Download OSNR Model to Consider Physical Layer

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OSNR Model to Consider Physical Layer Impairments in
Transparent Optical Networks
Helder A. Pereira · Daniel A. R. Chaves · Carmelo J. A. Bastos-Filho ·
Joaquim F. Martins-Filho
Received: date / Accepted: date
Abstract We propose a model that considers several
physical impairments in all-optical networks based on
the optical signal-to-noise degradation. Our model considers gain saturation effect and amplified spontaneous
emission depletion in optical amplifiers, coherent crosstalk in optical switches, and four wave mixing in the
transmission fibers. We apply our model to investigate
the impact of different physical impairments in the performance of all-optical networks. The simulation results
show the impact of each impairment on network performance in terms of blocking probability as a function
of device parameters. We also apply the model as a
metric for impairment-constraint routing in all-optical
networks. We show that our proposed routing and wavelength assignment algorithm outperforms two common
approaches.
Keywords Four Wave Mixing · Physical Impairments · Optical Communications · Optical
Noise · Optical Signal-to-Noise Ratio · Routing
and Wavelength Assignment · Wavelength Division
Multiplexing
Helder A. Pereira
University of Pernambuco, Department of Electrical Engineering,
52720-001, Recife-PE, Brazil.
E-mail: [email protected]
Daniel A. R. Chaves · Joaquim F. Martins-Filho
Federal University of Pernambuco, Department of Electronics
and Systems, 50740-530, Recife-PE, Brazil.
E-mail: [email protected]
Carmelo J. A. Bastos-Filho
University of Pernambuco, Department of Computing and Systems, 52720-001, Recife-PE, Brazil.
E-mail: [email protected]
1 Introduction
All-optical networks have been considered as the most
reliable and economic solution to achieve high transmission capacities with relative low cost. In these networks, the signal remains in the optical domain between the edge nodes, i.e., the signal propagates along
the core of the optical network without any opticalelectrical-optical conversion. There are two main challenges to manage these networks providing quality of
service (QoS): design an appropriate routing and wavelength assignment algorithm (RWA) and obtain an acceptable optical signal-to-noise ratio (OSNR) for every
optical signal at the destination node [1; 2]. Linear
and non-linear effects in fibers, and noise added by the
network elements along transmission can lead to OSNR
degradation, which have impact on the QoS. The main
physical impairments that impact the optical network
performance are the amplifier gain saturation, amplified
spontaneous emission (ASE) and its saturation process,
coherent crosstalk in switches, chromatic dispersion,
polarization mode dispersion (PMD) and nonlinear effects in fibers [1; 3–11].
Furthermore, the routing process has a significant
impact on the network performance. Some routing algorithms use heuristics based on pre-defined metrics.
Some examples are: the shortest path (SP) [12], minor delay [12], load balance [12], hops count (HW),
available wavelength (AW), hop count and available
wavelengths (HAW), total wavelengths and available
wavelengths (TAW), hop count and total wavelengths
and available wavelengths (HTAW) [13], and least resistance weight (LRW) [14]. The main aim of these
approaches is to achieve an improved load distribution,
or to optimize network resources such as wavelength
usage, to obtain lower blocking probabilities.
2
Many efforts have been made to develop RWA algorithms that consider physical impairments. In the optical network constricted by impairments, most reported
studies concerning the solution of the RWA problem can
be classified into three major categories. In the first category the RWA algorithm is treated in two steps: first
a lightpath computation in a network layer module is
provided, followed by a lightpath verification performed
by the physical layer module. Different routing schemes
have been proposed using this approach. In [4], Ramamurthy et al modeled their impairment-aware RWA
algorithm taking into account the ASE noise generated
in EDFA and cross talk added by the optical switch and
compared the estimated bit error rate (BER) against
a determined threshold. In [3], Huang et al modeled
their impairment-aware RWA algorithm taking into account the PMD and OSNR performance parameters
separately and compared them against two threshold
levels at the end of the route.
In the second category, the RWA algorithm is treated in three steps: first a lightpath computation in a network layer module is provided resulting in one (or none)
feasible lightpath for each wavelength in the network.
Then, for each feasible lightpath found, a verification
is performed by the physical layer module. Among the
lightpaths that passed in physical layer module verification the best one is chosen, considering some metric.
Pointurier et al. [15] used this approach and developed
a routing scheme based on Q-factor, which incorporates
the effects of the compounded crosstalk in both physical
layer module verification and choosing lightpath to set
up the call. In [16], Anagnostopoulos et al developed
a similar approach, nevertheless, considering the four
wave mixing, cross phase modulation and EDFA ASE
noise effects.
In the third category, RWA algorithm itself is aware
of physical impairments and uses the impairments information for routing procedures. Martins-Filho et al
proposed in [8] a dynamic routing algorithm that selects
the route based on the lowest physical impairments,
including ASE accumulation, amplifier gain saturation
and wavelength dependent gain along the path, and
then calculate BER to check for the required signal
quality. In [17], Cardillo et al proposed to use the OSNR
model considered in [3] with some enhancements to
consider non-linear penalties as well as the linear effects
that occur along lightpath transmission. In [18], Kulkarni et al utilized the Q-factor as a performance parameter, and integrates the interplay of linear impairments
(chromatic dispersion, PMD, ASE noise, cross-talk and
filter concatenation).
