A generalized method for estimating transmission penalties from spectrally-shaped crosstalk in cascaded multi-port WSS networks is derived, including effects of ASE, signal filtering, and crosstalk filtering. The weighted crosstalk value is computed by multiplying the shaped interfering signal by the power spectral density of the primary signal. This value is used to predict OSNR penalties in networks with cascaded WSSs of arbitrary port count. Theoretical treatment is supported by extensive numerical simulations and experiments for a variety of network configurations. Examples are presented for 43 Gb/s DPSK and 120 Gb/s DP-QPSK in cascaded ROADM networks with three distinct WSS types.
© 2012 OSA
Crosstalk occurring within the receiver bandwidth, commonly known as in-band, or homodyne crosstalk, is one of the most significant impairments which limits the transmission distance in optical fiber networks, and has been the subject of extensive studies since the advent of DWDM systems . In-band crosstalk can be generated by multiple back-reflections from discrete points along the fiber (e.g. imperfect connectors or splices), by distributed back-reflections (Rayleigh backscattering or stimulated Brillouin scattering), by four-wave mixing products, or by imperfect isolation of filters used to add and drop wavelengths within a DWDM system. This latter source of in-band crosstalk has become of more concern recently as DWDM networks have evolved to support an increasing number of reconfigurable optical add/drop multiplexer (ROADM) nodes based on wavelength selective switches (WSS) .
This has motivated the effort to quantify the impact on transmission performance of imperfect crosstalk isolation of the wavelength-selective switches employed at ROADM nodes across a fiber optic link. The standard crosstalk definition (the ratio between the total primary and interfering signal powers) is not a reliable indicator of the crosstalk impact on transmission performance of modern DWDM networks due to the wide bandwidth of 40 Gb/s and 100 Gb/s signals and the relatively narrow and non-uniform isolation spectrum of WSSs. This yields a spectrally shaped crosstalk and a transmission penalty determined by the specific spectral shaping. Consequently, crosstalk-induced transmission penalties for a given transceiver type depend on specific conditions determined by the number of WSSs in the link, their specific isolation magnitudes and shapes [3–11], their passband widths and shapes [12–15], the ASE in the crosstalk bandwidth, relative frequency detuning of signal and stopband , and relative signal-to-crosstalk power. It is therefore necessary to define a crosstalk parameter to account for the diversity of network conditions, and one that uniquely determines a transmission penalty for a given signal modulation format and receiver implementation.
Addressing this issue, Zami et al. proposed the weighting of isolation spectral response by the normalized power spectral density (PSD) of the interfering signal to define isolation over the stop band [3–5]. Bissessur and Bastide studied the frequency dependence of the crosstalk penalty as the interfering signal center frequency was detuned from the primary signal . Collings et al. investigated the crosstalk penalty dependence on the shape of port isolation profiles in 50 GHz-spaced WSS ROADMs .
This paper presents for the first time a general definition and procedure for computing the weighted crosstalk which determines transmission penalty of a given modulation format regardless of the crosstalk spectral shape and how it was generated. The weighted crosstalk concept is discussed in Section 2, with the principle described in detail and the derivation of the appropriate weighting function presented. Section 3 expands this concept in applying it to the case of networks with M cascaded Nx1 WSSs. Proof-of-concept in the form of experiments and numerical simulations is presented in Section 4, with section 4.1 demonstrating the concept in the case of a single 2x1 WSS with 43 Gb/s signals as a stepping stone to more complex crosstalk scenarios. Section 4.2 then expands the study to account for N ports on a single WSS, while section 4.3 presents results of a network with M cascaded Nx1 WSSs and 43 Gb/s and 120 Gb/s signals. Section 5 contains analysis of a sample DWDM network using the weighted crosstalk approach applied to measured isolation and passband functions of WSS units in a cascade. Different evolutions of weighted crosstalk with number of WSSs are found depending on signal modulation format (DPSK or DP-QPSK) and on WSS transmission and isolation spectra. Concluding remarks are stated in Section 6.
