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Mar 30, 2006 - processing (DSP) can remove the need for optical chromatic disper- sion compensation, either through pre-distortion at the transmitter. [3, 4] or ...

Optimum electronic dispersion compensation strategies for nonlinear transmission

100% (all at the transmitter) is investigated, with the total dispersion compensation equal to the dispersion of the fibre (16 320 ps nm1).

S.J. Savory

Nonlinear simulation: Nonlinear simulations of a single-channel system (l ¼ 1550 nm) were carried out using the split-step Fourier algorithm, with the BER and Q estimated using 1024 data bits (NRZ format) at 10 Gbits. (10 Gbit=s was chosen due to the emergence of 20 GSa=s DSP.) The fibre was standard singlemode fibre (a ¼ 0.25 dB km1, Aeff ¼ 80 mm2, D ¼ 17 ps nm1 km1) with the signal with amplifiers having a noise figure 4.5 dB and gain 20 dB, resulting in Gaussian optical noise. The power was swept from 10 to 5 dBm in steps of 0.5 dB. This was then repeated for various values of pre-compensation. Fig. 2 shows the results of the nonlinear simulations as a colour map of 20 log(Q), with the lighter colours corresponding to improved performance. From Fig. 2, it can be seen that the maximum value of Q ¼ 21.9 dB is obtained when the compensation is shared equally between the transmitter and receiver (50% precompensation), and the launch power is 1 dBm. This indicates that there is an optimum value for the pre-compensation.

Digital signal processing combined with either pre-distortion at the transmitter or coherent detection at the receiver can eliminate penalties due to fibre dispersion. The nonlinearity of transmission fibre results in an optimal balance of pre-distortion and receiver equalisation.

Introduction: It is well established that the nonlinear performance of an optical transmission system can be improved by managing the dispersion [1, 2]. Recent developments have shown that digital signal processing (DSP) can remove the need for optical chromatic dispersion compensation, either through pre-distortion at the transmitter [3, 4] or using receiver equalisation with coherent detection [5]. These techniques exploit the fact that chromatic dispersion operates linearly on the optical field, enabling 10 Gbit=s transmission over 5120 km of standard dispersion (G652) fibre with no inline optical dispersion compensation [3]. The lack of inline dispersion compensation results in the optical waveform being highly dispersed and therefore more susceptible to fibre nonlinearities. To reduce the impact of nonlinearities, we propose to use both pre-distortion at the transmitter and equalisation with a coherent receiver. This will result in an optimum electronic dispersion compensation strategy for nonlinear transmission, a concept that will be investigated in this Letter.

Fig. 1 Schematic of transmission system under consideration Pre-comp and post-comp model pre-distortion at transmitter and equalisation with coherent receiver, respectively 100 20

Fig. 3 Effect of pre-compensation on optimum launch power obtained by fitting (1) to simulation data with typical RMS error of 0.5 dBQ

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optimum (dBQ = 21.9)

dBQ = 20 log(Q )

pre-compensation, %

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16 14 12 10

20 8

0 -10

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launch power, dBm

Fig. 2 Colour map dBQ ¼ 20 log(Q) as launch power and pre-compensation are varied Maximum Q obtained for 50% pre-compensation

Methodology: The impact of transmitter pre-distortion and receiver equalisation is investigated for nonlinear propagation over 960 km (12  80 km spans) of standard singlemode fibre, with no inline optical dispersion compensation. As the key concern is nonlinear propagation, the impact of the digitisation will be neglected, enabling the model to be simplified. We assume the electrical signals in the transmitter and receiver are proportional to the optical field. This allows the transmitter pre-distortion and receiver equalisation to be modelled in the optical domain as lossless linear dispersion compensating elements combined with a conventional intensity modulated=direct detection transceiver (IM=DD), as shown in Fig. 1. In this Letter the impact of pre-compensation, from 0% (all at the receiver) to

