外文翻譯--高比特率傳輸系統(tǒng)中非線性失真的表征

1、<p><b>　　中文4940字</b></p><p>　　出處：Optical Communication Theory and Techniques. Springer US, 2005: 137-150</p><p>　　Characterization of Intrachannel Nonlinear Distortion in Ultra-

2、high Bit-rate Transmission SystemsInvited Paper</p><p>　　Robert I. Killey, Vitaly Mikhailov, Shamil Appathurai, and Polina Bayvel</p><p>　　Optical Networks Group, Department of Electronic and E

3、lectrical Engineering,</p><p>　　University College London, Torrington Place, London WC1E 7JE, UK</p><p>　　r.killey@ee.ucl.ac.uk</p><p>　　Abstract: Signal distortion due to intrachan

4、nel cross-phase modulation and four-wavemixing limits transmission distances in ultra-high bit-rate optical communications.To gain an understanding of the effects of nonlinear pulse interactions and to quantify the effec

5、tiveness of new methods to suppress them, accurate characterization techniques are required to isolate the effects of fibre nonlinearity from the other impairments which occur in transmission. In this paper, we discuss t

6、wo techniques: f</p><p>　　distortion (pulse timing jitter, amplitude fluctuations, and FWM-induced ‘ghost’pulse power) and, secondly, measurements of the BER-dependence on optical signal launch power. We des

7、cribe the use of these characterization methods to investigate the suppression of nonlinear distortion through the use of optimized dispersion maps, alternate-polarization and alternate-phase return-to-zero signal forma

8、ts.</p><p>　　Key words: dispersion management; optical fiber nonlinearity; four wave mixing; cross phase modulation.</p><p>　　INTRODUCTION</p><p>　　Limits to the transmission distan

9、ces achievable in high bit-rate systems are imposed by nonlinear refraction. The intensity modulation of the signals induces optical phase shifts due to the intensity-dependence of the refractive index of the transmissio

10、n fibres. In WDM systems with narrow channel spacing, the nonlinear refraction leads to interactions between channels through cross-phase modulation (XPM) and four-wave-mixing (FWM). As the channel bit-rate and channel w

11、avelength spacing is increa</p><p>　　As in the multi-channel case, the pulse overlap leads to cross-phase modulation</p><p>　　and four-wave-mixing. These effects were investigated experimentally

12、 and numerically in [1–10] and a number of methods have been proposed and demonstrated aimed at suppressing intrachannel nonlinear distortion, through optimization of the dispersion map and pre-compensation [11–16], the

13、use of optimized signal formats [17], in particular the use of phase modulated returnto-</p><p>　　zero formats [18–26], alternate-polarization RZ [27–29], subchannel multiplexing[30], polarization mode dispe

14、rsion-supported transmission [31] and channel precoding [32].</p><p>　　In this paper, we describe experimental and numerical techniques developed to characterize intrachannel cross-phase modulation and four-

15、wave-mixing in long-haul 40 Gbit/s systems. We explain how these techniques can be used to quantify the improvements in performance achievable using new methods, including optimized dispersion maps and novel modulation f

16、ormats.</p><p>　　2. CHARACTERIZING INTRACHANNEL NONLINEAR DISTORTION</p><p>　　One challenge faced in characterizing any physical effect in optical signal transmission is that of isolating it fro

17、m the numerous other effects which occur simultaneously. The goal of our research was to isolate and quantify the impact on the system performance of intrachannel XPM and FWM, separating it from other effects including a

18、mplifier noise, chromatic dispersion, polarization mode dispersion and transmitter and receiver patterning.</p><p>　　Methods of measuring the nonlinear distortion include direct BER and Qfactor</p>&l

19、t;p>　　measurements, and measurements of the signal eye diagrams and signal waveforms using sampling oscilloscopes, for a range of signal launch powers and transmission distances. In the following sections, simulations

20、 and experimental measurements of nonlinear pulse interactions in 40 Gbit/s transmission,carried out with the group’s recirculating fibre loop testbed, are described</p><p>　　2.1 Signal waveform distortion&l

21、t;/p><p>　　An effective method of characterizing the effects of intrachannel nonlinear distortion is the direct measurement or calculation of the signal waveform distortion after transmission. Three measures of

