I. INTRODUCTION

Nowadays, many metropolitan core networks utilize existing WDM systems engineered for a long-haul network[1]. While point-to-point topology is predominantly used for long-haul WDM networks, ring topology is particularly used for metropolitan WDM networks because SONET/SDHare usually configured in a ring architecture [2]. Regardless of the network’s topology, dispersion is one of the major impairments in a WDM transmission system, especially for bit rates of 10 Gb/s or higher. The most popular way of compensating for dispersion is to use dispersion-compensation fibers (DCFs). Commercially available DCF modules are most suitable for compensating chromatic dispersion across the C band (1525~1565 nm in wavelength) of a conventional single-mode fiber (ITU G.652), which is deployed widely for terrestrial networks [3]. However, a DCF module requires additional cost and higher amplification of signals to compensate for its insertion loss. Therefore, it is necessary to design a network with a minimal set of DCFs.

In a long-haul WDM system it is relatively easy to design a dispersion map, because the signal’s transmission distance (i.e. the fiber length) is fixed. Therefore, DCFscan be placed periodically. An “optimum” dispersion map in a long haul WDM system usually refers to optimization of the signal’s power level, to mitigate fiber nonlinearities while keeping OSNR as large as possible [4-9]. However,in a metro ring network with the capability of wavelength reconfiguration, designing the dispersion map can be a more challenging task, because the distances (fiber lengths)between each node are inevitably irregular, which makes it impossible to place DCFs in a regular pattern. Furthermore,if there are N nodes in the network, then we need to consider N × (N-1) dispersion maps, because a wavelength path starting at any given node can terminate at any of the remaining (N-1) nodes. Residual dispersions of all N ×(N-1) cases should be below a certain value to meet the performance criterion, even though the criterion may not be as strict as in a long-haul WDM system.

Figure 1 shows the typical structure of a node with the capability of wavelength reconfiguration. Any wavelength can be dropped or added at the node, while the remaining optical channels will pass through the node. One (or two)optical amplifiers should be placed before (and after) the node to compensate power loss due to not only fibers but also optical devices such as a multiplexer/demultiplexer, optical cross-connect, etc. in the node. A DCF is usually placed with an optical amplifier [2].

FIG. 1. Typical node structure capable of wavelength reconfiguration.

Although many reports have been published on dispersion compensation in a long-haul WDM system [4-9], no work has been reported on an algorithm to design a dispersion map for a ring network, to our knowledge. In this paper, we present a novel algorithm to find the minimum set of DCFS in a ring network that will keep the residual dispersion at every node below a predetermined value.

II. METHODOLOGY FOR DESIGNING AN OPTIMUM DISPERSION MAP FOR A WDM RING NETWORK

Most metro core networks today are built on two unidirectional (clockwise and counterclockwise) fiber rings. However, for simplicity, we will consider counterclockwise traffic only, as shown in Fig. 2. Basically there are two configurations to compensate fiber dispersion, namely, post compensation (Fig. 2(a)) and precompensation (Fig.2(b)). If we ignore the fiber’s nonlinearities, there will be no difference in signal quality between these two configurations, because chromatic dispersion in fiber is a linear phenomenon [1].

FIG. 2. 5-node ring network with counterclockwise traffic: (a) post compensation configuration, (b) precompensation configuration.

First, let us consider optical signals traveling one link only from each node in a ring network with N nodes. With the post compensation configuration shown in Fig. 3(a),the accumulated dispersions should meet the following conditions:

FIG. 3. Signal travel starting from each node: (a) one-link travel, (b) two-link travel.

\(\begin{array}{l} D_{1} l_{1}+\bar{d}_{2} \leq d_{\text {tod }} \\ D_{2} l_{2}+\bar{d}_{3} \leq d_{\text {tod }} \\ \vdots \\ D_{N} l_{N}+\bar{d}_{1} \leq d_{\text {tod }} \end{array}\)       (1)

where D_i [ps/(nm ‧ km)] and l_i [km] are the dispersion parameter and the length of the ith link fiber respectively. i^th [ps/nm] (<0) is the dispersion of DCF at the ith node and d_tol [ps/nm] is the allowed residual dispersion in the network.

