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160 JOURNAL OF NETWORKS, VOL. 5, NO. 2, FEBRUARY 2010 ps/nm pre-compensation, or if the improvement of one method is very high. a) b) c) Figure 3. Q gain [dB] with respect to the conventional receiver vs. residual dispersion [ps/nm] for the combined method MEAN + MSPE with different pre-compensations and a) 4 dBm, b) 6 dBm and c) 8 dBm average fibre input power. C. Summary The performance of three strategies for compensation of phase noise effects: the compensation of the mean nonlinear phase shift, the multi-symbol phase estimation and the combination of both methods for 43 Gbit/s RZ- DQPSK multi-span transmission was obtained by Monte- Carlo simulations for various dispersion maps and different fibre input powers. In general, all three methods exhibit the same optimum dispersion map with respect to the residual dispersion as is given for the conventional receiver. Thus, it is not required to change the dispersion map if receivers are upgraded with one of these phase noise compensation methods. Furthermore, it was shown that the MEAN is most efficient for systems with high performance loss due to the influence of nonlinearities and therefore also for non-optimised dispersion maps (0.9 dB Q gain for 6 dBm input power and 2.3 dB for 8 dBm with 38 ps/nm residual dispersion). The improvement of this method for systems with low influence of nonlinearities however is very poor (0.35 dB Q gain for 4 dBm with 38 ps/nm residual dispersion). The Q gain of MSPE is almost independent of the dispersion map that is used. The maximum Q gain decreases with increasing fibre input power (1.4 dB Q gain for 4 dBm input power, 0.9 dB for 6 dBm and 0.7 dB for 8 dBm with 38 ps/nm residual dispersion). The improvement of the combination of MEAN and MSPE is approximately equal to the sum of the improvement from each individual method (1.8 dB Q gain for 4 dBm input power, 1.9 dB for 6 dBm and 2.7 dB for 8 dBm with 38 ps/nm residual dispersion). Therefore, depending on the system setup, it has to be decided if the additional gain of implementing both methods, MEAN and MSPE, is reasonable. © 2010 ACADEMY PUBLISHER III. ELECTRONIC EQUALIZERS IN COHERENT PSK-RECEIVERS In a second part we investigate electronic equalization in coherent receivers in combination with multi-level modulation and nonlinear fiber effects. The next bitrate in the Ethernet hierarchy is expected to be 100Gb/s. For this bitrate, multi-level modulation formats should be used to reduce the bandwidth requirements. In conjunction with a coherent receiver the multi-level formats can be detected in the electrical domain with digital signal processing (DSP), due to the availability of high-speed digital signal processors. Similarly carrier and phase recovery as well as the equalization can be achieved with DSP [5]. A. Simulation Setup At the transmitter side either 53.5GBaud RZ-QPSK [6], 35.7GBaud RZ-8PSK [7] or 26.75GBaud Star-RZ- 16QAM are generated to achieve 107Gb/s for all modulation formats according to Fig. 4 (top). Star-RZ- 16QAM is generated from RZ-8PSK with an additional Mach-Zehnder modulator (MZM). The advantage of this setup is the necessity of only binary driving signals, contrary to multi-level driving signals in the case of pure I/Q-modulation. All data signals are differentially encoded due to the phase ambiguity of the carrier recovery. The transmission channel is modelled as a single span with variable length to adjust the chromatic dispersion (CD). A linear channel (only CD, D=17ps/nm/km) as well as a nonlinear channel (self-phase-modulation (SPM) and CD, γ=1.6215 1/W/km, α=0.21dB/km, Pfiber in, average=5dBm) is assumed. At the receiver side an EDFA with a Gaussian optical bandpass filter (BP, f3dB= 4.1x Baudrate) is used for noise loading. The received signal is combined with the signal of a local oscillator (LO) in a 2x4 90º hybrid (for this contribution ideal homodyne detection is assumed) and detected with two balanced photo-detectors. Afterwards the resulting electrical inphase and quadrature signals are lowpass (LP) filtered (Butterworth 3 rd order, f3dB= 1x