Abstract

Recently, the single photon avalanche diode optical wireless communication (SPAD OWC) has attracted much attention due to its potential underwater applications. For such system, the channel noise is additive Poisson noise (APN) rather than the commonly encountered additive white Gaussian noise (AWGN) and the corresponding maximum likelihood (ML) detection is hard to provide a useful insight into energy-efficient signal design. By using the previously proposed Hellinger distance design criterion, we design an energy-efficient multi-dimensional constellation within the nonnegative integer set by minimizing the average optical power for a fixed minimum Hellinger distance. Comprehensive simulations indicate that our designed constellation can substantially outperform the currently available pulse amplitude modulation (PAM) and squared PAM for SPAD OWC systems.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  43. 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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    [Crossref]

2017 (2)

T. Mao, Z. Wang, and Q. Wang, “Receiver design for SPAD-based VLC systems under Possion-Gaussian mixed noise model,” Opt. Express 25(2), 799–809 (2017).
[Crossref] [PubMed]

L.-H. Si-Ma, J. Zhang, B. Wang, and Y.-Y. Zhang, “Hellinger-distance-optimal space constellations for SPAD underwater MIMO-OWC systems,” IEEE Commun. Lett. 21(4), 765–768 (2017).
[Crossref]

2016 (4)

J. Zhang, L.-H. Si-Ma, B.-Q. Wang, J.-K. Zhang, and Y.-Y. Zhang, “Low-complexity receivers and energy-efficient constellations for SPAD VLC systems,” IEEE Photon. Technol. Lett. 28(17), 1799–1802 (2016).
[Crossref]

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).

C. Wang, H. Y. Yu, and Y. J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

Y. Y. Zhang, H. Y. Yu, J. K. Zhang, and Y. J. Zhu, “On the optimality of spatial repetition coding for MIMO optical wireless communications,” IEEE Commun. Lett. 20(5), 846–849 (2016).
[Crossref]

2015 (2)

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. J. Zhu, W. F. Liang, J. K. Zhang, and Y. Y. Zhang, “Space-collaborative constellation designs for MIMO indoor visible light communications,” IEEE Photon. Technol. Lett. 27(15), 1667–1670 (2015).
[Crossref]

2014 (8)

P. A. Hiskett and R. A. Lamb, “Underwater optical communications with a single photon-counting system,” Proc. SPIE 9114, 91140P (2014).
[Crossref]

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 558–565 (2014).
[Crossref]

S. K. Routray, “The changing trends of optical communication,” IEEE Potentials 33(1), 28–33 (2014).
[Crossref]

D. Chitnis and S. Collins, “A SPAD-based photon detecting system for optical communications,” J. Lightw. Technol. 32(10), 2028–2034 (2014).
[Crossref]

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part I: General properties and numerical techniques,” IEEE Trans. Commun. 62(1), 194–202 (2014).
[Crossref]

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part II: Binary inputs,” IEEE Trans. Commun. 62(1), 203–213 (2014).
[Crossref]

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
[Crossref]

2013 (2)

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]

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]

2012 (1)

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wirel. Commun. Netw. 91(1), 1–28 (2012).

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]

2009 (2)

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

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science in China Series F: Information Sciences 52(8), 1483–1490 (2009).
[Crossref]

2008 (2)

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection?” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

C. Yuen, Y. L. Guan, and T. T. Tjhung, “Power-balanced orthogonal space–time block code,” IEEE Trans. Veh. Technol. 57(5), 3304–3309 (2008).
[Crossref]

2005 (1)

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[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]

2003 (1)

S. Hranilovic and F. R. Kschischang, “Optical intensity-modulated direct detection channels: signal space and lattice codes,” IEEE Trans. Inf. Theory 49(6), 1385–1399 (2003).
[Crossref]

1999 (1)

V. Tarokh, A. Naguib, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Trans. Commun. 47(2), 199–207 (1999).
[Crossref]

1998 (1)

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

1989 (2)

G. D. Forney and L.-F. Wei, “Multidimensional constellations–Part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7(6), 877–892 (1989).
[Crossref]

G. D. Forney, “Multidimensional constellations–Part II: Voronoi constellations,” IEEE J. Sel. Areas Commun. 7(6), 941–958 (1989).
[Crossref]

1987 (2)

G. Ungerboeck, “Trellis-coded modulation with redundant signal sets Part I: Introduction,” IEEE Commun. Mag. 25(2), 5–11 (1987).
[Crossref]

G. Ungerboeck, “Trellis-coded modulation with redundant signal sets Part II: State of the art,” IEEE Commun. Mag. 25(2), 12–21 (1987).
[Crossref]

1969 (1)

I. Bar-David, “Communication under the Poisson regime,” IEEE Trans. Inf. Theory 15(1), 31–37 (1969).
[Crossref]

1948 (1)

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

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 Communication Conference (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

Alexander, S. N. J.

