Coherent superposition of light waves has long been used in various fields of science, and recent advances in digital coherent detection and space-division multiplexing have enabled the coherent superposition of information-carrying optical signals to achieve better communication fidelity on amplified-spontaneous-noise limited communication links. However, fiber nonlinearity introduces highly correlated distortions on identical signals and diminishes the benefit of coherent superposition in nonlinear transmission regime. Here we experimentally demonstrate that through coordinated scrambling of signal constellations at the transmitter, together with appropriate unscrambling at the receiver, the full benefit of coherent superposition is retained in the nonlinear transmission regime of a space-diversity fiber link based on an innovatively engineered multi-core fiber. This scrambled coherent superposition may provide the flexibility of trading communication capacity for performance in future optical fiber networks, and may open new possibilities in high-performance and secure optical communications.
© 2012 OSA
Modern optical fiber communication has become the backbone of the internet era, thanks to breakthroughs such as low-loss optical fiber, the erbium-doped fiber amplifier, and wavelength-division multiplexing (WDM). As internet communication demands continue to increase exponentially, the once thought unlimited fiber bandwidth is facing a “capacity crunch”. To sustain the growth of communication capacity, spectrally efficient modulation formats such as polarization-division multiplexed (PDM) quadrature phase shift keying (QPSK) have recently been introduced to optical fiber communications [1, 2]. The success of these phase-encoded signals is based on digital coherent detection which allows for the full recovery of the E-field of the optical signal. To further increase the fiber communication capacity, space-division multiplexing (SDM) is considered a promising new technology [3–6]. Record per-fiber capacities of 112 Tb/s  and 305 Tb/s  have been demonstrated using SDM in multi-core fiber (MCF). An aggregate spectral-efficiency-distance-product of 40,320 km⋅b/s/Hz  and an intrachannel spectral-efficiency of 60 b/s/Hz  have also been experimentally demonstrated using a single MCF.
Coherent superposition of light waves has long been known, most notably through Young's double-slit interference experiment  dating back to 1803, which helped to establish the principle of wave-particle duality. Recent advances in digital coherent detection and SDM have enabled the digital coherent superposition (DCS) of information-carrying optical signals, which are identical at the transmitter and are space-diversified in a single MCF, to achieve better communication fidelity in link-budget-stressed applications . The signal quality after DCS was found to be improved in the amplified spontaneous noise (ASE) limited case, with the resulting optical signal-to-noise ratio (OSNR) being proportional to the number of superimposed signals. This phenomenon reflects the well-known diversity gain exploited in wireless communications, including multiple-input-multiple-output (MIMO) systems . However, optical transmission systems are plagued by fiber nonlinearity, resulting in highly correlated distortions on the various signal copies transmitted for diversity, which diminishes the benefit of the DCS in the nonlinear transmission regime . We show that the correlation among the nonlinear distortions of the superimposing signals can be effectively eliminated and the full benefit of coherent superposition can be retained in the nonlinear regime by scrambling the signal constellations at the transmitter and unscrambling them after transmission prior to coherent superposition. We refer to this scheme as scrambled coherent superposition (SCS), which may also mitigate other correlated and uncorrelated signal distortions, resulting from effects such as inter-symbol interference, receiver thermal noise, and quantization noise. Both SCS and DCS are naturally compatible with the emerging class of MCF-based SDM transmission, as the transit times among the different cores are essentially the same, allowing for a natural application of the concept of coherent superposition.
2. Principle of scrambled coherent superposition
The implementation of SCS or DCS in a SDM optical fiber transmission system (Fig. 1(a) ) is similar to that of single-input-multiple-output (SIMO) transmission in wireless communications. SIMO can be considered as a degenerate case of MIMO, which has revolutionized wireless communications  and was suggested for use in optical communications . Optical SIMO detection has also been proposed to be implemented in the optical domain through the use of adaptive optical phase and time shifters . Unlike SIMO and DCS, where the transmitted signals are identical, the individual transmitted signals in SCS are different from each other in that they contain scrambled versions of a same data sequence using a pre-determined scrambling function. The optical transmitter considered in this proof-of-concept experiment is a PDM Cartesian modulator (Fig. 1(b)) that is capable of modulating the real and imaginary parts of each of the two orthogonal polarization components of an optical carrier to form a 128-Gb/s PDM-QPSK signal (Fig. 1(c)). The fiber link consists of MCF spans with fan-out connectors to standard single-mode fibers (Fig. 1(d)). The cross section of a seven-core fiber is shown in Fig. 1(e). Erbium-doped fiber amplifiers are used to compensate for the transmission loss. At the receiver, digital coherent detection (Fig. 1(f)) is used to convert the E-fields of two orthogonal polarization components of each received SDM signal to the digital domain. A digital signal processor is then used to compensate for linear transmission impairments such as chromatic dispersion, and to phase-align all the signals. For SCS, the phase alignment process involves the unscrambling of the constellation of each recovered signal field (), i.e., dividing the received field by its corresponding scrambling function , before performing the coherent superposition (Fig. 1(g)).
