Abstract

In this Letter, we present a photonic compressive sampling scheme based on optical sampling and random demodulation for microwave spectral analysis. A novel (to our knowledge) approach to realizing the multiplication of a pseudorandom binary sequence and the input microwave signal of interest in the optical domain is proposed, which largely simplifies the implementation of the compressive sampling. A spectrally sparse signal can be successfully captured by an electrical digitizer with a sampling rate much lower than the Nyquist rate with the help of random demodulation and the sparse reconstruction algorithm. Identification of the signals with multiple frequency components is successfully demonstrated.

© 2012 Optical Society of America

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References

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  1. J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
    [CrossRef]
  2. R. A. Minasian, IEEE Trans. Microwave Theor. Tech. 54, 832 (2006).
    [CrossRef]
  3. L. V. T. Nguyen and D. B. Hunter, IEEE Photon. Technol. Lett. 18, 1188 (2006).
    [CrossRef]
  4. H. Chi, X. H. Zou, and J. P. Yao, IEEE Photon. Technol. Lett. 20, 1249 (2008).
    [CrossRef]
  5. S. T. Winnall and A. C. Lindsay, IEEE Trans. Microwave Theor. Tech. 47, 1385 (1999).
    [CrossRef]
  6. W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
    [CrossRef]
  7. R. E. Saperstein, D. Panasenko, and Y. Fainman, Opt. Lett. 29, 501 (2004).
    [CrossRef]
  8. B. Vidal, T. Mengual, and J. Marti, IEEE Trans. Microwave Theor. Tech. 58, 3103 (2010).
    [CrossRef]
  9. Y. Wang, H. Chi, X. Zhang, S. Zheng, and X. Jin, Opt. Lett. 36, 3897 (2011).
    [CrossRef]
  10. L. V. T. Nguyen, IEEE Photon. Technol. Lett. 21, 642 (2009).
    [CrossRef]
  11. J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
    [CrossRef]
  12. H. Nan, Y. Gu, and H. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
    [CrossRef]
  13. L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
    [CrossRef]
  14. J. M. Nicholes and F. Bucholz, Opt. Express 19, 7339 (2011).
    [CrossRef]
  15. M. Mishali and Y. C. Eldar, IEEE J. Sel. Top. Signal Proc. 4, 375 (2010).
    [CrossRef]
  16. S. Boyd and L. Vandenberghe, Convex Optimization(Cambridge Univ., 2004).

2012 (1)

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

2011 (3)

2010 (3)

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

B. Vidal, T. Mengual, and J. Marti, IEEE Trans. Microwave Theor. Tech. 58, 3103 (2010).
[CrossRef]

M. Mishali and Y. C. Eldar, IEEE J. Sel. Top. Signal Proc. 4, 375 (2010).
[CrossRef]

2009 (1)

L. V. T. Nguyen, IEEE Photon. Technol. Lett. 21, 642 (2009).
[CrossRef]

2008 (1)

H. Chi, X. H. Zou, and J. P. Yao, IEEE Photon. Technol. Lett. 20, 1249 (2008).
[CrossRef]

2007 (1)

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

2006 (2)

R. A. Minasian, IEEE Trans. Microwave Theor. Tech. 54, 832 (2006).
[CrossRef]

L. V. T. Nguyen and D. B. Hunter, IEEE Photon. Technol. Lett. 18, 1188 (2006).
[CrossRef]

2004 (1)

2001 (1)

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

1999 (1)

S. T. Winnall and A. C. Lindsay, IEEE Trans. Microwave Theor. Tech. 47, 1385 (1999).
[CrossRef]

Baraniuk, R. G.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Boyd, S.

S. Boyd and L. Vandenberghe, Convex Optimization(Cambridge Univ., 2004).

Brock, J. C.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Bucholz, F.

Capmany, J.

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

Chi, H.

Y. Wang, H. Chi, X. Zhang, S. Zheng, and X. Jin, Opt. Lett. 36, 3897 (2011).
[CrossRef]

H. Chi, X. H. Zou, and J. P. Yao, IEEE Photon. Technol. Lett. 20, 1249 (2008).
[CrossRef]

Dai, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Davis, R. L.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Duarte, M. F.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Eldar, Y. C.

M. Mishali and Y. C. Eldar, IEEE J. Sel. Top. Signal Proc. 4, 375 (2010).
[CrossRef]

Fainman, Y.

Gu, Y.

H. Nan, Y. Gu, and H. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

Hunter, D. B.

L. V. T. Nguyen and D. B. Hunter, IEEE Photon. Technol. Lett. 18, 1188 (2006).
[CrossRef]

Ji, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Jin, X.

Jung, T. J.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Laska, J. N.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Lembo, L. J.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Li, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Lin, J.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Lindsay, A. C.