2. Weighted crosstalk concept
In a DWDM system, a signal described in the frequency domain by function S(f) (“primary signal”) may encounter crosstalk with spectral content X(f) (“interfering signal”) in two general scenarios: (a) X(f) is similar to S(f) in terms of having identical bit rate, modulation format, spectral shape, or (b) X(f) is different from S(f), having a different bit rate, modulation format, and/or being spectrally shaped (e.g., from imperfect WSS stop-band isolation, upstream ROADM passband narrowing, etc). Figure 1 shows an example of crosstalk scenario with a 43 Gb/s NRZ-DPSK primary signal S(f), along with a similar 43 Gb/s NRZ-DPSK interfering signal which has been spectrally shaped by imperfect isolation on the blocking port of a WSS.
Crosstalk is traditionally defined as the ratio of the total power in the primary signal to the total power in the interfering signal, computed as:Fig. 1), the method of crosstalk calculation should be modified to account for the fact that the spectral components of X(f) which are closest to the center frequency of the power spectral envelope of S(f) have much greater impact on signal quality than the spectral components concentrated towards the edges [6, 16].
This is accomplished by an appropriate weighting function W(f) applied to the interfering signal shape X(f) before the calculation of the crosstalk value. A similar spectral weighting approach has been previously used to define a group delay ripple parameter, which correlates with transmission performance . The weighting function should be related to the spectral shape of the primary signal, i.e., a normalized and scaled version of the power spectral density (PSD) of S(f). It may therefore be defined as W(f) = k∙S(f), where k represents the scaling factor. The weighted crosstalk calculation can then be performed as in Eq. (1) with the additional weighting term, as follows:Eq. (2) equals the unweighted crosstalk result of Eq. (1). Setting W(f) = k∙S(f) in Eq. (2) and solving for k gives:Eq. (2) using the definition W(f) = k∙S(f), where the scaling factor k is defined as Eq. (3). This result is equal to the unweighted crosstalk of Eq. (1) for the case when crosstalk is an attenuated copy of the signal. In the more general case when signal and crosstalk have different spectral distribution, the above crosstalk definition will properly account for the spectral content of the interfering signal.
3. Weighted crosstalk adapted to cascaded WSS networks
The weighted crosstalk approach described in Sec. 2 may be applied to the case of a network with M cascaded WSSs, each of which has N input ports and one output port (Fig. 2 ).
At WSS 1, the input signal Sin(f) is transmitted into the Nth port of the WSS, with potential interfering signals S1,1(f), S1,2(f), …, S1,N-1(f) of the same wavelength being input and (imperfectly) blocked at each of the remaining N-1 ports. The blocking filter shapes are given by H1,1(f), H1,2(f), …, H1,N-1(f). The combined primary and interfering signals are then propagated to the next WSS, where by convention they are input to the Hm,N(f) port, and the same addition of primary and interfering signals occurs. This continues until the Mth WSS is reached, where potential interferers SM,1(f), SM,2(f), …, SM,N-1(f) are filtered through stopbands by HM,1(f), HM,2(f), …, HM,N-1(f) and combined with the HM,N(f)-filtered output of WSS M-1. Note that the interfering signals Sm,n(f) are arbitrary and can be of mixed modulation formats, baud rates, OSNR levels, etc from that of the primary signal Sin(f). Likewise, the WSS transmittances Hm,n(f) are defined arbitrarily and can take any shape. In the absence of additional spectral shaping (e.g., due to high fiber nonlinearities), the total signal at the output of the Mth WSS is given by:Eq. (2), the weighted crosstalk can then be given by:Eq. (4)), as defined in Sec 2. Note that W(f) is based on the spectral content of the received primary signal and not of the transmitted signal. Also, note that the weighted crosstalk expression (5) is reduced to the simpler form (2) in the case of M = 1 and N = 2.
In the following section, a study is presented in which arbitrarily-shaped interferers were generated in order to demonstrate efficacy of the weighted approach in describing the impact of crosstalk on transmission performance. As part of this study, measurements were performed on a 2x1 WSS in order to test the effectiveness of applying the methodology to a physical WSS prototype with typical filtering characteristics. The study is then expanded to the cases of practical networks with a single Nx1 WSS, and then more generally to those with M cascaded Nx1 WSS devices.