3. Correlation and de-correlation of nonlinear distortions
To emulate the scrambling, seven signals (where n = 1,2…7) are delayed copies of an original signal, which is encoded with a pseudo random bit sequence (PRBS) of length 215-1 The delays are introduced at the transmitter through different optical delays, and known at the receiver through offline signal processing. Note that the scrambling functions can be short PRBSs. In this work, the scrambling functions are simply the delayed signal fields divided by the original signal field . These signals are space-diversified and transmitted over a 76.8-km seven-core fiber in a re-circulating loop configuration. In practice, the outputs of the MCF need to measured simultaneously. Due to the limited experimental resource in this proof-of-concept experiment, we use one coherent receiver to measure the outputs sequentially and store their E-fields. We then process the stored E-fields in an offline digital signal processor. The optical fields of all the received signals are first processed individually to compensate for the channel response and the frequency and phase offsets between the transmit laser and the receiver’s local oscillator laser. The recovered signal fields of all the SDM signals are then unscrambled, through division by their corresponding scrambling functions (or keys) , before being synchronized, phase-aligned , and coherently superimposed to obtain a reconstructed version of the original signal, , which is expected to have improved fidelity compared to that obtained with DCS, (Fig. 1(g)), as will be shown later. The number of superposed signals (m) can be varied as desired.
In the absence of fiber nonlinearity, the capacity of an optical channel is determined by the OSNR, as governed by the Shannon limit . It has been found that in the presence of fiber nonlinearity, nonlinear signal-to-signal and single-to-noise interactions impose a lower capacity limit, which is often referred to as the nonlinear Shannon limit [17–19]. The dominating nonlinear interaction is the signal-to-signal interaction originating from four-photon mixing or four-wave mixing (FWM) [20–22]. For identical signals transmitted over optical fiber links with similar physical parameters such as nonlinearity and dispersion, as in the case of DCS , the nonlinear distortions on these signals tend to be identical. To verify this, we plot the distortion (or deviation from the original signal) on the real part of the received signal from core 1 after SDM transmission over the 76.8-km MCF as a function of that from core 2. The correlation can be quantified by using Pearson's correlation coefficient (ρ) between two real variables x and y, which is defined as the covariance of the two variables divided by the product of their standard deviations and , orFig. 2(a) ). Note that the partial decorrelation is due to ASE noise induced signal distortions, which are uncorrelated. At an increased signal power of 10 dBm per core, the distortions become highly correlated with ρ~0.9 (Fig. 2(b)), confirming the correlated nature of the dominating signal-to-signal nonlinear interaction. Remarkably, with the scrambling of the signal constellations (by introducing a delay of 100 symbols between the two signals), the correlation coefficient is dramatically reduced from 0.9 to ~0.004 (Fig. 2(c)).
To illustrate the potential benefit of the constellation scrambling in coherent superposition, we assume that three signals are superimposed in a transmission system where the variance of the ASE noise induced linear distortions () equals that of the nonlinear distortions () for each signal. In the case of DCS (Fig. 2(d)), the ASE-noise contribution to the final signal variance () is reduced by a factor of three as the noises add incoherently and the signals add coherently, but the nonlinearity contribution to remains the same as both signals and nonlinear distortions are highly correlated. On the other hand, in the case of SCS (Fig. 2(e)), both the ASE-noise contribution and the nonlinearity contribution are reduced by a factor of three as the nonlinear distortions also add incoherently. The final signal variance after SCS is thus half of that after DCS, showing the benefit of the constellation scrambling in achieving the full potential of coherent superposition.