Baudrate), sampled twice per symbol and then processed in a digital signal processing unit (fig. 5). CW laser SSMF RZ pulse train MZM clock Var. att. 3 dB coupler EDFA BP LO data 1 MZM MZM 90º data 2 90º Hybrid 3 dB coupler RZ-QPSK Inphase component LP LP data 3 PM Quadrature component data 4 MZM RZ-8PSK Star- RZ-16QAM ADC X r X i EDC & phase estimation DSP data' 1 data' 2 data' 3 data' 4 Figure 4. Transceiver (top), channel and receiver (bottom) setup; PM: Phase Modulator. For EDC, linear transversal filters for all investigated equalizers are used. The performance of equalizers with only a feed forward filter (FFE[x], where x denotes the
JOURNAL OF NETWORKS, VOL. 5, NO. 2, FEBRUARY 2010 161 number of filter coefficients) and with an additional decision feedback equalizer (DFE[x], where feedback of the decision to the EDC is necessary (Fig. 5) are examined. The equalizer has a complex baseband structure and the coefficients are determined with a zeroforcing (ZF) approach based on the MMSE criterion with the use of a training sequence [8]. The symbol decision in the DSP is made on phases with an additional decision on the amplitude for Star-RZ- 16QAM. After decision the differential decoding and mapping into two, three or four data streams (depending on the modulation format) takes place. x r x i EDC y r y i phase estimation decoding mapping data' 1 data' 2 data' 3 data' 4 Figure 5. Digital signal processing unit for a 16-level modulation format. B. Simulation Results Fig. 6 shows the OSNR penalty at a BER of 10 -4 versus CD without EDC for all modulation formats for the linear and nonlinear channel. Due to the short transmission distances the effective nonlinear length is small and therefore the influence of the nonlinear effects is small as well. The dispersion tolerance for RZ-QPSK (53.5GBaud) and RZ-8PSK (35.7GBaud) is almost equal. Obviously the expected improvement due to the reduced bandwidth of RZ-8PSK is just compensated for by the narrower symbol spacing. For Star-RZ-16QAM (26.75GBaud) the bandwidth is reduced further, whereas the minimum distance of the double-ring constellation is reduced only slightly compared to RZ-8PSK. w/o EDC linear nonlinear 5dBm Figure 6. OSNR penalty vs. CD without EDC for RZ-QPSK, RZ- 8PSK and Star-RZ-16QAM for the linear (solid) and the nonlinear (dashed) channel with 5dBm input power. Now, EDC with the ZF-equalizer for the linear channel is applied (Fig. 7). First of all an improvement of at least one order of magnitude can be observed (note the abscissa scales of Fig. 6 and 7). Comparing the various modulation formats the dispersion tolerance increases with decreasing bandwidth of the format. For each modulation format the dispersion tolerance can be enlarged further by increasing the equalizer filter length. For Star-RZ-16QAM e.g. the dispersion tolerance at 2 dB OSNR penalty can be increased from ±550ps/nm with FFE[9] to greater than ±800 ps/nm with FFE[15]. © 2010 ACADEMY PUBLISHER However in general the overall improvement with an additional DFE is rather small. b) FFE[15] DFE[0] DFE[2] FFE[9] DFE[0] DFE[2] Figure 7. OSNR penalty vs. CD for the linear channel for RZ-QPSK, RZ-8PSK and Star-RZ-16QAM for a) FFE[9] and b) FFE[15] without DFE (DFE[0], solid) and with DFE 2 nd order (DFE[2], dashed). Fig. 8 depicts the performance of the ZF-equalizer for the nonlinear channel. For RZ-QPSK and RZ-8PSK the performance is almost the same as for the linear case. However for Star-RZ-16QAM the dispersion tolerance degrades compared to the linear case. Here the equalizer design has to consider the different SPM induced nonlinear phase shifts of the two amplitude rings. a) a) b) FFE[9] DFE[0] DFE[2] FFE[15] DFE[0] DFE[2] Figure 8. OSNR penalty vs. CD for the nonlinear channel with 5dBm input power for RZ-QPSK, RZ-8PSK and Star-RZ-16QAM for a) FFE[9] and b) FFE[15] without DFE (DFE[0], solid) and with DFE 2 nd order (DFE[2], dashed). The determined coefficients are a compromise for the compensation of both phase shifts. Thus for such multiring constellations equalization should be supported by a
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