C. J. Horton and S. N. J. Alexander, Sphere Packings, Lattices and Groups (Springer-Verlag, 1993).

Amphawan, A.

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 558–565 (2014).
[Crossref]

Anscombe, F. J.

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

Arnon, S.

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).
[Crossref]

Bar-David, I.

I. Bar-David, “Communication under the Poisson regime,” IEEE Trans. Inf. Theory 15(1), 31–37 (1969).
[Crossref]

Barry, J.

S. Arnon, J. Barry, G. Karagiannidis, R. Schober, and M. Uysal, Advanced Optical Wireless Communication Systems (Cambridge University, 2012).
[Crossref]

Borah, D. K.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wirel. Commun. Netw. 91(1), 1–28 (2012).

Boucouvalas, A. C.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wirel. Commun. Netw. 91(1), 1–28 (2012).

Calderbank, A. R.

V. Tarokh, A. Naguib, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Trans. Commun. 47(2), 199–207 (1999).
[Crossref]

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

Cao, J.

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part I: General properties and numerical techniques,” IEEE Trans. Commun. 62(1), 194–202 (2014).
[Crossref]

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part II: Binary inputs,” IEEE Trans. Commun. 62(1), 203–213 (2014).
[Crossref]

Chaudhary, S.

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 558–565 (2014).
[Crossref]

Chen, J.

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part II: Binary inputs,” IEEE Trans. Commun. 62(1), 203–213 (2014).
[Crossref]

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part I: General properties and numerical techniques,” IEEE Trans. Commun. 62(1), 194–202 (2014).
[Crossref]

Chitnis, D.

D. Chitnis and S. Collins, “A SPAD-based photon detecting system for optical communications,” J. Lightw. Technol. 32(10), 2028–2034 (2014).
[Crossref]

Collins, S.

D. Chitnis and S. Collins, “A SPAD-based photon detecting system for optical communications,” J. Lightw. Technol. 32(10), 2028–2034 (2014).
[Crossref]

Davis, C. C.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wirel. Commun. Netw. 91(1), 1–28 (2012).

Dong, Y.

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
[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]

Faulkner, G.

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

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]

Forney, G. D.

G. D. Forney and L.-F. Wei, “Multidimensional constellations–Part I: Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7(6), 877–892 (1989).
[Crossref]

G. D. Forney, “Multidimensional constellations–Part II: Voronoi constellations,” IEEE J. Sel. Areas Commun. 7(6), 941–958 (1989).
[Crossref]

Gallager, R. G.

R. G. Gallager, Principles of Digital Communication (Cambridge University Press, 2008).
[Crossref]

Gao, Q.

C. Gong, Q. Gao, and Z. Xu, “Analysis and design of amplitude modulation for optical wireless communication with shot noise,” in Proceedings of IEEE International Conference on Communications (ICC) (IEEE, 2016), pp. 1–6.

Gauss, C. F.

C. F. Gauss, Disquisitiones Arithmeticae (Yale University, 1966).

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).

C. Gong, Q. Gao, and Z. Xu, “Analysis and design of amplitude modulation for optical wireless communication with shot noise,” in Proceedings of IEEE International Conference on Communications (ICC) (IEEE, 2016), pp. 1–6.

Grosswald, E.

E. Grosswald, Representations of Integers as Sums of Squares (Springer-Verlag, 1985).
[Crossref]

Guan, Y. L.

C. Yuen, Y. L. Guan, and T. T. Tjhung, “Power-balanced orthogonal space–time block code,” IEEE Trans. Veh. Technol. 57(5), 3304–3309 (2008).
[Crossref]

C. Yuen, Y. L. Guan, and T. T. Tjhung, “Orthogonal space-time block code from amicable complex orthogonal design,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, 2004), pp. 469–472.

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]

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]

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 Communication Conference (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

Hardy, G. H.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Oxford University, 1979).

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]

Hiskett, P. A.

P. A. Hiskett and R. A. Lamb, “Underwater optical communications with a single photon-counting system,” Proc. SPIE 9114, 91140P (2014).
[Crossref]

Horton, C. J.

C. J. Horton and S. N. J. Alexander, Sphere Packings, Lattices and Groups (Springer-Verlag, 1993).

Hranilovic, S.

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part II: Binary inputs,” IEEE Trans. Commun. 62(1), 203–213 (2014).
[Crossref]

J. Cao, S. Hranilovic, and J. Chen, “Capacity-achieving distributions for the discrete-time poisson channel - part I: General properties and numerical techniques,” IEEE Trans. Commun. 62(1), 194–202 (2014).
[Crossref]

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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 Communication Conference (GLOBECOM) (IEEE, 2014), pp. 2108–2113.

