A new amplifier placement scheme to reduce noise in WDM networks. M. DE MERCADO (), I. DE MIUEL (2), F. OZÁLEZ (3),. FERÁDEZ, J.C. AUADO, R.M. LOREZO, J. BLAS, E.J. ABRIL, M. LÓEZ Dpt. of Signal Theory, Communications and Telematic Engineering University of Valladolid E.T.S.I. de Telecomunicación, Campus Miguel Delibes, 470 Valladolid SAI Abstract: In this paper, we introduce a new placement scheme for Erbium Doped Fiber Amplifiers in Wavelength Division Multiplexing (WDM) Local/Metropolitan Area etworks (LA/MA). This method can be used when the number of amplifiers and the total gain to be supplied per link are known. The aim is to place amplifiers so that the noise at the receivers is minimized. A comparison with previous placement schemes is performed to show that our method obtains a higher noise reduction. Key-Words: - Wavelength Division Multiplexing (WDM), Optical Metro etworks, Erbium-Doped Fiber Amplifiers (EDFA), lacement Schemes, ain Splitting, Amplified Spontaneous Emission () oise. Introduction The continuous increase on the demand of telecommunication services makes Wavelength Division Multiplexing (WDM) networks to be one of the preferred techniques to upgrade present architectures and to support high-bandwidth services. The development of optical amplifiers has made WDM a feasible technology by means of increasing transmission distances in optical links. There are several types of optical amplifiers, but the most widespread-used ones are the Erbium-Doped Fiber Amplifiers (EDFA) [,2]. Despite their advantages, such as high gain, high bandwidth and low noise figure, EDFAs have some disadvantages. They are very expensive devices and they need maintenance [-5]. These reasons make network designers to develop techniques to minimize the number of amplifiers needed. Several algorithms have been proposed to find an optimal solution to this problem [3-7]. These algorithms can be classified into two groups: the link-by-link algorithms [3] and the global optimization algorithms [4-7]. The first group obtains the number of amplifiers in the network by analyzing link by link. The second group analyzes the whole network. Better results are obtained with these global algorithms because more information is used [4-7]. Once the number of amplifiers required is known, the problem is to find their exact location in the network. This is very important, because it can reduce noise at reception. If signal levels are maintained at the receivers, and the noise power is reduced, the result is an increase in the Signal-to- oise Ratio (SR) at those receivers. In this paper, we propose a method to place optical amplifiers reducing noise power at reception. The rest of the paper is organized as follows. In section 2, some considerations about the EDFA model employed are made. Section 3 shows previous amplifier placement schemes. In section 4, we describe our placement scheme. Finally, in section 5 results are given to prove that our method reduces noise at the receivers when compared to previous schemes. 2 EDFA model We use the amplifier model described in [4-8]. It is defined by the following expression: sat = ( ) ln in 0 () where in is the total input signal power to the amplifier, sat is the internal saturation power, 0 the small-signal gain and the gain, (in absolute scale, not db). Two more constraints are applied to the model. If max is the maximum small-signal gain and max is the maximum output power an amplifier can supply, the model must verify: 0 max (2) in max (3)
