Abstract

A new technique, which can compensate for the lack of channel bandwidth in an optical wireless orthogonal frequency division multiplexing (OFDM) link based on a light emitting diode (LED), is proposed. It uses an adaptive sampling and an inverse discrete cosine transform in order to convert an OFDM signal into a sparse waveform so that not only is the important data obtained efficiently but the redundancy one is removed. In compressive sensing (CS), a sparse signal that is sampled below the Nyquist/Shannon limit can be reconstructed successively with enough measurement. This means that the CS technique can increase the data rate of visible light communication (VLC) systems based on LEDs. It is observed that the data rate of the proposed CS-based VLC-OFDM link can be made 1.7 times greater than a conventional VLC-OFDM link (from 30.72 Mb/s to 51.2 Mb/s). We see that the error vector magnitude (EVM) of the quadrature phase shift keying (QPSK) symbol is 31% (FEC limit: EVM of 32%) at a compression ratio of 40%.

© 2014 Optical Society of America

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References

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  1. 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]
  2. J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.
  3. H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
    [Crossref]
  4. H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
    [Crossref]
  5. C. Kottke, J. Hilt, K. Habel, J. Vucic, and K.-D. Langer, “1.25 Gbit/s visible light WDM link based on DMT modulation of a single RGB LED luminary,” in Proceedings of 38th European Conference and Exhibition on Optical Communication (Amsterdam, 2012), paper We.3.B.4.
    [Crossref]
  6. J. Vucic, C. Kottke, S. Nerreter, K.-D. Langer, and J. W. Walewski, “513 Mbit/s visible light communications link based on DMT-modulation of a white LED,” J. Lightwave Technol. 28(24), 3512–3518 (2010).
  7. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
    [Crossref]
  8. D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ll minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
    [Crossref] [PubMed]
  9. E. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
    [Crossref]
  10. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev. 43(1), 129–159 (2001).
    [Crossref]
  11. J. A. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
    [Crossref]
  12. R. A. Shafik, S. Rahman, and R. Islam, “On the extended relationships among EVM, BER, and SNR as performance metrics,” in Proceedings of 4th International Conference on Electrical and Computer Engineering (Dhaka, 2006), pp. 408–411.
    [Crossref]
  13. Application note, “8 hints for making and interpreting EVM measurements” (Agilent Technologies, 2005), cp.literature.agilent.com/litweb/pdf/5989–3144EN.pdf .

2013 (1)

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]

2010 (1)

2009 (1)

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

2008 (1)

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

2006 (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2005 (1)

E. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

2004 (1)

J. A. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

2003 (1)

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ll minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

2001 (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev. 43(1), 129–159 (2001).
[Crossref]

Candès, E.

E. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

Chen, S. S.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev. 43(1), 129–159 (2001).
[Crossref]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ll minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev. 43(1), 129–159 (2001).
[Crossref]

Elad, M.

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ll minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

Faulkner, G.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

Gruber, J.

J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.

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]

Jung, D.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

Koonen, T.

J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.

Kottke, C.

Langer, K.-D.

J. Vucic, C. Kottke, S. Nerreter, K.-D. Langer, and J. W. Walewski, “513 Mbit/s visible light communications link based on DMT-modulation of a white LED,” J. Lightwave Technol. 28(24), 3512–3518 (2010).

J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.

Lee, K.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

Lee, S. C. J.

J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.

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]

Minh, H. L.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

Nerreter, S.

O’Brien, D.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

Oh, Y.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

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]

Saunders, M. A.

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev. 43(1), 129–159 (2001).
[Crossref]

Tao, T.

E. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

Tropp, J. A.

J. A. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

Vucic, J.

Walewski, J. W.

J. Vucic, C. Kottke, S. Nerreter, K.-D. Langer, and J. W. Walewski, “513 Mbit/s visible light communications link based on DMT-modulation of a white LED,” J. Lightwave Technol. 28(24), 3512–3518 (2010).

J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.

Won, E. T.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

Zeng, L.

