High-performance TDM demultiplexing of coherent Nyquist pulses using time-domain orthogonality Koudai Harako,* David Odeke Otuya, Keisuke Kasai, Toshihiko Hirooka, and Masataka Nakazawa Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai-shi, Miyagiken, 980-8577 Japan * [email protected]
Abstract: We propose a simple and high-performance scheme for demultiplexing coherent Nyquist TDM signals by photo-mixing on a photodetector with Nyquist LO pulses. This scheme takes advantage of the timedomain orthogonality of Nyquist pulses, which enables high-SNR demultiplexing and homodyne detection simultaneously in spite of a strong overlap with adjacent pulses in the time domain. The feasibility of this scheme is demonstrated through a demultiplexing experiment employing 80 Gbaud, 64 QAM Nyquist pulse OTDM signals. This scheme exhibits excellent demultiplexing performance with a much simpler configuration than a conventional ultrafast all-optical sampling scheme. ©2014 Optical Society of America OCIS codes: (060.1660) Coherent communications; (060.4080) Modulation; (060.4230) Multiplexing; (320.5550) Pulses.
References and links 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13.
T. Richter, E. Palushani, C. Schmidt-Langhorst, M. Nölle, R. Ludwig, and C. Schubert, “Single wavelength channel 10.2 Tb/s TDM-capacity using 16-QAM and coherent detection,” Proceedings of the Optical Fiber Communication Conference (OFC) 2011, PDPA9. E. Palushani, C. Schmidt-Langhorst, T. Richter, M. Nölle, R. Ludwig, and C. Schubert, “Transmission of a serial 5.1-Tb/s data signal using 16-QAM and coherent detection,” Proceedings of the European Conference on Optical Communication (ECOC) 2011, We.8.B.5. D. O. Otuya, K. Kasai, M. Yoshida, T. Hirooka, and M. Nakazawa, “A single-channel 1.92 Tbit/s, 64 QAM coherent optical pulse transmission over 150 km using frequency-domain equalization,” Opt. Express 21(19), 22808–22816 (2013). M. Nakazawa, T. Hirooka, P. Ruan, and P. Guan, “Ultrahigh-speed “orthogonal” TDM transmission with an optical Nyquist pulse train,” Opt. Express 20(2), 1129–1140 (2012). K. Harako, D. Seya, T. Hirooka, and M. Nakazawa, “640 Gbaud (1.28 Tbit/s/ch) optical Nyquist pulse transmission over 525 km with substantial PMD tolerance,” Opt. Express 21(18), 21062–21075 (2013). D. O. Otuya, K. Kasai, T. Hirooka, M. Yoshida, and M. Nakazawa, “1.92 Tbit/s, 64 QAM coherent Nyquist pulse transmission over 150 km with a spectral efficiency of 7.5 bit/s/Hz,” Proceedings of the Optical Fiber Conference (OFC) 2014, W1A.4. H. Hu, D. Kong, E. Palushani, J. D. Andersen, A. Rasmussen, B. M. Sørensen, M. Galili, H. C. H. Mulvad, K. J. Larsen, S. Forchhammer, P. Jeppesen, and L. K. Oxenløwe, “1.28 Tbaud Nyquist signal transmission using timedomain optical Fourier transformation based receiver,” Proceedings of the Conference on Lasers and ElectroOptics (CLEO) 2013, CTh5D.5. T. Richter, M. Nölle, F. Frey, and C. Schubert, “Generation and coherent reception of 107-GBd optical Nyquist BPSK, QPSK, and 16 QAM,” IEEE Photon. Technol. Lett. 26(9), 877–880 (2014). J. Zhang, J. Yu, Y. Fang, and N. Chi, “High speed all optical Nyquist signal generation and full-band coherent detection,” Sci. Rep. 4, 6156 (2014). F. Ito, “Interferometry demultiplexing experiment using linear coherent correlation with modulated local oscillator,” Electron. Lett. 32(1), 14–15 (1996). C. Zhang, Y. Mori, K. Igarashi, K. Katoh, and K. Kikuchi, “Ultrafast operation of digital coherent receivers using their time-division demultiplexing function,” J. Lightwave Technol. 27(3), 224–232 (2009). M. Nakazawa, K. Kasai, M. Yoshida, and T. Hirooka, “Novel RZ-CW conversion scheme for ultra multi-level, high-speed coherent OTDM transmission,” Opt. Express 19(26), B574–B580 (2011). G. Baxter, S. Frisken, D. Abakoumov, H. Z. I. Clarke, A. Bartos, and S. Poole, “Highly programmable wavelength selective switch based on liquid crystal on silicon switching elements,” Proceedings of OFC/NFOEC2006, OTuF2, 2006.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29456