Although impairment-constraint routing schemes outperform the most common impairment unaware ap-
proaches, the use of these algorithms implies in higher
computational complexity. Therefore, the development
of models that use simple analytical equations is of
paramount importance. Some models consider the SNR
degradation or Q factor [4; 16; 19–22]. Another approach is to consider the degradation of the OSNR [3;
23–28].
In this paper we report on the development of an
analytical model based on OSNR degradation to take
into account the effect of the gain saturation and ASE
noise depletion in amplifiers, coherent crosstalk in optical switches, FWM and PMD in the optical fibers. Differently from the previously reported work, our model
considers these effects all together and it uses simple
analytical equations obtained from well known fundamental or experimental behavior of network devices.
We apply our model to investigate the impact of each
physical impairment in the network performance [29],
for two different network topologies. Network performance is evaluated in terms of blocking probability as
a function of device parameters and network load. We
also apply our model for impairment-constraint routing.
We present a RWA algorithm that finds the route based
on the OSNR using our proposed model (OSNR-R),
and we compare its performance with other RWA algorithms. In Section II we describe in details our model
that considers physical impairments in all-optical networks. In Section III we present the general characteristics and parameters used in our simulations considering
two different optical network topologies. In Section IV
we show the simulation results for the analysis of the
impact of the physical impairments on the network performance using our proposed model. In Section V we
present the proposed OSNR-R algorithm and we show
the simulation results for network performance for three
different RWA algorithms, including the OSNR-R. In
Section VI we give our conclusions.
2 Physical impairments modeling
Our formulation quantifies the OSNR degradation along the optical signal propagation in the all-optical
networks. The impact of physical layer impairments is
taken into account by considering the signal power and
the noise power at the destination node, both affected
by gains and losses along the lightpath. Moreover, some
network elements add noise components or have a nonlinear response. The optical amplifiers add ASE noise
power and are also affected by gain saturation and ASE
depletion as the total input signal power increases. The
optical switches add noise due to non-ideal isolation
between ports. And the transmission fibers add noise
due to FWM when the signal wavelength is close to
3
zero dispersion wavelength (λ0 ) and also induce pulse
broadening due to PMD. In this paper, we neglect the
effect of chromatic dispersion assuming that it is totally
compensated in the network links. The consideration
of residual dispersion in under development and will
be the subject of future publication. Fig. 1 shows the
configuration of the network wavelength routing node.
It is similar to the one assumed in [4].
Switch
1
1
1
Switch
2
2
.
.
.
.
2
.
.
.
.
.
.
Switch
W
M
Optical
fiber
Optical
amplifier
M
DEMUX
1
MUX
2
..
W W
TX
..
2
Optical
amplifier
Optical
fiber
1
RX
WAVELENGTH ROUTING NODE
Fig. 1 Network wavelength routing node configuration, for
M fibers with W wavelengths.
Fig. 2 shows the network devices considered in our
model in each link. The links have the following elements: transmitter, optical switch, multiplexer, booster
amplifier, optical fiber, pre-amplifier, demultiplexer, optical switch and receiver. The points a to h in Fig. 2
are evaluation points where the signal and noise can
be determined in the optical domain. In point a, we
have the input optical signal power (Pin ) and the input
optical noise power (Nin ). The ratio between Pin and
Nin defines the OSNR of the transmitter (OSNRin ).
For the lightpath with i links, the elements between b
and h are repeated i − 1 times before the signal reaches
the receiver in the destination node.
TX
a
X
b
c
d
e
f
g
X
h
RX
generated by each optical switch in one wavelength is
given by [30]:
NSwitch = ε
n
X
PSwj (λ),
(1)
j=1
where PSwj (λ) is the optical power from the jth optical
fiber in the same wavelength of the reference optical signal, ε is the switch isolation factor and n is the number
of signals in the same wavelength at the switch input
ports. For the node configuration used here, shown in
Fig. 1, n = M . Pointurier et al [31], considered that ε
has a dynamic effect depending on the network status,
whereas in [32] the authors considered that fiber nonlinearities enhance the detuned crosstalk when signals
are transmitted over long distances. For the sake of
simplicity, we considered here that ε is the same for
every wavelength, i. e. it is not channel-dependent.
At points c and g we consider the contribution of
the multiplexer and demultiplexer elements. BrandtPearce et al [33] considered a source of crosstalk due
to imperfect WDM demultiplexing. They found that it
is significant for high density of channels in the network.
However, in this paper we take into account the MUX
and DEMUX losses only.
