Abstract

Nyquist sinc-pulse shaping provides spectral efficiencies close to the theoretical limit. In this paper we discuss the analogy to optical orthogonal frequency division multiplexing and compare both techniques with respect to spectral efficiency and peak to average power ratio. We then show that using appropriate algorithms, Nyquist pulse shaped modulation formats can be encoded on a single wavelength at speeds beyond 100 Gbit/s in real-time. Finally we discuss the proper reception of Nyquist pulses.

© 2011 OSA

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2011 (7)

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

G. Bosco, V. Curri, A. Carena, P. Poggiolini, and F. Forghieri, “On the Performance of Nyquist-WDM Terabit Superchannels Based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM Subcarriers,” J. Lightwave Technol. 29(1), 53–61 (2011).
[CrossRef]

X. Liu, S. Chandrasekhar, B. Zhu, P. Winzer, A. Gnauck, and D. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011).
[CrossRef]

M. Sjödin, P. Johannisson, H. Wymeersch, P. A. Andrekson, and M. Karlsson, “Comparison of polarization-switched QPSK and polarization-multiplexed QPSK at 30 Gbit/s,” Opt. Express 19(8), 7839–7846 (2011).
[CrossRef] [PubMed]

D. Rafique and A. D. Ellis, “Nonlinear penalties in long-haul optical networks employing dynamic transponders,” Opt. Express 19(10), 9044–9049 (2011).
[CrossRef] [PubMed]

Z. Dong, J. Yu, H. C. Chien, N. Chi, L. Chen, and G. K. Chang, “Ultra-dense WDM-PON delivering carrier-centralized Nyquist-WDM uplink with digital coherent detection,” Opt. Express 19(12), 11100–11105 (2011).
[CrossRef] [PubMed]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

2010 (3)

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

A. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28(4), 423–433 (2010).
[CrossRef]

R. Essiambre, G. Kramer, P. Winzer, G. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[CrossRef]

2008 (1)

1989 (1)

L. Lo Presti and M. Mondin, “Design of optimal FIR raised-cosine filters,” Electron. Lett. 25(7), 467–468 (1989).
[CrossRef]

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).

Altenhain, L.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Andrekson, P. A.

Bao, H.

Becker, J.

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Ben-Ezra, S.

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Bonk, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Bosco, G.

Carena, A.

Chandrasekhar, S.

Chang, G. K.

Chen, L.

Chi, N.

Chien, H. C.

Cotter, D.

Curri, V.

Dong, Z.

Dreschmann, M.

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Ellermeyer, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Ellis, A.

Ellis, A. D.

Essiambre, R.

Forghieri, F.

Foschini, G.

Freude, W.

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Frey, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Gnauck, A.

Goebel, B.

Hillerkuss, D.

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Huber, G.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Huebner, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Johannisson, P.

Jordan, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Karlsson, M.

Kleinow, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Koenig, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Koos, C.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Kramer, G.

Leuthold, J.

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Li, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Lindenmann, N.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Liu, X.

Lo Presti, L.

L. Lo Presti and M. Mondin, “Design of optimal FIR raised-cosine filters,” Electron. Lett. 25(7), 467–468 (1989).
[CrossRef]

Ludwig, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Lutz, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Marculescu, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Melikyan, A.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Meyer, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Meyer, M.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Moeller, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Mondin, M.

L. Lo Presti and M. Mondin, “Design of optimal FIR raised-cosine filters,” Electron. Lett. 25(7), 467–468 (1989).
[CrossRef]

Narkiss, N.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Nebendahl, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47(2), 617–644 (1928).

Oehler, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Parmigiani, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Peckham, D.

Petropoulos, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Poggiolini, P.

Rafique, D.

Resan, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Roeger, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Schellinger, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Schindler, P.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Schmogrow, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Shieh, W.

Sjödin, M.

Tang, Y.

Vallaitis, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

Weingarten, K.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Winter, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[CrossRef]

R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time OFDM transmitter beyond 100 Gbit/s,” Opt. Express 19(13), 12740–12749 (2011).
[CrossRef] [PubMed]

R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
[CrossRef]

Winzer, P.