22、 distortion can be used: pulse timing jitter, resulting from XPM, pulse amplitude fluctuations arising from both FWM and XPM, and ‘ghost’ pulse power, transferred from the pulses to the zero bit slots through FWM. The ef

23、fectiveness of the use of novel signal formats and optimized dispersion maps in r</p><p>　　2.1.1 Optimization of pre-compensation</p><p>　　In our initial studies, timing jitter and ghost pulse p

24、ower were calculated for typical system parameters using the split-step Fourier algorithm for a single channel 40 Gbit/s link employing standard single-mode fibre (SMF), with dispersion D = 17 ps/(nm·km),fibre nonli

25、near coefficientγ=1.2（W.km)-1and lossα=0.21dB/km.Each</p><p>　　span comprised 60 km of SMF with dispersion compensating fibre following each span (Fig. 1) [8].</p><p>　　Figure 1. Transmission sy

26、stem with N spans, pre-compensation dispersion Dpre and residual dispersion per span Dres</p><p>　　Unchirped RZ pulses, which are more robust than NRZ [17], with 9 ps FWHM were transmitted, encoded with 25

27、6-bit random bit sequences. Ideal transmitter and receiver characteristics and the assumption of noiseless amplifiers allowed the investigation of distortion due solely to the fibre nonlinearity. The system considered wa

28、s a 12 span link, with each span exactly post-compensated by DCF and the optical launch power was 6 dBm.An effective technique to suppress intrachannel nonlinear effects is t</p><p>　　Figure 2. Intrachannel

29、cross-phase modulation (IXPM) timing jitter and intrachannel fourwave-</p><p>　　mixing (IFWM) power (normalised to peak power of ‘ones’) after transmission over 12 spans.</p><p>　　Figure 3. Opti

30、cal eye diagrams, with Dpre=1(left), –240 (centre) and –400 ps/nm (right).</p><p>　　The growth of the four-wave-mixing induced ghost pulse power was also calculated for the same systems. The plot shows that

31、this transmission impairment is also strongly dependent on the input signal waveform, with excessive pre-compensation leading to greater pulse overlap and hence increased FWM.As for the case of timing jitter, the ghost p

32、ulse power was minimized with precompensation at the transmitter of approximately -200 ps/nm. Fig. 3 shows the eye diagrams of the received signals for three</p><p>　　2.1.2 Alternate-polarization RZ format t

33、ransmission. </p><p>　　Following the simulations characterizing nonlinear pulse interactions in 40 Gbit/s transmis-sion, recirculating fibre loop experiments were carried out in which the timing and amplitud

34、e jitter, and ghost pulse power, were measured using a high speed sampling oscilloscope (Fig. 4) [28]. An optical time-division-multiplexing transmitter was used to obtain the 40 Gbit/s signal, allowing the effects of va

35、rying the relative states of polarization of adjacent pulses to be investigated.</p><p>　　Figure 4. Recirculating loop experimental set-up with optical time-division multiplexed transmitter (EAM – electroabs

36、orption modulator, SC-DCF – slope compensating dispersion compensating fibre, PC – polarization controller, AOM – acousto-optic modulator).</p><p>　　Standard single-mode fibre was employed, with the paramete

37、rs used in the simulations described in the previous section. The amplifier span length was 61 km and the signal launch power into each span was kept constant at 7 dBm. Multiple signal traces were measured, and the timin

38、g and amplitude jitter were extracted from the measured waveforms [28]. The measured values of jitter are plotted in Fig. 5. With parallel polarization states of the pulses, the increase in the experimentally observed ti

39、mi</p><p>　　The effect of using alternating pulse polarization states was to reduce δζ by 32 %, to 1.6 ps after 7 spans, and this was in good agreement with the reduction predicted by the split-step Fourier

40、 simulations. The XPM from adjacent pulses reduces by 2/3, assuming linear polarization is maintained during transmission,and reduced by approximately 1/2 if the polarization varies randomly. However,pulses spaced by two

41、 bit-slots are still co-polarised, and, as the pulses spread over multiple bit period</p><p>　　Figure 5. Experimental (left) and calculated (right) values of XPM-induced timing jitter with parallel (squares,

