Optical cross-connects (OXC) introduce crosstalk and intersymbolic interference due to filtering in the optical signal. We show experimentally and by simulation that higher optical signal-to-noise ratio (OSNR) penalties are obtained for the combined effect of both impairments compared to the sum of the penalties taken independently. Furthermore, the Modified Chernoff Bound is applied for performance estimation, with good accuracy and fast computation time. By using the correct OSNR penalty, the maximum number of cascaded OXC is reduced by 17% relatively to when the penalties are considered separately, for a 2 dB maximum penalty.
©2009 Optical Society of America
Optical cross-connects (OXC) are being adopted in optical networks, enabling traffic to be switched in the optical domain, providing flexibility, and avoiding the costly optical-electrical-optical (OEO) conversions. However, each OXC reduces the available bandwidth of switched signals and introduces in-band crosstalk between channels due to limited isolation . At the end of the transmission link, the optical signal accumulates a number of crosstalk interferers and is severely filtered, which results in a degraded signal bit error rate (BER) performance . Therefore, it is important to accurately assess the impact of the impairments on the signal so that the maximum number of cascaded OXC is correctly predicted.
The impact of crosstalk on the signal performance has been extensively studied , as well as the impact of optical and electrical filtering, namely on systems affected by amplified spontaneous emission (ASE) . Recently, the combined effects of crosstalk and filtering have also been investigated . It was shown that for a filtered crosstalk signal, a weighted isolation should be used for performance assessment instead of the isolation at the crosstalk wavelength. More recently, we have shown that the combined effect of self phase modulation and group velocity dispersion in the crosstalk signal can cause a crosstalk induced optical signal to noise ratio (OSNR) penalty higher than compared to an unimpaired crosstalk signal, due to the distortion of the crosstalk signal shape . Therefore, the combined effect of various impairments should be studied, since penalties larger than expected can arise when compared to a separate assessment of the same impairments.
Since both crosstalk and inter-symbolic interference (ISI) due to filtering are generated at OXC, along this paper we investigate the combined impact of narrow and detuned filtering on the optical signal and on the crosstalk signal. We show that the crosstalk induced penalties when the signal is narrowly or detuned filtered are larger than when the signal is not filtered. Additionally, we investigate the same effect in the case of narrow electrical filtering. The penalty increase arises from the eye closure of the signal, which penalty adds super-linearly to the crosstalk penalty. Furthermore, we introduce the use of the Modified Chernoff Bound (MCB) based method in a way to include the ISI effect along with the crosstalk to estimate the BER. Due to its computational simplicity, such method provides a quick and accurate estimation of the network performance when both ISI and crosstalk are an issue. In Sections 2 and 3, a single crosstalk signal is used, for a better understanding of the phenomenon, but results with a larger number of crosstalk interferers are presented in Section 4 to support that the same conclusions hold for more than one crosstalk channel.
2. Optical network equivalent system setup
In an optical meshed network, an optical signal can cross several OXCs. In each OXC, the signal is filtered and, possibly, an amount of crosstalk is introduced. Considering that the signal and crosstalk signal have different origins, their path will be different and therefore they are filtered by different filters. To emulate such effects, different optical filters with tunable bandwidth are used for the signal and crosstalk signal, to emulate the filter transfer function of the cascaded OXCs.
2.1 Experimental and simulation setup
The conceptual setup for studying the effects of both crosstalk and ISI due to filtering is now described. An optical transmitter (Tx) produces a 10 Gb/s signal that is split into the signal part and the crosstalk signal part. The signal and the crosstalk signal are each filtered by an independent optical filter, with tunable bandwidth. The crosstalk signal phase is decorrelated from the signal phase and its amplitude is adjusted for the desired signal to crosstalk ratio (SXR). The crosstalk signal is then coupled to the signal and also to ASE noise. An attenuator after the ASE noise source sets the optical signal to noise ratio (OSNR). A large bandwidth optical filter filters the ASE noise before the impaired signal is fed to the square-law bandwidth limited photo-receiver. The electrical signal is then fed to the BER tester (BERT). The BER is determined with optimum decision threshold. The OSNR penalty is given by the difference of the OSNR required to achieve a BER of 10-4 between the signal with and without crosstalk, with the same filter conditions. The SXR is 20 dB throughout the paper.
