Abstract

Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.

© 2017 Optical Society of America

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References

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  1. L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
    [Crossref]
  2. A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Mag. 51(12), 26–32 (2013).
    [Crossref]
  3. J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
    [Crossref]
  4. E. Fisher, I. Underwood, and R. Henderson, “A reconfigurable single-photon-counting integrating receiver for optical communications,” IEEE J. Solid-State Circuits 48(7), 1638–1650 (2013).
    [Crossref]
  5. X. Liu, C. Gong, S. Li, and Z. Xu, “Signal characterization and receiver design for visible light communication under weak illuminance,” IEEE Commun. Lett. 20(7), 1349–1352 (2016).
  6. N. Faramarzpour, M. Deen, S. Shirani, and Q. Fang, “Fully integrated single photon avalanche diode detector in standard CMOS 0.18 Îijm technology,” IEEE Trans. Electron. Dev. 55(3), 760–767 (2008).
    [Crossref]
  7. O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.
  8. T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. 50(1), 100–107 (2004).
    [Crossref]
  9. Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
    [Crossref]
  10. J. Zhang, L. Si-Ma, B. Wang, J. Zhang, and Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1041–1135 (2016).
    [Crossref]
  11. F. Anscombe, “The transformation of Poisson, binomial and negativebinomial data,” Biometrika 35(3–4), 246–254 (1948).
    [Crossref]
  12. D. Chitnis and S. Collins, “A SPAD-based photon detecting system for optical communications,” J. Lightwave Technol. 32(16), 2028–2034 (2014).
    [Crossref]
  13. Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.
  14. J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).
  15. K. Doris, A. Roermund, and D. Leenaerts, Wide-Bandwidth High Dynamic Range D/A Converters (The Springer International Series in Engineering and Computer Science Series) (Springer, 2006).
  16. Z. Cheng, X. Zheng, D. Palubiak, M. Deen, and H. Peng, “A comprehensive and accurate analytical SPAD model for circuit simulation,” IEEE Trans. Elec. Dev. 63(5), 1940–1948 (2016).
    [Crossref]
  17. J. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis (Cambridge University, 1998).
    [Crossref]
  18. Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Proceedings of IEEE Global Commun. Conf. Workshops (GC Wkshps) (IEEE, 2015), pp. 1–6.
  19. C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. 14(4), 630–640 (1978).
    [Crossref]
  20. D. Snyder, C. Helstrom, A. Lanterman, M. Faisal, and R. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, (2), 272–283 (1995).
    [Crossref]

2016 (3)

X. Liu, C. Gong, S. Li, and Z. Xu, “Signal characterization and receiver design for visible light communication under weak illuminance,” IEEE Commun. Lett. 20(7), 1349–1352 (2016).

J. Zhang, L. Si-Ma, B. Wang, J. Zhang, and Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1041–1135 (2016).
[Crossref]

Z. Cheng, X. Zheng, D. Palubiak, M. Deen, and H. Peng, “A comprehensive and accurate analytical SPAD model for circuit simulation,” IEEE Trans. Elec. Dev. 63(5), 1940–1948 (2016).
[Crossref]

2015 (1)

Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
[Crossref]

2014 (1)

2013 (2)

A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Mag. 51(12), 26–32 (2013).
[Crossref]

E. Fisher, I. Underwood, and R. Henderson, “A reconfigurable single-photon-counting integrating receiver for optical communications,” IEEE J. Solid-State Circuits 48(7), 1638–1650 (2013).
[Crossref]

2012 (2)

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

2008 (1)

N. Faramarzpour, M. Deen, S. Shirani, and Q. Fang, “Fully integrated single photon avalanche diode detector in standard CMOS 0.18 Îijm technology,” IEEE Trans. Electron. Dev. 55(3), 760–767 (2008).
[Crossref]

2004 (1)

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

1997 (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

1995 (1)

1978 (1)

C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. 14(4), 630–640 (1978).
[Crossref]

1948 (1)

F. Anscombe, “The transformation of Poisson, binomial and negativebinomial data,” Biometrika 35(3–4), 246–254 (1948).
[Crossref]

Abbas, T.

