy of the point-source model of a multi-led array in high-speed visible light communication channel characterization,” IEEE Photon. J. 7(4), 1600714 (2015).
[Crossref]

Hranilovic, S.

M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communications using OFDM and multiple LEDs,” IEEE Trans. on Commun. 63(11), 4304–4313 (2015).
[Crossref]

Hsieh, Y. T.

Jiang, R.

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

Juang, Y. Z.

Kamalakis, T.

G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
[Crossref]

Komine, T.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

Lampe, L.

M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communications using OFDM and multiple LEDs,” IEEE Trans. on Commun. 63(11), 4304–4313 (2015).
[Crossref]

Li, J.

J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.

Lin, Y. H.

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

Little, T. D. C.

H. Elgala and T. D. C. Little, “Reverse polarity optical RPO-OFDM-OFDM: dimming compatible OFDM for gigabit VLC links,” Opt. Exp. 21(20), 24288–24299 (2013).
[Crossref]

Lowery, A. J.

J. Armstrong and A. J. Lowery, “Power effcient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

Luo, Y.

J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.

Mesleh, R.

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proceedings of IEEE International Conf. Telecommun. (IEEE2009), pp. 25–29.

Mossaad, M. S. A.

M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communications using OFDM and multiple LEDs,” IEEE Trans. on Commun. 63(11), 4304–4313 (2015).
[Crossref]

Nakagawa, M.

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

Ntogari, G.

G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
[Crossref]

Sphicopoulos, T.

G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
[Crossref]

Walewski, J. W.

G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
[Crossref]

Wang, F.

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

Wang, Q.

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM for visible light communications with dimming control,” IEEE Photon. Technol. Lett. 27(9), 974–977 (2015).
[Crossref]

Wang, Z.

Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM for visible light communications with dimming control,” IEEE Photon. Technol. Lett. 27(9), 974–977 (2015).
[Crossref]

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

Z. Wang, W.-D. Zhong, C. Yu, J. Chen, C. P. S. Francois, and W. Chen, “Performance of dimming control scheme in visible light communication system,” Opt. Express 20(17), 18861–18868 (2012).
[Crossref] [PubMed]

Xu, Z.

J. Ding, Z. Xu, and L. Hanzo, “Accuracy of the point-source model of a multi-led array in high-speed visible light communication channel characterization,” IEEE Photon. J. 7(4), 1600714 (2015).
[Crossref]

Yang, Y.

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
[Crossref]

Yu, C.

Zeng, Z.

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
[Crossref]

Zhang, X.

J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.

Zhong, W.-D.

Electron. Lett. (1)

J. Armstrong and A. J. Lowery, “Power effcient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006).
[Crossref]

IEEE Photon. J. (2)

Y. Yang, Z. Zeng, J. Cheng, and C. Guo, “An enhanced DCO-OFDM scheme for dimming control in visible light communication systems,” IEEE Photon. J. 8(3), 7904813 (2016).
[Crossref]

J. Ding, Z. Xu, and L. Hanzo, “Accuracy of the point-source model of a multi-led array in high-speed visible light communication channel characterization,” IEEE Photon. J. 7(4), 1600714 (2015).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Q. Wang, Z. Wang, and L. Dai, “Asymmetrical hybrid optical OFDM for visible light communications with dimming control,” IEEE Photon. Technol. Lett. 27(9), 974–977 (2015).
[Crossref]

IEEE Trans. on Commun. (2)

T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. on Commun. 61(2), 733–742 (2013).
[Crossref]

M. S. A. Mossaad, S. Hranilovic, and L. Lampe, “Visible light communications using OFDM and multiple LEDs,” IEEE Trans. on Commun. 63(11), 4304–4313 (2015).
[Crossref]

IEEE Trans. on Consumer Electron. (1)

T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. on Consumer Electron. 50(1), 100–107 (2004).
[Crossref]

IET Power Electron. (1)

H. L. Cheng, Y. N. Chang, C. A. Cheng, C. H. Chang, and Y. H. Lin, “High-power-factor dimmable LED driver with low-frequency pulse-width modulation,” IET Power Electron. 9(10), 2139–2146 (2016).
[Crossref]

J. Display Technol. (1)

J. Lightw. Technol. (2)

J. Armstrong, “OFDM for optical communications,” J. Lightw. Technol. 27(3), 189–204 (2009).
[Crossref]

S. Dimitrov and H. Haas, “Information rate of OFDM-based optical wireless communication systems with nonlinear distortion,” J. Lightw. Technol. 31(6), 918–929 (2013).
[Crossref]

J. Optical Commun. and Net. (1)

G. Ntogari, T. Kamalakis, J. W. Walewski, and T. Sphicopoulos, “Combining illumination dimming based on pulse-width modulation with visible-light communications based on discrete multitone,” J. Optical Commun. and Net. 3(1), 56–65 (2011).
[Crossref]

Opt. Commun. (1)

R. Jiang, Q. Wang, F. Wang, L. Dai, and Z. Wang, “An optimal scaling scheme for DCO-OFDM based visible light communications,” Opt. Commun. 356, 136–140 (2015).
[Crossref]

Opt. Exp. (1)

H. Elgala and T. D. C. Little, “Reverse polarity optical RPO-OFDM-OFDM: dimming compatible OFDM for gigabit VLC links,” Opt. Exp. 21(20), 24288–24299 (2013).
[Crossref]

Opt. Express (1)

Other (2)

J. Li, X. Zhang, Q. Gao, Y. Luo, and D. Gu, “Exact BEP analysis for coherent M-ary PAM and QAM over AWGN and Rayleigh fading channels,” in Proceedings of IEEE Vehicular Technol. Conf.-Spring (IEEE2008), pp. 390–394.