The amplifier model with these constraints is shown in Fig.. It is assumed that the amplifier has a flat gain over the bandwidth of interest. Amplifier ain (db) 20 5 0 = 5 db 0 = 20 db T i = nsphf cbo ( αl ) 2 exp Ti i= + 2n sp ( ) hf i = i j= c B O j ( ) exp( αl ) exp ( αl ) j (6) (7) 0 5 0 = 0 db 0 = 5 db where i is the gain of the i-th amplifier of the cascade, and l j is the distance between the j-th amplifier and the end of the link. These equations will be used to obtain the power later. 0-30 -25-20 -5-0 -5 0 Total Input ower of all Wavelengths Fig.: Amplifier model. Dashed lines show the model of equation (). The constraint (3) restricts the model to the solid lines. The dominant noise contribution in EDFAs is the Amplified Spontaneous Emission () noise [,2]. The output noise power generated by an EDFA of gain can be calculated as follows [9]: sp c ( ) B O = 2n hf (4) where the parameters, their meanings and the values used in this paper are shown in Table. The gain is in natural units. When propagating through the link, noise is attenuated. Let us suppose that we have a link of length L and we put an amplifier l 0 km downstream. The noise power at the end of the link will be [8]: ( ) B exp( [ L ]) = 2n hf α l (5) sp c Symbol arameter Value used max Maximum small-signal 00 (20 db) ain of the EDFA sat Internal saturation power of the.298 mw EDFA max Maximum output power of an mw (0 dbm) amplifier α db Fiber attenuation (db/km) 0.2 db/km α Fiber attenuation (natural units) 0.04605 n sp Spontaneous emission factor.4 h lanck s constant 6.625 0-34 J s f c Central optical carrier frequency 93.4 THz B O Optical channel bandwidth 50 Hz Table : arameters and values used in this study. When we have a cascade of EDFAs, the noise at the end of the link is [8]: O 0 3 revious work. Several placement schemes have been proposed by different authors. Our start point is the work by Ramamurthy et al. [4-6], which focuses on WDM Local/Metropolitan Area etworks (LA/MA). They propose two mathematical formulations to minimize the number of amplifiers required in a network. When attempting to minimize this number, it is necessary to set upper and lower limits to the optical power propagating through the link. The upper limit is set by the maximum output power of an amplifier ( max ) or by the maximum power such that the nonlinear effects in the fiber are despicable. We assume the tighter bound is max. The lower bound is due to the sensitivity of network devices, and in this study it is set to 30 dbm per channel. The outputs of these formulations are the number of amplifiers per link and the aggregate gain they must supply. Then, their exact location is determined by using one of the algorithms also proposed in [4-6]: As Late As ossible (ALA) or As Soon As ossible (ASA). ALA places the amplifiers as follows: Each link is traversed downstream, and each of the - first amplifiers is placed when the power level of the signal have reached its minimum acceptable value. These - first amplifiers operate at their maximum possible gain. The last one gives the remaining gain needed in the link, and it is placed in the same way as previous amplifiers. The ASA scheme is similar to ALA, but instead of being the last amplifier the one with lowest gain, it is the first one. Differences between the two methods can be seen in Figs. 7 and 8 of [6]. A small variation of the ALA method is the Last Amplifier as Soon As ossible (LASA) scheme [8]. In this method, the - first amplifiers are placed in the same way as in the ALA scheme, but the last one is placed as soon as it is possible for it to give the remaining gain.
To illustrate how these methods place the amplifiers, let us consider a 50 km link with two amplifiers, where the total gain needed is 35 db. There are 0 channels propagating through the link (for simplicity, we will assume that they have the same power levels) and the power at the beginning of the link is set to 20 dbm per channel. The results of the different placements are shown in Figs. 2 to 4. 20 db 5 db 50 km 00 km 0 km Fig.2: Amplifier placement using the ALA method. 5 db 20 db 25 km 00 km 25 km Fig.3: Amplifier placement using the ASA method. 