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Abdallah, M.

Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

Almer, O.

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Anscombe, F.

F. Anscombe, “The transformation of Poisson, binomial and negativebinomial data,” Biometrika 35(3–4), 246–254 (1948).
[Crossref]

Bailey, R.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

Bijaoui, A.

J. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis (Cambridge University, 1998).
[Crossref]

Brattain, M.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Busacker, D.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Cheng, Z.

Z. Cheng, X. Zheng, D. Palubiak, M. Deen, and H. Peng, “A comprehensive and accurate analytical SPAD model for circuit simulation,” IEEE Trans. Elec. Dev. 63(5), 1940–1948 (2016).
[Crossref]

Chitnis, D.

Collins, S.

Deen, M.

Z. Cheng, X. Zheng, D. Palubiak, M. Deen, and H. Peng, “A comprehensive and accurate analytical SPAD model for circuit simulation,” IEEE Trans. Elec. Dev. 63(5), 1940–1948 (2016).
[Crossref]

N. Faramarzpour, M. Deen, S. Shirani, and Q. Fang, “Fully integrated single photon avalanche diode detector in standard CMOS 0.18 Îijm technology,” IEEE Trans. Electron. Dev. 55(3), 760–767 (2008).
[Crossref]

Doris, K.

K. Doris, A. Roermund, and D. Leenaerts, Wide-Bandwidth High Dynamic Range D/A Converters (The Springer International Series in Engineering and Computer Science Series) (Springer, 2006).

Duerr, E.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Dutton, N.

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Faisal, M.

Fang, Q.

N. Faramarzpour, M. Deen, S. Shirani, and Q. Fang, “Fully integrated single photon avalanche diode detector in standard CMOS 0.18 Îijm technology,” IEEE Trans. Electron. Dev. 55(3), 760–767 (2008).
[Crossref]

Faramarzpour, N.

N. Faramarzpour, M. Deen, S. Shirani, and Q. Fang, “Fully integrated single photon avalanche diode detector in standard CMOS 0.18 Îijm technology,” IEEE Trans. Electron. Dev. 55(3), 760–767 (2008).
[Crossref]

Fisher, E.

E. Fisher, I. Underwood, and R. Henderson, “A reconfigurable single-photon-counting integrating receiver for optical communications,” IEEE J. Solid-State Circuits 48(7), 1638–1650 (2013).
[Crossref]

Frechette, J.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Funk, J.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Gnecchi, S.

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Gong, C.

X. Liu, C. Gong, S. Li, and Z. Xu, “Signal characterization and receiver design for visible light communication under weak illuminance,” IEEE Commun. Lett. 20(7), 1349–1352 (2016).

Grossmann, P.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Gyongyosi, L.

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

Haas, H.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
[Crossref]

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Proceedings of IEEE Global Commun. Conf. Workshops (GC Wkshps) (IEEE, 2015), pp. 1–6.

Hanzo, L.

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

Helstrom, C.

D. Snyder, C. Helstrom, A. Lanterman, M. Faisal, and R. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, (2), 272–283 (1995).
[Crossref]

C. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst. 14(4), 630–640 (1978).
[Crossref]

Henderson, R.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
[Crossref]

E. Fisher, I. Underwood, and R. Henderson, “A reconfigurable single-photon-counting integrating receiver for optical communications,” IEEE J. Solid-State Circuits 48(7), 1638–1650 (2013).
[Crossref]

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Proceedings of IEEE Global Commun. Conf. Workshops (GC Wkshps) (IEEE, 2015), pp. 1–6.

Imre, S.

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

Jordy, G.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Jovicic, A.

A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Mag. 51(12), 26–32 (2013).
[Crossref]

Kahn, J. M.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

Komine, T.

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

Lanterman, A.

Leenaerts, D.

K. Doris, A. Roermund, and D. Leenaerts, Wide-Bandwidth High Dynamic Range D/A Converters (The Springer International Series in Engineering and Computer Science Series) (Springer, 2006).

Li, J.

A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Mag. 51(12), 26–32 (2013).
[Crossref]

Li, S.

