Abstract

We report on a record spectral efficient terahertz communication system using a coherent radio-over-fiber (CRoF) approach. High spectral efficient back-to-back and wireless THz transmission around 325 GHz is experimentally demonstrated using a 64-QAM-OFDM modulation format and a 10 GHz wide wireless channel resulting in a data rate of 59 Gbit/s.

© 2017 Optical Society of America

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References

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  1. “Cisco Visual Networking Index: Forecast and Methodology,” 2015–2020, white paper, http://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/complete-white-paper-c11-481360.pdf .
  2. T. Nagatsuma, G. Ducournau, and C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).
  3. Radio Regulations, Articles, International Telecommunication Union, Edition of 2016.
  4. ERC REPORT 25, The European Table of Frequency Allocations and applications in the frequency range 8.3 kHz to 3000 GHz (ECA Table), Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT), (Approved June 2016).
  5. 47 C.F.R. § 2.106, FCC Online Table of Frequency Allocations, Federal Communications Commission, Office of Engineering and Technology, Policy and Rules Division, Revised on August 31, 2016.
  6. H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
    [Crossref]
  7. T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, N. Yoshimoto, J. Terada, and H. Takahashi, “Terahertz wireless communications based on photonics technologies,” Opt. Express 21(20), 23736–23747 (2013).
    [Crossref] [PubMed]
  8. A. Kanno, N. Sekine, I. Hosako, T. Kawanishi, Y. Yoshida, and K.-I. Kitayama, “Fiber-remoted 20-Gbaud QPSK transmission at 300 GHz,” in Tech. Dig. of IEEE International Topical Meeting on Microwave Photonics, (MWP 2015).
    [Crossref]
  9. I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).
  10. X. Yu, R. Asif, M. Piels, D. Zibar, M. Galili, T. Morioka, P. U. Jepsen, and L. K. Oxenløwe, “60 Gbit/s 400 GHz wireless transmission,” in International Conference on Photonics in Switching (PS), Florence, 4–6, (2015).
    [Crossref]
  11. C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
    [Crossref]
  12. M. Weiß, A. Stöhr, F. Lecoche, and B. Charbonnier, “27 Gbit/s photonic wireless 60 GHz transmission system using 16-QAM OFDM,” in Tech. Dig. of IEEE International Topical Meeting on Microwave Photonics, (MWP 2009), postdeadline paper.
  13. S. Koenig, D. Lopez-Diaz, J. Antes, R. Henneberger, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, I. Kallfass, and J. Leuthold, “100 Gbit/s wireless link with mm-wave photonics,” in Tech. Dig. of Optical Fiber Communication Conference and Exposition and the National Fiber Optics Engineers Conference, (OFC/NFOEC 2013), postdeadline paper.
  14. X. Pang, A. Caballero, A. Dogadaev, V. Arlunno, R. Borkowski, J. S. Pedersen, L. Deng, F. Karinou, F. Roubeau, D. Zibar, X. Yu, and I. T. Monroy, “100 Gbit/s hybrid optical fiber-wireless link in the W-band (75-110 GHz),” Opt. Express 19(25), 24944–24949 (2011).
    [Crossref] [PubMed]
  15. X. Li, J. Yu, J. Zhang, Z. Dong, F. Li, and N. Chi, “A 400G optical wireless integration delivery system,” Opt. Express 21(16), 18812–18819 (2013).
    [Crossref] [PubMed]
  16. A. Stöhr, O. Cojucari, F. van Dijk, G. Carpintero, T. Tekin, S. Formont, I. Flammia, V. Rymanov, B. Khani, and R. Chuenchom, “Robust 71-76 GHz Radio-over-Fiber Wireless Link with High-Dynamic Range Photonic Assisted Transmitter and Laser Phase-Noise Insensitive SBD Receiver,” in Tech. Dig. of Optical Fiber Communication Conference and Exposition and the National Fiber Optics Engineers Conference, (OFC/NFOEC 2014).
    [Crossref]
  17. A. Stöhr, B. Shih, S. T. Abraha, A. G. Steffan, and A. Ng’oma, “High Spectral-Efficient 512-QAM-OFDM 60 GHz CRoF System using a Coherent Photonic Mixer (CPX) and an RF Envelope Detector,” in Tech. Dig. of Optical Fiber Communication Conference and Exposition and the National Fiber Optics Engineers Conference, (OFC/NFOEC 2016).
    [Crossref]
  18. N. J. Gomes, M. Morant, A. Alphones, B. Cabon, J. E. Mitchell, C. Lethien, M. Csörnye, A. Stöhr, and S. lezekiel, “Radio-over-fiber transport for the support of wireless broadband services [Invited],” J. Opt. Netw. 8(2), 156–178 (2009).
    [Crossref]
  19. . Chuenchom, X. Zou, V. Rymanov, B. Khani, M. Steeg, S. Dulme, S. Babiel, A. Stohr, J. Honecker, and A. G. Steffan, “Integrated 110 GHz coherent photonic mixer for CRoF mobile backhaul links,” in IEEE International Topic Meeting on Microwave Photonics (MWP 2015), Paphos, Cyprus, (2015).
    [Crossref]
  20. R. Chuenchom, S. Babiel, M. Steeg, and A. Stöhr, “Impact of WDM channel spacing on millimeter-wave wireless access using wireless coherent Radio-over-Fiber (CRoF) channels,” in Optical Fiber Communication Conference (OFC 2015), Los Angeles, Unites States, (2015).
    [Crossref]
  21. W. Idler and F. Buchali, “Higher-Order Modulation Formats - Concepts and Enabling Devices,” in Fiber Optic Communication, 2nd edition, N. Grote and H. Venghaus, Eds, Springer Series in Optical Science (Springer, 2017), in press.