At points d and f in Fig. 2, we take into account
the noise induced by the optical amplifiers, as well as
the gain saturation effect. Considering the signal-spontaneous beating as the main noise source, this noise can
be quantified by [34]:
Namp = PASE =
hf Bo Gamp Famp
,
2
(2)
where h is the Planck constant, f is the optical signal
frequency, Bo is the optical filter bandwidth, Gamp is
the linear dynamic amplifier gain and Famp is the amplifier noise factor.
The amplifier gain saturation effect is taken into
account by using the following expression [8; 9]:
G0
,
Pout
1+
Psat
Fig. 2 The link configuration for adjacent nodes, with optical
devices considered in our analytical model.
Gamp =
At points b and h in Fig. 2, we consider the noise
induced by coherent crosstalk in the optical switches assuming that incoherent crosstalk can be filtered out on
the switch output. This effect occurs basically because
of energy leakage from other co-propagating signals to
the reference optical signal, in the same wavelength, due
to non-ideal optical switches. The optical noise power
where G0 is the non-saturated amplifier gain, Pout is
the optical power at the amplifier output and Psat is the
amplifier output saturation power. One can note in (3)
that Gamp depends on the optical power at amplifier
input.
Since Famp also depends on the input optical power,
we empirically developed the following expression to
(3)
4
obtain the real behavior of Famp as a function of the
input optical power:



Famp = F0 
1 + A1 −
A1 
,
Pin 
1+
A2
(4)
5
10
15
30
10
25
9
20
8
15
7
10
6
5
5
0
4
-30 -25 -20 -15 -10 -5
0
5
10
η
= D2 γ 2 Pi Pj Pk e−αd
9
"
1 − e−αd
α2
2 #
,
(5)
′
where η is the FWM efficiency, D is the degeneracy
factor which is equal to three or six for degenerate
and nondegenerate FWM, γ is the nonlinear coefficient,
Pi , Pj and Pk are the input powers for the signals at
frequencies fi , fj and fk , respectively, α is the fiber
attenuation coefficient and d is the fiber length. The
frequencies generated by FWM process can be determined by [36]:
fijk = fi + fj − fk ,
(6)
where indexes i and j are different from k.
Considering every optical power component generated by FWM in the reference signal wavelength, we
have:
Amplifier noise figure (dB)
Amplifier gain (dB)
0
PF W M (λ) = Pijk (λ)
′
where F0 is the amplifier noise factor for low input
optical powers, A1 and A2 are function parameters.
These parameters can be obtained by fitting experimental results.
Fig. 3 shows the amplifier gain and noise figure as
a function of input optical power per channel from an
Erbium doped fiber amplifier (EDFA) built in our laboratories. The experimental results are typical from EDFAs and are represented by symbols and the model
results are represented by solid curves. The function
parameters of equations (3) and (4) that fit the experimental results of Fig. 3 are: G0 = 1000 (30 dB),
F0 = 3 (4.77 dB), Psat = 15 dBm, A1 = 500 and
A2 = 2 W.
-30 -25 -20 -15 -10 -5
power can be evaluated using the following equation
proposed by Song et al [37]:
15
Input optical power per channel (dBm)
Fig. 3 Amplifier gain and amplifier noise figure as a function
of input optical power per channel obtained from experimental
results (symbols) and fitting model (solid curves).
In real optical amplifiers, both the ASE and the
amplifier gain decrease as the input optical power increases [35]. In Fig. 3 one can observe that the noise figure increases with the input optical power. However, the
amplifier gain decays faster than the increase in noise
figure. As a consequence, using (2), the ASE power
decreases when the optical power increases.
At point e in Fig. 2, we consider the noise generated
by FWM effect [36]. This nonlinear effect depends on
the channel spacing, optical signal power per channel,
number of wavelengths propagating in the optical fiber,
fiber dispersion coefficient and the zero dispersion wavelength of the transmission fiber. Each FWM generated
NF W M =
m
X
PF W Mj (λ),
(7)
j=1
where NF W M is the noise power due to FWM and
PF W Mj (λ) is one of the m optical power components
generated by the FWM effect that falls into the same
propagating signal wavelength.
Finally, at the point h in Fig. 2, one can evaluate
the output optical signal power (Pout ) and the output
optical noise power (Nout ). Pout is evaluated according
to the gains and losses along the signal propagation and
it is given by:
Pout =
Gamp1 e−αd Gamp2
Pin ,
L2Switch LMux LDemux
(8)
where Gamp1 and Gamp2 are the dynamic linear gains of
the booster and pre-amplifier, α is the fiber loss coefficient, d is the fiber length, LSwitch , LMux and LDemux
are the optical switch, multiplexer and demultiplexer
losses.
Nout is evaluated from the source node to the destination node, including the noise components in the
respective points of evaluation (a to h in Fig. 2) along
the lightpath and it is given by:
5
Nout =
where B is the transmission bit rate, DP MD (j) is the
PMD coefficient, and d (j) is the length of the jth link
belonging to the lightpath. The ∆t should be lower than
a pre-determined maximum pulse broadening (δ).