Wolf, S.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Wymeersch, H.

Yang, X.

D. Hillerkuss, R. Schmogrow, M. Meyer, S. Wolf, M. Jordan, P. Kleinow, N. Lindenmann, P. Schindler, A. Melikyan, X. Yang, S. Ben-Ezra, B. Nebendahl, M. Dreschmann, J. Meyer, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, L. Altenhain, T. Ellermeyer, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “32.5 Tbit/s 16QAM Nyquist – WDM transmission, Opt. Express (submitted).

Yu, J.

Zhao, J.

Zhu, B.

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R. Schmogrow, D. Hillerkuss, M. Dreschmann, M. Huebner, M. Winter, J. Meyer, B. Nebendahl, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Real-time software-defined multiformat transmitter generating 64QAM at 28 GBd,” IEEE Photon. Technol. Lett. 22(21), 1601–1603 (2010).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, B. Nebendahl, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse modulation transmitter generating rectangular shaped spectra of 112 Gbit/s 16QAM signals,” in Signal Processing in Photonic Communications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SPMA5. http://www.opticsinfobase.org/abstract.cfm?URI=SPPCom-2011-SPMA5

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256 QAM (64 Gbit/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” in Optical Fiber Communications Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMJ5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMJ5

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R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” Photon. Technol. Lett., DOI: 10.1109/LPT.2011.2172405.
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Figures (12)

Fig. 1
Fig. 1

Reducing the required channel spacing in WDM systems by removing spectral portions outside the Nyquist bandwidth Fs through filtering. Minimum channel spacing for crosstalk free systems is fixed by Fs. (a) Unfiltered M-ary QAM channels with theoretically infinitely wide spectrum. (b) Nyquist channel center frequencies can be spaced apart by the Nyquist bandwidth Fs. Basically, no guard bands are required.

Fig. 2
Fig. 2

Pre-filtering of optical M-QAM signals for generating sinc-shaped Nyquist pulses. (a) An optical filter can be applied to carve an ideal rectangle out of an NRZ spectrum. Such an optical filter requires a frequency response S21(f) that would be difficult – if not impossible – to realize. (b) Alternatively, two analog electrical filters can be used to form an appropriate output signal with an ideal rectangularly shaped spectrum. These filters would also need a non-standard transfer function S21(f). (c) By digital filtering as a part of the digital signal processing (DSP) block in the transmitter one can efficiently remove redundant parts of the spectrum. Resulting signals show almost ideal rectangular spectra, and additional off-the-shelf analog electrical or optical filters can easily remove spurious spectra.

Fig. 3
Fig. 3

Comparison between OFDM (left column) and Nyquist sinc-pulses (right column) in time and frequency domain. (a) The upper graph shows the real parts of three on-off keyed sinusoidal subcarriers xk(t), the sum of which represents one specific time-domain OFDM symbol centered at t = 0. The lower graph shows the corresponding spectra Xk(f) of the subcarriers centered at frequencies fk-1, fk, and fk+1. (b) The upper graph shows three Nyquist pulses yk(t) (“temporal subcarriers”) centered at times tk-1, tk, and tk+1. The lower graph shows the corresponding real parts of the spectra Yk(f) with three spectral sinusoidals, the sum of which represents one specific frequency-domain Nyquist symbol centered at f = 0. (c) The upper graph shows the envelopes (green rectangles as in Fig. 3(a) of three temporal OFDM symbols located at times (i−1)Ts, iTs, and (i + 1)Ts. For simplicity, each temporal OFDM symbol is composed of the same single zero-frequency subcarrier f0 = 0 for k = 0, The lower graph shows the corresponding real parts of the spectra within a sinc-shaped envelope (green). The three spectral sinusoidals within correspond to three temporal positions of the temporal OFDM symbol. (d) The upper graph shows the real parts of three Nyquist pulses within a sinc-shaped envelope (green). The three temporal sinusoidals within correspond to three spectral positions of the spectral Nyquist symbols. The lower graph shows the envelopes (green rectangles as in Fig. 3(b) of the three spectral Nyquist symbols located at frequencies (i−1)Fs, iFs, and (i + 1)Fs. For simplicity, each spectral Nyquist symbol is composed of the same single zero-time Nyquist “subcarrier” t0 = 0 for k = 0.

