Abstract

In this paper, a photonic-assisted multi-channel compressive sampling scheme is proposed with one pseudo-random binary sequence (PRBS) source and Wavelength Division Multiplexing-based time delay. Meanwhile, the restricted isometry property of sensing matrix determined by the optimized time delay pattern is analyzed. In experiment, a four-channel photonic-assisted system with 5-GHz bandwidth was set up, where four-channel PRBS signals were generated by adding fiber-induced constant time delays to four-wavelength modulated PRBS signal, and a signal composed of twenty tones was recovered faithfully with four analog-to-digital converters (ADCs) with only 120-MHz-bandwidth.

© 2013 Optical Society of America

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  1. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
    [CrossRef]
  2. R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
    [CrossRef]
  3. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
    [CrossRef]
  4. R. Horisaki, X. Xiao, J. Tanida, and B. Javidi, “Feasibility study for compressive multi-dimensional integral imaging,” Opt. Express21(4), 4263–4279 (2013).
    [CrossRef] [PubMed]
  5. J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
    [CrossRef]
  6. M. Mishali and Y. C. Eldar, “From theory to practice: Sub-nyquist sampling of sparse wideband analog signals,” J. Sel. Top. Signal Process.4(2), 375–391 (2010).
    [CrossRef]
  7. J. M. Nichols and F. Bucholtz, “Beating nyquist with light: a compressively sampled photonic link,” Opt. Express19(8), 7339–7348 (2011).
    [CrossRef] [PubMed]
  8. L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).
  9. H. Chi, Y. Mei, Y. Chen, D. Wang, S. Zheng, X. Jin, and X. Zhang, “Microwave spectral analysis based on photonic compressive sampling with random demodulation,” Opt. Lett.37(22), 4636–4638 (2012).
    [CrossRef] [PubMed]
  10. P. Timothy, P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, Jr., “Wideband Photonic Compressive Sampling Analog-to-Digital Converter for RF Spectrum Estimation,” in Proceedings of Optical Fiber Communication Conference, (Anaheim, Calif., 2013), paper OTh3D.1.
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    [CrossRef] [PubMed]
  12. H. Nan, Y. Gu, and H. Zhang, “Optical analog-to-digital conversion system based on compressive sampling,” IEEE Photon. Technol. Lett.23(2), 67–69 (2011).
    [CrossRef]
  13. Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.
  14. E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. Int.346(9), 717–772 (2008).
  15. J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory53(12), 4655–4666 (2007).
    [CrossRef]
  16. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process1(4), 586–597 (2007).
    [CrossRef]

2013 (1)

2012 (3)

2011 (2)

H. Nan, Y. Gu, and H. Zhang, “Optical analog-to-digital conversion system based on compressive sampling,” IEEE Photon. Technol. Lett.23(2), 67–69 (2011).
[CrossRef]

J. M. Nichols and F. Bucholtz, “Beating nyquist with light: a compressively sampled photonic link,” Opt. Express19(8), 7339–7348 (2011).
[CrossRef] [PubMed]

2010 (1)

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-nyquist sampling of sparse wideband analog signals,” J. Sel. Top. Signal Process.4(2), 375–391 (2010).
[CrossRef]

2008 (2)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. Int.346(9), 717–772 (2008).

2007 (3)

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory53(12), 4655–4666 (2007).
[CrossRef]

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process1(4), 586–597 (2007).
[CrossRef]

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
[CrossRef]

2006 (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
[CrossRef]

Baraniuk, R. G.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

Bucholtz, F.

Candès, E. J.

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. Int.346(9), 717–772 (2008).

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

Chen, H.

Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.

Chen, M.

Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.

Chen, Y.

Chi, H.

Dai, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

Duarte, M. F.

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

Eldar, Y. C.

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-nyquist sampling of sparse wideband analog signals,” J. Sel. Top. Signal Process.4(2), 375–391 (2010).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process1(4), 586–597 (2007).
[CrossRef]

Gilbert, A.

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory53(12), 4655–4666 (2007).
[CrossRef]

Gu, Y.

H. Nan, Y. Gu, and H. Zhang, “Optical analog-to-digital conversion system based on compressive sampling,” IEEE Photon. Technol. Lett.23(2), 67–69 (2011).
[CrossRef]

Horisaki, R.

Javidi, B.

Ji, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Jin, X.

Kelly, K. F.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

Kirolos, S.

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

Laska, J. N.

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

Li, R.

Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.

Li, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Liang, Y.

Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.

Lin, J.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Massoud, Y.

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

Mei, Y.

Mishali, M.

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-nyquist sampling of sparse wideband analog signals,” J. Sel. Top. Signal Process.4(2), 375–391 (2010).
[CrossRef]

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

Nan, H.

H. Nan, Y. Gu, and H. Zhang, “Optical analog-to-digital conversion system based on compressive sampling,” IEEE Photon. Technol. Lett.23(2), 67–69 (2011).
[CrossRef]

Nichols, J. M.

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process1(4), 586–597 (2007).
[CrossRef]

Ragheb, T.