Gamp1 e−αd Gamp2
Nin +
LMux LDemux L2Switch
n
X
Gamp1 e−αd Gamp2
ε
PSw1,j (λ)+
+
LMux LDemux LSwitch j=1
Gamp1 e−αd Gamp2
+
LDemux LSwitch
hν (λ) Bo
Famp2
+
Famp1 + −αd
2
e
Gamp1
m
X
Gamp2
PF W Mj (λ)+
+
LDemux LSwitch j=1
+ε
s
X
3 Simulation characteristics
(9)
Fig. 4 shows the flowchart of our simulation algorithm
using the shortest path as the routing metrics. This
algorithm is used in Section 4 for physical impairments
analysis purposes.
Call request
PSw2,j (λ),
j=1
where Nin is the noise power at the transmitter output.
Dividing Pout by Nout , one can obtain the OSNR at
destination node (OSNRout ). A threshold OSNR can
be established to guarantee the QoS (OSNRQoS ) for
call requests on the network.
Considering a route with i links, we have:
Pouti =
Gampi,1 e−αdi Gampi,2
LMux LDemux LSwitch
!
(10)
Pouti−1
Nouti =
Gamp1,i e−αdi Gamp2,i
Nouti−1 +
LMux LDemux LSwitch
Gamp1,i e−αdi Gamp2,i hν (λ) Bo
+
LDemux LSwitch
2
Famp2,i
Famp1,i + −αdi
+
e
Gamp1,i
m
X
Gamp2,i
PF W Mi,j (λ)+
+
LDemux LSwitch j=1
+ε
s
X
where Pout0
Yes
Acceptable OSNR
(11)
Pin
and Nout0
LSwitch
=
Nin
+
LSwitch
PSw1,j (λ).
Futhermore, we also consider the pulse broadening
effect caused by PMD in a route using the following
expression [38]:
P MD
j=1
(j) d (j),
No
Yes
Fig. 4 Flowchart of the routing and wavelength assignment
algorithm employed in the network simulations presented in
Section 4.
j=1
v
u i
uX 2
D
∆t = B t
No
Establish call request
PSwi+1,j (λ),
=
Block call request
Yes
j=1
n
X
No
Wavelength available
Acceptable pulse
broadening
and
ε
Route selection
(12)
For each network simulation, a set of at least 105
calls are generated choosing randomly the source-destination pair. The call request process is characterized
as a Poisson process and the time duration for each established call is characterized as a exponential process.
Our simulation algorithm works as follows: upon a
call request it determines a route using a pre-defined
metric. Then, it selects an available wavelength from a
list using the first fit algorithm. The lightpath OSNR
is evaluated. If it is above the pre-determined level the
call is established (OSNRQoS ). Our algorithm blocks
6
a call if the pulse broadening (∆t) is above the maximum level (δ), if there is no available wavelength or
if the OSNR for the respective wavelength is below
the OSNRQoS . The blocked calls are lost. The blocking
probability is obtained from the ratio of the number of
blocked calls and the number of requested calls. We assume circuit-switched bidirectional connections in two
fibers and no wavelength conversion capabilities. We
used two different networks in our simulations to avoid
any particularity that may raise from a specific network
topology. Fig. 5(a) shows a regular network topology.
Whereas the network presented in Fig. 5(b) has a irregular topology and it is similar to the NSFnet, but with
different distances. The amplifier gains are initially set
to compensate for the total link losses and the default
parameters used in our simulations are shown in Table 1. The network parameters (mainly the number of
wavelengths) were chosen such that the call blockings
were mainly due to OSNR degradation, instead of lack
of available wavelenghts.
120 km
1
2
60
km
km
60
70 km
70 km
70 km
8
60
km
km
60
3
(a)
11
76 km
km
m
24 k
22 km
35 km
7
5
6
9
8
72 km
55 km
12
45
km
65 km
3
4
km
35 km
21 km
22 km
25 km
26
km
27
42 km
1
30 km
km
25
km
48
2
100
Value
Psat
16 dBm
OSNRin
30 dB
OSNRQoS
23 dB
B
Bo
W
40 Gbps
100 GHz
36
∆f
λi
100 GHz
1550.12 nm
λ0
α
LM ux
LDemux
LSwitch
F0 (NF)
1510 nm
0.2 dB/km
3 dB
3 dB
3 dB
3.162 (5 dB)
A1
100
A2
4W
ǫ
δ
DP M D
Load
−40 dB
10%
√
0.05 ps/ km
60 Erlangs
Definition
Amplifier output saturation
power.
Input optical signal-to-noise
ratio.
Optical signal-to-noise ratio
for QoS criterion.
Transmission bit rate.
Optical filter bandwidth.
Number of wavelengths in an
optical link.
Channel spacing.
The lower wavelength of the
grid.
Zero dispersion wavelength.
Fiber loss coefficient.
Multiplexer loss.
Demultiplexer loss.
Optical switch loss.
Amplifier noise factor (Noise
figure).
Noise factor model parameter.
Noise factor model parameter.
Switch isolation factor.
Maximum pulse broadening.
PMD coefficient.