Fig. 4
Fig. 4

Schematic of OFDM signal and Nyquist pulse generation, both in frequency domain and time domain. For a better understanding we keep either k or i of Eq. (1) - (4) constant at zero while varying the other quantity. (a) OFDM spectrum, OFDM symbol at t0 = 0 (i = 0) only: N sinc-shaped sub-spectra for a finite number of k = 0…N − 1 keyed subcarriers are frequency shifted by kFs and modulated with complex coefficients cik. The superposition of all modulated sub-spectra results in the total OFDM spectrum X(f) = X(0)(f). (b) Nyquist pulse, Nyquist symbol with f0 = 0 (i = 0) only: Infinitely many sinc-shaped pulses (Nyquist “subcarriers”, k = −∞… + ∞) time shifted from t = 0 by increments kTs and modulated with complex coefficients cik. The superposition of all modulated pulses results in the total Nyquist time signal y(t) = y(0)(t). (c) OFDM symbol, OFDM spectrum with f0 = 0 (k = 0) only: Infinitely many rect-shaped temporal pulses (i = −∞… + ∞) time shifted from t = 0 by increments iTs and modulated with complex coefficients cik. The superposition of all modulated pulses results in the total OFDM time signal x(t). (d) Nyquist symbol, Nyquist pulse at t0 = 0 (k = 0) only: N rect-shaped sub-spectra for a finite number of i = 0…N − 1 keyed spectral symbols are frequency shifted by iFs and modulated with coefficients cik. The superposition of all modulated spectra results in the total Nyquist spectrum Y (f).

Fig. 5
Fig. 5

Finite impulse response filter (FIR, direct form I) of order R. A series of R delay elements Ts / q are located in-between the R + 1 taps. Tapped signals are weighed by R filter coefficients hr and summed to form the filter output.

Fig. 6
Fig. 6

Impulse responses and transfer functions of FIR filters with various orders R. Left column: Impulse responses. The durations of the impulse response is marked with a rectangular window (green). Middle column: Power spectra on a linear scale. Right column: Power spectra on a logarithmic scale. Colored noisy curves represent the average power spectra for a pulse train with a repetition period Ts = 1 / Fs, which has been encoded with random complex data. The white curves reproduce the power spectra from the middle column. For all power spectra a possibly existent discrete carrier line is omitted. (a) A single NRZ impulse “shaped” by a one-tap “filter” of order R = 0 leads to a sinc-shaped spectrum. (b) An ideal sinc-impulse is truncated by a rectangular window. The corresponding filter is of order R = 16. The power spectrum results from the convolution of the rect-shaped spectrum of the sinc-impulse with the sinc-shaped spectrum of the rect-window. (c) An increased filter order of R = 32 leads to a larger time window, and therefore the resulting spectrum evolves towards an ideal rectangular shape. (d) A filter with very high order R = 1024 closely approximates a rect-shaped power spectrum. Overshoots and ringing are due to Gibbs’ phenomenon. All pulses in these plots have been q-fold oversampled with q = 2.

Fig. 7
Fig. 7

Spectral efficiency (SE) and peak-to-average power ratio (PAPR) for Nyquist pulses and OFDM signals as a function of the number R of filter taps and the IFFT size N, respectively. (a) Normalized spectral efficiency (SE) for single-polarization M-ary QAM modulation. Nyquist shaped signals and OFDM signals show almost identical SE. (b) PAPR increases with filter order R for single-carrier Nyquist signals slower than the PAPR for OFDM with the number of subcarriers N.