1. Introduction In recent years, a transmission capacity exceeding 1 Tbit/s/ch has become an important research target because of the need to cope with the rapid growth in Internet traffic. The optical time division multiplexing (OTDM) of coherent pulses is a simple and direct approach for increasing the single-channel transmission capacity, and transmission experiments with coherent OTDM signals exceeding 1 Tbit/s/ch have already been reported that adopted QAM [1–3]. In general, OTDM requires ultrashort optical pulses as the symbol rate increases, and the inherently broad bandwidth of RZ optical pulses is disadvantageous in terms of spectral efficiency. Recently, optical Nyquist pulses were proposed for spectrally efficient high-speed OTDM transmission [4], and they have attracted a lot of attention as new pulses for high-speed and highly spectral efficient OTDM transmission [5–7]. The shape of an optical Nyquist pulse is the impulse response of a Nyquist filter. In contrast to ordinary RZ pulses, the tail of a Nyquist pulse decays with ripples that periodically cross zero. Therefore, the pulses can be bit-interleaved to an extremely high symbol rate without intersymbol interference (ISI) even if the neighboring pulses are strongly overlapping. This narrowband Nyquist pulse results in a significant bandwidth reduction in OTDM transmission, which can be ultimately made as low as the TDM symbol rate. The coherent detection of optical Nyquist pulses with a CW-LO and a high-speed digital oscilloscope has recently been demonstrated at a symbol rate lower than the bandwidth of the AD converter [8,9]. However, for symbol rates exceeding the receiver bandwidth, OTDM demultiplexing becomes mandatory. An ultrafast optical sampling technique was used to extract only an ISI-free component from an overlapping Nyquist pulse train [4]. This leads to SNR degradation as the sampling gate width decreases. On the other hand, a coherent OTDM demultiplexing scheme has been proposed by using homodyne detection with an RZ-pulsed local oscillator (LO) [10,11]. However, this scheme is affected by SNR degradation by the bandwidth limiting of a digital coherent receiver owing to the broad spectral width of RZ pulses [12]. In addition, no time-domain orthogonality was used. In this paper, we propose a novel scheme for high-performance and highly efficient coherent Nyquist pulse TDM demultiplexing using a Nyquist pulse as both a data signal and an LO. Based on the time-domain orthogonality of Nyquist pulses, we show that photomixing on a photo-detector (PD) with a Nyquist LO pulse can extract a tributary from the overlapping data sequence with a high SNR, and the leakage from other channels can be completely suppressed. By adopting this scheme, an 80 Gbaud, 64 QAM Nyquist TDM signal was successfully demultiplexed to 10 Gbaud. 2. Principle of coherent Nyquist pulse TDM demultiplexing The proposed scheme takes advantage of the time-domain orthogonality of Nyquist pulses among different time slots described in [4]. This scheme is analogous to OFDM, which involves the orthogonality of sinusoidal functions among different frequencies and thus the overlapping FDM channels can be demultiplexed by means of FFT. Similarly, even when an adjacent pulse overlaps, a TDM channel can be extracted completely by means of photomixing between Nyquist TDM data and LO pulses as we describe below. To explain the principle of the demultiplexing of Nyquist TDM signals using orthogonality, we define the time-interleaved optical Nyquist pulses as n(t) = r(tnT) and the symbol data at t = nT as gn. According to the sampling theorem, when α = 0 the TDM Nyquist data train u(t) = Σgnn(t) is equivalent to an analog signal g(t), which is given by:
u (t ) g (t ) g nn (t )
(1)
n
Furthermore, n(t) satisfies the following orthogonality condition when the roll-off factor α = 0:
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29457
0 (n m) 1 n (t )m (t )dt T 1 (n m)
(2)
Using Eqs. (1) and (2), gn can be expressed as follows.
gn
1 u (t )n (t )dt T
(3)
The product of u(t) and n(t) can be realized by the square-law detection of u(t) and n(t) on a PD. This indicates that gn can be extracted simply by synchronously launching the data and LO pulses (u(t) and n(t), respectively) into a PD. In OFDM, where n(t) is regarded as cos(2 nt / T ) , this formula is equivalent to the Fourier transformation for an OFDM demodulation [4].
Fig. 1. Basic configuration of TDM demultiplexing using Nyquist LO pulses.
Figure 1 shows the basic configuration for TDM demultiplexing using Nyquist LO pulses. When OTDM data signal u(t) and Nyquist LO pulses n(t) are coupled into two inputs of a coherent photo-detection circuit, the two outputs are written as follows.
