sponds to a different template, sharing a particular spectral shape. The remaining points correspond to isolated cases. It is worth noting that eqn. 4 is exactly the relation for the ctitical delay derived in [3] in the very particular case of coherent oscillations (when the limit cycle corresponds to identical instantaneous state components). We can say that eqn. 4 applies to general oscillatory behaviour for reciprocal CNNs with ‘large’ gain. Note that the maximum and minimum eigevalues of A are approximately independent of N . This follows observing that increasing N corresponds simply to sampling the template spectrum on a denser grid. So the above expressions for the critical delay are independent of the network size. Application to planar arrays: Practical realisations of CNNs are based on planar rather than toroidal arrays. For planar arrays, eqn. 2 does not apply. However, in usual applications, CNNs have the number of cells far larger than the template dimension, i.e. N >> r. In these cases, the eigenvalues of matrix A are well approximated by eqn. 2 [6]. We verified this fact for the templates used in our simulations. The maximum deviation of the true eigenvalues (obtained by the QR algorithm) from the eigenvalues obtained by eqn. 2, was 23% for N = 8, 7% for N = 16 and 3% for N = 25. So the template spectrum can be used as a practical design guideline even for planar CNNs, provided that the number of cells is sufficiently large. 0 IEE 1995 31 July 1995 Electronics Letters Online No: 19951349 M. Finocchiaro (Info-Com. Department, University of Rome ‘La Sapienza’, Rome, Italy) Introduction: In long-haul soliton systems, the main performance limitation is due to Gordon-Haus jitter accumulation and signalto-noise ( S N ) degradation, resulting from the amplified spontaneous emission noise (ASE) induced by optical amplifiers. In such a system, the jitter variance is proportional to F(G)/Ae8where A, is the fibre effective area and F(G) is a penalty function, resulting from the use of high-gain lumped amplifiers, that evolves with the amplifier spacing [l]. In addition, the S/N ratio is inversely proportional to this F(G)/Aef/function. It then appears that the use of large effective area (LEA) fibres will increase the system performance, in particular by allowing a higher F(G‘) penalty and a corresponding higher amplifier spacing which is important from an industrial point of view. It has been shown that by a proper index profile design, the effective area can be increased 121. In this Letter, we experimentally demonstrate the relevance of LEA fibres, by soliton transmission at 5Gbit/s in a loop configuration with fixed in-line filters. It should be noted that the potentiality of the proposed technique can also be extended to the soliton sliding frequency-guiding filter technique as well as to NRZ transmission systems [3] since in this last case the signal noise ratio is also inversely proportional to the function F(G)/Sefi The F(G)/Aef/function is expressed as [3] where C, and C, are, respectively, the input and output coupling loss, and G is the amplifier gain that compensates for fibre loss; it is expressed against amplifier spacing 2,and attenuation a by G = exP(G). 10.00~.......~....... ..,.............................-........................... R. Perfetti (Institute of Electronics, University of Perugia, via S. Luciu Canetola, 1-06131 Perugia, Italy) References 1 2 3 4 5 6 7 and CHUA, L.o.: ‘Cellular neural networks: theory and circuit design’, Int. J. Circuit Theory Appl., 1992, 20, pp. 533-553 SARGENI, F.: ‘Digitally programmable transconductance amplifier for CNN applications’, Electron. Lett., 1994, 30, (1 l), pp. 87G872 MARCUS, c.M., and WESTERVELT, R.M.: ‘Stability of analog neural networks with delay’, Ph,vs. Rev. A, 1989, 39, (l), pp. 347-359 ROSKA, T., wu, c.w., and CHUA, L.o.: ‘Stability of cellular neural networks with dominant nonlinear and delay-type templates’, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1993, 40, (4), pp. 270-272 CIVALLERI, P.P., GILLI, M., and PANDOLFI, L.: ‘On stability of cellular neural networks with delay’, IEEE Trans. Circuits Syst. L Fundam. Theory Appl., 1993, 40, (3), pp. 157-165 PERFETTI, R.: ‘Relation between template spectrum and convergence of discrete-time cellular neural networks’, Electron. Lett., 1993, 29, (25), pp. 2208-2209 ROSKA, T , and KEK, L. (Eds): ‘Analogic CNN program library, Version 6.1’. Analogic and Neural Computing Laboratory, Computer and Automation Institute, Hungarian Academy of Sciences, December 1994 NOSSEK, J.A., SEILER, G., ROSKA, T., nhancement of soliton system performance by use of new large effective area fibres B. Biotteau, J.