S. T. Winnall and A. C. Lindsay, IEEE Trans. Microwave Theor. Tech. 47, 1385 (1999).
[CrossRef]

Lodenkamper, R.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Marti, J.

B. Vidal, T. Mengual, and J. Marti, IEEE Trans. Microwave Theor. Tech. 58, 3103 (2010).
[CrossRef]

Mengual, T.

B. Vidal, T. Mengual, and J. Marti, IEEE Trans. Microwave Theor. Tech. 58, 3103 (2010).
[CrossRef]

Minasian, R. A.

R. A. Minasian, IEEE Trans. Microwave Theor. Tech. 54, 832 (2006).
[CrossRef]

Mishali, M.

M. Mishali and Y. C. Eldar, IEEE J. Sel. Top. Signal Proc. 4, 375 (2010).
[CrossRef]

Nan, H.

H. Nan, Y. Gu, and H. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

Nguyen, L. V. T.

L. V. T. Nguyen, IEEE Photon. Technol. Lett. 21, 642 (2009).
[CrossRef]

L. V. T. Nguyen and D. B. Hunter, IEEE Photon. Technol. Lett. 18, 1188 (2006).
[CrossRef]

Nicholes, J. M.

Novak, D.

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

Panasenko, D.

Romberg, J. K.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Saperstein, R. E.

Tropp, J. A.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Vandenberghe, L.

S. Boyd and L. Vandenberghe, Convex Optimization(Cambridge Univ., 2004).

Vidal, B.

B. Vidal, T. Mengual, and J. Marti, IEEE Trans. Microwave Theor. Tech. 58, 3103 (2010).
[CrossRef]

Wang, W. S.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Wang, Y.

Winnall, S. T.

S. T. Winnall and A. C. Lindsay, IEEE Trans. Microwave Theor. Tech. 47, 1385 (1999).
[CrossRef]

Wu, J.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Wu, M. C.

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

Xu, K.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Yan, L.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Yao, J. P.

H. Chi, X. H. Zou, and J. P. Yao, IEEE Photon. Technol. Lett. 20, 1249 (2008).
[CrossRef]

Zhang, H.

H. Nan, Y. Gu, and H. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

Zhang, X.

Zheng, S.

Zou, X. H.

H. Chi, X. H. Zou, and J. P. Yao, IEEE Photon. Technol. Lett. 20, 1249 (2008).
[CrossRef]

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

M. Mishali and Y. C. Eldar, IEEE J. Sel. Top. Signal Proc. 4, 375 (2010).
[CrossRef]

IEEE Photon. J. (1)

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

H. Nan, Y. Gu, and H. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

L. V. T. Nguyen and D. B. Hunter, IEEE Photon. Technol. Lett. 18, 1188 (2006).
[CrossRef]

H. Chi, X. H. Zou, and J. P. Yao, IEEE Photon. Technol. Lett. 20, 1249 (2008).
[CrossRef]

L. V. T. Nguyen, IEEE Photon. Technol. Lett. 21, 642 (2009).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (4)

R. A. Minasian, IEEE Trans. Microwave Theor. Tech. 54, 832 (2006).
[CrossRef]

S. T. Winnall and A. C. Lindsay, IEEE Trans. Microwave Theor. Tech. 47, 1385 (1999).
[CrossRef]

W. S. Wang, R. L. Davis, T. J. Jung, R. Lodenkamper, L. J. Lembo, J. C. Brock, and M. C. Wu, IEEE Trans. Microwave Theor. Tech. 49, 1996 (2001).
[CrossRef]

B. Vidal, T. Mengual, and J. Marti, IEEE Trans. Microwave Theor. Tech. 58, 3103 (2010).
[CrossRef]

Nat. Photonics (1)

J. Capmany and D. Novak, Nat. Photonics 1, 319 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (1)

S. Boyd and L. Vandenberghe, Convex Optimization(Cambridge Univ., 2004).

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Figures (3)

Fig. 1.
Fig. 1.

Photonic compressive sampling with a random demodulator (O/E: optical-to-electrical conversion).

Fig. 2.
Fig. 2.

Optical modulation module for realizing the multiplication of the signal of interest and the PRBS.

Fig. 3.
Fig. 3.

Simulation results. (a) Spectrum of the original signal, (b) reconstructed spectrum (N=4096, R=16), (c) comparison of the original and the recovered signal in the time domain (N=4096, R=16), (d) reconstructed spectrum (N=1024, R=16).

Equations (5)

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

Vout(t)=RZp(t)αβr(t)x(t)=Cp(t)r(t)x(t),
Vout(t)[kr(tkT)x(tkT)]*g(t).
Vd(t)=Vout(t)*h(t)=[kr(tkT)x(tkT)]*[g(t)*h(t)].
y(t)=Vd(t)kδ(tkRT)=kδ(tkRT){[kr(tkT)x(tkT)]*[g(t)*h(t)]}.
y=DHRx=DHRWθ,

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