Abstract

We demonstrate measurement of RF signals in the 2-19 GHz band using a photonic compressive sensing (CS) receiver. The RF is modulated onto chirped optical pulses that then propagate through a multimode fiber that produces the random projections needed for CS via optical speckle. Our system makes 16 independent measurements per optical pulse and we demonstrate several calibration techniques to obtain the CS measurement matrix from these measurements. Then a standard penalized l1 norm method recovers amplitude, phase, and frequency of single-tone and two-tone RF signals with about 100 MHz resolution in a single 4.5 ns pulse. A novel subspace method recovers the frequency to about 20 kHz resolution over 100 pulses in a 2.8 microsecond time window. These experiments use discrete fiber-coupled optical components, but all necessary functions can be realized in photonic and electronic integrated circuits.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

2017 (2)

M. Piels and D. Zibar, “Compact silicon multimode waveguide spectrometer with enhanced bandwidth,” Sci. Rep. 7(1), 43454 (2017).
[Crossref] [PubMed]

G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Calibration of a speckle-based compressive sensing receiver,” Proc. SPIE 10103, 101030Z (2017).
[Crossref]

2016 (4)

2015 (4)

2014 (2)

2013 (8)

B. Redding, S. M. Popoff, and H. Cao, “All-fiber spectrometer based on speckle pattern reconstruction,” Opt. Express 21(5), 6584–6600 (2013).
[Crossref] [PubMed]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

Y. Liang, M. Chen, H. Chen, C. Lei, P. Li, and S. Xie, “Photonic-assisted multi-channel compressive sampling based on effective time delay pattern,” Opt. Express 21(22), 25700–25707 (2013).
[Crossref] [PubMed]

H. Chi, Y. Chen, Y. Mei, X. Jin, S. Zheng, and X. Zhang, “Microwave spectrum sensing based on photonic time stretch and compressive sampling,” Opt. Lett. 38(2), 136–138 (2013).
[Crossref] [PubMed]

Y. Chen, H. Chi, T. Jin, S. Zheng, X. Jin, and X. Zhang, “Sub-Nyquist sampled analog-to-digital conversion based on photonic time stretch and compressive sensing with optical random mixing,” J. Lightwave Technol. 31(21), 3395–3401 (2013).
[Crossref]

F. Yin, Y. Gao, Y. Dai, J. Zhang, K. Xu, Z. Zhang, J. Li, and J. Lin, “Multifrequency radio frequency sensing with photonics-assisted spectrum compression,” Opt. Lett. 38(21), 4386–4388 (2013).
[Crossref] [PubMed]

B. T. Bosworth and M. A. Foster, “High-speed ultrawideband photonically enabled compressed sensing of sparse radio frequency signals,” Opt. Lett. 38(22), 4892–4895 (2013).
[Crossref] [PubMed]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Sensing RF signals with the optical wideband converter,” Proc. SPIE 8645, 86450P (2013).
[Crossref]

2012 (3)

2011 (3)

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5(1), 8–20 (2011).
[Crossref]

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

J. M. Nichols and F. Bucholtz, “Beating Nyquist with light: a compressively sampled photonic link,” Opt. Express 19(8), 7339–7348 (2011).
[Crossref] [PubMed]

2010 (3)

G. C. Valley and G. A. Sefler, “Optical time-domain mixer,” Proc. SPIE 7797, 77970F (2010).
[Crossref]

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010).
[Crossref]

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

2008 (1)

I. Loris, “L1Packv2: A Mathematica package for minimizing an l 1-penalized functional,” Comput. Phys. Commun. 179(12), 895–902 (2008).

2006 (3)

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l 1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59(6), 797–829 (2006).
[Crossref]

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

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

1986 (1)

R. O. Schmidt, “Multiple Emitter Location and Signal Parameter Estimation,” IEEE Trans. Antenn. Propag. 34(3), 276–280 (1986).
[Crossref]

Alam, M.

Baraniuk, R. G.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010).
[Crossref]

Bosworth, B. T.

Bromberg, Y.

Bucholtz, F.

Caltagirone, F.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

Candes, E. J.

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

Cao, H.

Carron, I.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

Chen, H.

Chen, M.

Chen, Y.

Chi, H.

Chin, S.

Clark, T. R.