4.1 Spectral shaping study and 2x1 WSS
In order to assess the validity of the weighted crosstalk approach presented above, a set of simulations were performed which employed stop-band filters of varying properties, with the purpose of demonstrating the usefulness of the weighted crosstalk in predicting the impact of arbitrarily-shaped interferers on the transmission performance. The simulation diagram is shown in Fig. 3 . Stop-band filter shapes were generated with variable parameters as depicted in Fig. 4(a) –4(e). Filter profile (a) has uniform isolation across the full bandwidth, and this result is taken as the reference crosstalk performance in subsequent calculations. The profiles in (b-e) are variations of a realistic WSS stop-band shape, sweeping over parameters such as isolation floor level (b), center frequency offset (c), stop-band width (d), and stop-band edge slope (e). The black dotted curves in the plots are mux-filtered 43 Gb/s NRZ-DPSK spectra overlaid on the filter functions for reference.
For the simulations (Fig. 3), the transmitter consisted of a differentially-driven MZI NRZ-DPSK modulator at 43 Gb/s, with a PRBS bit pattern over 213 simulated bits. Optical mux and demux for 50 GHz channel spacing were modeled by optical filters of Gaussian order 4 and 3-dB bandwidth 41 GHz. Gaussian-distributed optical white noise was added to the signal in order to set the OSNR. An interfering signal (uncorrelated bit sequence, swept over optical phase) was then added to the signal, having been shaped by the filter functions shown in Fig. 4(a)–4(e). The optical receiver consisted of a balanced detector with a demodulator free-spectral range of 66 GHz (~65% of bit period) .
Figure 4(i) and 4(ii) illustrate the resulting OSNR penalties as a function of the crosstalk without and with the weighting term W(f), respectively. Figure 4(i) shows a fairly large variation in OSNR penalty as a function of unweighted crosstalk due to the unevenly-distributed crosstalk signal spectra. However, in Fig. 4(ii), it can be seen that by accounting for the shape of the signal and appropriately weighting it before computing the crosstalk, the data points fall on the same curve, and there is very high correlation between OSNR penalty and the weighted crosstalk parameter for all filter cases studied.
These simulations were repeated for the case in which the primary and interfering signals were of different modulation formats and bandwidths; specifically, 43 Gb/s NRZ-DPSK and 43 Gb/s RZ-DQPSK, respectively. The same filtering scenarios were applied as in Fig. 4(a)–4(e), and the results were nearly identical, showing a large spread in OSNR penalty when plotted against unweighted crosstalk, but all curves coinciding once the weighted calculation is applied .
Measurements were performed to validate the numerical simulation results, as well as to demonstrate the feasibility of using the weighted crosstalk metric on WSS devices typically found in commercial DWDM networks. For the measurement, a 2x1 WSS prototype with distorted stop-bands was selected to quantify the performance impact on a 43 Gb/s NRZ-DPSK primary signal by an identical split, delayed, decorrelated, and polarization-scrambled interfering signal which was shaped by the stop-band of the WSS. Three channels were chosen on the WSS, each of which exhibited different stop-bandwidths, center frequency offsets, and isolation floors (Fig. 5(a) ). For each channel, OSNR penalties were measured as a function of increasing crosstalk power. As predicted by simulations, plotting the penalty against the weighted crosstalk leads to a common OSNR penalty curve. Figure 5(b) shows the measured penalties (filled markers) overlaid with the crosstalk reference curve (i.e., DPSK interfered with a decorrelated, spectrally-unaltered copy of itself). The lab measurements were also simulated (hollow markers) using the measured WSS isolation profiles, and good agreement is obtained between measurement and simulation, with matching within 0.2 dB for OSNR penalties up to 2 dB.
