Abstract

We demonstrate a new architecture for high-speed compressed sensing using chirp processing with ultrafast laser pulses, presently applied to the measurement of sparse-frequency microwave signals. We spectrally encode highly chirped ultrafast laser pulses with pseudorandom bit sequences such that every laser pulse acquires a unique spectral pattern. The pulses are partially compressed in time, extending the effective sampling rate beyond the electronic limit, and then modulated with a sparse microwave signal. Finally the pulses are fully compressed and detected, effectively integrating the measurement. We achieve 100 usable features per pattern allowing for 100 points in the reconstructed microwave spectra and experimentally demonstrate reconstruction of two- and three-tone microwave signals spanning from 900 MHz to 14.76 GHz. These spectra are reconstructed by measuring the energy of only 23 to 38 consecutive laser pulses acquired in a single shot with a 500 MHz real-time oscilloscope.

© 2013 Optical Society of America

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References

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  1. A. Bleicher, IEEE Spectrum 50, 42 (2013).
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  2. E. Candès and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
    [CrossRef]
  3. J. M. Nichols and F. Bucholtz, Opt. Express 19, 7339 (2011).
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    [CrossRef]
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  9. H. Chi, Y. Chen, Y. Mei, X. Jin, S. Zheng, and X. Zhang, Opt. Lett. 38, 136 (2013).
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  10. F. Coppinger, A. S. Bhushan, and B. Jalali, IEEE Trans. Microw. Theory Tech. 47, 1309 (1999).
    [CrossRef]
  11. M. Figueiredo, R. Nowak, and S. Wright, IEEE J. Sel. Topics Signal Process. 1, 586 (2007).
    [CrossRef]
  12. E. Candès and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
    [CrossRef]

2013 (2)

2012 (3)

2011 (2)

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

J. M. Nichols and F. Bucholtz, Opt. Express 19, 7339 (2011).
[CrossRef]

2010 (1)

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

2008 (1)

E. Candès and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

2007 (1)

M. Figueiredo, R. Nowak, and S. Wright, IEEE J. Sel. Topics Signal Process. 1, 586 (2007).
[CrossRef]

2006 (1)

E. Candès and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

1999 (1)

F. Coppinger, A. S. Bhushan, and B. Jalali, IEEE Trans. Microw. Theory Tech. 47, 1309 (1999).
[CrossRef]

Baraniuk, R.

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

Bhushan, A. S.

F. Coppinger, A. S. Bhushan, and B. Jalali, IEEE Trans. Microw. Theory Tech. 47, 1309 (1999).
[CrossRef]

Bleicher, A.

A. Bleicher, IEEE Spectrum 50, 42 (2013).
[CrossRef]

Bucholtz, F.

Candès, E.

E. Candès and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

E. Candès and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

Chen, Y.

Chi, H.

Coppinger, F.

F. Coppinger, A. S. Bhushan, and B. Jalali, IEEE Trans. Microw. Theory Tech. 47, 1309 (1999).
[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]

Duarte, M.

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

Figueiredo, M.

M. Figueiredo, R. Nowak, and S. Wright, IEEE J. Sel. Topics Signal Process. 1, 586 (2007).
[CrossRef]

Gu, Y.

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

Jalali, B.

F. Coppinger, A. S. Bhushan, and B. Jalali, IEEE Trans. Microw. Theory Tech. 47, 1309 (1999).
[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.

Laska, J.

J. Tropp, J. Laska, M. Duarte, J. Romberg, and R. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[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]

Mei, Y.

Nan, H.

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

Nichols, J. M.

Nowak, R.

M. Figueiredo, R. Nowak, and S. Wright, IEEE J. Sel. Topics Signal Process. 1, 586 (2007).
[CrossRef]

Romberg, J.

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

Sefler, G. A.

Shaw, T. J.

Tao, T.

E. Candès and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

Tropp, J.

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

Valley, G. C.

Wakin, M.

E. Candès and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

Wang, D.

Wright, S.

M. Figueiredo, R. Nowak, and S. Wright, IEEE J. Sel. Topics Signal Process. 1, 586 (2007).
[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]

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]

Zhang, H.

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

Zhang, X.

Zheng, S.

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

M. Figueiredo, R. Nowak, and S. Wright, IEEE J. Sel. Topics Signal Process. 1, 586 (2007).
[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. (1)

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

IEEE Signal Process. Mag. (1)

E. Candès and M. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

IEEE Spectrum (1)

A. Bleicher, IEEE Spectrum 50, 42 (2013).
[CrossRef]

IEEE Trans. Inf. Theory (2)

E. Candès and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

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

IEEE Trans. Microw. Theory Tech. (1)

F. Coppinger, A. S. Bhushan, and B. Jalali, IEEE Trans. Microw. Theory Tech. 47, 1309 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

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Figures (3)

Fig. 1.
Fig. 1.

(a) Conceptual operation and (b) detailed experimental system.

Fig. 2.
Fig. 2.

Example optical spectra showing (a) 0101… (blue curve) and 1010… (red curve) pattern modulation and (b) an example PRBS pattern (red curve) plotted with the high and low envelopes (blue curves) for pattern modulation used by the reconstruction matrix A in Eq. (6).

Fig. 3.
Fig. 3.

(a) Temporal RF measurement derived from the difference in optical spectrum with and without RF modulation shown spectrally due to wavelength-to-time mapping (red curve). The envelope from the spectral shape is overlaid for reference (blue curve). (b) Temporal RF measurement with the effect of the envelope removed and the reconstruction from the RF spectrum shown in panel (c) overlaid. (c) Two-tone reconstruction of peaks at 4.95 and 14.76 GHz, with N=100, M=23, τ=0.04, and MSE=0.00031. (d) Two-tone reconstruction of peaks at 2.43 and 9.90 GHz, with N=100, M=28, τ=0.068, and MSE=0.00072. (e) Three-tone reconstruction of peaks at 900 MHz, 4.95 and 14.76 GHz, with N=100, M=38, τ=0.05, and MSE=0.00056.

Equations (7)

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

yk=x,ϕk,k=1M
y=Φx,
ND1L1ΔλRPRBS.
P(t)=R(t)[1+αx(t)],
yk=tr/2tr/2R(t)[1+αx(t)]dttr/2tr/2R(t)dt,
y=As+n,
mins(12yAs22+τs1),

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