42、 dashed line) and orthogonal (circles, solid line) adjacent pulse polarization states.</p><p>　　Intrachannel four-wave mixing leads to the transferral of energy between the pulses, resulting in pulse amplitu

43、de distortion,δa 。After transmission over 7 spans, the increase in δa ，was 0.046, normalised to the average pulse amplitude (Fig. 6) [28]. The use of alternate polarization states was expected to be effective at reducing

44、 the amplitude distortion, as the FWM efficiency reduces to zero for waves with orthogonal polarization states. This was experimentally confirmed, with a reduction in δ</p><p>　　Figure 6. Experimental (left

45、) and calculated (right) values of FWM- and XPM-induced pulse amplitude distortion with parallel (squares, dashed line) and orthogonal (circles, solid line) adjacent pulse polarisation states.</p><p>　　2.1.3

46、 Alternate-phase RZ format transmission</p><p>　　The work of a number of groups has shown that alternate-phase return-to-zero (AP-RZ) signal format is effective in reducing the distortion caused by nonlinear

47、 pulse interactions [18,20–25]. To investigate this technique, a comprehensive set of experiments were carried out to characterize the effects of intrachannel XPM and FWM through measurements of the signal waveform, take

48、n with a sampling oscilloscope. The AP-RZ transmitter is shown in Fig. 7 [25].</p><p>　　Figure 7. AP-RZ transmitter</p><p>　　Conventional RZ and alternate-phase RZ, with a sinusoidal phase modul

49、ation with peak-to-peak amplitude of ∏ rad and a time period twice the bit period, were compared. Initially, the optimum values of pre-compensation were found through simulations, with 5 dBm launch power, which predict

50、ed that the optimum amount of pre-compensation is dependent on the format used. The values of -250 ps/nm and -100 ps/nm were optimum for the conventional RZ and AP-RZ formats respectively.</p><p>　　Next, the

51、 systems were experimentally tested using the recirculating fibre loop. The experimental set-up, shown in Fig. 8, employed two cascaded electro-absorption modulators (EAMs) driven by the 40 Gbit/s pattern generator (223

52、-1 PRBS)and a 40 GHz clock signal respectively, to generate an RZ signal with pulse width of approximately 11 ps [25]. A phase modulator driven by a 20 GHz clock signal was then used to impose a ∏ rad optical phase dif

53、ference between adjacent pulses to generate the AP-</p><p>　　with optimum values of dispersion determined by the simulations, were experimentally implemented by cascading appropriate lengths of normal and an

54、omalous dispersion fiber, ensuring that the cumulative dispersion over the entire transmission distance was zero. The signal power launched into the preand post-compensation was approximately 0 dBm.</p><p>

55、　　Figure 8. Experimental recirculating loop set-up with AP-RZ transmitter and precompensation</p><p>　　The received RZ and AP-RZ signal waveforms, back-to-back and after transmission over 240 km with 10 dBm

56、launch power, with and without precompensation,were measured using a high speed sampling oscilloscope. The waveform of the signals encoding the 11111011111 bit sequence at the input of the link is plotted in Fig. 9(a) [2

57、5]. The effect of intrachannel four-wave-mixing can be clearly seen in the waveforms after transmission in Figs. 9(b) and 9(c). With the conventional RZ format, the bit slot ca</p><p>　　Methods of characteri

58、zing nonlinear pulse interactions through the measurementand calculation of the distortion of the received signal waveforms have been described in this section. These techniques are useful in understanding the nonlinear

59、effects and demonstrating their suppression through optimized signal formats and dispersion maps. A second method of quantifying the nonlinear pulse interactions is to measure the effect of varying the signal launch powe

60、r on the received signal Q-factor and b</p><p>　　Figure 9. Experimentally measured 11111011111 bit sequence before and after transmission over 240 km of standard single-mode fibre with 10 dBm launch power s

61、howing the FWM induced ghost pulse and its suppression through the use of the AP-RZ signal format and optimized pre-compensation. (a) Output from transmitter. Signals after transmission: (b) RZ with no pre-compensation,