X. Liu, C. Gong, S. Li, and Z. Xu, “Signal characterization and receiver design for visible light communication under weak illuminance,” IEEE Commun. Lett. 20(7), 1349–1352 (2016).

Li, Y.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
[Crossref]

Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Proceedings of IEEE Global Commun. Conf. Workshops (GC Wkshps) (IEEE, 2015), pp. 1–6.

Liu, X.

X. Liu, C. Gong, S. Li, and Z. Xu, “Signal characterization and receiver design for visible light communication under weak illuminance,” IEEE Commun. Lett. 20(7), 1349–1352 (2016).

MacDonald, J.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

McIntosh, K.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Murtagh, F.

J. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis (Cambridge University, 1998).
[Crossref]

Nakagawa, M.

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

O’Brien, D. C.

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

Oakley, D.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Palubiak, D.

Z. Cheng, X. Zheng, D. Palubiak, M. Deen, and H. Peng, “A comprehensive and accurate analytical SPAD model for circuit simulation,” IEEE Trans. Elec. Dev. 63(5), 1940–1948 (2016).
[Crossref]

Peng, H.

Z. Cheng, X. Zheng, D. Palubiak, M. Deen, and H. Peng, “A comprehensive and accurate analytical SPAD model for circuit simulation,” IEEE Trans. Elec. Dev. 63(5), 1940–1948 (2016).
[Crossref]

Qaraqe, K.

Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

Richardson, T.

A. Jovicic, J. Li, and T. Richardson, “Visible light communication: opportunities, challenges and the path to market,” IEEE Commun. Mag. 51(12), 26–32 (2013).
[Crossref]

Roermund, A.

K. Doris, A. Roermund, and D. Leenaerts, Wide-Bandwidth High Dynamic Range D/A Converters (The Springer International Series in Engineering and Computer Science Series) (Springer, 2006).

Ruff, A.

J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Rupp, M.

L. Hanzo, H. Haas, S. Imre, D. C. O’Brien, M. Rupp, and L. Gyongyosi, “Wireless myths, realities, and futures: from 3G/4G to optical and quantum wireless,” Proc. IEEE 100, 1853–1888 (2012).
[Crossref]

Safari, M.

Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
[Crossref]

Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Proceedings of IEEE Global Commun. Conf. Workshops (GC Wkshps) (IEEE, 2015), pp. 1–6.

Shirani, S.

N. Faramarzpour, M. Deen, S. Shirani, and Q. Fang, “Fully integrated single photon avalanche diode detector in standard CMOS 0.18 Îijm technology,” IEEE Trans. Electron. Dev. 55(3), 760–767 (2008).
[Crossref]

Si-Ma, L.

J. Zhang, L. Si-Ma, B. Wang, J. Zhang, and Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1041–1135 (2016).
[Crossref]

Snyder, D.

Starck, J.

J. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis (Cambridge University, 1998).
[Crossref]

Tsonev, D.

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

Underwood, I.

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J. Frechette, P. Grossmann, D. Busacker, G. Jordy, E. Duerr, K. McIntosh, D. Oakley, R. Bailey, A. Ruff, M. Brattain, J. Funk, J. MacDonald, and S. Verghese, “Readout circuitry for continuous high-rate photon detection with arrays of InP Geiger-mode avalanche photodiodes,” Proc. SPIE 8375, 83750W (2012).

Videv, S.

Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

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J. Zhang, L. Si-Ma, B. Wang, J. Zhang, and Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1041–1135 (2016).
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J. Zhang, L. Si-Ma, B. Wang, J. Zhang, and Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1041–1135 (2016).
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Y. Li, M. Safari, R. Henderson, and H. Haas, “Optical OFDM with single-photon avalanche diode,” IEEE Photon. Technol. Lett. 27(9), 943–946 (2015).
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J. Zhang, L. Si-Ma, B. Wang, J. Zhang, and Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1041–1135 (2016).
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Y. Li, S. Videv, M. Abdallah, K. Qaraqe, M. Uysal, and H. Haas, “Single photon avalanche diode (SPAD) VLC system and application to downhole monitoring,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

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Y. Li, M. Safari, R. Henderson, and H. Haas, “Nonlinear distortion in SPAD-based optical OFDM systems,” in Proceedings of IEEE Global Commun. Conf. Workshops (GC Wkshps) (IEEE, 2015), pp. 1–6.