E1
1 2
u(t ) n (t ) ,
E2
1 2
u(t ) n (t ) ,
(4)
After balanced detection of E1 and E2, the output becomes
I (t ) E1 E2 u(t )n (t ) 2
2
(5)
The self-homodyne components, |u(t)|2 and |n(t)|2, are canceled by balanced detection, and only the product of u(t) and n(t) remain. By taking account of the time response of the PD or the bandwidth of the receiver, the output after coherent detection, Iout(t), can be given by
I out (t )
1 2
I ( ) H ( )e jt d
(6)
where H(ω) is a transfer function of the coherent PD, and I ( ) is the Fourier transformation of Iout(t):
I ( ) I (t )e jt dt
(7)
By substituting Eq. (7) into Eq. (6), the output signal Iout(t) can be obtained as follows.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29458
1 2 1 2
I out (t )
I (t )e jt dt H ( )e jt d (8)
I (t ) H ( )e j (t t ) d dt
In particular, if H(ω) is a low pass filter whose bandwidth is Ω, Eq. (8) is rewritten as
1 2 1 2
I out (t )
1 2 2
I (t ) e j ( t t ) d dt 0
I (t )
e j (t t ) 1 dt j (t t )
(9)
1 j(t t ) 1dt I (t ) j (t t )
I (t )dt
By choosing a filter bandwidth of Ω = 2π/T, Iout(t) is written as follows from Eqs. (5) and (9):
I out (t )
1 u (t )n (t )dt T
(10)
This result indicates that coherent homodyne mixing between u(t) and n(t) yields the extraction of the data gn at t = nT from Eq. (3). When α 0, Eq. (2) is expressed as
1 3 5 n (t )m (t )dt (1 )sinc (1 )(m n) (1 )sinc (1 )(m n) T 8 8
8
cos (m n) sinc (1 (m n)) sinc (1 (m n))
(11)
When n m, the right-hand side of Eq. (11) is not exactly zero, and hence the orthogonality relationship is not rigorously satisfied when α 0. The integration value of Eq. (11) when α = 0.5 is plotted in Fig. 2 as a function of mn. It can be seen that the overlap integral between n(t) and m(t) does not become zero for n m. However, it is still a very small value of less than 0.12 even when |mn| = 1, where the pulse overlap is largest, and it approaches zero rapidly as |mn| increases. Figure 3 shows the overlap integral for 0α1 when mn = 0 and 1. The overlap integral remains less than 0.13 for all α values despite exhibiting the strongest overlap under mn = 1. These results indicate that the quasi-orthogonality property can be maintained for α 0.
Fig. 2. Overlap integral of Nyquist pulses when α = 0.5.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29459
Fig. 3. Overlap integral of Nyquist pluses for each roll-off factors when mn = 0 and 1.
3. TDM demultiplexing experiment of 80 Gbaud, 64 QAM coherent Nyquist pulses
Fig. 4. Experimental setup for 80 Gbaud, 64 QAM coherent Nyquist TDM demultiplexing using a Nyquist LO pulse (a) and an ultrafast NOLM sampling gate (b). The present scheme (a) is much simpler than the previous scheme (b).
We applied the proposed scheme to the 80 to 10 Gbaud demultiplexing of 64 QAM Nyquist TDM signals. Figure 4 shows the experimental setup. At the transmitter, we used an acetylene (C2H2) frequency-stabilized fiber laser as a CW coherent optical source. The output signal was fed into an optical comb generator consisting of a dual-drive LiNbO3 (LN) MachZehnder modulator. Its spectrum was then manipulated into a Nyquist profile to generate a 10 GHz coherent Nyquist pulse train using a pulse shaper [13]. The spectra of the optical Nyquist pulses generated with α = 0, 0.5, and 1 are shown in Fig. 5. It can be seen that these spectra closely fit the ideal Nyquist profile as shown by the black curves. The Nyquist pulse train was modulated with a 10 Gbaud 64 QAM signal supplied from an arbitary waveform generator (AWG), and multiplexed to 80 Gbaud using a delay-line bit interleaver.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29460
0
10
=0
Normalized power [dB]
Normalized power [dB]
10
-10 -20 -30 -40 -50 -60
0
= 0.5
-10 -20 -30 -40 -50 -60
1538
1539
1538
Wavelength [nm]
1539 Wavelength [nm]
(a)
(b)
Normalized power [dB]
10 0
=1
-10 -20 -30 -40 -50 -60 1538
1539 Wavelength [nm]
(c) Fig. 5. Optical spectra of Nyquist pulses generated with α = 0 (a), 0.5 (b), and 1 (c). The black curves show the ideal Nyquist spectral profile.
At the receiver, we adopted the two demultiplexing configrations shown in Fig. 4(a) and 4(b). As shown in Fig. 4(a), another 10 GHz Nyquist pulse train was generated from a frequency-tunable CW fiber laser, optical comb generator driven by the 10 GHz clock extracted from the data, and a pulse shaper, in the same way as the transmitter. Here, the rolloff factor of the Nyquist LO pulse was chosen to be the same as the data pulse. Its phase was synchronized with that of the data signal via a pilot tone by the OPLL circuit. This coherent phase-locked Nyquist pulse was used as an LO for coherent detection. Coherent detection with the Nyquist LO pulse enables demultiplexing and homodyne detection simultaneously. Figure 4(b) shows the other demultiplexing scheme based on conventional ultrafast sampling using a nonlinear optical loop mirror (NOLM). Here, a 10 GHz, 860 fs Gaussian pulse train was used as an optical sampling