Network load.
on the network performance. We evaluate the network
performance in terms of blocking probabilities using the
shortest path algorithm to determine routes between
the source and destination nodes, as described in Section 3. Otherwise stated, the simulation parameters are
given in Table 1.
7
120 km
4
Parameter
120 km
6
70 km
120 km
5
Table 1 Default simulation parameters.
m 13
28 k
14
10
(b)
Fig. 5 The optical networks used in our simulations: (a) regular
topology and (b) american topology. Node distances are shown.
4 Physical impairments analysis
In this section we apply our proposed model for the
evaluation of the impact of each physical impairment
Fig. 6 shows the blocking probability as a function
of input optical power per channel for different network
loads, considering two different optical network topologies, and for a amplifier output saturation power equal
to 19 dBm. Note that for each network topology the
minimum blocking probability is obtained for a different
input optical power per channel, which is −1 dBm for
Fig. 6(a), and −3 dBm for Fig. 6(b). For higher laser
powers, the coherent crosstalk, FWM effect and gain
saturation effect are responsible for the increase in the
blocking probability, since they increase with the increase in the signal power, as seen in Eq. (1), (3), (5)
and (7). For lower laser powers, the ASE becomes more
relevant, since this noise source does not decrease with
the decrease in the signal power, as seen in Eq. (2).
The blocking probability of requested calls increases
when the network load increases. In fact, as the network traffic becomes higher, the physical impairments
become more relevant, causing more OSNR degradation
7
to the signals. However, we verified in our simulations
that for network loads of 80 Erlangs or higher the call
blockings due to lack of available wavelengths is no
longer negligible.
1
Blocking probability
0.1
0.01
Regular topology
40 Erlangs
in Fig. 7 (60 Erlangs). Fig. 7 also shows that the amplifier saturation power has a big impact on the network
performance when the blocking probability is limited by
the QoS constraint (i. e. for more than 30 wavelengths
available). A 3 dB increase in its value (from 16 dBm
to 19 dBm) leads to a drop in the blocking probability
by one order of magnitude for the regular topology and
by two orders of magnitude for the american topology.
However, when the network blockings are due to lack of
available wavelengths (i. e. for less than 20 wavelengths
in the networks studied here), the physical impairments
have little impact.
60 Erlangs
1E-3
80 Erlangs
1
100 Erlangs
120 Erlangs
1E-4
-15
-10
-5
0
5
Input optical power per channel (dBm)
(a)
1
0.1
Blocking probability
0.1
10
Blocking probability
-20
0.01
0.01
Regular topology
1E-3
Psat = 16dBm
Psat = 19dBm
American topology
1E-4
Psat = 16dBm
Psat = 19dBm
1E-3
1E-5
1E-4
0
American topology
60 Erlangs
1E-5
20
30
40
50
60
Fig. 7 Blocking probability as a function of number of wavelengths in a link, considering two different optical network
topologies for different amplifier output saturation powers.
80 Erlangs
100 Erlangs
1E-6
10
Number of wavelengths in a link
40 Erlangs
120 Erlangs
1E-7
-20
-15
-10
-5
0
5
10
Input optical power per channel (dBm)
(b)
Fig. 6 Blocking probability as a function of input optical power
per channel for different network loads, considering two different
optical network topologies: (a) regular topology and (b) american
topology, and for amplifier output saturation power equal to
19 dBm.
Fig. 7 shows the blocking probability as a function
of the number of wavelengths in a link, considering
two different optical network topologies, for different
amplifier output saturation powers. The network load
is 60 Erlangs. There is a threshold in terms of number of
wavelengths in each network, above which the blocking
probability is due to the physical impairments (OSNR
degradation). For less than this threshold, the blocking
probability is caused basically by the lack of available
wavelengths. One can verify that 36 wavelengths in
a link are necessary to obtain the minimum blocking
probability for both amplifier output saturation powers
in both network topologies considered. Adding more
wavelengths would not result in any improvement of the
network performance, for the network load considered
Fig. 8 shows the blocking probability as a function
of the switch isolation factor, considering two different
optical network topologies for different amplifier output
saturation powers. We note that for ε below −40 dB
the effect of coherent crosstalk can be neglected, and
the network blockings are limited by other physical
impairments. When ε is increased beyond −40 dB, we
observe that the impact of coherent crosstalk increases
sharply. Fig. 8 shows that the switch isolation factor
is a critical device parameter for the performance of
all-optical networks.
Fig. 9 shows the blocking probability as a function of
input optical power per channel, considering two different optical network topologies for different noise figures
and amplifier output saturation powers. We observe
that only 2 dB difference in the amplifier noise figure has
a considerable impact on network performance. Also,
one can note that for higher noise figures, the input
optical power that achieves lowest blocking probability
shifts toward high powers. This is because the ASE
noise increases for higher noise figures.