4 A heuristic scheme In this section, we propose a heuristic method that reduces noise when compared with previous schemes. To prove this, numerical results are provided in section 5. revious studies show that if an amplifier providing a gain level is replaced with more amplifiers providing jointly the same gain as the original one, the power is reduced [0]. Besides, [] demonstrates that if the total gain needed by the link is equally distributed among all amplifiers, the Signal-to-oise Ratio at the end of the link can be increased. We are going to adapt these considerations to our case, where we have a fixed number of amplifiers and the total gain required by the network links is known. Let us equally distribute the total gain required by the link among the amplifiers, and place them as soon as the amplifier can provide the maximum output power ( max ). For the example link of section 3, the placement result is shown in Fig. 5. 7.5 db 7.5 db 20 db 5 db 37.5 km 87.5 km 25 km 50 km 75 km 25 km Fig.4: Amplifier placement using the LASA method. We are looking for a way to place amplifiers that obtains the lowest power at the end of the links. To obtain this noise power, equation (6) must be applied. We can also calculate the noise reduction (R) obtained with the different methods when they are compared to ALA using the following equation: scheme (%) = R 00 (8) ALA For the example shown, LASA and ASA methods obtain the best noise performance at the end of the link, 33.8% better than ALA scheme. These three methods assume that the number of optical amplifiers () and the total gain (S) needed are known for any link of the network. When these restrictions are imposed, other placement schemes, such as the ones shown in [0,], cannot be applied. Fig.5: Amplifier placement using the new method. Using equation (8), the noise reduction at the end of the link when compared to ALA scheme is 43.6%. In some cases where the first amplifier is located at the beginning of the link, it may not provide simultaneously max and the required gain. To show this, let us consider a 00 km link with two amplifiers, where the total gain needed is 42.74 db. There are 20 equally-powered channels propagating through the link and the input power of the link is -29.3449 dbm per channel (aggregate power of -6.334 dbm). The results of the placement for ALA, ASA, LASA and the equally distributed scheme are shown in Figs. 6 to 9. With the equally distributed method, the total output power of the first amplifier is -.089 dbm, which is lower than max. In this example, the best noise performance is obtained when LASA method is used, 26.4% better that ALA applying equation (8). The equally distributed method obtains a noise reduction of 23.4% when compared with ALA. In order to improve the behavior of the method
proposed, let us increase the gain of the first amplifier so that max can be obtained at its output without changing its location. The other amplifier provides the remaining gain. The new placement is shown in Fig. 0. Comparing power at the end of the link between ALA and this new placement, we can see that the result is 30.8% better than ALA result (and therefore also better than LASA). 6.99 db 3.5 db 3.28 km 84.94 km.78 km Fig.6: Amplifier placement using the ALA method for the new link. 3.5 db 6.99 db 0 km 84.95 km 5.05 km Fig.7: Amplifier placement using the ASA method for the new link. 6.99 db 3.5 db 3.28 km 67.43 km 29.29 km Fig.8: Amplifier placement using the LASA method for the new link. 5.245 db 5.245 db 0 km 70.78 km 29.22 km Fig.9: Amplifier placement using the equallydistributed method for the new link. 6.334 db 4.56 db 0 km 70.78 km 29.22 km Fig.0: Corrections to the placement. Hence, we propose a heuristic method, called DASA (Distributed As Soon As ossible) which is described by the following rules: If a link has only one amplifier, it is placed as soon