By summing Eq. (1), we obtain the condition for DCFs, \(\bar{d}_{D C F:} \leq-d_{\text {loop}}+N d_{\text {tal}}\), where \(\bar{d}_{D C F s}=\sum_{i=1}^{N} \bar{d}_{i}\) is the total dispersion of DCFs in the network, and \(d_{\text {loop}}=\sum_{i=1}^{N} D_{i} i_{i}\) is the total dispersion in the network due to link fibers.

Now, if we consider optical signals traveling two links only from each node (Fig. 3(b)), then the accumulated dispersion should meet the following conditions.

\(\begin{array}{l} D_{1} l_{1}+D_{2} l_{2}+\bar{d}_{2}+\bar{d}_{3} \leq d_{t a l} \\ D_{2} l_{2}+D_{3} l_{3}+\bar{d}_{3}+\bar{d}_{4} \leq d_{t a l} \\ D_{N} l_{N}+D_{1} l_{1}+\bar{d}_{1}+\bar{d}_{2} \leq d_{t a l} \end{array}\)       (2)

Again, by summing Eq. (2) we get \(\bar{d}_{D C F_{8}} \leq-d_{\text {loop}}+\frac{N}{2} d_{\text {tol}}\) , which is now a stricter condition than the previous one. Similarly, if we consider optical signals traveling the farthest, that is (N-1) links from each node, we get

\(\bar{d}_{D C F_{s}} \leq-d_{\text {loop}}+\frac{N}{N-1} d_{\text {tol}}\)       (3)

which is the strictest condition for the total dispersion of DCFs,\(\bar{d}_{D C F_{s}}\) . Therefore the condition in Eq. (3) will guarantee that all of the accumulated dispersions of N ×(N-1) cases are below d_tol. In a similar way, we can obtain the same result for the precompensation configuration.

Now, from Eq. (3) the total dispersion of the minimum set of DCFs is

\(\bar{d}_{D C F ; \max }=-d_{\text {loop}}+\frac{N}{N-1} d_{\text {tol}}\)       (4)

If d_tol is close to zero, \(\bar{d}_{D C F_{3}, \max }\) should be equal to\(\left(-d_{\text {loop}}\right)\), which can be achieved by letting the dispersion of each DCF compensate the previous link exactly. Fortunately, most metropolitan networks do not use a very high bit rate, say 40 Gb/s or above. In that case we can have a more relaxed condition for  \(\bar{d}_{D C F s^{*}}\) . For example, it is known that the maximum allowed dispersions for a bit rate of 10 Gb/s in NRZ format are 1200 ps/nm and 1900 ps/nm for a power penalty of 1 dB and 2 dB respectively [2].

2.1. Ideal Compensation with a Given Dispersion Tolerance

Let us consider a signal traveling farthest, starting from each node. The accumulated dispersions should meet the following conditions:

\(\begin{array}{l} d_{\text {loop}}-D_{N} l_{N}+\bar{d}_{D C F_{s}}-\bar{d}_{1} \leq d_{\text {tol}} \\ d_{\text {loop}}-D_{1} l_{1}+\bar{d}_{D C F^{3}}-\bar{d}_{2} \leq d_{\text {tol}} \\ d_{\text {loop}}-D_{N-1} l_{N-1}+\bar{d}_{\text {DCF}_{8}}-\bar{d}_{N} \leq d_{\text {tol}} \end{array}\)       (5)

Then the minimum requirement for each DCF can beobtained when \(\bar{d}_{D C F_{S}}\) is given by Eq. (4). That is,

\(\begin{aligned} \left(-\bar{d}_{1}\right)_{\min } &=\frac{-1}{N-1} d_{t a l}+D_{N} l_{N} \\ \left(-\bar{d}_{2}\right)_{\min } &=\frac{-1}{N-1} d_{t a l}+D_{1} l_{1} \\ \left(-\bar{d}_{N}\right)_{\min } &=\frac{i}{N-1} d_{t o l}+D_{N-1} l_{N-1} \end{aligned}\)       (6)

With the precompensation configuration, the minimumset of DCFs is modified as below.