4. Theoretical performance gain
It is useful to find a closed-form solution for the improvement on signal quality brought by SCS. Commonly, the signal quality is quantified by the Q2-factor19, 23], we can express the Q2-factor asFig. 3(a) . The number of superimposed signals (m) for DCS and SCS is fixed at 3. Evidently, SCS provides better signal quality than DCS in the nonlinear transmission regime, especially when.
5. Experimental setup and results
To experimentally assess the performance gain of SCS over DCS in long-haul optical transmission, we perform a multi-MCF span experiment where one 76.8-km span of a 7-core fiber is placed inside a re-circulating loop  and optical signals are transmitted over a distance of 2688 km, corresponding to 35 spans of MCF. Ten 50-GHz-spaced 128-Gb/s PDM-QPSK channels in the wavelength range between 1550 nm and 1554 nm are generated with de-correlation between even and odd channels, before being launched into the seven-core-fiber link. A 7-by-1 optical switch is used to sequentially direct the seven outputs from the link to a wavelength selective switch, where the center WDM channel at 1552 nm is selected for digital coherent detection. Each sampled waveform contains 1 million samples at 80 GS/s. As all the signals of the center channel exiting from the seven cores contain the same repetitive patterns, they can be stored and processed offline to find their relative delays (using known pilot symbols) in this proof-of-concept experiment. Figure 3(b) shows the measured Q2 factor, derived from the measured BER, as a function of the signal launch power per core for three cases, (i) without coherent superposition, (ii) with DCS (m = 3), and (iii) with SCS (m = 3). The experimental results (Fig. 3(b)) are in reasonably good agreement with the theoretical results (Fig. 3(a)). At 4-dBm signal launch power per core, or ~4 dB higher than P0, the recovered signal constellation after SCS (Fig. 3(c)) is much clearer than that recovered after DCS (Fig. 3(d)), visualizing the performance gain of SCS over DCS.
Figure 4(a) shows the signal quality improvement as a function of the number of superimposed signals for SCS and DCS. When m signals are superimposed, they are coming from cores 1 to m as labeled in Fig. 1(e). Thanks to the low crosstalk among the cores, the transmission performances of the seven cores of the MCF are very similar. The optimum signal launch power per core without coherent superposition is ~0 dBm, at which the Q2 factor is 7.9 dB. After SCS with m = 2, the signal Q2 factor is increased by nearly 3 dB. Note that the performance improvement comes at the expense of halved SDM transmission capacity, but SCS provides the flexibility to trade capacity for performance (or transmission distance), and can be valuable in applications where the link budget is insufficient to achieve a desired transparent reach. Note also that simply reducing the modulation speed by half may not provide as large a Q2 factor improvement because the optimum signal power is usually reduced as the modulation speed is reduced (due to a lower dispersive effect and stronger FWM strength, resulting from the smaller spectral extent of the speed-reduced signal). For example, when the data rate of a PDM-QPSK signal is halved from 85.4 Gb/s to 42.7 Gb/s, the optimum signal launch power is reduced by ~2 dB and the Q2 factor improvement is only ~1 dB . With the increase of the number of superimposed signals, the measured performance gain of SCS increases at a rate close to that predicted by theory, and is substantially higher than that obtained with DCS (Fig. 4(a)). The measured performance gains by SCS are slightly smaller than that predicted by the simple theory, probably due to imperfect scrambling of the signal patterns in the cores. The recovered signal constellations after SCS with m = 2, 3, and 5 (Fig. 4(b)-4(d)) are shown in comparison with those after DCS with m = 2, 3, and 5 (Fig. 4(e)-4(g)), again visualizing the additional performance gains of SCS over DCS.
6. Discussion and conclusion
The proposed technique of scrambled coherent superposition is naturally compatible with the emerging class of multi-core fiber and few-mode-fiber based space-division multiplexed transmission systems. The concept of SCS can also be readily applied to orthogonal frequency division multiplexing based transmission  by performing constellation scrambling in the frequency dimension. Furthermore, a more secured communication link can be established by limiting the individual performances of the SDM signals to be much below the forward-error correction threshold such that meaningful communication can only be achieved by SCS of multiple SDM signals, which may arrive at the same receiver from different spatial paths. The communication security can be further increased by using quantum key distribution [26–28] to distribute the scrambling functions or keys used in SCS. This scrambled coherent superposition may thus provide the flexibility of trading communication capacity for performance and/or security in future optical fiber networks.