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Y. Y. Zhang, H. Y. Yu, J. K. Zhang, and Y. J. Zhu, “On the optimality of spatial repetition coding for MIMO optical wireless communications,” IEEE Commun. Lett. 20(5), 846–849 (2016).
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Y. Y. Zhang, H. Y. Yu, J. K. Zhang, and Y. J. Zhu, “On the optimality of spatial repetition coding for MIMO optical wireless communications,” IEEE Commun. Lett. 20(5), 846–849 (2016).
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Y. J. Zhu, W. F. Liang, J. K. Zhang, and Y. Y. Zhang, “Space-collaborative constellation designs for MIMO indoor visible light communications,” IEEE Photon. Technol. Lett. 27(15), 1667–1670 (2015).
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EURASIP J. Wirel. Commun. Netw. (1)

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wirel. Commun. Netw. 91(1), 1–28 (2012).

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Y. Y. Zhang, H. Y. Yu, J. K. Zhang, and Y. J. Zhu, “On the optimality of spatial repetition coding for MIMO optical wireless communications,” IEEE Commun. Lett. 20(5), 846–849 (2016).
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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).

L.-H. Si-Ma, J. Zhang, B. Wang, and Y.-Y. Zhang, “Hellinger-distance-optimal space constellations for SPAD underwater MIMO-OWC systems,” IEEE Commun. Lett. 21(4), 765–768 (2017).
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G. Ungerboeck, “Trellis-coded modulation with redundant signal sets Part II: State of the art,” IEEE Commun. Mag. 25(2), 12–21 (1987).
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IEEE J. Sel. Areas Commun. (3)

L. Zeng, D. O’Brien, H. Minh, G. Faulkner, K. Lee, D. Jung, Y. Oh, and E. T. Won, “High data rate multiple input multiple output (MIMO) optical wireless communications using white led lighting,” IEEE J. Sel. Areas Commun. 27(9), 1654–1662 (2009).
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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).
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IEEE Photon. J. (1)

C. Wang, H. Y. Yu, and Y. J. Zhu, “A long distance underwater visible light communication system with single photon avalanche diode,” IEEE Photon. J. 8(5), 1–11 (2016).
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IEEE Photon. Technol. Lett. (3)

Y. J. Zhu, W. F. Liang, J. K. Zhang, and Y. Y. Zhang, “Space-collaborative constellation designs for MIMO indoor visible light communications,” IEEE Photon. Technol. Lett. 27(15), 1667–1670 (2015).
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IEEE Trans. Commun. (4)

S. Tang, Y. Dong, and X. Zhang, “Impulse response modeling for underwater wireless optical communication links,” IEEE Trans. Commun. 62(1), 226–234 (2014).
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IEEE Trans. Inf. Theory (3)

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IEEE Trans. Wireless Commun. (2)

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
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M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection?” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
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Proc. SPIE (1)

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Science in China Series F: Information Sciences (1)

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science in China Series F: Information Sciences 52(8), 1483–1490 (2009).
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[Crossref]

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Figures (8)

Fig. 1
Fig. 1 PAM, SPAM and our proposed constellations with L = 2 and different K.
Fig. 2
Fig. 2 Proposed constellations for L = 3 and different K.
Fig. 3
Fig. 3 Comparisons for the PDF estimation of and Gaussian distribution with various optical irradiance
Fig. 4
Fig. 4 Receiver performance comparisons for L = 2, various K and different constellation.
Fig. 5
Fig. 5 Comparisons among PAM, SPAM and proposed constellation for AR receiver with L = 2 and different K.
Fig. 6
Fig. 6 Comparisons among PAM, SPAM and proposed constellation for AR receiver with L = 3 and different K.
Fig. 7
Fig. 7 Comparisons between SPAM and proposed constellation for AR receiver with L = 4 and different K.
Fig. 8
Fig. 8 Comparisons between SPAM and proposed constellation for AR receiver with L = 5 and different K.

Equations (7)

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r = α x + β 1 L × 1 + p
r ( AR ) = 2 r + 3 / 8 , = 1 , 2 , , L .
r ( AR ) x ¯ + ξ
r ( AR ) x ¯ + ξ .
HD ( 𝒳 ) = min x x ^ , x , x ^ 𝒳 = 1 L | x x ^ | 2 .
𝒳 ˜ = i = 1 i = I 1 𝒳 ˜ n i 𝒳 ¯ n I ,
𝒳 ˜ n I { x : 1 T x = n I , x 1 2 + L }

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