pulse, and the pulse was optimized by taking account of the trade-off between SNR and ISI. The demultiplexed RZ pulse was converted into a quasi-CW data signal by using an RZ-CW conversion circuit [12]. The RZ-CW conversion circuit was adopted to compress the spectrum within the receiver bandwidth for high-SNR demodulation. In this case, the demultiplexed channel is homodyne-detected with a CW-LO. After coherent detection between data and a Nyquist- or CW-LO with a 90-degree optical hybrid circuit and a balanced PD, the received signal was A/D-converted at a sampling rate of 80 Gsamples/s. Here, the bandwidth of the balanced PD was 43 GHz. Finally, the QAM signal was demodulated in the digital signal processor in an offline condition. Figures 6 and 7 show the constellation maps of the demultiplexed 64 QAM when α = 0 and 0.5, respectively. In these figures, (a) and (b) correspond to the results obtained using a Nyquist LO scheme and a conventional ultrafast sampling scheme, respectively. It can be clearly seen that the SNR degradation is larger with an ultrafast sampling scheme (EVM = 4.1% in Fig. 6 and 3.6% in Fig. 7). This is due to the insufficient SNR that resulted from the ultra-narrow gating used for the sampling. On the other hand, with the Nyquist LO, the demodulation result is greatly improved (EVM = 3.4% in Fig. 6 and 3.0% in Fig. 7). Figure 8 #222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29461
shows the bit error rate (BER) performance obtained with the optical sampling scheme and the Nyquist LO scheme. When α = 0, the Nyquist LO scheme outperforms the optical sampling scheme as shown by the red squares in Fig. 8, where the OSNR required for the FEC threshold (2 × 103) is improved by 3.9 dB. Even when α = 0.5, a better BER performance was obtained with the Nyquist LO scheme. However, the BER improvement was smaller than for α = 0. This is because of the broad bandwidth requirement resulting from the non-zero α and also owing to the fact that the orthogonality is not rigorously satisfied when α = 0.5. When α = 1, the BER performance is similar to that for α = 0.5. The results in Fig. 8 indicate that the BER performance for α = 0 is lower than that for α = 0.5 and 1 in spite of its ideal orthogonality. This can be attributed to the higher SNR requirement for signals with a higher spectral efficiency, or equivalently a lower α value. To explain this, Fig. 9(a) shows the theoretical BER curves for 64 QAM signals when the spectral efficiency is SE = 3, 4 and 6 bit/s/Hz. This figure can be obtained from the theoretical BER curve of 64 QAM signals as a function of Eb/N0, BER (7 / 24)erfc (1/ 7)(Eb / N0 ) , and by converting Eb/N0 to OSNR through the equation OSNR = [Rb/N(1 + α)Δν](Eb/N0), where N is the OTDM multiplicity (here N = 8), Rb is the bit rate before demultiplexing (i.e., Rb/N = 60 Gbit/s represents the bit rate after demultiplexing) and Δν = 12.5 GHz (0.1 nm) is the noise detection bandwidth. Here the factor (1 + α) is explicitly included to take account of the conversion from the original signal bandwidth B = (1 + α)Rs to the demodulation bandwidth B/N(1 + α). Here, Rs is the symbol rate before demultiplexing i.e. Rs = 80 Gbaud and B/N(1 + α) is equal to 10 GHz. The spectral efficiency is related to the roll-off factor of a Nyquist pulse through SE = 6/(1 + α) bit/s/Hz for 64 QAM, which is plotted in Fig. 9(b). From Fig. 9(b), α = 0, 0.5 and 1 correspond to SE = 3, 4 and 6 bit/s/Hz, respectively. The curves in Fig. 9(a) indicate that a Nyquist pulse with a lower α value requires a higher SNR. Figure 10 shows the BER measured for all the tributaries with the Nyquist LO scheme (α = 0, OSNR = 25 dB). This indicates that all tributaries perform similarly with a low BER compared with an optical sampling scheme.
Fig. 6. Constellations of a 64 QAM Nyquist pulse with α = 0 received with the proposed scheme (a) and the previous ultrafast sampling scheme (b), respectively.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29462
Fig. 7. Constellations of a 64 QAM Nyquist pulse with α = 0.5 received with the proposed scheme (a) and the previous ultrafast sampling scheme (b), respectively.
2 =0
Nyquist LO scheme Optical sampling scheme
-log (BER)
FEC threshold 2x10-3 3.9 dB
3 = 0.5
4 =1
5
19
21
23
25
27
29
OSNR [dB]@0.1 nm Fig. 8. Back-to-back BER vs. OSNR for demultiplexed 10 Gbaud 64 QAM Nyquist pulses with α = 0 (squares), 0.5 (diamonds) and 1 (circles).
Fig. 9. Theoretical BER curves of 64 QAM signals as a function of OSNR with SE = 6 bit/s/Hz (α = 0, blue), SE = 4 bit/s/Hz (α = 0.5, red) and SE = 3 bit/s/Hz (α = 1, black) (a), and the relationship between the roll-off factor and spectral efficiency for 64 QAM (b).
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29463
3
-log(BER)
4 5 6 7 8 1
2
3 4 5 6 7 Tributary number
8
Fig. 10. BERs for all the tributaries of the demultiplexed 10 Gbaud 64 QAM Nyquist pulses with the Nyquist LO scheme (α = 0, OSNR = 25 dB).