2016 (1)

T. Nagatsuma, G. Ducournau, and C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).

2015 (1)

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

2014 (1)

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

2013 (2)

2012 (1)

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

2011 (1)

2009 (1)

Ajito, K.

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

Alphones, A.

Antes, P.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Arlunno, V.

Borkowski, R.

Caballero, A.

Cabon, B.

Chen, Q.

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

Chi, N.

Csörnye, M.

Dan, J.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Deng, L.

Deng, X.

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

Dogadaev, A.

Dong, Z.

Ducournau, G.

T. Nagatsuma, G. Ducournau, and C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).

Gomes, N. J.

Hisatake, S.

Horiguchi, S.

Kallfass, I.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Karinou, F.

Kukutsu, N.

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

Kuri, M.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Kürner, T.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Kuwano, S.

Lethien, C.

Leuther, A.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

lezekiel, S.

Li, F.

Li, X.

Lin, C.

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

Lu, B.

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

Massler, H.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Merkle, T.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Minamikata, Y.

Mitchell, J. E.

Monroy, I. T.

Morant, M.

Muramoto, Y.

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

Nagatsuma, T.

T. Nagatsuma, G. Ducournau, and C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).

T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, N. Yoshimoto, J. Terada, and H. Takahashi, “Terahertz wireless communications based on photonics technologies,” Opt. Express 21(20), 23736–23747 (2013).
[Crossref] [PubMed]

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

Pang, X.

Pedersen, J. S.

Renaud, C.

T. Nagatsuma, G. Ducournau, and C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).

Roubeau, F.

Song, H. J.

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

Stöhr, A.

Takahashi, H.

Terada, J.

Tessmann, A.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Wagner, S.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Wakatsuki, A.

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

Wang, C.

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

Weber, R.

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

Yoshimizu, Y.

Yoshimoto, N.

Yu, J.

Yu, X.

Zhang, J.

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

X. Li, J. Yu, J. Zhang, Z. Dong, F. Li, and N. Chi, “A 400G optical wireless integration delivery system,” Opt. Express 21(16), 18812–18819 (2013).
[Crossref] [PubMed]

Zibar, D.