Fig. 8
Fig. 8

FPGA parallel processing. In each computation window the FPGA produces a series of 64 sinc-pulses with different weighting coefficients cik = ±1 and for i = 0. (a) Products of modulation coefficients and windowed sinc-pulses (two-fold oversampled, q = 2) are stored within 64 lookup tables (LUT). Stored samples within the LUT are marked as dots. Each of the 64 LUT outputs is delayed in time such that (b) sinc-maxima (red dots) fall on the zeros of neighboring sinc-functions corresponding to a spacing by Ts. For each of the 128 sampling times inside the computation window the non-zero samples are added (c), clipped (d), and eventually produce the output waveform (e).

Fig. 9
Fig. 9

Experimental setup for a real-time Nyquist pulse transmitter comprising FPGAI,Q and DACI,Q, an externally coupled laser (ECL), an optical I/Q-modulator and an EDFA. An “ideal” elementary output pulse along with its corresponding spectrum is shown as an inset (green). The PDM stage emulates polarization division multiplexing. The signal is loaded with noise by adding a variable amount of amplified spontaneous emission (ASE). The receiver comprises an EDFA along with an Agilent N4391A optical modulation analyzer (OMA) for BER and EVM measurements, and an optical spectrum analyzer (OSA) for OSNR measurements.

Fig. 10
Fig. 10

Spectra, constellation diagrams and BER versus OSNR and EVM results for PDM-16QAM and PDM-QPSK signals generated with R = 0 (black, raw NRZ), R = 16 (red), and R = 32 (blue) filters. Plotted constellation diagrams comprise data from both polarizations. (a) Ensemble averages of measured (black, red, and blue) and VHDL simulated (white) spectra. It may be seen that with an increasing number of taps the spectrum evolves towards an ideal rectangle. The observed noise floors next to the spectra are due to quantization noise and do not significantly degrade the signal quality [11]. (b) Constellation diagrams for PDM-QPSK and PDM-16QAM at highest possible OSNR. (c) Measured BER (symbols) versus OSNR (lower axis). Calculated equivalent BER [‎18] derived from measured EVM (dashed lines, upper axis) are plotted for Nyquist signals generated with filter of order 16 and 32 and raw NRZ. Calculated EVM values [‎18] corresponding to the measured OSNR are specified on the upper axis.

Fig. 11
Fig. 11

Constellation diagrams for Nyquist and NRZ signals received with different bandwidths. (a) A 14 GBd Nyquist signal is well received with a Nyquist bandwidth of 7 GHz. (b) An NRZ of 14 GBd performs poorly with ADCs bandwidth-limited to 7 GHz. (c) Increasing the bandwidth to 9.33 GHz enhances the reception of the NRZ signal. Nevertheless, the Nyquist signal shows best performance.

Fig. 12
Fig. 12

Clock phase recovery for M-QAM modulation of raised-cosine and Nyquist pulses, respectively. (a) Spectrum of a squared raised-cosine signal. The clock phase can be extracted from the peaks at the symbol rate. (b) Spectrum of a squared Nyquist sinc-pulse train. The peaks at the symbol rate have vanished. (c) Standard deviation of the modulus of four measured (solid lines) and noiseless (dashed lines) Nyquist signals plotted over the sampling clock phase. Noise leads to a vertical shift of the curves’ minima. The initial points of the graphs are arbitrary and depend on the timing of the data acquisition. (d) Dependence of Nyquist signal quality on the clock phase error. Solid line: simulation; squares: measurement.

Tables (1)

Tables Icon

Table 1 Commonly used terms for OFDM and Nyquist signal description

Equations (38)