4. Conclusion We described a novel scheme for demultiplexing coherent Nyquist TDM signals using photomixing with an optical Nyquist LO pulse. This scheme takes advantage of the time-domain orthogonality to extract data from an overlapped data sequence, and enables highperformance demultiplexing with a simple configuration. 80 Gbaud, 64 QAM Nyquist pulses with α = 0 were successfully demultiplexed to 10 Gbaud, which is difficult to realize with a conventional ultrafast sampling scheme. Since the present method has a superior SNR performance and simpler configuration than an optical sampling technique, this scheme is especially advantageous for QAM transmission with a higher multiplicity. Acknowledgment This work was supported by the Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Specially Promoted Research, 26000009.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29464
Abstract: We propose a simple and high-performance scheme for demultiplexing coherent Nyquist TDM signals by photo-mixing on a photodetector with Nyquist LO pulses. This scheme takes advantage of the timedomain orthogonality of Nyquist pulses, which enables high-SNR demultiplexing and homodyne detection simultaneously in spite of a strong overlap with adjacent pulses in the time domain. The feasibility of this scheme is demonstrated through a demultiplexing experiment employing 80 Gbaud, 64 QAM Nyquist pulse OTDM signals. This scheme exhibits excellent demultiplexing performance with a much simpler configuration than a conventional ultrafast all-optical sampling scheme. ©2014 Optical Society of America OCIS codes: (060.1660) Coherent communications; (060.4080) Modulation; (060.4230) Multiplexing; (320.5550) Pulses.
References and links 1. 2. 3. 4. 5. 6. 7.
8. 9. 10. 11. 12. 13.
T. Richter, E. Palushani, C. Schmidt-Langhorst, M. Nölle, R. Ludwig, and C. Schubert, “Single wavelength channel 10.2 Tb/s TDM-capacity using 16-QAM and coherent detection,” Proceedings of the Optical Fiber Communication Conference (OFC) 2011, PDPA9. E. Palushani, C. Schmidt-Langhorst, T. Richter, M. Nölle, R. Ludwig, and C. Schubert, “Transmission of a serial 5.1-Tb/s data signal using 16-QAM and coherent detection,” Proceedings of the European Conference on Optical Communication (ECOC) 2011, We.8.B.5. D. O. Otuya, K. Kasai, M. Yoshida, T. Hirooka, and M. Nakazawa, “A single-channel 1.92 Tbit/s, 64 QAM coherent optical pulse transmission over 150 km using frequency-domain equalization,” Opt. Express 21(19), 22808–22816 (2013). M. Nakazawa, T. Hirooka, P. Ruan, and P. Guan, “Ultrahigh-speed “orthogonal” TDM transmission with an optical Nyquist pulse train,” Opt. Express 20(2), 1129–1140 (2012). K. Harako, D. Seya, T. Hirooka, and M. Nakazawa, “640 Gbaud (1.28 Tbit/s/ch) optical Nyquist pulse transmission over 525 km with substantial PMD tolerance,” Opt. Express 21(18), 21062–21075 (2013). D. O. Otuya, K. Kasai, T. Hirooka, M. Yoshida, and M. Nakazawa, “1.92 Tbit/s, 64 QAM coherent Nyquist pulse transmission over 150 km with a spectral efficiency of 7.5 bit/s/Hz,” Proceedings of the Optical Fiber Conference (OFC) 2014, W1A.4. H. Hu, D. Kong, E. Palushani, J. D. Andersen, A. Rasmussen, B. M. Sørensen, M. Galili, H. C. H. Mulvad, K. J. Larsen, S. Forchhammer, P. Jeppesen, and L. K. Oxenløwe, “1.28 Tbaud Nyquist signal transmission using timedomain optical Fourier transformation based receiver,” Proceedings of the Conference on Lasers and ElectroOptics (CLEO) 2013, CTh5D.5. T. Richter, M. Nölle, F. Frey, and C. Schubert, “Generation and coherent reception of 107-GBd optical Nyquist BPSK, QPSK, and 16 QAM,” IEEE Photon. Technol. Lett. 26(9), 877–880 (2014). J. Zhang, J. Yu, Y. Fang, and N. Chi, “High speed all optical Nyquist signal generation and full-band coherent detection,” Sci. Rep. 4, 6156 (2014). F. Ito, “Interferometry demultiplexing experiment using linear coherent correlation with modulated local oscillator,” Electron. Lett. 32(1), 14–15 (1996). C. Zhang, Y. Mori, K. Igarashi, K. Katoh, and K. Kikuchi, “Ultrafast operation of digital coherent receivers using their time-division demultiplexing function,” J. Lightwave Technol. 27(3), 224–232 (2009). M. Nakazawa, K. Kasai, M. Yoshida, and T. Hirooka, “Novel RZ-CW conversion scheme for ultra multi-level, high-speed coherent OTDM transmission,” Opt. Express 19(26), B574–B580 (2011). G. Baxter, S. Frisken, D. Abakoumov, H. Z. I. Clarke, A. Bartos, and S. Poole, “Highly programmable wavelength selective switch based on liquid crystal on silicon switching elements,” Proceedings of OFC/NFOEC2006, OTuF2, 2006.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29456
1. Introduction In recent years, a transmission capacity exceeding 1 Tbit/s/ch has become an important research target because of the need to cope with the rapid growth in Internet traffic. The optical time division multiplexing (OTDM) of coherent pulses is a simple and direct approach for increasing the single-channel transmission capacity, and transmission experiments with coherent OTDM signals exceeding 1 Tbit/s/ch have already been reported that adopted QAM [1–3]. In general, OTDM requires ultrashort optical pulses as the symbol rate increases, and the inherently broad bandwidth of RZ optical pulses is disadvantageous in terms of spectral efficiency. Recently, optical Nyquist pulses were proposed for spectrally efficient high-speed OTDM transmission [4], and they have attracted a lot of attention as new pulses for high-speed and highly spectral efficient OTDM transmission [5–7]. The shape of an optical Nyquist pulse is the impulse response of a Nyquist filter. In contrast to ordinary RZ pulses, the tail of a Nyquist pulse decays with ripples that periodically cross zero. Therefore, the pulses can be bit-interleaved to an extremely high