T. P. McKenna, J. H. Kalkavage, M. D. Sharp, and T. R. Clark, “Wideband Photonic Compressive Sampling System,” J. Lightwave Technol. 34(11), 2848–2855 (2016).
[Crossref]

J. R. Stroud, B. T. Bosworth, D. N. Tran, T. P. McKenna, T. R. Clark, T. D. Tran, and M. A. Foster, “Continuous 119.2-GSample/s photonic compressed sensing of sparse microwave signals,” In 2015 Conference on Lasers and Electro-Optics (CLEO)IEEE, (2015).
[Crossref]

Dai, Y.

Daudet, L.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

de Hoog, F.

M. Yang, F. de Hoog, Y. Fan, and W. Hu, “Adaptive sampling by dictionary learning for hyperspectral imaging,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(9), 4501–4509 (2016).
[Crossref]

Donoho, D. L.

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

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l 1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59(6), 797–829 (2006).
[Crossref]

Dounaevsky, O.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5(1), 8–20 (2011).
[Crossref]

Dremeau, A.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

Duarte, M. F.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010).
[Crossref]

Eldar, Y.

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

Eldar, Y. C.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5(1), 8–20 (2011).
[Crossref]

Fan, Y.

M. Yang, F. de Hoog, Y. Fan, and W. Hu, “Adaptive sampling by dictionary learning for hyperspectral imaging,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(9), 4501–4509 (2016).
[Crossref]

Foster, M. A.

Galili, M.

Gao, Y.

Gigan, S.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

Gu, Y.

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

Guo, Q.

Hu, W.

M. Yang, F. de Hoog, Y. Fan, and W. Hu, “Adaptive sampling by dictionary learning for hyperspectral imaging,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(9), 4501–4509 (2016).
[Crossref]

Jin, T.

Jin, X.

Johannson, L.

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

Justin Shaw, T.

Kalkavage, J. H.

Krzakala, F.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

Laska, J. N.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010).
[Crossref]

Lei, C.

Li, J.

Li, P.

Liang, Y.

Liew, S. F.

B. Redding, S. F. Liew, Y. Bromberg, R. Sarma, and H. Cao, “Evanescently coupled multimode spiral spectrometer,” Optica 3(9), 956–962 (2016).
[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

Lin, J.

Loris, I.

I. Loris, “L1Packv2: A Mathematica package for minimizing an l 1-penalized functional,” Comput. Phys. Commun. 179(12), 895–902 (2008).

McKenna, T. P.

T. P. McKenna, J. H. Kalkavage, M. D. Sharp, and T. R. Clark, “Wideband Photonic Compressive Sampling System,” J. Lightwave Technol. 34(11), 2848–2855 (2016).
[Crossref]

J. R. Stroud, B. T. Bosworth, D. N. Tran, T. P. McKenna, T. R. Clark, T. D. Tran, and M. A. Foster, “Continuous 119.2-GSample/s photonic compressed sensing of sparse microwave signals,” In 2015 Conference on Lasers and Electro-Optics (CLEO)IEEE, (2015).
[Crossref]

Mei, Y.

Mishali, M.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5(1), 8–20 (2011).
[Crossref]

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

Nan, H.

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

Nichols, J. M.

Piels, M.

M. Piels and D. Zibar, “Compact silicon multimode waveguide spectrometer with enhanced bandwidth,” Sci. Rep. 7(1), 43454 (2017).
[Crossref] [PubMed]

Popoff, S. M.

Redding, B.

Romberg, J. K.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010).
[Crossref]

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

Saade, A.

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

Sarma, R.

B. Redding, S. F. Liew, Y. Bromberg, R. Sarma, and H. Cao, “Evanescently coupled multimode spiral spectrometer,” Optica 3(9), 956–962 (2016).
[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

Schmidt, R. O.

R. O. Schmidt, “Multiple Emitter Location and Signal Parameter Estimation,” IEEE Trans. Antenn. Propag. 34(3), 276–280 (1986).
[Crossref]

Scofield, A. C.

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

A. C. Scofield, G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Demonstration of GHz-band RF receiver and spectrometer using random speckle patterns,” in Conference on Lasers and Electro-optics (CLEO), (2018).
[Crossref]

Sefler, G. A.

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Calibration of a speckle-based compressive sensing receiver,” Proc. SPIE 10103, 101030Z (2017).
[Crossref]

G. C. Valley, G. A. Sefler, and T. Justin Shaw, “Multimode waveguide speckle patterns for compressive sensing,” Opt. Lett. 41(11), 2529–2532 (2016).
[Crossref] [PubMed]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Optical multi-coset sampling of GHz-band chirped signals,” Proc. SPIE 9362, 93620M (2015).