as it can provide an output power equal to max, while supplying the gain required by the link. If a link has more than one amplifier, the total gain required by the link is equally distributed among all amplifiers, and they are placed as soon as an output power equal to max can be provided. If an amplifier has to be placed at the beginning of the link, its gain has to be modified so that it provides an output power equal to max. The rest of the gain is equally distributed among the remaining amplifiers, and they are placed as soon as they can provide max. 5 umerical results. We have applied DASA method to the sample networks shown in Figs. and 2, to compare with the results obtained with ALA, LASA and ASA methods. These networks are assive Optical etworks (O) with non-reflective assive Star Couplers (SC) [4,5,7]. The power has been obtained using equation (6) with Table parameters, and the results are shown in Tables 2 and 3. The tables also show the noise reduction achieved with the different placement schemes when compared with ALA method. In the worst case, our method has proved to obtain the same results as the other schemes. In links with only one amplifier, DASA and LASA obtain the same placement, but the noise results can be different because of the power entering the link from previous links of the network. More important than the fact of reducing power is the increase experimented in the SR, given that the signal levels at the end of the links maintain approximately constant (± 0.04%) for all schemes
6 Conclusion In this paper we have proposed a heuristic method to reduce power at the end of network links. It has been called DASA (Distributed As Soon As ossible). umerical results have shown that this method obtains better noise reductions that previous proposed placement schemes, and therefore improves SR at reception. References: [].. Agrawal, Fiber-Optic Communication Systems, John Wiley and Sons, Inc, ew York, 992. [2] S. Shimada, H. Ishido (ed), Optical Amplifiers and their Applications. John Wiley & Sons, Inc, West Sussex, England, 994. [3] C.-S. Li, F. F. Tong, C. J. eorgiou, M. Chen, ain Equalization in Metropolitan and Wide Area Optical etworks using Optical Amplifiers, roceedings, IEEE IFOCOM 94, Toronto, Canada, pp. 30 37, June 994. [4] B. Ramamurthy, Efficient design of wavelength division multiplexing (WDM)-based optical networks, h.d. dissertation, Dep. Comput. Sci., Univ. California, Davis, CA, July 998. [5] B. Ramamurthy, J. Iness, B. Mukherjee, Optimizing Amplifier lacements in a roup : 20 stations roup 2: 5 stations Link 00 km Link 5 Link 2 Link 4 3 2 4 50 km 00 km Link 3 Link 6 roup 3: 28 stations Fig.: Sample network used in this study and in [4,5,8]. Multiwavelength Optical LA/MA: The Equally owered-wavelengths Case, Journal of Lightwave Technology, vol. 6, nº 9, pp. 560 569, September 998. [6] B. Ramamurthy, J. Iness, B. Mukherjee, Optimizing Amplifier lacements in a Multiwavelength Optical LA/MA: The Unequally owered-wavelengths Case, IEEE/ACM Transactions on etworking, vol. 6, nº 6, pp. 755 767, December 998. [7] J.Iness, Efficient Use of Optical Components in WDM-Based Optical etworks, h.d Dissertation, Universitiy of California, Davis, Department of Computer Science, 997. [8] I. de Miguel, J. C. Aguado,. Fernández, R. M. Lorenzo, E. J. Abril, M. López, A Simple Method to lace Amplifiers in a WDM LA/MA, ELECO 99 International Conference on Electrical and Electronics Engineering, pp. 43 47, 999. [9] R. Ramaswami, K.. Sivarajan, Optical etworks: A ractical erspective. Morgan Kaufmann ublishers, Inc. 998 [0]. E. reen, Jr., Fiber Optic etworks, rentice Hall Inc, Englewood Cliffs, ew Jersey, 993. [] H.-D. Lin, ain Splitting and lacement of Distributed Amplifiers, Technical report RC 626 (#7200), IBM, October 990. roup 2: 6 stations roup : 9 stations 0 Km 0 km 0 km Link 7 Link 2 2 00 km 3 00 km Link 6 Link 3 5 Link Link 5 00 km 4 200 km Link 4 roup 4: 0 stations roup 4: 0 stations Fig.2: Sample network 2 used in this study and in [6,7].