O. Almer, D. Tsonev, N. Dutton, T. Abbas, S. Videv, S. Gnecchi, H. Haas, and R. Henderson, “A SPAD-based visible light communications receiver employing higher order modulation,” in Proceedings of IEEE Global Commun. Conf. (GLOBECOM) (IEEE, 2015), pp. 1–6.

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Figures (4)

Fig. 1
Fig. 1 SPAD-based PAM system model.
Fig. 2
Fig. 2 Performance comparison between the proposed quasi-ML detector, the GAT-based detector, and the receivers illustrated in [10] (this graph shows the BER of each receiver versus SNR of the Gaussian component whilst the noise in the Poisson component is constant due to the fixed optical irradiance of −70dBm, where the average photon count equals 4.5 × 104).
Fig. 3
Fig. 3 Performance comparison between the proposed quasi-ML detector, the GAT-based detector, and the receivers illustrated in [10] with respect to the optical irradiance.
Fig. 4
Fig. 4 Performance comparison between the SPAD-based VLC systems with the proposed quasi-ML detector and the GAT-based detector.

Tables (1)

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Algorithm 1 The proposed GAT-based detector for PAM systems using SPAD

Equations (22)

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z i = η p i + n i , i = 0 , 1 , , N 1 ,
λ i = ( Q T / E ) x i + N d T = α x i + β ,
P r ( p i = n | λ i ) = e λ i λ i n n ! .
p ( z i | λ i , σ ) = n = 0 + ( λ i n e λ i n ! × 1 2 π σ 2 exp ( ( z i n ) 2 2 σ 2 ) ) .
x ^ b i a s = arg max x ^ i C { p ( z i | α x ^ i + β , σ ) } ,
{ p ( z i | λ i , σ ) } ( s ) = + p ( x | λ i , σ ) e s x d x = exp ( λ i ( e s 1 ) + 0.5 σ 2 s 2 ) .
p ( z i | λ i , σ ) = 1 2 π j c j c + j exp ( f ( s ) ) d s ,
p ( z i | λ i , σ ) 1 ( 2 π f ( s ^ ) ) exp ( f ( s ^ ) ) ,
f ( s ) = 2 f ( s ) s 2 = λ i e s + σ 2 ,
f ( s ^ ) = z i + σ 2 s ^ λ i exp ( s ^ ) = 0 .
s ^ n e w = s ^ p r e z i + σ 2 s ^ p r e λ i e s ^ p r e σ 2 + λ i e s ^ p r e ,
exp ( s ^ ) 1 s ^ , 1 < s ^ < 1 ,
s ^ 0 = λ i z i λ i + σ 2 .
x ^ i = arg max x ^ i C { p ( z i | α x ^ i + β , σ ) } = arg max x ^ i C { 1 ( 2 π f ( s ^ ) ) exp ( f ( s ^ ) ) } .
T ( z i ) = { 2 z i + 0.375 + σ 2 , z i + 0.375 + σ 2 > 0 ; 0 , z i + 0.375 + σ 2 0 .
T ( z i ) = E { T ( z i ) | λ i , σ } + n i ,
e i = + T ( z i ) p ( z i | λ i , σ ) d z i .
e i + T ( z i ) 1 2 π f ( s ^ i ) exp { f ( s ^ i ) } d z i ,
e i u i 2 λ i e s ^ i σ 2 s ^ i + 0.375 + σ 2 × exp { λ i ( e s ^ i s + e s ^ i 1 ) } λ i e s ^ i + σ 2 2 π d s ^ i ,
Φ ( λ i , u i ) = λ i exp ( u i ) σ 2 u i + 0.375 + σ 2 = 0 .
g ( c i ) = u i 2 λ i e s σ 2 s + 0.375 + σ 2 × exp { λ i ( e s s + e s 1 ) } λ i e s + σ 2 2 π d s ,
D i = ( g ( c i ) + g ( c i + 1 ) ) / 2 , i = 0 , 1 , , M 2 .

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