References and links
1. P. J. Winzer and R.-J. Essiambre, “Advanced optical modulation formats,” Proc. IEEE 94(5), 952–985 (2006). [CrossRef]
2. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010). [CrossRef]
3. A. R. Chraplyvy, “The coming capacity crunch,” in Proceedings of the2009European Conference on Optical Communication (Vienna, Austria), Plenary Talk.
5. M. Nakazawa, “Giant leaps in optical communication technologies towards 2030 and beyond,” in Proceedings of the2010European Conference on Optical Communication (Turin, Italy), Plenary Talk.
7. B. Zhu, T. F. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “112-Tb/s Space-division multiplexed DWDM transmission with 14-b/s/Hz aggregate spectral efficiency over a 76.8-km seven-core fiber,” Opt. Express 19(17), 16665–16671 (2011). [CrossRef] [PubMed]
8. J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proceedings of the 2012 Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 2012), PDP5C.1.
9. S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. C. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “WDM/SDM transmission of 10 x 128-Gb/s PDM-QPSK over 2688-km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 40,320 km·b/s/Hz,” Opt. Express 20(2), 706–711 (2012). [CrossRef] [PubMed]
10. X. Liu, S. Chandrasekhar, X. Chen, P. J. Winzer, Y. Pan, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, “1.12-Tb/s 32-QAM-OFDM superchannel with 8.6-b/s/Hz intrachannel spectral efficiency and space-division multiplexed transmission with 60-b/s/Hz aggregate spectral efficiency,” Opt. Express 19(26), B958–B964 (2011). [CrossRef] [PubMed]
11. T. Young, “Experimental demonstration of the general law of the interference of light,” Philos. Trans. R. Soc. Lond. 94, 1-16.(1804).
12. X. Liu, S. Chandrasekhar, A. H. Gnauck, P. J. Winzer, A. R. Chraplyvy, B. Zhu, T. Taunay, and M. Fishteyn, “Performance improvement of space-division multiplexed 128-Gb/s PDM-QPSK signals by constructive superposition in a single-input-multiple-output configuration,” in Proceedings of the 2012 Optical Fiber Communication Conference (Optical Society of America, Washington, DC, 2012), OTu1D3.
13. G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Tech. J. 1(2), 41–59 (1996). [CrossRef]
15. S. Naderi Shahi and S. Kumar, “Reduction of nonlinear impairments in fiber transmission system using fiber diversity,” in Proceedings of the 2011 OSA Summer Topical Meeting on Signal Processing in Photonic Communications (Toronto, Canada), SPWA3.
16. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
19. W. Shieh and X. Chen, “Information spectral efficiency and launch power density limits due to fiber nonlinearity for coherent optical OFDM system,” IEEE Photon. J. 3(2), 158–173 (2011). [CrossRef]
20. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, “Four-photon mixing and high speed WDM systems,” J. Lightwave Technol. 13(5), 841–849 (1995). [CrossRef]
21. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, and A. H. Gnauck, “Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses,” IEEE Photon. Technol. Lett. 13(5), 445–447 (2001). [CrossRef]
22. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press 2007).
23. A. Carena, G. Bosco, G. V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proceedings of the 2010 European Conference on Optical Communication (Turin, Italy), P4.07.
24. D. M. Millar, S. Makovejs, V. Mikhailov, R. I. Killey, P. Bayvel, and S. J. Savory, “Experimental comparison of nonlinear compensation in long-haul PDM-QPSK transmission at 42.7 and 85.4 Gb/s,” in Proceedings of the 2009 European Conference on Optical Communication (Vienna, Austria), paper 9.4.4.
25. X. Liu, S. Chandrasekhar, A. H. Gnauck, P. J. Winzer, S. Randel, S. Corteselli, B. Zhu, T. Taunay, and M. Fishteyn, “Digital coherent superposition for performance improvement of spatially multiplexed 676-Gb/s OFDM-16QAM superchannels,”in Proceedings of the 2012 European Conference on Optical Communication (Amsterdam, Netherlands), paper Tu.3.C.2 (2012).
28. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single photon detectors,” Nat. Photonics 1(6), 343–348 (2007). [CrossRef]