The experimental setup is depicted in Fig. 1. A 231-1 PRBS is used. The crosstalk signal phase is decorrelated from the signal phase by traveling over 4 km of standard single mode fiber (SSMF), with negligible dispersion impact. The delay between signal and crosstalk signal is controlled by a variable optical delay line (VODL) so that the bit transitions occur at the same time in both signal and crosstalk signal, when they are added later on in an optical coupler. A polarization controller (PC) sets the crosstalk signal state of polarization to match that of the signal, which corresponds to the worst case of crosstalk effect on the performance degradation, and an attenuator (Att.) controls the SXR.
In the simulation setup, the random phase fluctuations between the signal and crosstalk signal due the different paths are simulated by a random phase walk between both signals, to emulate the effect of the 4 km SSMF in the experimental setup. As in a Monte Carlo simulation, each simulation is run 1000 times using a 210 deBruijn sequence with a different phase. However, the ASE noise is accounted for analytically . The electrical frequency response of the circuit comprising the photodiode and subsequent transimpedance amplifier is modeled as a 3rd order Bessel low pass filter with bandwidth at -3 dB of 10 GHz. The optical filter is modeled as super Gaussian band pass filter with order and bandwidth that best match the experimental characteristics.
2.2 Modified Chernoff bound with inter-symbolic interference
The MCB method has proved to be an accurate and computationally fast way of calculating BER and power penalties for signals impaired by crosstalk . To assess the accuracy of such method in the conditions here investigated, we consider a MCB approach with separate bounds for mark and space levels , where the moment generating functions are derived from the in-band crosstalk arc-sin statistics . However, the MCB in  and  does not take into account the ISI effect caused either by optical or electric filtering. To overcome this limitation, we calculate a histogram of the signal at the time instant of maximum eye aperture considering a noiseless and crosstalk free transmission. Each of the histogram electric current values is then used in the MCB, instead of the steady state mark and space power levels. The final MCB result is the weighted averaged of all the bounds obtained from each power level, where the weights are the occurrences of each current level of the signal histogram. The ASE noise variances for each histogram current value are rigorously calculated considering the proper optical filter shape , but assuming constant signal power . Hence, a BER estimate for a crosstalk and ISI impaired signal is obtained with a single simulation run.
In all the results of Section 3 the MCB BER estimate was, in average, 240 times faster to compute than the simulation.
3.1 Optical filter bandwidth dependence
The dependence of the crosstalk induced OSNR penalty has been studied as a function of the optical filter bandwidth in the signal path. The OSNR penalty is defined as the difference between the required OSNR for a BER of 10-4 of the crosstalk impaired signal and the crosstalk free signal, considering in both cases the same optical filter in the signal path. Using this definition of OSNR penalty, the penalty of optical filtering on the signal is removed, since the reference required OSNR is taken already for the optically filtered signal. Hence, the effect of the crosstalk penalty is isolated from the penalty induced from optical filtering. The results are presented in Fig. 2. The experimental optical filter is simulated as a super-Gaussian optical filter with order 1.5, which best fits the amplitude response of the used filter. The agreement between the experimental, simulation and MCB results is within 0.2 dB. The OSNR penalty is constant (and equal to 0.9 dB) for bandwidths above 15 GHz, which is the classical crosstalk-induced OSNR penalty. However, for bandwidths below 15 GHz, a steep rise in the OSNR penalty is observed due to ISI. To support this, Fig. 2 also shows the experimental eye diagrams of the crosstalk free signal. It is noticeable that 15 GHz is precisely the bandwidth of the optical filter that starts to cause eye closure due to ISI.