symbol rate without intersymbol interference (ISI) even if the neighboring pulses are strongly overlapping. This narrowband Nyquist pulse results in a significant bandwidth reduction in OTDM transmission, which can be ultimately made as low as the TDM symbol rate. The coherent detection of optical Nyquist pulses with a CW-LO and a high-speed digital oscilloscope has recently been demonstrated at a symbol rate lower than the bandwidth of the AD converter [8,9]. However, for symbol rates exceeding the receiver bandwidth, OTDM demultiplexing becomes mandatory. An ultrafast optical sampling technique was used to extract only an ISI-free component from an overlapping Nyquist pulse train [4]. This leads to SNR degradation as the sampling gate width decreases. On the other hand, a coherent OTDM demultiplexing scheme has been proposed by using homodyne detection with an RZ-pulsed local oscillator (LO) [10,11]. However, this scheme is affected by SNR degradation by the bandwidth limiting of a digital coherent receiver owing to the broad spectral width of RZ pulses [12]. In addition, no time-domain orthogonality was used. In this paper, we propose a novel scheme for high-performance and highly efficient coherent Nyquist pulse TDM demultiplexing using a Nyquist pulse as both a data signal and an LO. Based on the time-domain orthogonality of Nyquist pulses, we show that photomixing on a photo-detector (PD) with a Nyquist LO pulse can extract a tributary from the overlapping data sequence with a high SNR, and the leakage from other channels can be completely suppressed. By adopting this scheme, an 80 Gbaud, 64 QAM Nyquist TDM signal was successfully demultiplexed to 10 Gbaud. 2. Principle of coherent Nyquist pulse TDM demultiplexing The proposed scheme takes advantage of the time-domain orthogonality of Nyquist pulses among different time slots described in [4]. This scheme is analogous to OFDM, which involves the orthogonality of sinusoidal functions among different frequencies and thus the overlapping FDM channels can be demultiplexed by means of FFT. Similarly, even when an adjacent pulse overlaps, a TDM channel can be extracted completely by means of photomixing between Nyquist TDM data and LO pulses as we describe below. To explain the principle of the demultiplexing of Nyquist TDM signals using orthogonality, we define the time-interleaved optical Nyquist pulses as n(t) = r(tnT) and the symbol data at t = nT as gn. According to the sampling theorem, when α = 0 the TDM Nyquist data train u(t) = Σgnn(t) is equivalent to an analog signal g(t), which is given by:
u (t ) g (t ) g nn (t )
(1)
n
Furthermore, n(t) satisfies the following orthogonality condition when the roll-off factor α = 0:
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29457
0 (n m) 1 n (t )m (t )dt T 1 (n m)
(2)
Using Eqs. (1) and (2), gn can be expressed as follows.
gn
1 u (t )n (t )dt T
(3)
The product of u(t) and n(t) can be realized by the square-law detection of u(t) and n(t) on a PD. This indicates that gn can be extracted simply by synchronously launching the data and LO pulses (u(t) and n(t), respectively) into a PD. In OFDM, where n(t) is regarded as cos(2 nt / T ) , this formula is equivalent to the Fourier transformation for an OFDM demodulation [4].
Fig. 1. Basic configuration of TDM demultiplexing using Nyquist LO pulses.
Figure 1 shows the basic configuration for TDM demultiplexing using Nyquist LO pulses. When OTDM data signal u(t) and Nyquist LO pulses n(t) are coupled into two inputs of a coherent photo-detection circuit, the two outputs are written as follows.
E1
1 2
u(t ) n (t ) ,
E2
1 2
u(t ) n (t ) ,
(4)
After balanced detection of E1 and E2, the output becomes
I (t ) E1 E2 u(t )n (t ) 2
2
(5)
The self-homodyne components, |u(t)|2 and |n(t)|2, are canceled by balanced detection, and only the product of u(t) and n(t) remain. By taking account of the time response of the PD or the bandwidth of the receiver, the output after coherent detection, Iout(t), can be given by
I out (t )
1 2
I ( ) H ( )e jt d
(6)
where H(ω) is a transfer function of the coherent PD, and I ( ) is the Fourier transformation of Iout(t):
I ( ) I (t )e jt dt
(7)
By substituting Eq. (7) into Eq. (6), the output signal Iout(t) can be obtained as follows.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29458
1 2 1 2
I out (t )
I (t )e jt dt H ( )e jt d (8)
I (t ) H ( )e j (t t ) d dt
In particular, if H(ω) is a low pass filter whose bandwidth is Ω, Eq. (8) is rewritten as
1 2 1 2
I out (t )
1 2 2
I (t ) e j ( t t ) d dt 0
I (t )
e j (t t ) 1 dt j (t t )
(9)
1 j(t t ) 1dt I (t ) j (t t )
I (t )dt
By choosing a filter bandwidth of Ω = 2π/T, Iout(t) is written as follows from Eqs. (5) and (9):
I out (t )
1 u (t )n (t )dt T
(10)
This result indicates that coherent homodyne mixing between u(t) and n(t) yields the extraction of the data gn at t = nT from Eq. (3). When α 0, Eq. (2) is expressed as
1 3 5 n (t )m (t )dt (1 )sinc (1 )(m n) (1 )sinc (1 )(m n) T 8 8
8
cos (m n) sinc (1 (m n)) sinc (1 (m n))
(11)
When n m, the right-hand side of Eq. (11) is not exactly zero, and hence the orthogonality relationship is not rigorously satisfied when α 0. The integration value of Eq. (11) when α = 0.5 is plotted in Fig. 2 as a function of mn. It can be seen that the overlap integral between n(t) and m(t) does not become zero for n m. However, it is still a very small value of less than 0.12 even when |mn| = 1, where the pulse overlap is largest, and it approaches zero rapidly as |mn| increases. Figure 3 shows the overlap integral for 0α1 when mn = 0 and 1. The overlap integral remains less than 0.13 for all α values despite exhibiting the strongest overlap under mn = 1. These results indicate that the quasi-orthogonality property can be maintained for α 0.