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Sensing RF signals with the optical wideband converter,” Proc. SPIE 8645, 86450P (2013).
[Crossref]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Compressive sensing of sparse radio frequency signals using optical mixing,” Opt. Lett. 37(22), 4675–4677 (2012).
[Crossref] [PubMed]

G. C. Valley and G. A. Sefler, “Optical time-domain mixer,” Proc. SPIE 7797, 77970F (2010).
[Crossref]

A. C. Scofield, G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Demonstration of GHz-band RF receiver and spectrometer using random speckle patterns,” in Conference on Lasers and Electro-optics (CLEO), (2018).
[Crossref]

Seifert, M.

Sharp, M. D.

Shaw, T. J.

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Calibration of a speckle-based compressive sensing receiver,” Proc. SPIE 10103, 101030Z (2017).
[Crossref]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Optical multi-coset sampling of GHz-band chirped signals,” Proc. SPIE 9362, 93620M (2015).

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Sensing RF signals with the optical wideband converter,” Proc. SPIE 8645, 86450P (2013).
[Crossref]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Compressive sensing of sparse radio frequency signals using optical mixing,” Opt. Lett. 37(22), 4675–4677 (2012).
[Crossref] [PubMed]

A. C. Scofield, G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Demonstration of GHz-band RF receiver and spectrometer using random speckle patterns,” in Conference on Lasers and Electro-optics (CLEO), (2018).
[Crossref]

Shoshan, E.

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5(1), 8–20 (2011).
[Crossref]

Stapleton, A. D.

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Calibration of a speckle-based compressive sensing receiver,” Proc. SPIE 10103, 101030Z (2017).
[Crossref]

A. C. Scofield, G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Demonstration of GHz-band RF receiver and spectrometer using random speckle patterns,” in Conference on Lasers and Electro-optics (CLEO), (2018).
[Crossref]

Stroud, J. R.

Tao, T.

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
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Tran, T. D.

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J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010).
[Crossref]

Valley, G. C.

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Calibration of a speckle-based compressive sensing receiver,” Proc. SPIE 10103, 101030Z (2017).
[Crossref]

G. C. Valley, G. A. Sefler, and T. Justin Shaw, “Multimode waveguide speckle patterns for compressive sensing,” Opt. Lett. 41(11), 2529–2532 (2016).
[Crossref] [PubMed]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Optical multi-coset sampling of GHz-band chirped signals,” Proc. SPIE 9362, 93620M (2015).

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Sensing RF signals with the optical wideband converter,” Proc. SPIE 8645, 86450P (2013).
[Crossref]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Compressive sensing of sparse radio frequency signals using optical mixing,” Opt. Lett. 37(22), 4675–4677 (2012).
[Crossref] [PubMed]

G. C. Valley and G. A. Sefler, “Optical time-domain mixer,” Proc. SPIE 7797, 77970F (2010).
[Crossref]

A. C. Scofield, G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Demonstration of GHz-band RF receiver and spectrometer using random speckle patterns,” in Conference on Lasers and Electro-optics (CLEO), (2018).
[Crossref]

Wang, D.

Xie, S.

Xu, K.

Yang, M.

M. Yang, F. de Hoog, Y. Fan, and W. Hu, “Adaptive sampling by dictionary learning for hyperspectral imaging,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(9), 4501–4509 (2016).
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Yu, X.

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

Zhang, J.

Zhang, X.

Zhang, Z.

Zheng, S.

Zibar, D.

M. Piels and D. Zibar, “Compact silicon multimode waveguide spectrometer with enhanced bandwidth,” Sci. Rep. 7(1), 43454 (2017).
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Commun. Pure Appl. Math. (2)

D. L. Donoho, “For most large underdetermined systems of linear equations the minimal l 1-norm solution is also the sparsest solution,” Commun. Pure Appl. Math. 59(6), 797–829 (2006).
[Crossref]

E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

Comput. Phys. Commun. (1)

I. Loris, “L1Packv2: A Mathematica package for minimizing an l 1-penalized functional,” Comput. Phys. Commun. 179(12), 895–902 (2008).

IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. (1)

M. Yang, F. de Hoog, Y. Fan, and W. Hu, “Adaptive sampling by dictionary learning for hyperspectral imaging,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(9), 4501–4509 (2016).
[Crossref]

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

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

IEEE Photonics Technol. Lett. (1)

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

IEEE Trans. Antenn. Propag. (1)

R. O. Schmidt, “Multiple Emitter Location and Signal Parameter Estimation,” IEEE Trans. Antenn. Propag. 34(3), 276–280 (1986).
[Crossref]

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

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IET Circuits Dev. Syst. (1)

M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: analog to digital at sub-Nyquist rates,” IET Circuits Dev. Syst. 5(1), 8–20 (2011).
[Crossref]

J. Lightwave Technol. (2)

Nat. Photonics (1)

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7(9), 746–751 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (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]

G. C. Valley, G. A. Sefler, and T. Justin Shaw, “Multimode waveguide speckle patterns for compressive sensing,” Opt. Lett. 41(11), 2529–2532 (2016).
[Crossref] [PubMed]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Compressive sensing of sparse radio frequency signals using optical mixing,” Opt. Lett. 37(22), 4675–4677 (2012).
[Crossref] [PubMed]

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37(16), 3384–3386 (2012).
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H. Chi, Y. Chen, Y. Mei, X. Jin, S. Zheng, and X. Zhang, “Microwave spectrum sensing based on photonic time stretch and compressive sampling,” Opt. Lett. 38(2), 136–138 (2013).
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Optica (2)

Proc. SPIE (5)

G. C. Valley, T. J. Shaw, A. D. Stapleton, A. C. Scofield, G. A. Sefler, and L. Johannson, “Application of laser speckle to randomized numerical linear algebra,” Proc. SPIE 10551, 105510M (2018).

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Sensing RF signals with the optical wideband converter,” Proc. SPIE 8645, 86450P (2013).
[Crossref]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Optical multi-coset sampling of GHz-band chirped signals,” Proc. SPIE 9362, 93620M (2015).

G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Calibration of a speckle-based compressive sensing receiver,” Proc. SPIE 10103, 101030Z (2017).
[Crossref]

G. C. Valley and G. A. Sefler, “Optical time-domain mixer,” Proc. SPIE 7797, 77970F (2010).
[Crossref]

Sci. Rep. (1)

M. Piels and D. Zibar, “Compact silicon multimode waveguide spectrometer with enhanced bandwidth,” Sci. Rep. 7(1), 43454 (2017).
[Crossref] [PubMed]

Other (17)

M. Piels and D. Zibar, “Compact spectrometer based on a silicon multimode waveguide,” Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, (2017).

A. C. Scofield, G. A. Sefler, T. J. Shaw, A. D. Stapleton, and G. C. Valley, “Demonstration of GHz-band RF receiver and spectrometer using random speckle patterns,” in Conference on Lasers and Electro-optics (CLEO), (2018).
[Crossref]

A. Saade, F. Caltagirone, I. Carron, L. Daudet, A. Dremeau, S. Gigan, and F. Krzakala, “Random projections through multiple optical scattering: Approximating kernels at the speed of light,” 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 6215–6219 (2016).
[Crossref]

J. Dong, S. Gigan, F. Krzakala, and G. Wainrib, “Scaling up Echo-State Networks with multiple light scattering.” arXiv preprint arXiv:1609.05204 (2016).

Texas Instruments, http://www.ti.com/product/ADS52J90/description (2018).

G. C. Valley and G. A. Sefler, “Systems and methods for converting wideband signals in the optical domain,” U.S. Patent No. 8,026,837, (2011).

M. Mishali and Y. C. Eldar, “Xampling: Compressed sensing for analog signals,” in Compressed Sensing: Theory and Applications, ed. by Y. C. Eldar and G. Kutyniok, (Cambridge University, 2012).

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications, (Cambridge University, 2012).

S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing, (Springer, 2013).

G. A. Sefler, G. C. Valley, and T. J. Shaw, “Photonic compressive sensing of GHz-band RF signals,” Proc. 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa) 109–113 (2015).
[Crossref]

G. C. Valley and G. A. Sefler, “Systems and methods for converting radio frequency signals into the digital domain using multi-mode optics,” U.S. Patent No. 9,413,372, (2016).

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Systems and methods for converting wideband signals into the digital domain using electronics or guided-wave optics,” U.S. Patent No. 8,902,096, (2014).

T. 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,” OFC/NFOEC Tech. Dig. OTHD.1 (2013).

Q. Guo, H. Chen, M. Chen, S. Yang, and S. Xie, “Photonics-assisted compressive sampling systems,” In SPIE/COS Photonics Asia (pp. 100260E–100260E). International Society for Optics and Photonics, (2016).