The detailed explanation for the crosstalk induced penalty increase with the decrease of the optical filter bandwidth lies in the shape of the filtered signal. When the optical filter is very narrow, it causes ISI on the signal. However, in the measurements presented in Fig. 2, such impact has been removed due to the definition of OSNR penalty used. As a consequence, we can conclude that the ISI and crosstalk impairments do not add linearly. As an example, consider a signal that is strongly impaired by ISI, but the eye is still open and, therefore, the OSNR for a BER of 10-4 is still attainable. However, due to the arc-sin statistics of crosstalk, a small amount of crosstalk will cause the eye of the signal to close and an error floor to appear. Consequently, the required OSNR increases steeply and becomes infinite if the eye is completely closed. If the eye is not completely closed, the required OSNR is attainable, but a small quantity of crosstalk will cause a large penalty. If the eye had not been previously impaired by ISI, the crosstalk induced penalty would have been the classical crosstalk penalty. Therefore, it is not possible to calculate the OSNR penalty of signal impaired by both crosstalk and ISI by calculating independently the OSNR penalties for a signal impaired by ISI and for a signal impaired by crosstalk and add them together. Instead, their effect must be accounted for simultaneously, as the results in Fig. 2 show.
The effect of the bandwidth of the optical filter in the crosstalk signal path was also investigated. Further results have shown that the bandwidth of the optical filter affecting the crosstalk signal does not influence (within the accuracy) the crosstalk penalty, provided that the SXR (or weighted isolation ratio) is maintained, which agrees with previous results .
3.2 Optical filter detuning dependence
The effect of the detuning of the optical filter in the signal path has also been studied. The results are presented in Fig. 3, for an optical filter bandwidth of 15 GHz with super-Gaussian shape with order 1.5. The OSNR penalty was determined as previously explained, considering the same filtering conditions in both crosstalk impaired and unimpaired measurements. The results show that the OSNR penalty increases as the detuning of the filter increases. As the detuning increases, ISI and some eye closure is introduced, and as in the case of narrow filtering this causes a larger crosstalk penalty. The insets of Fig. 3, which show the crosstalk unimpaired eye diagrams, again support this conclusion. The eye diagram where the crosstalk penalty is higher is slightly closed in the “1” level due to the filter detuning. The agreement between experimental, simulation and MCB results is within 0.1 dB, except for a detuning of 6 GHz, where the discrepancy is 0.3 dB. From 0 to 6 GHz of detuning, the crosstalk-induced OSNR penalty shows, respectively, an increase from about 1 dB to 1.5 dB in the case of the experimental results and from 1 to 1.8 dB for the simulation and MCB results. The optical filter characteristic is not so well matched to the simulated shape at the cut-off frequency, and therefore, for a detuning of 6 GHz, the simulated ISI impaired eye diagram is not so well characterized relatively to the experiment. As a consequence, the calculated and experimentally measured OSNR penalties are slightly different for 6 GHz of detuning.
By detuning the filter in the crosstalk signal path, the crosstalk penalty is constant if the SXR is maintained, therefore verifying the weighted isolation rule .
3.3 Electrical filter bandwidth dependence
The impact of the ISI caused by the electrical filter on the crosstalk induced penalties has also been investigated. Although the electrical filters used in an optical network are usually well known and fixed, unlike the equivalent optical filter which is dependent on the signal path, increasing crosstalk penalties have been observed for narrow electrical bandwidths. The simulation and MCB results are shown in Fig. 4, for a 3rd order Bessel electrical filter. The optical filters for both signal and crosstalk signal have second order super Gaussian shape and 30 GHz bandwidth. The agreement between the simulation and MCB is within 0.15 dB. As in the case of narrow optical filtering, the crosstalk induced penalty increases for reduced filter bandwidths. The penalty increase happens when the electrical filter starts to close the eye diagram at the sampling instant (around 6 GHz in the case depicted in Fig. 4). Further results have shown that, for other filter shapes, the same conclusions hold, but the rate of penalty increase and the bandwidth at which penalty increases are different.
4. Network impact
The previous section has shown that higher crosstalk induced OSNR penalties arise when the signal is itself already impaired by ISI. This section will provide some results of the crosstalk penalty in a network scenario with cascaded OXC, where each OXC filters the signal.
Each OXC is modeled as a cascade of two second order super-Gaussian optical filters with 25 GHz of bandwidth at -3 dB that are tuned to the signal frequency. Transmission effects between OXC are not considered. After crossing a number of OXC the signal is filtered by a second order super Gaussian optical filter of 40 GHz bandwidth, before being fed to the photo-receiver and an electrical filter modeled by a 3rd order Bessel function with 7GHz bandwidth at -3 dB. The signal is impaired by one crosstalk interferer.