Fig. 10 shows the blocking probability as a function
of input optical power per channel, considering two
8
1
Blocking probability
0.1
0.01
1E-3
Regular topology
Psat = 16dBm
1E-4
Psat = 19dBm
American topology
1E-5
Psat = 16dBm
Psat = 19dBm
1E-6
-60
-50
-40
-30
-20
-10
Switch isolation factor (dB)
Fig. 8 Blocking probability as a function of switch isolation
factor, considering two different optical network topologies for
different amplifier output saturation powers.
dispersion shifted fiber (DSF) is used, λ0 = 1550 nm,
we observe that the network blocking probabilities are
higher than in the NZ-DSF case. In this case the use of
amplifiers with higher output saturation power, such as
Psat = 19 dBm, does not bring much improvement to
the network performance. It occurs basically because
the FWM effect becomes more relevant for this type
of optical fiber. Fig. 10 also shows that for DSF fibers
it is necessary to use lower input optical powers for
achieving lower blocking probabilities. However, for the
regular topology the blocking probability is very high
and in this case one should use larger channel spacing
to reduce the FWM effect. A FWM aware wavelength
assignment algorithm, rather than first fit, should also
improve network performance.
1
0.1
Blocking probability
Blocking probability
1
Regular topology
Psat = 16dBm
NF = 5dB
0.01
NF = 7dB
Psat = 19dBm
NF = 5dB
0.1
Regular topology
Psat = 16dBm
0
0.01
0
0
0
1E-3
-15
-10
-5
0
5
10
= 1550nm
Psat = 19dBm
NF = 7dB
-20
= 1510nm
= 1510nm
= 1550nm
1E-3
Input optical power per channel (dBm)
-20
(a)
-15
-10
-5
0
5
10
Input optical power per channel (dBm)
(a)
1
1
0.1
Blocking probability
Blocking probability
0.1
0.01
American topology
Psat = 16dBm
1E-3
NF = 5dB
NF = 7dB
1E-4
Psat= 19dBm
NF = 5dB
NF = 7dB
0.01
American topology
Psat = 16dBm
0
1E-3
0
1E-4
0
0
-15
-10
-5
0
5
10
Input optical power per channel (dBm)
(b)
= 1550nm
Psat = 19dBm
1E-5
-20
= 1510nm
= 1510nm
= 1550nm
1E-5
-20
-15
-10
-5
0
5
10
Input optical power per channel (dBm)
(b)
Fig. 9 Blocking probability as a function of input optical power
per channel, considering two different optical network topologies:
(a) regular topology and (b) american topology, for different noise
figures and amplifier output saturation powers.
different optical network topologies for optical fibers
with different zero dispersion wavelengths and amplifier
output saturation powers. When the non-zero dispersion shifted fiber (NZ-DSF) is used, λ0 = 1510 nm, we
obtain the minimum blocking probabilities. When the
Fig. 10 Blocking probability as a function of input optical power
per channel, considering two different optical network topologies:
(a) regular topology and (b) american topology, for optical fibers
with different zero dispersion wavelengths and amplifier output
saturation powers.
Fig. 11 shows the blocking probability as a function of the PMD coefficient, considering two different
optical network topologies for different amplifier out-
9
put saturation powers, for a bit rate of 40 Gbps. We
note that there is a threshold behavior for the PMD
coefficient (DPT hMD ). For DP MD below the threshold,
the PMD can be neglected and the call blockings occur
by the OSNR degradation. For DP MD above DPT hMD ,
the PMD effect becomes more relevant and it is the
cause of most of the call blockings. And in this case, the
blocking probability can not be improved by increasing
the amplifier saturation power because the PMD affects
the signals in the time domain.√
For the regular topology
the amerwe found DPT hMD = 0.16 ps/ km, and for √
Th
ican topology we found DP MD = 0.19 ps/ km. The
regular topology is more sensitive to PMD because its
average route length is longer (124.02 km) than for the
american topology (84.99 km).
1
Blocking probability
0.1
OSNRQoS the connection is blocked. The wavelength
assignment problem is solved by using the first fit algorithm [39]. It must be highlighted that for all wavelengths the route found by SP weight function is the
same. This is not the case for LRW and OSNR-R algorithms. For the OSNR-R algorithm the different wavelengths in the same route may show different noise
accumulation. The OSNR-R algorithm works as follows: upon a call request it selects a wavelength from
a list using first fit algorithm. The route is determined
by using the OSNR as the cost function in the Dijkstra algorithm. If the OSNR of the lightpath is above
the pre-determined level (OSNRQoS ) the call is established. The algorithm blocks a call if the pulse broadening (∆t) is above the maximum level (δ), if there is no
wavelength available or if the OSNR for the respective
wavelength is below the OSNRQoS . Fig 4 shows the
flowchart of SP and LRW algorithms and Fig 12 shows
the flowchart of the OSNR-R algorithm employed in
our network simulations.
0.01
Regular topology
1E-3
Psat = 16dBm
Psat = 19dBm
American topology
1E-4
Psat = 16dBm
Call request
Psat = 19dBm
1E-5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Polarization mode dispersion coefficient (ps/km
1/2
)
Fig. 11 Blocking probability as a function of PMD coefficient,
considering two different optical network topologies for different
amplifier output saturation powers, for a bit rate of 40 Gbps.