Electron. Lett. (1)

H. J. Song, K. Ajito, Y. Muramoto, A. Wakatsuki, T. Nagatsuma, and N. Kukutsu, “24 Gbit/s data transmission in 300 GHz band for future terahertz communications,” Electron. Lett. 48(15), 953–954 (2012).
[Crossref]

IEEE Trans. Terahertz Sci. Technol. (1)

C. Wang, B. Lu, C. Lin, Q. Chen, X. Deng, and J. Zhang, “0.34-THz Wirelss link based on higher-order modulation for future wireless local area network applications,” IEEE Trans. Terahertz Sci. Technol. 4(1), 75–85 (2014).
[Crossref]

IEICE Trans. Electron. (1)

I. Kallfass, J. Dan, P. Antes, A. Tessmann, S. Wagner, M. Kuri, R. Weber, H. Massler, A. Leuther, T. Merkle, and T. Kürner, “Towards MMIC-based 300 GHz indoor wireless communication systems,” IEICE Trans. Electron. E98(12), 1081(2015).

J. Opt. Netw. (1)

Nat. Photonics (1)

T. Nagatsuma, G. Ducournau, and C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photonics 10, 371–379 (2016).

Opt. Express (3)

Other (13)

A. Stöhr, O. Cojucari, F. van Dijk, G. Carpintero, T. Tekin, S. Formont, I. Flammia, V. Rymanov, B. Khani, and R. Chuenchom, “Robust 71-76 GHz Radio-over-Fiber Wireless Link with High-Dynamic Range Photonic Assisted Transmitter and Laser Phase-Noise Insensitive SBD Receiver,” in Tech. Dig. of Optical Fiber Communication Conference and Exposition and the National Fiber Optics Engineers Conference, (OFC/NFOEC 2014).
[Crossref]

A. Stöhr, B. Shih, S. T. Abraha, A. G. Steffan, and A. Ng’oma, “High Spectral-Efficient 512-QAM-OFDM 60 GHz CRoF System using a Coherent Photonic Mixer (CPX) and an RF Envelope Detector,” in Tech. Dig. of Optical Fiber Communication Conference and Exposition and the National Fiber Optics Engineers Conference, (OFC/NFOEC 2016).
[Crossref]

. Chuenchom, X. Zou, V. Rymanov, B. Khani, M. Steeg, S. Dulme, S. Babiel, A. Stohr, J. Honecker, and A. G. Steffan, “Integrated 110 GHz coherent photonic mixer for CRoF mobile backhaul links,” in IEEE International Topic Meeting on Microwave Photonics (MWP 2015), Paphos, Cyprus, (2015).
[Crossref]

R. Chuenchom, S. Babiel, M. Steeg, and A. Stöhr, “Impact of WDM channel spacing on millimeter-wave wireless access using wireless coherent Radio-over-Fiber (CRoF) channels,” in Optical Fiber Communication Conference (OFC 2015), Los Angeles, Unites States, (2015).
[Crossref]

W. Idler and F. Buchali, “Higher-Order Modulation Formats - Concepts and Enabling Devices,” in Fiber Optic Communication, 2nd edition, N. Grote and H. Venghaus, Eds, Springer Series in Optical Science (Springer, 2017), in press.

Radio Regulations, Articles, International Telecommunication Union, Edition of 2016.

ERC REPORT 25, The European Table of Frequency Allocations and applications in the frequency range 8.3 kHz to 3000 GHz (ECA Table), Electronic Communications Committee (ECC) within the European Conference of Postal and Telecommunications Administrations (CEPT), (Approved June 2016).

47 C.F.R. § 2.106, FCC Online Table of Frequency Allocations, Federal Communications Commission, Office of Engineering and Technology, Policy and Rules Division, Revised on August 31, 2016.