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

IEEE Commun. Mag. (1)

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]

IEEE Photon. Technol. Lett. (2)

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, and Y. Oh, “High-speed visible light communications using multiple resonant equalization,” IEEE Photon. Technol. Lett. 20(14), 1243–1245 (2008).
[Crossref]

H. L. Minh, D. O’Brien, G. Faulkner, L. Zeng, K. Lee, D. Jung, Y. Oh, and E. T. Won, “100-Mb/s NRZ visible light communications using a postequalized white LED,” IEEE Photon. Technol. Lett. 21(15), 1063–1065 (2009).
[Crossref]

IEEE Trans. Inf. Theory (3)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

E. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

J. A. Tropp, “Greed is good: Algorithmic results for sparse approximation,” IEEE Trans. Inf. Theory 50(10), 2231–2242 (2004).
[Crossref]

J. Lightwave Technol. (1)

Proc. Natl. Acad. Sci. U.S.A. (1)

D. L. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via ll minimization,” Proc. Natl. Acad. Sci. U.S.A. 100(5), 2197–2202 (2003).
[Crossref] [PubMed]

SIAM Rev. (1)

S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev. 43(1), 129–159 (2001).
[Crossref]

Other (4)

C. Kottke, J. Hilt, K. Habel, J. Vucic, and K.-D. Langer, “1.25 Gbit/s visible light WDM link based on DMT modulation of a single RGB LED luminary,” in Proceedings of 38th European Conference and Exhibition on Optical Communication (Amsterdam, 2012), paper We.3.B.4.
[Crossref]

J. Gruber, S. C. J. Lee, K.-D. Langer, T. Koonen, and J. W. Walewski, “Wireless high-speed data transmission with phosphorescent white-light LEDs,” in Proceedings of 33th European Conference and Exhibition on Optical Communication (Berlin, 2007), pp. 1–2.

R. A. Shafik, S. Rahman, and R. Islam, “On the extended relationships among EVM, BER, and SNR as performance metrics,” in Proceedings of 4th International Conference on Electrical and Computer Engineering (Dhaka, 2006), pp. 408–411.
[Crossref]

Application note, “8 hints for making and interpreting EVM measurements” (Agilent Technologies, 2005), cp.literature.agilent.com/litweb/pdf/5989–3144EN.pdf .

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Figures (10)

Fig. 1
Fig. 1 Compressed optical OFDM signal transmission and reconstruction in a VLC system using adaptive sampling with IDCT domain and L1-minimization.

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Fig. 2
Fig. 2 Process of sparse signal generation using adaptive sampling and IDCT.

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Fig. 3
Fig. 3 L1-minimization-based original signal reconstruction procedure.

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Fig. 4
Fig. 4 Experimental setup for reconstruction of the compressed OFDM/QPSK signal in an optical wireless link based on a white LED.

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Fig. 5
Fig. 5 Channel response of VLC-Tx, filled square line: 1st order equalizer with LNA, open circle line: only white LED.

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Fig. 6
Fig. 6 Sparse waveform generation using adaptive sampling and IDCT, (a) upper waveform: original OFDM/QPSK signal, lower waveform: adaptive sampled OFDM/QPSK signal, (b) upper waveform: result of OFDM/QPSK signal transformed by IDCT, lower waveform: result of adaptive sampled one transformed by IDCT.

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Fig. 7
Fig. 7 The variation of EVM as well as the effective data rate against the compression ratio. The dashed line indicates the FEC limit (EVM of 32% = BER of 10−3).

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Fig. 8
Fig. 8 Variation of SNR and BER against compression ratio according to the modulation format (QPSK and 16-QAM), filled squares: QPSK symbols, open squares: 16QAM symbols, filled inverse triangles: BER of QPSK symbols, open inverse triangles: BER of 16-QAM symbols.

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Fig. 9
Fig. 9 Used a rate 1/2 feed-forward convolutional encoder diagram.

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Fig. 10
Fig. 10 SNR change of reconstructed QPSK signal against compression ratio before and after the convolutional code.

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Equations (5)

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

x=Ψα
α= argmin α∈ ℜ m ‖ α ‖ 1 subject to ν=ΦΨα
x ^ =Ψα+ε
min Ψ,α ‖ α ‖ 1 subject to ‖ Φx−ΦΨα ‖ 2 ≤ε
Compression ratio (%)=( 1− Length of compressed data Length of original data )×100

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