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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
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