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

Sefler, G. A.

Shaw, T. J.

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

Tanida, J.

Tropp, J.

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory53(12), 4655–4666 (2007).
[CrossRef]

Valley, G. C.

Wang, D.

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process1(4), 586–597 (2007).
[CrossRef]

Wu, J.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Xiao, X.

Xie, S.

Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.

Xu, K.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Yan, L.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

Zhang, H.

H. Nan, Y. Gu, and H. Zhang, “Optical analog-to-digital conversion system based on compressive sampling,” IEEE Photon. Technol. Lett.23(2), 67–69 (2011).
[CrossRef]

Zhang, X.

Zheng, S.

Appl. Phys. Lett. (1)

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93(12), 121105 (2008).
[CrossRef]

C. R. Acad. Sci. Int. (1)

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. Int.346(9), 717–772 (2008).

IEEE J. Sel. Top. Signal Process (1)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process1(4), 586–597 (2007).
[CrossRef]

IEEE Photon. J. (1)

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, “Integrated Multi-frequency Recognition and Down-conversion based on Photonics-assisted Compressive Sampling,” IEEE Photon. J.4(3), 664–670 (2012).

IEEE Photon. Technol. Lett. (1)

H. Nan, Y. Gu, and H. Zhang, “Optical analog-to-digital conversion system based on compressive sampling,” IEEE Photon. Technol. Lett.23(2), 67–69 (2011).
[CrossRef]

IEEE Signal Process. Mag. (1)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–121 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (2)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

J. Tropp and A. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory53(12), 4655–4666 (2007).
[CrossRef]

J. Sel. Top. Signal Process. (1)

M. Mishali and Y. C. Eldar, “From theory to practice: Sub-nyquist sampling of sparse wideband analog signals,” J. Sel. Top. Signal Process.4(2), 375–391 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Other (3)

P. Timothy, P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, Jr., “Wideband Photonic Compressive Sampling Analog-to-Digital Converter for RF Spectrum Estimation,” in Proceedings of Optical Fiber Communication Conference, (Anaheim, Calif., 2013), paper OTh3D.1.

Y. Liang, M. Chen, R. Li, H. Chen, and S. Xie, “A photonic-assisted compressive sampling system,” in Proceedings of IEEE Microwave photonics Conference, (Netherlands, 2012), pp. 184–187.

J. N. Laska, S. Kirolos, M. F. Duarte, T. Ragheb, R. G. Baraniuk, and Y. Massoud, “Theory and implementation of an analog-to-information conversion using random demodulation,” IEEE Int. Symp. Circuits and Systems (ISCAS), 1959–1962 (2007).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

The diagram of proposed CS system (CW: continuous wave; MZM: Mach-Zehnder modulator; PD: photodetector; LPF: low-pass filter; DSP: Digital signal processor).

Fig. 2
Fig. 2

The spectrums of modulated PRBS signals, RF signal and low-pass filtered mixed signal.

Fig. 3
Fig. 3

For random vectors X, the values of AX 2 2 X 2 2 achieved with: (a) Multiple individual-and-different PRBSs; (b) PRBS signals of nonuniform time delays; (c) PRBS signals of uniform time delays.

Fig. 4
Fig. 4

Experimental setup (DFB: Distributed-feedback laser; MUX: Multiplexer; DeMUX: Demultiplexer; PD: Photodetector;; DSP: Digital signal processor)

Fig. 5
Fig. 5

The waveforms of four-channel PRBS signals.

Fig. 6
Fig. 6

(a) Original RF spectrum; (b) four-channel compressed spectrum; (c) and (d) recovered spectrums for L = 3 and L = 5.

Equations (7)

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V i (t)=[1+πm(tΔ τ i )/ V pi1 ][1+πx(t)/ V pi2 ]
V i (f)=1+π/ V pi2 X(f)+ M i (f)+π/ V pi2 k= N N a k e j2πk f p Δ τ i X(fk f P )
V i (f)=1+ M i (f)+π/ V pi2 k= N N a k e j2πk f p Δ τ i X(fk f P ), f[0.5L f P ,0.5L f P ]
Y i ( f )=π/ V pi2 k= N N a k e j2πk f p Δ τ i X(fj f P )
[ Y i (f L f p ) Y i (f) Y i (f+ L f p ) ] Y i = π V pi2 [ a ( N L ) e j2π( N L ) f p Δ τ i a N e j2π N f p Δ τ i a ( N + L ) e j2π( N + L ) f p Δ τ i a N + L e j2π( N L ) f p Δ τ i a 1 e -j2π f p Δ τ i a 0 a 1 e j2π f p Δ τ i a N e j2π N f p Δ τ i a ( N L ) e j2π( N + L ) f p Δ τ i ] A i [ X(f N f p ) X(f) X(f+ N f p ) ] X
[ Y 1 Y i Y M ] Y = [ A 1 A i A M ] A [ X(f N f p ) X(f) X(f+ N f p ) ] X
(1 δ K ) AX 2 2 X 2 2 (1+ δ K )

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