H. Elgala, R. Mesleh, and H. Haas, “Practical considerations for indoor wireless optical system implementation using OFDM,” in Proceedings of IEEE International Conf. Telecommun. (IEEE2009), pp. 25–29.

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Figures (6)

Fig. 1
Fig. 1 Block diagram of the considered MIMO-OFDM system.
Fig. 2
Fig. 2 Numerical results of clipping noise comparison between a spatial dimming scheme and an analogue dimming scheme. Nt = 10 and the parameters shown in Table 1 are adopted.
Fig. 3
Fig. 3 Numerical results of the effective SNR Γb(elec) versus ηnorm and the scaling factor a with the parameters shown in Table 1, M = 16, SNR = 105dB and Nt = 10.
Fig. 4
Fig. 4 Analytical and simulated BERs of the proposed SD-OFDM with different dimming levels.
Fig. 5
Fig. 5 Numerical results of the minimum required Nt versus ηnorm for different spectral efficiency.
Fig. 6
Fig. 6 Simulation results of the spectral efficiency comparison.

Tables (1)

Tables Icon

Table 1 Simulation Parameters.

Equations (19)

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{ X ( N k ) = X * ( k ) , k = 1 , 2 , , N 1 , X ( 0 ) = X ( N 2 ) = 0
s i ( n ) = { I H , if x ( n ) I H B DC a ; a x ( n ) + B DC , if I H B DC a > x ( n ) I L B DC a ; I L , if x ( n ) < I L B DC a
r = H s + z
g h ( o p t ) = { ( m + 1 ) A 2 π d 2 T s ( ψ ) g ( ψ ) cos m ( ϕ ) cos ( ψ ) , 0 < ψ < Ψ c 0 , ψ > Ψ c
g ( ψ ) = { n 2 sin 2 Ψ c , 0 ψ Ψ c , 0 , 0 Ψ c
r com ( n ) = g h ( o p t ) s ( n ) + 1 N t N r i = 1 N r z i ( n ) .
y ( n ) = r com ( n ) B DC g h ( o p t ) a g h ( o p t ) = { I H B DC a + w ( n ) a g h ( o p t ) , if x ( n ) I H B DC a ; x ( n ) + w ( n ) a g h ( o p t ) , if I H B DC a > x ( n ) I L B DC a ; I L B DC a + w ( n ) a g h ( o p t ) , if x ( n ) < I L B DC a
η norm = N glared N t 100 %
y ( n ) = K x ( n ) + v ( n )
K = cov [ x ( n ) , y ( n ) ] σ 2 = Q ( I L B DC a σ ) Q ( I H B DC a σ )
σ v 2 = E [ [ y ( n ) K x ( n ) ] 2 ] E [ y ( n ) K x ( n ) ] 2 = E [ y 2 ( n ) ] K 2 σ 2 E [ y ( n ) ] 2 .
E [ y ( n ) ] = I H B DC a Q ( I H B DC a σ ) + I L B DC a [ 1 Q ( I L B DC a σ ) ] σ 2 π [ exp ( ( I H B DC ) 2 2 a 2 σ 2 ) exp ( ( I L B DC ) 2 2 a 2 σ 2 ) ]
E [ y 2 ( n ) ] = ( g h ( o p t ) 2 ( I H B DC ) 2 + σ w 2 ) a 2 g h ( o p t ) 2 Q ( I H B DC a σ ) + ( g h ( o p t ) 2 ( I L B DC ) 2 + σ w 2 ) a 2 g h ( o p t ) 2 [ 1 Q ( I L B DC a σ ) ] + σ 2 π [ I L B DC a exp ( ( I L B DC ) 2 2 a 2 σ 2 ) I H B DC a exp ( ( I H B DC ) 2 2 a 2 σ 2 ) ] + [ σ 2 + σ w 2 a 2 g h ( o p t ) 2 ] [ Q ( I L B DC a σ ) Q ( I H B DC a σ ) ]
σ c l i p 2 = σ v 2 σ w 2 K 2 a 2 g h ( o p t ) 2 .
Γ b ( elec ) = K 2 σ 2 G B σ v 2 log 2 M
max a Γ b ( elec ) = K 2 σ 2 G B σ v 2 log 2 M s . t . 1 ) : B DC = I L + I H 2 2 ) : N glared = η norm N t 3 ) : a 0 .
B E R = 4 ( M 1 ) M log 2 ( M ) Q ( 3 log 2 ( M ) M 1 Γ b ( elec ) ) + 4 ( M 2 ) M log 2 ( M ) Q ( 3 3 log 2 ( M ) M 1 Γ b ( elec ) ) .
β SD = ( N 2 ) log 2 ( M ) 2 ( N + N cp )
B E R = ( N 2 ) ( 2 N β SD N 2 1 ) N β SD 2 N β SD N 2 1 Q ( 6 N β SD ( 2 2 N β SD N 2 1 ) ( N 2 ) Γ b ( elec ) ) + ( N 2 ) ( 2 N β SD N 2 2 ) N β SD 2 N β SD N 2 1 Q ( 3 6 N β SD ( 2 2 N β SD N 2 1 ) ( N 2 ) Γ b ( elec ) ) .

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