No
Wavelength available
Block call request
Yes
Route selection
5 RWA analysis
In this section we apply our model as a metric for a
impairment-constraint routing and wavelength assignment algorithm. We present a RWA algorithm that finds the routes based on the minimum OSNR for a given
available wavelength. Our OSNR based routing algorithm (OSNR-R) is compared to the shortest path (SP)
[13] and to the least resistance weight (LRW) [14] algorithms in terms of blocking probability and computation costs. Each of these algorithms have their own
metrics or weight functions. These weight functions are
used as a cost function in Dijkstra’s shortest cost algorithm to solve the routing problem considering physical
impairments along the lightpath. For the sake of fairness in the comparison among algorithms we use our
proposed model to calculate the OSNR of the lightpaths
determined by each routing algorithm. If the route found by the routing algorithm has an OSNR below the
Acceptable pulse
broadening
No
Yes
Acceptable OSNR
No
Yes
Establish call request
Fig. 12 Flowchart of the OSNR based routing and wavelength
assignment algorithm employed in our network simulations.
10
5.1 Shortest Path
Then, the route found by OSNR-R in λ can be expressed by
The link weight function wi,j is computed on a per-link
basis for a given link between nodes i and j. The weight
function is given by [13]
wi,j = di,j ,
(13)
where di,j is the physical link length between nodes i
and j.
5.2 Least Resistance Weight
The link weight function wi,j is computed on a per-link
basis for a given link between nodes i and j. The LRW
weight function is given by [14]
wi,j

T

 Cmax
A
Ci,j
=

∞
A
6= 0,
if Ci,j
(14)
A
if Ci,j
= 0,
A
where Ci,j
denotes the current number of available waT
velengths on the link, Ci,j
denotes the total number of
T
wavelengths on the link, and Cmax
represents the maxT
imum number of wavelengths in the link; i.e., Cmax
=
T
max(Ci,j ).
5.3 OSNR based routing
The idea behind this weight function is finding a route
with minor OSNR degradation for a given wavelength.
One can note from the noise formulation (Eq. (11) in
Section 2) that the output OSNR in a chain of i links is
dependent on the previous links in the chain. Therefore,
the relative magnitude of the noise penalty induced
by the ith link is dependent on noise accumulation
in previous links in the chain. Thus, for the OSNR-R
algorithm it is not correct to model a weight function for a given link independent of the chosen route
as considered in the other two approaches (SP and
LRW). However, OSNR-R can be easily implemented
with Dijkstra’s minimum cost algorithm. It can recalculate total accumulated OSNR from source node to
the currently visited node. It must be highlighted that a
higher OSNR in lightpath means a better signal quality.
Therefore, Dijkstra’s algorithm must be set to find the
maximum value for OSNR instead of the common use
of this algorithm that tries to minimize some metrics.
Mathematically, if π(s, d) represents all possible routes
between nodes s and d, and fOSN R [π(s, d), λ] represents
the output OSNR for these routes in the wavelength λ.
λ
= max {fOSN R [π (s, d) , λ]} .
Rs,d
(15)
Fig. 13 shows the blocking probability as a function of network load, considering two different optical
network topologies, for the three different routing algorithms. One can note that for both network topologies
the OSNR-R algorithm presents lower blocking probabilities for all network loads. This is because the OSNRR algorithm finds the route with minor OSNR degradation. Thus, it provides load balance to the network,
since if some links become busier, the OSNR of the signal passing these links will degrade and, therefore, the
OSNR-R algorithm will tend to avoid such links, finding
alternative routes. As a result, the blocking probability
due to low QoS (unacceptable OSNR) is lower for the
OSNR-R than for the other algorithms that do not take
into account the physical impairments in the routing
process.
Fig. 13 shows that the OSNR-R algorithm outperforms the SP and LRW algorithms in terms of blocking
probability. However, we must also compare the time
spent by these approaches to solve the RWA problem.
We used a Pentium Core 2 Duo with 2.13 GHz and
3 GB of RAM to perform this comparison. The results
for the average time spent by the OSNR-R algorithm
to solve the RWA per call are shown in Fig. 14, for
the regular and American topologies, as a function of
network load. The average time is obtained from 5 simulations of 10, 000 calls each. Fig. 14(a) shows that the
OSNR-R algorithm can take up to 63 ms and 134 ms
to find a route in the regular and American topologies, respectively. And also that the average route computation time has a linear dependence with network
load, with a slope of 0.4 ms/Erlang for the regular and
1.0 ms/Erlang for the American topologies. Whereas
the LRW algorithm solves the RWA problem in about
0.7 ms for the regular topology and about 1.2 ms for
the American topology, and it presents no dependence
with network load. It should be noted that the LRW
algorithm considered here performs a QoS verification
after route definition by calculating the signal OSNR
at the end of the chosen route and checking it against
the acceptable value (OSNRQoS ). We found that this
OSNR evaluation is the main contribution to the LRW
algorithm computation times. The results for the LRW
are not shown in Fig. 14. Therefore, the OSNR-R algorithm solves the RWA problem up to 112 times slower
than LRW. This is because of the time consuming calculations to evaluate the physical impairments performed
by the OSNR-R.