-P. Hamaide, F. Pitel, 0. Audouin, P. Nouchi and P. Sansonetti Indexing terms: Soliton transmission, Optical communication, Optical$bres 7 0 p 2 large effective area fibres are exploited in a SGbitis soliton transmission system over transoceanic distances. It is shown that the use of large effective area fibres improves the system performance by enhancing either the total transmission distance or the amplifier spacing. 2026 000 , 4 0 . LA . I 10 20 30 40 50 60 amplifier spacing ,km 70 80 j853111 Fig. 1 Penalty (50/Aef) against amplifier spacing for A , = 5 0 p 2 and Aef = 7 0 ~ ’ OdB level corresponds to ideal distributed amplification with A, = 5Opd 0 Acg 5 0 ~ 1 ’ 0 A, - 7 0 ~ ’ This function is plotted in Fig. 1 against the amplifier spacing Z, for a conventional effective area of 5 0 w 2 and for the larger effective area of 7 0 p 2 corresponding to the available fibre [2]. The values of the other parameters are chosen to correspond with the experiment described below, i.e. C, = ldB, C, = 3dB and a = 0.26dBikm. The curves show that an optimal amplifier spacing exists near 30km and that increasing the effective area clearly improves the penalty function. Starting from the reference point R, there are two ways to take advantage of LEA fibres. First, at constant amplifier spacing, as shown by arrow A, the penalty decreases allowing either a higher margin for a given link length or a longer total transmission distance. Secondly, according to arrow B, it allows an extension of the amplifier spacing to about 50km keeping the same penalty level, transmission length and BER performance. The loop experiment, described in this Letter is, to our knowledge, the first experimental demonstration of the two types of improvement brought about by the use of large effective area fibres in soliton systems. Experimental setup: Fig. 2 shows the experimental setup. The soliton source is an electro-absorption modulator generating 35ps wide pulses at a 5GHz repetition rate. The optical pulse train at a 1557.5nm wavelength is modulated by a pseudo-random (27-1) sequence generator. Then it is launched into the recirculating loop ELECTRONICS LETTERS 9th November 1995 Vol. 31 No. 23 receiver wurce - A-0 coupler filter Fig. 2 Experimental setup through a high extinction ratio acousto-optic switch. The recirculating pulses are extracted through a 3dB coupler and detected on a SGbitIs soliton receiver with a 90ps acceptance window. A transmission analyser used in a ‘burst’ mode measures the BER at propagation distances selected by way of a delay generator. Two I.lnm in-line filters are used as frequency guides to reduce the Gordon-Haus jitter. The loop contains three 1480nm pumped amplifiers to balance fibre loss and one extra amplifier to compensate for the coupler, filters and in-line acousto-optic switch loss. For the reference experiment, the recirculating loop consists of two 30km spans of dispersion-shifted fibre with a conventional 5 0 p 2 effective area. Average dispersion and loss including splices and connectors are 0.7psinm.km and 0.26dB/km, respectively. In a second experiment the fibre is replaced by two 30km spans of 7 0 p 2 effective area of the fibre developed recently. To obtain the same average dispersion as before, 0.8km of singlemode fibre (17psinm.km) is added. The global fibre loss is also -0.26dBikm. In a last experiment, the loop fibre consists of only one 50km span of 7 0 w z effective area. Again, the average dispersion and loss remain close to the values in the reference experiment. Both in-line filters are maintained in the loop. 0 IO 12 14 16 distance, krn (x lo3) 15 contribution of the extra amplifier is comparatively higher in this single-span loop. We assume that both effects cancel each other out and that the observed results effectively reflect the penalty function evolution. To confirm this assumption, analytical BER are shown in Fig. 3. The filter-damped Gordon-Haus and filterdamped electrostrictional jitter variances, including experimental parameters, are calculated by analytical expressions given in [5]. The sum of both jitter variances are then converted into the corresponding BER using