Fig. 4 Two extremes of performance, indicating 4.3 dB improvement by exploiting pre-distortion and receiver equalisation The Figure gives excellent agreement with proposed analytical model

Analysis of results: The impairments due to nonlinear propagation are characterised by the optimum launch power for a particular value of pre-compensation. To determine the optimum launch power, it is beneficial to fit an analytical curve to the simulation data. At low powers, the system is linear Q2 / P (where P is the launch power); however, at high powers it behaves as Q2 / 1=P x where x > 1. We therefore propose to fit a curve of the form

ELECTRONICS LETTERS 30th March 2006 Vol. 42 No. 7

1 1 Px þ ¼ 2 Q aP b

ð1Þ

where a, b and x are constants to be determined. For a curve of the form of (1) the maximum value of Q2 corresponds to the optimum launch power, which is given by  ð1=xþ1Þ b ð2Þ Popt ¼ xa We determined the optimum launch power from the results shown in Fig. 2 as a function of pre-compensation, as shown in Fig. 3. It can be observed that there is an optimum value for pre-compensation of 50%, the two extremes of performance corresponding to 100 and 50% precompensation, giving the worst and best performances, respectively. The performance against launch power is shown for these two cases in Fig. 4. By comparing the two curves, we note that there is a 4.3 dB benefit in exploiting both transmitter pre-distortion and receiver compensation (50% pre-compensation) compared to the case of using only transmitter pre-distortion (100% pre-compensation). To determine if it is always optimal to share the compensation we investigated the cases of 0, 50 and 100% pre-compensation for a number of additional systems, summarised in Table 1. In each case 50% pre-compensation was found to offer improved performance over 0 and 100% precompensation, revealing that it is optimal to use both transmitter pre-distortion and receiver equalisation.

Table 1: Nonlinear improvement in launch power afforded using 50% pre-compensation compared to 100% pre-compensation for additional systems (with 0% pre-compensation being marginally better than 100%)

compensation. The optimum strategy for both WDM and singlechannel propagation is to share the electronic compensation between the transmitter and receiver. Acknowledgments: The author thanks P. Bayvel and R. Killey for valuable discussions, and EPSRC and the EU NOBEL project for financial support. # IEE 2006 Electronics Letters online no: 20063903 doi: 10.1049/el:20063903

S.J. Savory (Optical Networks Group, Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom) E-mail: [email protected] References 1 2

3 4

Bit rate Channels Distance Nonlinear (Gbit=s) (25 GHz spacing) (km) improvement (dB) 10

5

960

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1

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Frignac, Y., Antona, J.-C., Bigo, S., and Hamaide, J.-P.: ‘Numerical optimization of pre- and in-line dispersion compensation in dispersionmanaged systems at 40 Gbit/s’. Proc OFC 2002, Paper ThFF5 Lenihan, A.S., Sinkin, O.V., Marks, B.S., Tudury, G.E., Runser, R.J., Goldman, A., Menyuk, C.R., and Carter, G.M.: ‘Nonlinear timing jitter in an installed fiber network with balanced dispersion compensation’, IEEE Photonics Technol. Lett., 2005, 17, (7), pp. 1558–1560 McNicol, J., O’Sullivan, M., Roberts, K., Comeau, A., McGhan, D., and Strawczynski, L.: ‘Electrical domain compensation of optical dispersion’. Proc OFC 2005, Paper OThJ3 Killey, R.I., Watts, P.M., Mikhailov, V., Glick, M., and Bayvel, P.: ‘Electronic dispersion compensation by signal predistortion using digital processing and a dual-drive Mach–Zehnder modulator’, IEEE Photonics Technol. Lett., 2005, 17, (3), pp. 714–716 Taylor, M.G.: ‘Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments’, IEEE Photonics Technol. Lett., 2004, 16, (2), pp. 674–676

Conclusions: The nonlinearity of the fibre results in an optimum compensation strategy when relying solely on electronic dispersion

ELECTRONICS LETTERS 30th March 2006

Vol. 42 No. 7

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