Fig. 2. Overlap integral of Nyquist pulses when α = 0.5.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29459
Fig. 3. Overlap integral of Nyquist pluses for each roll-off factors when mn = 0 and 1.
3. TDM demultiplexing experiment of 80 Gbaud, 64 QAM coherent Nyquist pulses
Fig. 4. Experimental setup for 80 Gbaud, 64 QAM coherent Nyquist TDM demultiplexing using a Nyquist LO pulse (a) and an ultrafast NOLM sampling gate (b). The present scheme (a) is much simpler than the previous scheme (b).
We applied the proposed scheme to the 80 to 10 Gbaud demultiplexing of 64 QAM Nyquist TDM signals. Figure 4 shows the experimental setup. At the transmitter, we used an acetylene (C2H2) frequency-stabilized fiber laser as a CW coherent optical source. The output signal was fed into an optical comb generator consisting of a dual-drive LiNbO3 (LN) MachZehnder modulator. Its spectrum was then manipulated into a Nyquist profile to generate a 10 GHz coherent Nyquist pulse train using a pulse shaper [13]. The spectra of the optical Nyquist pulses generated with α = 0, 0.5, and 1 are shown in Fig. 5. It can be seen that these spectra closely fit the ideal Nyquist profile as shown by the black curves. The Nyquist pulse train was modulated with a 10 Gbaud 64 QAM signal supplied from an arbitary waveform generator (AWG), and multiplexed to 80 Gbaud using a delay-line bit interleaver.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29460
0
10
=0
Normalized power [dB]
Normalized power [dB]
10
-10 -20 -30 -40 -50 -60
0
= 0.5
-10 -20 -30 -40 -50 -60
1538
1539
1538
Wavelength [nm]
1539 Wavelength [nm]
(a)
(b)
Normalized power [dB]
10 0
=1
-10 -20 -30 -40 -50 -60 1538
1539 Wavelength [nm]
(c) Fig. 5. Optical spectra of Nyquist pulses generated with α = 0 (a), 0.5 (b), and 1 (c). The black curves show the ideal Nyquist spectral profile.
At the receiver, we adopted the two demultiplexing configrations shown in Fig. 4(a) and 4(b). As shown in Fig. 4(a), another 10 GHz Nyquist pulse train was generated from a frequency-tunable CW fiber laser, optical comb generator driven by the 10 GHz clock extracted from the data, and a pulse shaper, in the same way as the transmitter. Here, the rolloff factor of the Nyquist LO pulse was chosen to be the same as the data pulse. Its phase was synchronized with that of the data signal via a pilot tone by the OPLL circuit. This coherent phase-locked Nyquist pulse was used as an LO for coherent detection. Coherent detection with the Nyquist LO pulse enables demultiplexing and homodyne detection simultaneously. Figure 4(b) shows the other demultiplexing scheme based on conventional ultrafast sampling using a nonlinear optical loop mirror (NOLM). Here, a 10 GHz, 860 fs Gaussian pulse train was used as an optical sampling pulse, and the pulse was optimized by taking account of the trade-off between SNR and ISI. The demultiplexed RZ pulse was converted into a quasi-CW data signal by using an RZ-CW conversion circuit [12]. The RZ-CW conversion circuit was adopted to compress the spectrum within the receiver bandwidth for high-SNR demodulation. In this case, the demultiplexed channel is homodyne-detected with a CW-LO. After coherent detection between data and a Nyquist- or CW-LO with a 90-degree optical hybrid circuit and a balanced PD, the received signal was A/D-converted at a sampling rate of 80 Gsamples/s. Here, the bandwidth of the balanced PD was 43 GHz. Finally, the QAM signal was demodulated in the digital signal processor in an offline condition. Figures 6 and 7 show the constellation maps of the demultiplexed 64 QAM when α = 0 and 0.5, respectively. In these figures, (a) and (b) correspond to the results obtained using a Nyquist LO scheme and a conventional ultrafast sampling scheme, respectively. It can be clearly seen that the SNR degradation is larger with an ultrafast sampling scheme (EVM = 4.1% in Fig. 6 and 3.6% in Fig. 7). This is due to the insufficient SNR that resulted from the ultra-narrow gating used for the sampling. On the other hand, with the Nyquist LO, the demodulation result is greatly improved (EVM = 3.4% in Fig. 6 and 3.0% in Fig. 7). Figure 8 #222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29461