the 90ps receiver acceptance window. For the three configurations, theoretical EFDs are 10.6, 13.3 and 10.8mm, to compare with the experimental 10, 13 and 9.6mm EFDs, respectively. First, these results show that experiments and calculations are in fair agreement. The systematic difference is attributed to the simplicity of the model that does not take into account polarisation effects. Secondly, they show that the stronger filtering and higher noise in the third experiment effectively compensate for each other. Conclusion: We showed that LEA fibres dramatically improve soliton system performance. Two ways to exploit this new kind of fibre at a given transmission length are demonstrated, by increasing the amplifier spacing or by increasing the operation margin. Moreover, such improvement can be applied to other types of amplified link, for instance soliton systems with sliding frequencyguiding filters and even NRZ transmission systems. 13 September 1995 0 IEE 1995 Electronics Letters Online No: 19951368 B. Biotteau, J.-P. Hamaide, F. Pitel, 0. Audouin, P. Nouchi and P. Sansonetti (Alcatel Alsthom Recherche, Route de Nozay, F-91460 Marcoussis, France) References and MOLLENAUER, L.F.: ‘Effects of fiber nonlinearities and amplifier spacing on ultra-long distance transmission’, J. Lightwave Technol., 1991, LT-9, pp. 170-173 GORDON, J.P., NOUCHI, P., SANSONETTI, P., LANDAIS, S., BARRE, G., BREHM, C., BONIORT, J.Y., PERRIN, B., GIRARD, J.J., and AUGE, J.: ‘Low-loss single- mode fiber with high nonlinear effective area’. Proc. OFC’95, 1995, pp. 260-261 AUDOUIN, o., and HAMAIDE, J.P.: ‘Enhancement of amplifier spacing in long-haul optical links through the use of large-effective area transmission fiber’, IEEE Photonics Technol. Lett., 1995, (to be published) MOLLENAUER, L.F., LICHTMAN, E., HARVEY, G.T., NEUBELT, M.J., and NYMAN, B.M.: ‘Demonstration of error-free soliton transmission over more than 15000 km at 5 Gbith single-channel, and over more than 11OOOkm at 1OGbitis in two-channel WDM’, Electron. Lett., 1992, 28, pp. 792-194 GOLOVCHENKO, EA., and PILIPETSKII, A.N.: ‘Acoustic effect and the polarization of adjacent bits in soliton communication lines’, J. Lightwave Technol., 1994, LT-12, pp. 1052-1056 20 Fig. 3 Experimental and theoretical BER against distance Filled symbols: experimental, open symbols: theoretical 0, W Z, = 30km, A , = 5 0 p z 0 0 Z, = 30km, A , = 7 0 p 2 A, A Z, = 50km, A , = 7 0 p z Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission Results and discussion: The BER is plotted in Fig. 3 against transmission distance for the three experiments. First, the error-free for the reference experiment is 10mm. distance EFD (BER < The difference from the 14mm result in [4] is explained by the relatively small acceptance window (90ps compared with -2OOps in [4]) of our receiver. Secondly, when the conventional 50 pmz fibre is switched into a 7 0 p 2 fibre, the EFD increases to 13mm. This improvement is attributed to the penalty decrease shown by arrow A in Fig. 1. It also means that LEA fibres improve the system margin for a given distance. Thirdly, an EFD of 9.6mm is obtained when using a 50km amplifier spacing with the 7 O p d fibre. This 65% amplifier spacing improvement with respect to the reference experiment, was expected from arrow B in Fig. 1, as the penalty levels are equal in both cases. However, it should be noted that in the last experiment, the filtering function is a little stronger with two filters at every 5 0 h instead of every 60km in the reference experiment, while the noise M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga and S. Akiba ELECTRONICS LETTERS Indexing terms: Jitter, Soliton transmission A novel soliton transmission scheme to suppress the accumulation of the Gordon-Haus jitter using periodic dispersion compensation and inline optical filters has been proposed. With 90% dispersion compensation rate and optimum optical filters, a of 19dB and a large power window of 2dB were confirmed for a 20Gbit/s, 9000km transmission system by using a 1000km-long recirculating loop. In the development of long-haul, ultra-high-speed soliton transmission systems, considerable efforts have been made to suppress the Uordon-Haus jitter [I], which limits the transmission distance significantly. Soliton control techniques using inline sliding 9th November 7995 Vol. 37 No. 23 2027

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