J. R. Stroud, B. T. Bosworth, D. N. Tran, T. P. McKenna, T. R. Clark, T. D. Tran, and M. A. Foster, “Continuous 119.2-GSample/s photonic compressed sensing of sparse microwave signals,” In 2015 Conference on Lasers and Electro-Optics (CLEO)IEEE, (2015).
[Crossref]

J. M. Nichols, F. Bucholtz, C. V. McLaughlin, A. K. Oh, and R. M. Willett, “Fixing basis mismatch in compressively sampled photonic link,” SPIE Sensing Technology + Applications. International Society for Optics and Photonics, (2014).

H. Sun, B. T. Bosworth, B. C. Grubel, M. R. Kossey, M. A. Foster, and A. C. Foster, “Compressed sensing of sparse RF signals based on silicon photonic microcavities,” In CLEO: Science and Innovations, pp. SM1O–5. Optical Society of America, (2017).

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Figures (11)

Fig. 1
Fig. 1 Experimental setup (MLL: Mode-locked laser; MZM: Mach-Zehnder modulator; PD: Photodiode; EDFA: Erbium-doped fiber amplifier; MMF: Multimode fiber; AWG: Arbitrary waveform generator).
Fig. 2
Fig. 2 Amplitude of the 16-channel measurement vector y as a function of Δϕij/(2π) for an illustrative RF frequency: data in red and fits in blue.
Fig. 3
Fig. 3 Recovered in-phase and quadrature amplitudes for a two-tone signal as a function of frequency for 100 pulses. Figure 3(a) used SVD to calculate the measurement matrix; (b) used the phase-fit method and (c) used the two-pulse method. The solid vertical lines are the locations of the RF frequencies.
Fig. 4
Fig. 4 Amplitude as a function of frequency for the two-tone signal recovered from a single 5 ns pulse: (a) shows a pulse where the in-phase of one frequency is zero and the quadrature of the other is zero; (b) the in-phase is the dominant component at both frequencies; (c) where the in-phase and quadrature components are non-zero for both frequencies. The black lines indicate the input signal frequencies.
Fig. 5
Fig. 5 In-phase and quadrature amplitude as a function of frequency and pulse number for 100 5-ns pulses of a two-tone signal.
Fig. 6
Fig. 6 Array plot of average recovered amplitude as a function of recovered frequency and time with one frequency held constant at 9.75 GHz and the second frequency scanned from 8.77 to 10.73 GHz in steps of 35 MHz.
Fig. 7
Fig. 7 Histogram amplitude as a function of frequency for 100 pulses. (a) Two well separated frequencies. (b) Two frequencies separated by 175 MHz, the smallest separation for which 2 separate peaks are resolved. (c) Two frequencies separated by 70 MHz that cannot be resolved. The solid lines indicate the input frequencies.
Fig. 8
Fig. 8 Array plot of amplitude as a function of recovered frequency and time. (a) for a pulse length of 4.5 ns and input frequency scanned from 2 to 20 GHz in 75 MHz steps, (b) for a pulse length of 4.5 ns and 13-19 GHz in 25 MHz steps, (c) for a pulse length of 18 ns and 2 to 10 GHz in 35 MHz steps.
Fig. 9
Fig. 9 Recovered amplitude as a function of frequency. Red curve: single scan with 4.5 ns pulses from 2 to 20 GHz. Blue curve: 4.5 ns pulses from13 to 19 GHz. Magenta curve: 18 ns pulses from 2 to 10 GHz.
Fig. 10
Fig. 10 Frequency error as a function of frequency. (a) Input frequency ranged from 8.77 to 10.73 GHz in steps of 35 MHz. (b) 17.45 to 18.55 GHz in steps of 25 MHz.
Fig. 11
Fig. 11 Phase as a function of pulse number for 56 frequencies from 8.77 to 10.695 GHz in units of 35 MHz.

Equations (8)

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

y=Φx= ΦΨ 1 s=Θs
x i = a i cos(2π f i t+ ϕ i )
s i =2 n 1/2 a i {0, ,exp( i ϕ i ), 0, ,exp( i ϕ i ), 0,}
Δ ϕ i,j =mod(2πj f i / f L ,2π)
s ij '=2 n 1/2 a i {0, ,exp( iΔ ϕ ij ), 0, ,exp( iΔ ϕ ij ), 0,}
Θ i +' =exp(i ϕ i0 ) Θ i +  and Θ i ' =exp(i ϕ i0 ) Θ i
Δϕ=arg( B 0 * . B 1 )
f F =1/( 2π )dϕ/dt=1/(2π)Δϕ f L .

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