Electronic dispersion compensation by signal predistortion using a dual-drive Mach-Zehnder modulator Robert I. Killey, Phillip M. Watts, Vitaly Mikhailov, Madeleine Glick, Polina Bayvel IRC-TR-04-28 March 2004
OFC
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Intel Research Cambridge
Electronic dispersion compensation by signal predistortion using a dual-drive Mach-Zehnder modulator Robert I. Killey1, Phillip M. Watts1, Vitaly Mikhailov1, Madeleine Glick2, Polina Bayvel1 1. Optical Networks Group, Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
[email protected] 2. Intel Research, 15 J.J. Thomson Avenue, Cambridge CB3 0FD, UK
Abstract: We propose the technique of signal predistortion using a dual-drive Mach-Zehnder modulator and nonlinear digital filters, and demonstrate compensation of 13600ps/nm, equivalent to 800 km of standard single mode fibre, at 10Gb/s. ©2005 Optical Society of America OCIS codes: (060.2360) Fiber optics links and subsystems; (060.4510) Optical communications
1. Introduction The use of electronic signal processing for the compensation of transmission impairments such as fibre dispersion removes the need for expensive and bulky optical components and offers adaptive compensation which will be required in future dynamic optical networks. In particular, digital techniques offer significant advantages in terms of the functionality and reproducibility of electronic dispersion compensation (EDC). Predicted future increases in speed and reduction in power consumption of CMOS-based DSPs, A/D and D/A converters [1, 2] will make the use of digital EDC increasingly feasible. Compensation at the receiver, using techniques such as feedforward equalization (FFE), decision feedback equalization (DFE) [3]-[5] and maximum likelihood sequence estimation (MLSE) [6, 7] have been shown to be effective in increasing the dispersion tolerance by up to a factor of two. However, the loss of the optical phase information, after direct detection of the intensity modulated signals, limits the amount of group velocity dispersion that can be effectively compensated [7, 8]. An alternative method, which we propose for the first time, is the use of electronic precompensation, in which the amplitude and phase waveforms of the transmitted signal are predistorted to achieve compensation of the fibre dispersion. While advanced phase modulated schemes such as prechirped NRZ and RZ extend the dispersion limit [9], the scheme we propose optimises the phase and amplitude of each pulse individually, depending on the sequence of the adjacent bits, offering significantly improved performance. We describe how a precompensating transmitter can be implemented using two digital electronic filters controlling a dual-drive Mach-Zehnder modulator, and propose a filter architecture based on a look-up table and a D/A converter. Results of simulations are presented, assessing the performance of the technique in compensating group velocity dispersion for 10 Gb/s transmission over standard single-mode fibre (SSMF) with dispersion of 17 ps/(nm.km). 2. Theory The precompensating transmitter, shown in Fig. 1, generates predistorted signals in such a way that the fibre dispersion reverses the distortion during transmission, resulting in the desired signal waveform at the receiver. Processor
D/A
Amp
d1
Input bit sequence 10110001…
Laser
ETX
Ein d2
Processor
D/A
MZM
Amp
Fig. 1 Proposed precompensating transmitter. If the signal is affected by the accumulated dispersion of the link, β2L, where β2 is the fibre dispersion and L is the length of the fibre, then the predistorted optical signal waveform, ETX(t) is found by
calculating the transmitted signal optical spectrum from the desired received signal spectrum, ERX(ω) = ETX(ω)exp(-iβ2ω2L/2), and taking the inverse Fourier transform of ETX(ω), where ETX and ERX are the electric fields of the transmitted and received optical signals respectively, and ω is the optical frequency. The predistorted signal is generated using a dual-drive Mach-Zehnder modulator, driven by voltages d1(t) and d2(t), as shown in Fig. 1. The output of the modulator is given by: ⎛ π (d1 (t ) − d 2 (t )) ⎞ ⎛ iπ (d1 (t ) + d 2 (t )) ⎞ ⎟⎟ ⎟⎟ exp⎜⎜ ETX (t ) = Ein cos⎜⎜ 2Vπ 2Vπ ⎠ ⎠ ⎝ ⎝
(1)
where Ein is the input to the modulator from a CW laser, assumed in the calculations described in the following sections to be a constant value. The drive voltages, d1(t) and d2(t), required to generate the predistorted waveform, ETX(t)=|ETX(t)|exp(iφ(t)), are found by rearranging (2): d 1 (t ) =
⎛ E (t ) ⎞ ⎞ Vπ ⎛⎜ φ (t ) + cos −1 ⎜⎜ TX ⎟⎟ ⎟ ⎜ ⎟ π ⎝ ⎝ E in ⎠ ⎠
d 2 (t ) =
⎛ E (t ) ⎞ ⎞ Vπ ⎛⎜ φ (t ) − cos −1 ⎜⎜ TX ⎟⎟ ⎟ ⎜ ⎟ π ⎝ ⎝ E in ⎠ ⎠
(2)
Feedback on the quality of the received signal from the receiver, in the form of Q-factor measurements or FEC measured error rate, can be used to optimize the amount of precompensation. Provided the transmission impairments do not vary rapidly, which is generally true for the chromatic dispersion of the transmission fibres, the amount of precompensation does not require rapid changes and the time delay in the feedback from the receiver does not affect the performance of the system. 3. Filter design and simulation results From (2), it can be seen that nonlinear filters are required to obtain d1 and d2. One possible implementation of the nonlinear digital filters, which we propose here, makes use of a look-up table stored in high speed SRAM (Fig. 2). memory Input bit sequence