Additional measurements were performed, with crosstalk generated by either a 43 Gb/s NRZ-DPSK or 43 Gb/s (21.5 Gbaud) RZ-DQPSK interfering signal on 43 Gb/s NRZ-DPSK primary signal, demonstrating that weighting the crosstalk also addresses any difference in modulation format and/or baud rate. In contrast to other experimental investigations performed with fixed isolation and bandpass profiles, this study also took advantage of the programmable continuous spectral shaping enabled by the WSS . The experimental setup described above was employed, with stop-band shape of the WSS modified and intentionally distorted in order to generate arbitrary bandwidths, center frequency offsets, isolation floors, and/or filter edge slopes. Figure 6(a) shows an OSA trace with the primary signal (in black) and the resulting interfering signals of three of the sample WSS filter scenarios, in which the center frequencies had been detuned and/or stopband edge slopes had been distorted.
Measured system impact, depicted in Fig. 6(b), shows the OSNR penalties plotted versus the unweighted crosstalk in the cases of DPSK (triangles) and DQPSK (squares) interferers. Figure 6(c) shows the same measurements plotted against weighted crosstalk. The dotted gray curve in both figures is the measured case of DPSK interfering with a decorrelated, spectrally-unaltered copy of itself, shown as reference. A much stronger relationship is found between system penalty and crosstalk level in the weighted case compared to the unweighted case. Crosstalk penalty data are well-fit by an exponential function, and taking the natural logarithm of the y-axis yields a linear relationship allowing correlation coefficients to be calculated. The correlation coefficient for the unweighted crosstalk data set (Fig. 6(b)) is relatively low at 41.9% and 58.4% for DPSK and DQPSK interferers, respectively, indicated by the large spread in OSNR penalty for given crosstalk levels. For the weighted crosstalk data (Fig. 6(c)), however, the correlation is increased to 89.5% and 89.4% for DPSK and DQPSK, respectively. Sources of uncertainty include temporal fluctuations in the stopband shape (from slight mirror adjustments made due to temperature control loops), and limited resolution of the measured spectra of the signals being used in the weighted crosstalk calculations.
4.2 Nx1 WSS
The methodology developed above for the 2x1 scenario was then applied to a system comprised of a single 9x1 WSS (i.e., M = 1, N = 9), as seen in Fig. 7 (dotted line at right of figure represents path taken for measurement). The inset to the figure shows the transmission spectra of all of the ports on WSS 1 for reference. A 43 Gb/s NRZ-DPSK transmitter was again chosen due to its large spectral width compared to other common modulation formats (43 Gb/s DQPSK or 120 Gb/s DP-QPSK), which yields the greatest impact from imperfect isolation of the WSS blocking ports.
The transmitted DPSK signal was split, polarization scrambled, and decorrelated from the original signal by passing through a sufficient length of fiber, and coupled with a variable-power ASE source to set the OSNR of the interfering signals. It was then further split and sent to each of the N-1 blocking ports of the WSS. Measurements were performed for three cases: (1) interferer as signal combined with ASE, (2) interferer as signal only, and (3) interferer as ASE only. For case (1), the ASE power level was adjusted such that the OSNR of the interferer was a constant 15 dB. For case (3), the ASE was held at the same level as case (1) while the modulated signal was disabled. The motivation behind looking at these three cases was to demonstrate the effectiveness of the weighted crosstalk approach regardless of interfering signal composition.
The power of the interfering signals in all three cases was varied in order to obtain OSNR penalties at multiple levels of crosstalk interference. A plot of BER versus OSNR with the interfering signals set to 9 dB higher than the primary signal at the WSS inputs (set at this level in order to generate measurable penalties) is shown below in Fig. 8(a) .
The plot of Fig. 8(a) shows the performance of the system in the absence of crosstalk (interferers disabled) in the curve with ◊’s. With this curve taken as reference, OSNR penalties are calculated for the three cases discussed above – interferer as (1) signal + ASE (□’s), (2) signal only (∆’s), and (3) ASE only (○’s). As is evident from the data, the effect of the added ASE to the interfering signals should not be neglected and additionally degrades the performance of the system.