Both simulation and MCB OSNR penalties are shown in Fig. 5. The OSNR penalties are measured relatively to zero OXC, i.e., only the receiver filter is considered. The penalty due to filtering, i.e. without crosstalk, increases steadily with the number of OXCs and becomes 1 and 2 dB after 15 and 26 OXCs, respectively. The expected crosstalk penalty, i.e. considering an ISI unimpaired signal is constant at about 0.7 dB, as it does not depend on the number of OXC, but only on the SXR. On the other hand, the correctly calculated crosstalk penalty taking into account the ISI induced by filtering depends on the number of OXCs. It reaches 1 and 1.5 dB at 15 and 27 OXCs, respectively. The expected and calculated total penalties are defined as the sum of the filtering penalty with the expected and calculated crosstalk penalties, respectively. Whereas the expected total penalty does not account for the increase of the crosstalk penalty due to the filtering ISI, the simulated total penalty accounts for this effect and therefore increases more steeply. Considering a maximum expected total penalty of 2 dB, the maximum number of cascaded OXC is 18. However, considering a maximum calculated total penalty of 2 dB, the maximum number of OXC is 15, which is a 17% decrease in the number of allowed OXC, when compared to the case of the expected total penalty. The MCB prediction is within ±1 OXC. Conversely, taking the maximum number of OXC predicted by the expected penalty at 2 dB would result in a calculated penalty larger of 2.5 dB.
Further results, with three crosstalk channels have yielded the same conclusions, where the maximum number of OXC was 14 at 2 dB penalty, 1 less comparing to only one crosstalk interferer. Considering the results, the filtering effects in the signal and crosstalk should not be considered separately, since their penalties do not add linearly. Therefore, correct network planning requires accurate assessment of the combined effect.
The OSNR penalty due to crosstalk increases whenever the signal is impaired by optical or electrical filtering, comparing to the case when no filtering is present, due to the signal eye closure. Although the electrical filter can be chosen to be wide enough to prevent this effect, the crosstalk penalty can significantly increase in networks with a large number of cascaded OXC due to changes in the bandwidth of the equivalent transfer function of the overall optical filter. For a maximum acceptable total OSNR penalty of 2 dB the number of admissible cascaded OXC reduces 17% from 18 to 15. To allow fast estimations of such changes, a MCB approach combined with noiseless simulation of the signal has been introduced, presenting an accuracy of ±1 OXC in the estimation of the maximum number of cascaded OXC.
This work has been supported by Fundação para a Ciência e a Tecnologia through grant SFRH/BDE/15565/2005.
References and links
1. T. Zami, B. Lavigne, and E. Balmefrezol, “Crosstalk analysis applied to wavelength selective switches,” Optical Fiber Communication Conference, paper OFP4 (2006).
2. J. Attard, J. Mitchell, and C. Rasmussen, “Performance Analysis of Interferometric Noise Due to Unequally Powered Interferers in Optical Networks,” J. Ligthwave Technol. 23, 1692–1703 (2005). [CrossRef]
3. M. Pfennigbauer, M. M. Strasser, M. Pauer, and P. J. Winzer, “Dependence of optically preamplified receiver sensitivity on optical and electrical filter bandwidths-measurement and simulation,” IEEE Photon. Technol. Lett. 14, 831–833 (2002). [CrossRef]
4. R. Meleiro, A. Buxens, D. Fonseca, J. Castro, P. André, and P. Monteiro, “Impact of Self Phase Modulation on In-band Crosstalk Penalties,” IEEE Photon. Technol. Lett. 20, 644–646 (2008). [CrossRef]
5. J. L. Rebola and A. V. T. Cartaxo, “Gaussian Approach for Performance Evaluation of Optically Preamplified Receivers with Arbitrary Optical and Electrical Filters,” IEE Proc.-J 146, 135–142 (2001).
6. J. J. O’Reilly and J. R. F. da Rocha, “Improved error probability evaluation methods for direct detection optical communication systems,” IEEE Trans. Inf. Theory 33, 839–848 (1987). [CrossRef]
7. J. Rebola and A. Cartaxo, “Q-factor estimation and impact of spontaneous-spontaneous beat noise on the performance of optically preamplified systems with arbitrary optical filtering,” J. Ligthwave Technol. 21, 87–95 (2003). [CrossRef]