ain (db) Distance (km) (W) (Reduction (%) Link when compared with ALA) ALA & ASA DASA ALA LASA ASA DASA ALA LASA ASA DASA LASA = 6.99 = 3.50 = 6.33 l 0 = 3.28 l 0 = 3.28 l 0 = 0 l 0 = 0 9.038 0-6 6.657 0-6.255 0-5 6.249 0-6 2 = 3.50 2 = 6.99 2 = 4.5 l = 84.94 l = 67.43 l = 84.95 l = 70.78 (26.34 %) (-38.85 %) (30.85 %) 2 = 3.67 =.87 = 2.77 l 0 = 40.67 l 0 = 3.69 l 0 = 36.9 4.400 0-5 3.77 0-5 2 =.87 2 = 3.67 2 = 2.77 l = 59.33 l = 68.35 l = 63.8 (4.29 %) = 3.9 = 8.68 =.68 l 0 = 40.67 l 0 = 8.3 l 0 = 33.4 3 2 = 3.9 2 = 3.9 2 =.68 l = 65.94 l = 65.95 l = 58.43 5.637 0-5 5.256 0-5 6.98 0-5 4.755 0-5 (6.76 %) (-26.34 %) (5.64 %) 3 = 8.68 3 = 3.9 3 =.68 l 2 = 43.39 l 2 = 65.95 l 2 = 58.43 = 7.47 = 4.77 = 6.04 l 0 = 7.3 l 0 = 0 l 0 = 0 4 2 = 7.47 2 = 7.47 2 = 6.04 l = 87.36 l = 27.3 l = 59.6 7.405 x 0-6 7.428 0-6 4.238 0-6 (-0.3 %) (42.76 %) 3 = 4.77 3 = 7.47 3 = 6.04 l 2 = 55.5 l 2 = 87.35 l 2 = 59.6 5 = 4.56 =.87 = 3.2 l 0 = 40.67 l 0 = 27.22 l 0 = 33.93 6.249 0 2 =.87 2 = 4.56 2 = 3.2 l = 59.33 l = 72.80 l = 66.07-5 5.726 0-5 7.088 0-5 4.802 0-5 (8.36 %) (-3.42 %) (23.5 %) 6 = 5.53 l 0 = 0.44.37 x 0-6.37 x 0-6 2 = 5.53 l = 77.64 (0 %) r. = 3.35 l 0 = 3.28 l 0 = 0 2.309 0-6 2.25 0-6.980 0-6 (2.5 %) (4.24 %) r. 2 = 2.57 l 0 = 7.3 l 0 = 0 3.025 0-5 2.797 0-6 3.249 0-6 2.557 0-6 (7.53 %) (-7.40 %) (5.57 %) r. 3 = 3.9 l 0 = 0.44 l 0 = 0 2.558 0-6 2.368 0-6 2.844 0-6 2.045 0-6 (7.42 %) (-.8 %) (20.05 %) Table 2: Results of the different methods for Fig. network. has been calculated at the end of each link. l i is the distance between amplifier i- and amplifier i. l 0 is the distance between the beginning of the link and the first amplifier. ain (db) Distance (km) (W) (Reduction (%) Link when compared with ALA) ALA & ASA DASA ALA LASA ASA DASA ALA LASA ASA DASA LASA = 8.2 = 6.33 = 7.58 l 0 = 36.7 l 0 = 36.7 l 0 = 5.53 l 0 = 2.82 2 = 8.2 2 = 8.2 2 = 7.58 l = 9.08 l = 9.08 l = 9.05 l = 87.94 3.858 0-5 3.792 0-5 2.50 0-5 2.455 0-5 (.68 %) (34.94 %) (36.36 %) 3 = 6.33 3 = 8.2 3 = 7.58 l 2 = 72.75 l 2 = 70.45 l 2 = 9.05 l 2 = 87.94 2 = 8.67 = 7.20 = 8.09 l 0 = 20.63 l 0 = 20.63 l 0 = 0 l 0 = 0.65 0 2 = 7.20 2 = 8.67 2 = 7.78 l = 79.37 l = 68.27 l = 88.88 l = 88.9-5.394 0-5 8.764 0-6 7.908 0-6 (3.68 %) (45.73 %) (5.03 %) 3 = 8.84 = 6.3 = 8.7 l 0 = 24.20 l 0 = 24.20 l 0 = 0 l 0 = 0.259 0-5.072 0-5 6.248 0-6 5.095 0-6 2 = 6.3 2 = 8.84 2 = 6.99 l = 75.80 l = 60.74 l = 84.89 l = 84.94 (4.85 %) (50.37 %) (59.53 %) 4 = 8.07 = 7.09 = 7.58 l 0 = 20 l 0 = 5.45 l 0 = 7.9 2.859 0 2 = 7.09 2 = 8.07 2 = 7.58 l = 80 l = 90.35 l = 87.9-5.674 0-5.664 0-5 (4.44 %) (4.80 %) = 6.92 = 7.70 = 3.85 l 0 = 76.4 l 0 = 30.75 l 0 = 6.50 5 2 = 6.92 2 = 6.92 2 = 3.85 l = 84.6 l = 84.60 l = 69.25 6.429 0-5 6.234 0-5 5.36 0-5 4.308 0-5 (3.03 %) (7.3 %) (32.97 %) 3 = 7.70 3 = 6.92 3 = 3.85 l 2 = 39.25 l 2 = 84.60 l 2 = 69.25 6 = 6.67 l 0 = 76.4.890 0-5.85 0-5.397 0-5.370 0-5 (2.03 %) (26.08 %) (27.5 %) 7 = 6.60 l 0 = 76.4.938 0-5.894 0-5.439 0-5.46 0-5 (2.23 %) (25.74 %) (26.93 %) 8 = 7.00 =.76 = 9.38 l 0 = 76.4 l 0 = 76.4 l 0 = 0 l 0 = 38.2 2.592 0-5 2.464 0-5.634 0-5.220 0-5 2 =.76 2 = 7.00 2 = 9.38 l = 23.84 l = 8.8 l = 67.34 l = 46.93 (4.85 %) (36.95 %) (52.92 %) r. -- -- 4.507 0-6 4.370 0-6 3.726 0-6 3.020 0-6 (3.03 %) (7.3 %) (32.97 %) r. 2 -- --.987 0-6.946 0-6.468 0-6.440 0-6 (2.03 %) (26.08 %) (27.5 %) r. 3 -- -- 2.445 0-6 2.390 0-6.85 0-6.768 0-6 (2.23 %) (25.74 %) (26.93 %) r. 4 -- --.03 0-6 9.809 0-7 6.500 0-7 4.856 0-7 (4.85 %) (36.95 %) (52.92 %) Table 3: Results of the different methods for Fig.2 network. has been calculated at the end of each link. l i is the distance between amplifier i- and amplifier i. l 0 is the distance between the beginning of the link and the first amplifier.