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x( t )= i= + x ( i ) ( t ), x ( i ) ( t )= k=0 N1 c ik x k ( ti T s ) , x k ( t )=rect( t T s ) e j2π f k t ,| f k+1 f k |= F s = 1 T s .
X( f )= i= + X ( i ) ( f ) , X ( i ) ( f )= k=0 N1 c ik X k ( f ) e j2πfi T s , X k ( f )= T s sinc( f f k F s ).
Y( f )= i=0 N1 Y ( i ) ( f ) , Y ( i ) ( f )= k= + c ik Y k ( fi F s ) , Y k ( f )= T s rect( f F s ) e j2πf t k ,| t k+1 t k |= T s = 1 F s .
y( t )= i=0 N1 y ( i ) ( t ), y ( i ) ( t )= k= + c ik y k ( t ) e +j2πi F s t , y k ( t )=sinc( t t k T s ).
Y ( 0 ) ( f,R )= T s π [ Si( πR f+ F s /2 q F s )Si( πR f F s /2 q F s ) ].
SE Nyquist ={ log 2 M 1+ 2.517 /R for 1R1024,q=2 log 2 M for R>1024,q=2
SE OFDM = log 2 M 1+1/N .
PAPR OFDM = N 2 1 2 N / k 2 =2 k 2 N.
P max = [ r=R/(2q)+1 R/(2q) | sinc( 1 2 r ) | ] 2 .
P ¯ = 1 T s + sinc( t T s )dt =1.
PAPR Nyquist = P max P ¯ k 2 [ r=R/(2q)+1 R/(2q) | sinc( 1 2 r ) | ] 2 .
rect( z Z )={ 1 for| z |<Z/2 0 else ,sinc( z Z )={ 1 z=0 sin( πz/Z ) πz/Z z0 .
1 Z Z/2 +Z/2 e j2πmz/Z e j2π m z/Z dz= δ m m form, m
1 Z + sinc( z Z m )sinc( z Z m ) dz= δ m m form, m
φ( z )= m= + φ m e j2πmz/Z ,
φ m = 1 Z Z/2 +Z/2 φ( z ) e j2πmz/Z dz
ψ( z )= m= + ψ m sinc( z Z m )
ψ m = 1 Z + ψ( z )sinc( z Z m )dz
1 Z Z/2 +Z/2 | φ( z ) | 2 dz= m= + | φ m | 2 ,
1 Z + | ψ( z ) | 2 dz= m= + | ψ m | 2 .
1 Z + sinc( z Z m )dz =1.
s (1) (z)= m= + sinc( z Z m ) =1.
s( z )= m= + ψ m sinc( z Z m ) = m=0 + ( 1 ) m sinc( z Z m )+ m= 1 ( 1 ) m+1 sinc( z Z m ) ,
s max ( 1 2 Z )= m= + | sinc( 1 2 m ) |
s Q,max ( 1 2 Z )= m=Q/2+1 Q/2 | sinc( 1 2 m ) |
ψ( z )=sinc( z Z )= m= + sinc( m q )sinc( q z Z m ) .
P ¯ = 1 Z + | ψ( z ) | 2 dz = 1 q m= + sin c 2 ( m q ) =1.
ψ( z )=sinc( z Z ) m=qQ/2+1 +qQ/2 sinc( m q )sinc( q z Z m ) .
P ( q,Q ) = 1 q m=qQ/2+1 +qQ/2 sinc 2 ( m q ) 1.
P ¯ P ( q,Q,k ) = P ( q,Q ) k 2 = 1 k 2 q m=qQ/2+1 qQ/2 sinc 2 ( m q )1 .
PAPR Nyquist = s Q,max 2 ( 1 2 Z ) P ¯ = k 2 [ m=Q/2+1 Q/2 | sinc( 1 2 m ) | ] 2 1 q m=qQ/2+1 +qQ/2 sinc 2 ( m q ) .
s( z )= m=1 Q 2 cos( 2πm z Z + α m ) .
s Q,max = 2 Q.
P ( Q ) = 1 Z Z/2 +Z/2 | s( z ) | 2 dz = m=1 Q 2 Z Z/2 +Z/2 cos 2 ( 2πm z Z + α m )dz = m=1 Q 2 Z 1 2 Z = m=1 Q 1 =Q.
P ¯ ( Q,k ) =Q/ k 2
PAPR OFDM,k=1 = s Q,max 2 P ¯ ( Q,k ) =2 k 2 Q
Y FIR ( 0 ) ( f,R )= Y ( 0 ) ( f )W( f,R )= T s rect( f F s ) R q T s sinc( R f q F s ).
Y FIR ( 0 ) ( f,R )= T s π [ Si( πR f+ F s /2 q F s )Si( πR f F s /2 q F s ) ].

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