shows the bit error rate (BER) performance obtained with the optical sampling scheme and the Nyquist LO scheme. When α = 0, the Nyquist LO scheme outperforms the optical sampling scheme as shown by the red squares in Fig. 8, where the OSNR required for the FEC threshold (2 × 103) is improved by 3.9 dB. Even when α = 0.5, a better BER performance was obtained with the Nyquist LO scheme. However, the BER improvement was smaller than for α = 0. This is because of the broad bandwidth requirement resulting from the non-zero α and also owing to the fact that the orthogonality is not rigorously satisfied when α = 0.5. When α = 1, the BER performance is similar to that for α = 0.5. The results in Fig. 8 indicate that the BER performance for α = 0 is lower than that for α = 0.5 and 1 in spite of its ideal orthogonality. This can be attributed to the higher SNR requirement for signals with a higher spectral efficiency, or equivalently a lower α value. To explain this, Fig. 9(a) shows the theoretical BER curves for 64 QAM signals when the spectral efficiency is SE = 3, 4 and 6 bit/s/Hz. This figure can be obtained from the theoretical BER curve of 64 QAM signals as a function of Eb/N0, BER (7 / 24)erfc (1/ 7)(Eb / N0 ) , and by converting Eb/N0 to OSNR through the equation OSNR = [Rb/N(1 + α)Δν](Eb/N0), where N is the OTDM multiplicity (here N = 8), Rb is the bit rate before demultiplexing (i.e., Rb/N = 60 Gbit/s represents the bit rate after demultiplexing) and Δν = 12.5 GHz (0.1 nm) is the noise detection bandwidth. Here the factor (1 + α) is explicitly included to take account of the conversion from the original signal bandwidth B = (1 + α)Rs to the demodulation bandwidth B/N(1 + α). Here, Rs is the symbol rate before demultiplexing i.e. Rs = 80 Gbaud and B/N(1 + α) is equal to 10 GHz. The spectral efficiency is related to the roll-off factor of a Nyquist pulse through SE = 6/(1 + α) bit/s/Hz for 64 QAM, which is plotted in Fig. 9(b). From Fig. 9(b), α = 0, 0.5 and 1 correspond to SE = 3, 4 and 6 bit/s/Hz, respectively. The curves in Fig. 9(a) indicate that a Nyquist pulse with a lower α value requires a higher SNR. Figure 10 shows the BER measured for all the tributaries with the Nyquist LO scheme (α = 0, OSNR = 25 dB). This indicates that all tributaries perform similarly with a low BER compared with an optical sampling scheme.
Fig. 6. Constellations of a 64 QAM Nyquist pulse with α = 0 received with the proposed scheme (a) and the previous ultrafast sampling scheme (b), respectively.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29462
Fig. 7. Constellations of a 64 QAM Nyquist pulse with α = 0.5 received with the proposed scheme (a) and the previous ultrafast sampling scheme (b), respectively.
2 =0
Nyquist LO scheme Optical sampling scheme
-log (BER)
FEC threshold 2x10-3 3.9 dB
3 = 0.5
4 =1
5
19
21
23
25
27
29
OSNR [dB]@0.1 nm Fig. 8. Back-to-back BER vs. OSNR for demultiplexed 10 Gbaud 64 QAM Nyquist pulses with α = 0 (squares), 0.5 (diamonds) and 1 (circles).
Fig. 9. Theoretical BER curves of 64 QAM signals as a function of OSNR with SE = 6 bit/s/Hz (α = 0, blue), SE = 4 bit/s/Hz (α = 0.5, red) and SE = 3 bit/s/Hz (α = 1, black) (a), and the relationship between the roll-off factor and spectral efficiency for 64 QAM (b).
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29463
3
-log(BER)
4 5 6 7 8 1
2
3 4 5 6 7 Tributary number
8
Fig. 10. BERs for all the tributaries of the demultiplexed 10 Gbaud 64 QAM Nyquist pulses with the Nyquist LO scheme (α = 0, OSNR = 25 dB).
4. Conclusion We described a novel scheme for demultiplexing coherent Nyquist TDM signals using photomixing with an optical Nyquist LO pulse. This scheme takes advantage of the time-domain orthogonality to extract data from an overlapped data sequence, and enables highperformance demultiplexing with a simple configuration. 80 Gbaud, 64 QAM Nyquist pulses with α = 0 were successfully demultiplexed to 10 Gbaud, which is difficult to realize with a conventional ultrafast sampling scheme. Since the present method has a superior SNR performance and simpler configuration than an optical sampling technique, this scheme is especially advantageous for QAM transmission with a higher multiplicity. Acknowledgment This work was supported by the Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Specially Promoted Research, 26000009.
#222587 - $15.00 USD Received 5 Sep 2014; revised 31 Oct 2014; accepted 10 Nov 2014; published 18 Nov 2014 (C) 2014 OSA 1 December 2014 | Vol. 22, No. 24 | DOI:10.1364/OE.22.029456 | OPTICS EXPRESS 29464