\(\begin{aligned} \left(-\bar{d}_{1}\right)_{\min } &=\frac{-1}{N-1} d_{\mathrm{tal}}+D_{1} l_{1} \\ \left(-\bar{d}_{2}\right)_{\min } &=\frac{-1}{N-1} d_{\mathrm{tad}}+D_{2} l_{2} \\ \left(-\bar{d}_{N}\right)_{\min } &=\frac{-1}{N-1} d_{t a t}+D_{N} l_{N} \end{aligned}\)       (7)

If we use DCFs for which dispersions are given by Eqs.(6) or (7) depending on the compensation configuration,all of the residual dispersions at each node will be lessthan or equal to d_tol.

2.2. Modular Compensation with Commercially Available DCMs

However, most commercial DCFs are provided in modularform, to compensate for dispersion over a length of 20 km,40 km,…100 km of standard single-mode fiber (G.652); letus denote them DCM20, DCM40, ..., DCM100. Dispersioncompensation modules (DCMs) based on fiber-Bragg-gratingtechnology are also provided in a similar manner. Therefore,we can only have a DCM at the ith node for which the dispersion is in the form of

\(\bar{d}_{i}=k_{i} \mathrm{DCM}_{\min }\)       (8)

where (-DCM_min) is the minimum dispersion of a DCM set available, and k_i is an integer.

DCMmin is usually DCM10 or DCM20, depending onthe vendor, and their values at the center of the C bandare around -164 ps/nm and -328 ps/nm respectively. If DCM_min = DCM20 and k_i = 3, then d_i should be DCM60.

k_i  = 0 means that no DCM is required at the i^th node.Now finding an optimum set of DCMs means finding aset of integers \(\left\{k_{i}\right\}_{i=1, \ldots, N}\) that will satisfy Eq. (5). First,we can estimate  as

\(\tilde{k}_{i}=\operatorname{round}\left(\frac{\left(\bar{d}_{i}\right)_{\min }}{-D C M_{\min }}\right)\)       (9)

where round(x) means rounding x to the nearest integer, and \(\left(-\bar{d}_{i}\right)_{\min }\)  is given by Eqs. (6) or (7).

However, the set of DCMs estimated by Eq. (9) may not make some of the accumulated dispersions in the network below d_tol . If that happens, one needs to find the most underestimated \(\left(-\bar{d}_{i}\right)\) compared to \(\left(-\bar{d}_{i}\right)_{\min }\) , and then increase k_i by one until all of the accumulated dispersions are less than or equal to d_tol . Numerical examples and discussions follow.

III. NUMERICAL EXAMPLES AND DISCUSSION

To demonstrate the methodology explained in the previous section, let us consider an example 10-node ring network with the post compensation configuration (Fig. 4). Link lengths are arbitrarily chosen, and the circumference of the ring is 492 km.

FIG. 4. Example 10-node ring network.

Even though the proposed method is not restricted to aspecific fiber type or compensation method, it is assumed that standard single-mode fibers are used for transmission and DCFs are used for dispersion compensation, because they are most popular in practice. Properties of commercially available fibers are summarized in Table 1. Parameter values from the table will be used for our numerical demonstration.

TABLE 1. Typical properties of optical fibers

The wavelength dependence of the fiber’s dispersion parameter is assumed to be linear, so that  \(D(\lambda)=D\left(\lambda_{0}\right)+\) \(S\left(\lambda_{0}\right)\left(\lambda-\lambda_{0}\right)\)( \(\lambda_{0}\)= 1545 nm). The wavelength dependence of the DCMs is also modeled linearly, for example,\(\operatorname{DCM} 20(\lambda)=L_{D C \operatorname{Mr} 20}\left\{D_{D C F}\left(\lambda_{0}\right)+S_{D C F}\left(\lambda_{0}\right)\left(\lambda-\lambda_{0}\right)\right\}\), where \(L_{D C M P 0}=20 \mathrm{km}\left|D_{\mathrm{SSMF}}\left(\lambda_{0}\right) / D_{D C F}\left(\lambda_{0}\right)\right|\). Other DCMs are modeled similarly.