n bit
10110001…
address
2n bit look-up table
output
m bit
D/A
Fig. 2 Proposed digital filter architecture. The incoming sequence of ones and zeros are stored in memory, and the D/A converter output voltage is set by the output word from the look-up table, addressed using the values of n consecutive input bits. The sample rate of the D/A converter is an integer multiple of the bit rate. The values stored in the look-up table are obtained from (2) for a signal waveform encoding a 2n-1 pseudorandom binary sequence (PRBS), in which the effect of the transmission impairments on the amplitude and phase of the centre bit of every possible sequence of n bits is determined. Simulations of the proposed system were carried out to assess the performance of the proposed technique in 10 Gb/s transmission systems for a range of SSMF fibre link lengths. In all the simulations described, the target signal format at the receiver was unchirped NRZ with 10-90% pulse rise- and fall-times of 30 ps. The outputs of the D/A converters were smoothed with 10 GHz Bessel filters, and the effects of fibre nonlinearity, ASE and D/A converter quantization noise were neglected. For each fibre length, the values to be stored in the look-up tables of the digital filters were calculated using (2) using a 2n-1 PRBS. The filters were then used to generate precompensated signals encoding 512 bit random sequences, and the effect of the fibre dispersion on the precompensated signals was calculated. The D/A converter sample rate was set at 4 samples/bit (40 Gsamples/s) and the dependence of the filter performance on the number of input bits, n, used to address the look-up table was investigated. Fig. 3 shows the eye-opening penalties vs transmission distance for n = 5, 9 and 13 bits. In the uncompensated case, an eye-opening penalty of 2 dB was reached after transmission over 80 km of SSMF (DL = 1360 ps/nm). With electronic precompensation, and with the transmitted waveform
optimised for each link length, this distance was increased to 273 km, 520 km and 802 km (DL = 4641, 8925 and 13634 ps/nm) with n = 5, 9 and 13 bits respectively.
Eye opening penalty (dB)
4 5 bit
9 bit
13 bit
3 1
2 0.5
1 0
0 0
200
400
600
800
1000
Time (50 ps/div)
Distance (km)
Fig. 3 Left: Eye-opening penalty versus SSMF length with no compensation (dashed line) and with compensation (solid lines) for n = 5, 9 and 13 bit look-up table addressing. Right: Received signal eye diagram following transmission over 700 km of SSMF (DL = 11900 ps/nm) with n = 13 bit look-up table addressing. Fig. 3 shows the compensated signal eye diagram following transmission over 700 km with n = 13 bits. Increasing the value of n further leads to an increase in the dispersion tolerance, although at the expense of larger memory capacity requirements. This predicted increase, by a factor of 10, of the dispersion tolerance demonstrates the potential of the proposed electronic precompensation scheme. In conclusion, we described a new method of electronic precompensation using a dual drive MachZehnder modulator, driven by nonlinear digital filters, based on look-up tables and D/A converters, to overcome distortion due to the group velocity dispersion of the transmission fibres. Simulation results demonstrated that the length of SSMF over which 10 Gbit/s signals could be transmitted with less than 2 dB EOP without optical compensation could be increased by a factor of 10, from 80 km to over 800 km. The technique is applicable to other types of signal format besides NRZ. References [1] P. Asbeck et al., ‘Digital signal processing – up to microwave frequencies’, IEEE Trans. Microwave Theory and Techniques 50, 3, pp. 900-909, March 2002. [2] C. –K. K. Yang, V. Stojanovic, S. Moditahedi, M. A. Horowitz, W. F. Allersick, ‘A serial-link transceiver based on 8GSamples/s A/D and D/A converters in 0.25-µm’, IEEE J. Solid-State Circuits 36, 11, pp. 1684-1692, Nov. 2001. [3] J. H. Winters and R. D. Gitlin, ‘Electrical signal processing techniques in long-haul fiber-optic systems’, IEEE Trans. Communications 38, 9, pp. 1439-1453, Sept. 1990. [4] F. Buchali, H. Bülow, W. Baumert, R. Ballentin, T. Wehren, ‘Reduction of the chromatic dispersion penalty at 10 Gbit/s by integrated electronic equalizers’, in Proc. Conference on Optical Fiber Communications (OFC 2000), vol. 3, pp. 268-270, Baltimore, MD. [5] J. Wang and J. M. Kahn, ‘Performance of electrical equalizers in optically amplified OOK and DPSK systems’, IEEE Photon. Technol. Lett. 16, 5, pp. 1397-1399, May 2004. [6] H. F. Haunstein, K. Sticht, A. Dittrich, W. Sauer-Greff, R. Urbansky, ‘Design of near optimum electrical equalisers for optical transmission in the presence of PMD’, in Proc. Conference on Optical Fiber Communications (OFC 2001), paper WAA4, Anaheim, CA. [7] M. Cavallari, C. R. S. Fludger, P. J. Anslow, ‘Electronic signal processing for differential phase modulation formats’, in Proc. Conference on Optical Fiber Communications (OFC 2004), paper TuG2, Los Angeles, CA. [8] M. G. Taylor, ‘Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments’, IEEE Photon. Technol. Lett. 16, 2, pp. 674-676, Feb. 2004. [9] N. Henmi, T. Saito and T. Ishida, ‘Prechirp technique as a linear dispersion compensation for ultrahigh-speed long-span intensity modulation direct detection optical communication systems’, J. Lightwave Technol. 12, 10, pp. 1706-1719, 1994.