M. Weiß, A. Stöhr, F. Lecoche, and B. Charbonnier, “27 Gbit/s photonic wireless 60 GHz transmission system using 16-QAM OFDM,” in Tech. Dig. of IEEE International Topical Meeting on Microwave Photonics, (MWP 2009), postdeadline paper.

S. Koenig, D. Lopez-Diaz, J. Antes, R. Henneberger, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, I. Kallfass, and J. Leuthold, “100 Gbit/s wireless link with mm-wave photonics,” in Tech. Dig. of Optical Fiber Communication Conference and Exposition and the National Fiber Optics Engineers Conference, (OFC/NFOEC 2013), postdeadline paper.

“Cisco Visual Networking Index: Forecast and Methodology,” 2015–2020, white paper, http://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/complete-white-paper-c11-481360.pdf .

X. Yu, R. Asif, M. Piels, D. Zibar, M. Galili, T. Morioka, P. U. Jepsen, and L. K. Oxenløwe, “60 Gbit/s 400 GHz wireless transmission,” in International Conference on Photonics in Switching (PS), Florence, 4–6, (2015).
[Crossref]

A. Kanno, N. Sekine, I. Hosako, T. Kawanishi, Y. Yoshida, and K.-I. Kitayama, “Fiber-remoted 20-Gbaud QPSK transmission at 300 GHz,” in Tech. Dig. of IEEE International Topical Meeting on Microwave Photonics, (MWP 2015).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Schematic description of the CRoF down-link system architecture enabling complex I/Q-modulation.

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Fig. 2
Fig. 2 Schematic of the THz communication link system set-up.

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Fig. 3
Fig. 3 Spectrum of the combined optical signal at the output of the 3-dB coupler.

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Fig. 4
Fig. 4 Measured spectrum (lower sideband and carrier) of the transmitted OFDM THz signal. Blue dots represent measurements, grey line illustrates the expected spectra.

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Fig. 5
Fig. 5 Frequency response of the THz transmission system.

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Fig. 6
Fig. 6 Measured drift of the THz carrier frequency versus time.

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Fig. 7
Fig. 7 Photograph of the THz communication link system set-up.

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Fig. 8
Fig. 8 IF spectrum after down-conversion using the envelope detector for back-to-back (left) and after 2 km fiber and 5 cm wireless transmission (right).

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Fig. 9
Fig. 9 Constellation of the demodulated 64-QAM-OFDM modulated signal at 59 Gbit/s for back-to-back (left) and after 2 km fiber and 5 cm wireless transmission (right).

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Fig. 10
Fig. 10 SNR versus subcarrier number of the demodulated OFDM signal.

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Equations (6)

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

E r (t)= E r0 (t)  e j ω r t+ ϕ r (t) ,
E s (t)= E s0 (t)  e j ω s t+ ϕ s (t) ,
E rec (t)= 1 2 (   E r (t)  e j π 2 + E s (t) 2 ⋅(  1+ π 2 V π Re{  m(t)  e j ω IF t } ) ).
i PD (t)= E rec (t)⋅ E rec * (t) ≈ E r0 (t) E s0 (t) 2 ⋅( 1+ π 2 V π Re{m(t)  e j ω IF t } )⋅cos( ω THz t+Δϕ(t) ),
i PD (t)≈ E r0 (t) E s0 (t) 2 ⋅( cos( ω THz t+Δϕ(t) ) + π 2 V π a(t)cos( ω IF t+θ(t) )cos( ω THz t+Δϕ(t) ) − π 2 V π a(t)sin( ω IF t+θ(t) )sin( ω THz t+Δϕ(t) ) ).
i ED (t)= ( i PD (t) ) 2 ≈ ( E r0 (t) E s0 (t) ) 2 2 ⋅( 1 2 + ( π 2 V π ) 2 a 2 (t) 2 + π 2 V π a(t)cos( ω IF t+θ(t) ) ).

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