Due to the slope mismatch, a DCF can exactly compensate the dispersion of the transmission fiber only at a single wavelength \(\lambda_0\). The slope-compensation efficiency of DCFs is assumed to be 60% (k_s = 0.6), which is guaranteed by most commercial products. The effect of the slope mismatch will be most significant at \(\lambda\) = 1565 nm, which is the longest wavelength in the C band, and therefore the required dispersion of the DCFs should be obtained at \(\lambda\) = 1565 nm.

3.1. Ideal Compensation with d_tol = 1200 ps/nm

The dispersions of the DCFs for ideal compensation can be easily obtained by Eq. (6); the results are summarized in Table 2. With these DCFs, all of the dispersion maps at \(\lambda\) = 1565 nm will end up at d_tol at their last nodes.

TABLE 2. Required dispersions for ideal compensation at λ = 1565 nm

Figure 5(a) shows three examples of these dispersion maps, and Fig. 5(b) shows the wavelength dependence of the dispersion map from node #2 to node #1, which has the longest path.

FIG. 5. Dispersion maps using ideal compensation with d_tol = 1200 ps/nm: (a) 3 maps at λ = 1565 nm, (b) maps from node #2 to node#1, at three different wavelengths.

3.2. Modular Compensation with Commercially AvailableDCMs

Now with DCM_min = DCM20, Eq. (9) gives us \(\left\{k_{i}\right\}_{i=1, \ldots, N}\) = {4, 0, 3, 1, 2, 3, 3, 1, 1, 4} at \(\lambda\) = 1565 nm.From \(\left\{k_{i}\right\}_{i=1, \ldots, N}\) we can identify which DCM should be placed at the i^th node: DCM20 i k_i = 1, DCM40 if  k_i  = 2, and so forth. Figure 6 shows the dispersion maps with the identified DCMs at each node. Note that all of the residual dispersions are under d_tol. Unlike the ideal-compensation case, the accumulated dispersions at their last nodes are less than d_tol.

FIG. 6. Dispersion maps at λ = 1565 nm using DCMmin = DCM20 with d_tol = 1200 ps/nm.

We can also design a dispersion map with DCMmin =DCM10, that is, with DCFs in a finer modular form, to compensate dispersion over lengths of 10 km, 20 km, 30km, ..., of standard single mode fiber

Now if d_tol were reduced to, say, 800 ps/nm, possibly due to increased imperfections of other devices, then we could expect that overall more DCMs would be required. We can identify which DCM should be placed at the ith node as before; the results are in Table 3. With d_tol = 800ps/nm, using DCM_min = DCM10 is a little more favorable compared to DCM_min = DCM20, since the total amount of dispersion by each DCM is reduced. Figure 7 compares the dispersion maps with DCM_min = DCM20 and with DCM_min = DCM10 when a signal travels from node #2 to node #1. If more than one set of DCMs can reduce the residual dispersions below a given d_tol , then other aspects of the network design, including the cost of DCMs, should be considered.

TABLE 3. Optimum DCMs for the 10-node ring network​​​​​​​

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FIG. 7. Comparison of dispersion maps when DCMmin =DCM20 and DCMmin = DCM10 (from node #2 to node #1,counterclockwise).

IV. CONCLUSION

We propose a simple but powerful methodology to design a dispersion map with an optimum set of DCMs for a WDM ring network. The methodology is restricted neither to a specific fiber nor dispersion-compensation method. In principle, for a given value of the maximum tolerable residual dispersion, it can be used with any modulation format and any bit rate. We apply the methodology to an example 10-node ring network of 492 km circumference and demonstrate how it works. Since no work has been reported to design a dispersion map for a ring network,the proposed method can be a good design tool for a ring network capable of wavelength reconfiguration.