11
150
Blocking probability
0.1
0.01
1E-3
Regular topology
1E-4
LRW
SP
OSNR-R
1E-5
20
40
60
80
100
Average route computation time (ms)
1
120
90
60
30
All physical impairments
Regular topology
American topology
120
0
Network load (Erlangs)
30
(a)
60
90
120
Network load (Erlangs)
(a)
1
2.0
0.01
1E-3
American topology
LRW
1E-4
SP
OSNR-R
1E-5
40
60
80
100
120
140
160
Network load (Erlangs)
(b)
Average route computation time (ms)
Blocking probability
0.1
1.5
1.0
0.5
No FWM effect
Regular topology
American topology
0.0
30
60
90
120
Network load (Erlangs)
Fig. 13 Blocking probability as a function of network load,
considering two different optical network topologies: (a) regular
topology and (b) american topology, for three different routing
algorithms.
These long route computation times presented by
the OSNR-R algorithm, reaching a hundred milliseconds, can be regarded as prohibitive for practical applications. However, we found that the FWM effect is
the main responsible for them. In Fig. 14(b) we present
similar results to Fig. 14(a), but considering no FWM
effect in the OSNR calculations. In this case one can
see that the OSNR-R algorithm can take up to 0.6 ms
and 1.5 ms to find a route in the regular and American
topologies, respectively. The average route computation time still presents a linear dependence with network load, with a slope of 0.003 ms/Erlang for the regular and 0.010 ms/Erlang for the American topologies.
Whereas the LRW algorithm solves the RWA problem
in about 0.06 ms for the regular topology and about
0.13 ms for the American topology, and again it presents
no dependence with network load. In this situation the
OSNR-R algorithm is up to 11.5 times slower than the
LRW algorithm. And more important, the OSNR-R
route computation times lie within the range of sub-
(b)
Fig. 14 Average time spent by the OSNR-R algorithm to solve
the RWA per call, for the regular and American topologies,
as a function of network load, considering: (a) all physical
impairments and (b) no FWM effect.
milliseconds, reaching just over a millisecond, which can
be considered reasonable for practical applications.
Moreover, the average route computation times can
be significantly reduced if one uses a more powerful
computer for route calculations. Also the FWM effect
evaluation algorithm should be further improved and
simplified to reduce its computation complexity. We did
not consider the SP algorithm for time analysis since it
is not an adaptive routing algorithm.
6 Conclusions
We presented a novel model to consider several physical
impairments in all-optical networks. Our model is based
on the degradation of OSNR along the lightpaths and
it considers the effects of gain saturation and ASE noise
in amplifiers, coherent crosstalk in optical switches, and
FWM in the optical fibers.
12
To our knowledge, we are the first to consider these
effects all together in a simple model based on OSNR,
using analytical equations obtained from well known
fundamental or experimental behavior of network devices. Moreover, we are also the first to consider the
dependence of gain, noise factor and overall amplifier
noise power on the total signal power.
We presented an application of our model for the
evaluation of network performance in terms of blocking probability. Our results show the impact of each
impairment on network performance as a function of
device parameters. For low signal powers the blocking probability is mainly due to the amplifiers noise,
whereas for high signal powers the main contribution to
the blocking probability comes from the FWM effect,
coherent crosstalk and gain saturation effect. We note
that the optimum signal power depends on network
topology and network device parameters.
Our simulation results also show that network performance is highly dependent on device parameters,
such as amplifier output saturation power, amplifier
noise figure, switch isolation factor, and fiber type. These device parameters have considerable impact on device costs. To our knowledge, we are the first to present
such type of evaluation, i. e. network performance in
terms of device parameters. Therefore, the model, as
well as the simulation results for the network cases
presented in this paper may be of great interest to
network designers.
We also presented an application of our proposed
model in impairment-constraint routing. The proposed
RWA algorithm finds the route based on the OSNR of
the lightpaths. The simulation results showed that our
OSNR-R algorithm outperforms the shortest path (SP)
and least resistance weight (LRW) algorithms in terms
of blocking probability. However, the OSNR-R is much
slower (about 100 times) than the LRW algorithm, reaching average route computation times in the order of
a hundred milliseconds. We also found that the most
time consuming part of the OSNR calculation is the
FWM effect evaluation. If we neglect the FWM effect
the average route computation time is reduced to about
one millisecond. The FWM effect can be neglected if
NZ-DSF or standard fibers are used.
Therefore, we believe our model has applications
in routing and wavelength assignment algorithms, and
also in network planning to balance costs and performance. Moreover, since our model is based on OSNR, it
is compatible with some signal monitoring techniques,
that may be implemented in some strategically chosen
points in the network to measure the actual OSNR
and feed this information to the model, improving its
accuracy and functionality.
Acknowledgments
The authors acknowledge the financial support from
FACEPE, CNPq and CAPES for scholarships and grant.
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