OSNR penalties at BER 1x10−5 are extracted from the plot in Fig. 8(a) and from similar BER versus OSNR data sets corresponding to different relative signal-to-crosstalk power (with up to 12 dB higher power applied to crosstalk ports relative to signal port). These OSNR penalties are plotted in Fig. 8(b) against the observed crosstalk levels using the weighted (hollow markers) and the unweighted (solid markers) methods of calculating crosstalk. The dotted black line is the measured back-to-back crosstalk performance of 43 Gb/s NRZ-DPSK when interfered with a decorrelated, spectrally-unaltered copy of itself, included as reference. As can be seen, when the weighted crosstalk approach is applied, the large spread in OSNR penalty versus crosstalk seen with the unweighted data points is eliminated, and the calculated weighted crosstalk falls very well in line with expected crosstalk performance. Additionally, the weighted crosstalk approach appears equally valid for all three interferer conditions (signal + ASE, signal only, and ASE only). Note that the crosstalk is calculated at the output of the WSS assuming a ± 50 GHz window (i.e., f0 = 50 GHz). Should a standard demux-type filter be included before the calculation, the calculated values of the unweighted crosstalk would be reduced but still far from the expected crosstalk performance. The calculated weighed crosstalk values would be negligibly affected.
4.3 M cascaded Nx1 WSSs
The measurement described in Sec 4.2 was repeated for a system comprised for 4 cascaded 9x1 WSSs (i.e., M = 4, N = 9). Measurements were done with the same 43 Gb/s NRZ-DPSK transponder, and additionally with a 120 Gb/s NRZ-PM-QPSK transponder utilizing coherent detection, real-time DSP and soft-decision FEC . In this configuration, the interfering signal was first split four ways before being sent to the 8x1 splitter and into the N-1 ports on the WSSs, as seen in Fig. 7. The setup was otherwise the same as in previous measurements for single Nx1 WSS. OSNR penalties were measured for various crosstalk levels (with up to 9 dB higher power applied to crosstalk ports relative to signal port) and different crosstalk sources (signal, ASE, and signal + ASE).
Figure 9 shows the result of the 4-WSS cascade measurements for 43 Gb/s NRZ-DPSK in (a), and 120 Gb/s NRZ-PM-QPSK in (b). Like all previous results, the OSNR penalties are well-predicted using the weighted crosstalk, even for this case where both the primary signal and interfering signals have been significantly shaped by the four cascaded WSSs.
With the backing support of extensive measurements and simulations, weighted crosstalk calculations may be utilized reliably in system analysis to predict the impact of crosstalk in a ROADM network under a variety of conditions. Only simple assumptions are required about WSS profile shapes, along with the power and spectral characteristics of the primary and interfering signals as determined by modulation formats and symbol rates. These weighted crosstalk calculations, combined with knowledge of the back-to-back crosstalk tolerance of the primary signal, yield expected OSNR penalties induced by the crosstalk arising in cascaded ROADM networks.
As an application of this crosstalk impact analysis, measured pass-through and blocking transmission profiles for three different WSS modules were used to calculate crosstalk evolution for cascaded 9x1 WSSs of the same type using Eq. (5). The weighted crosstalk was calculated for two common wide-bandwidth modulation formats, 43 Gb/s NRZ-DPSK and 120 Gb/s NRZ-DP-QPSK, to provide insight into the evolution of OSNR penalties in these three network scenarios and the impact of the different isolation profiles. For the purposes of the analysis, it was assumed that the interfering signals have the same modulation format and baud rate as the primary signal. Furthermore, it was assumed that the interfering signals are present on all ports of all WSSs, at the same power level as the primary signal, and that they have only been filtered by a 50-GHz mux prior to that point. Figure 10(a) shows the passband (thick line) and stopband (thin line; only the main blocking port shown for clarity) for each of the WSSs. As indicated by the figure, WSS B has a narrower pass-bandwidth but wider and deeper stop-bandwidth than WSS A, with WSS C lying somewhere in between.