62、 (c) AP-RZ with no pre-compensation, (d) RZ with -250 ps/nm precompensation and (e) AP-RZ with -100 ps/nm pre-compensation</p><p>　　2.2 Characterizing nonlinear distortion using BER measurements</p>&

63、lt;p>　　In this method, the signal power launched into the spans is varied, and the range of launch powers which achieve a given bit-error rate, for example BER<10-9 after transmission over a given distance is recor

64、ded. If the optical signal-to-noise ratio (OSNR) is kept constant while the signal launch power is varied, the measured BER values give a clear indication of the effects of signal distortion due to fibre nonlinearity. H

65、ence, in these measurements, it is important to be able to vary the signa</p><p>　　by changing the coupling ratio between the 40 Gbit/s channel and the CW channels whilst keeping constant the pump currents o

66、f the loop EDFA and therefore its gain, total output power and noise figure [25].</p><p>　　2.2.1 Optimizing the dispersion map.</p><p>　　Fig. 10 shows a measurement of the range of launch powers

67、 for which BER<10-9 for a single channel 40Gbit/s system employing conventional RZ signal format, non-zero dispersionshifted fibre (NZ-DSF) with D = 4 ps/(nm.km), with a 75 km amplifier span length and span dispersion

68、 compensation following each span. The lower values of the launch power represent the noise limit, below which the OSNR at</p><p>　　the receiver was too low to achieve BER<10-9 Increasing the signal la

69、unch power into the amplifier spans until the BER increased to 10-9 at each distance allowed the tolerance of the signal format to nonlinear effects to be determined. The plot in Fig. 10 shows launch power limits wit

70、hout pre-compensation at the transmitter, and with optimum pre-compensation of -40 ps/nm following the transmitter. In both cases, optimized post-compensation was used at the receiver. While the lower limit o</p>

71、<p>　　keeping the OSNR constant allowed the cause of the improved performance,the suppression of the intrachannel nonlinear effects, to be verified.</p><p>　　Figure 10. Measured upper and lower limits o

72、n optical launch powers in 40 Gbit/s transmission over non-zero dispersion-shifted fibre to achieve BER<10-9 </p><p>　　2.2.2 BER measurements with alternate-phase RZ signal format</p><p>　　T

73、he same measurement technique was employed to investigate the improvement in performance in the transmission of the AP-RZ signals described in the previous section. The measured upper limits to the signal launch power fo

74、r the 40 Gbit/s RZ and AP-RZ transmission are shown in Fig. 11 [25]. It can be seen that with no pre-compensation, the alternate-phases of adjacent pulses in the AP-RZ format signals resulted in a 2.6 dB increase in the

75、nonlinearity limited launch power after 240 km compared to </p><p>　　Figure 11.Experimentally measured nonlinearity limited launch powers to achieve BER<10-9 in transmission over standard single-mode fib

76、re with pre-compensation values of 0, -100 and -250 ps/nm.</p><p>　　CONCLUSIONS</p><p>　　We have described how intrachannel nonlinear effects lead to distortionin ultra-high bit-rate transmissio

77、n systems, and discussed the importance of isolating and characterizing these effects to determine optimum design rules for the suppression of pulse interactions. Techniques for characterizing intrachannel XPM and FWM, i

78、ncluding the calculation and measurement of the signal waveform distortion and measurements of the received signal BER,were discussed and examples of the use of these characte</p><p>　　improvement in the per

79、formance of this novel signal format compared to conventional RZ.</p><p>　　Measurements of bit-error-rates for a range of optical launch powers and transmission distances were carried out to characterize non

80、linear pulse interactions in systems employing both standard SMF and non-zero dispersion shifted fibre, with a variety of signal formats and dispersion maps. In conventional RZ transmission over non-zero dispersion-shift

81、ed fibre, the use of optimum pre-compensation was shown to allow an increase in the transmission distance from 825 km to 1125 km with BER<10-9 The </p><p>　　ACKNOWLEDGMENTS</p><p>　　The fina

82、ncial support for this work from Nortel Networks, EPSRC and the Royal Society is gratefully acknowledged. We also thank Anritsu, Agilent, Yokogawa and SHF for the loan of test and measurement equipment used in the experi

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