Figure 10(b) shows the evolution of the weighted crosstalk versus number of WSSs in the cascade up to 32 devices. An interesting feature to note is that, for the 43 Gb/s signal, the crosstalk (and therefore OSNR penalty) for WSS B actually decreases initially before beginning to increase again. This is explained by the fact that, for WSS B, the rate at which is signal is spectrally narrowed is higher than the rate at which additional crosstalk is accumulating. Decreasing OSNR penalty with number of crosstalk-generating nodes has been observed experimentally [10, 11] but not predicted by the standard crosstalk definition. This is not the case for the 120 Gb/s signal, however, since it initially has a much smaller bandwidth than the 43 Gb/s DPSK (43 Gbaud versus 28 Gbaud), but it also has a much lower initial crosstalk level. As the number of WSSs increases, the crosstalk levels for the two modulation formats converge due to the fact that the severe passband filtering makes the spectral content of the two signals look very similar.
Another interesting feature is the fact that initially WSS A and WSS C result in similar crosstalk levels, despite having quite different stop-band shapes. But, as the signals are filtered further through the cascade, the curves diverge quite significantly, resulting in a 6 dB better crosstalk performance for WSS C over WSS A after 32 devices.
Expected OSNR penalties due to crosstalk may be extracted directly from such a plot knowing the back-to-back crosstalk tolerance of a given modulation format and bit rate, e.g., dotted black curves of Fig. 9 for 43G DPSK in (a) and 120G QPSK in (b). Predicted OSNR penalties can be seen in Fig. 11 for 120 Gb/s DP-QPSK. An important consequence of this straightforward yet rigorous analysis is that expected penalties induced by crosstalk are significantly lower than might be expected from a simple calculation based on the worst-case isolation across the signal spectrum. As an example, consider the case of 120 Gb/s signal with signal bandwidth of 30 GHz transmitted through 32 WSSs of type A with maximum crosstalk within the signal bandwidth of −35 dB. Assuming the typical case of 9 input ports (8 crosstalk signals at each WSS) and additive crosstalk across ports and WSSs yields a total crosstalk after 32 WSSs of −35 + 10∙log(8) + 10∙log(32) = −11dB, a crosstalk level well above the receiver crosstalk tolerance. In contrast, weighted crosstalk analysis indicates a crosstalk-induced OSNR penalty of 1 dB at BER of 10−3 (Fig. 11) which can be included in the OSNR margin requirements for a network design.
A novel calculation method for in-band crosstalk in WSS networks based on the spectral isolation of the WSS weighted by the signal spectrum is defined and demonstrated through extensive simulations and experiments for a large variety of cases. The weighted crosstalk accounts for the increased impact of spectral crosstalk components closer to the central frequency of the signal, and therefore is a reliable indicator of the crosstalk impact on transmission performance. The weighted crosstalk definition has been expanded to be used with any number of concatenated WSSs, with any number of input ports on each WSS characterized by arbitrary isolation and transmission spectra, and with arbitrary spectra of the interfering signals (defined by modulation rate and format). This methodology was verified experimentally for two common signal formats, 43 Gb/s NRZ-DPSK and 120 Gb/s DP-QPSK, in a 4-WSS cascade, showing good agreement with expected results.
A significant benefit offered by the weighted crosstalk approach illustrated in this paper is the simplification of the procedure for estimating crosstalk-induced transmission penalties in practical DWDM networks. Crosstalk-induced OSNR penalties can be estimated for any ROADM network using the generalized weighted crosstalk formula and an independent simple OSNR penalty measurement for a single unfiltered crosstalk signal. This procedure has been used in this paper to determine the crosstalk penalty for 120 Gb/s DP-QPSK signals transmitted through up to 32 WSS units assuming 3 different measured isolation spectra. As expected, the OSNR penalties are shown to vary with the stopband and passband shapes. More interestingly and relevant for practical applications, the rigorous analysis offered by the weighted crosstalk calculation yields transmission penalties considerably lower than would be expected based on a simple addition of crosstalk contributions. While 120 Gb/s DP-QPSK transmission is shown in this study to have a high tolerance to in-band crosstalk generated by a large number of concatenated WSS units, higher-order modulation formats have comparatively higher crosstalk penalties . Nevertheless, the weighted crosstalk definition and analysis described in this paper should be applicable to other modulation formats as well.
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