1COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Performance Estimation of Performance Estimation of Bursty Wavelength Division Bursty Wavelength Division Multiplexing NetworksMultiplexing Networks
I. Neokosmidis, T. Kamalakis and T. SphicopoulosUniversity of Athens
Department of Informatics and TelecommunicationsEmail: [email protected]
2COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
People tend to calculate the performance of an WDM network assuming worst case scenarios:
Optical Sources always on (no bustiness) Phase difference between signals is zero (max
interference)Etc…
What happens in more “average” cases?
Introduction
3COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
IP over WDMexponential growth of IP traffic (almost doubles
every six months)WDM is a promising technology (high capacity)
Why IP directly over WDM?Lack of optical random access memories
(RAMs) required for all-optical packet switching
Need for infrastructures / schemes in order to “route” IP packets without optical buffering
Multiprotocol Lambda Switching
Bursty Traffic
4COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
The label of the packets is the wavelength on which they are transmitted
MPS network forwards and labels the IP packets according to their FEC
Each wavelength can be modeled as an M/G/1 system (short-range dependence)
The burstiness of each wavelength is characterized by the traffic load ρ
Bursty Traffic
5COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Inside a silent period (between two packets), the power of the source can be assumed zero
Silent periods can be considered as series of “0”s Within a packet, the “1”s and the “0”s appear
with equal likelihood The probability, Ppacket(t), that at any given time t,
a packet is being transmitted equals ρ The traffic load ρ essentially determines the
statistics of the bits
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
t1 t2 t3 t4
T
OFFp0=1-ρ/2
ONp1=ρ/2
t1+t2+t3+t4=ρT
Bursty Traffic
6COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Under the M/G/1 assumption:
0 bit "0" is transmitted 1 / 2p P
1 bit "1" is transmitted / 2p P
How does this affect the statistics of signal dependent noises (FWM, inband crosstalk,…)
Modelling Bursty Traffic
7COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
FWM is due to Kerr nonlinearity Generation of a fourth signal: f1+f2‑f3=f4
FWM is very useful in wavelength conversion In a WDM system, some of the products may
coincide with the wavelength channels This causes nonlinear crosstalk between the
WDM channels FWM-induced distortion is therefore signal
dependent!
Four Wave Mixing (FWM)
8COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
pqr
npqrpqr
rqpm nqnp
dBBBI cos
3
1
22
sin3
1cos
3
1
nrpqr
pqrpqr
rqp
nrpqr
pqrpqr
rqps nqnp
dBBB
nqnp
dBBBI
You can calculate the value of the FWM-induced distortion if you have the values of the bits being transmitted in all
channels (Bp) and their phases (θp)
Four Wave Mixing (FWM)
9COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
It is due to filtering imperfections at optical cross‑connects
It is at the same wavelength as the signal
It cannot be removed using additional filtering
Node 4
Node 1 Node 3
Node 2
2x2Switch
λ1
λ1
λ1 λ1
Inband Crosstalk
10COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
M
k
M
n
jkn
T
nkeDdttAS0 00
2)(
2
1
T
nknnkk
kn dttgtgcBcB
D )()(2
*
You can calculate the value of the inband crosstalk field if you have the values of the bits being transmitted in all channels
(Bp) and their phases (θp)
Inband Crosstalk
11COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Similarities…
In both cases you can calculate the value of the noise field if you have the values of the bits being transmitted in all
channels (Bp) and their phases (θp)
F()
z1
z2
z2N
Y
RVs with known PDF
RVs whose PDF we want to compute
12COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Standard Monte Carlo requires an excessive number of samples
(~10/EP)
MultiCanonical Monte Carlo increases the occurrence of samples in the
tail regions of the PDF (faster) it can easily be implemented in any general-
purpose programming language
How to model?
13COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Calculation of the PDF of a random variable Y which depends on random variables z1,…zN through Y=f(z1,…,zN)
In the first iteration, standard MC is performed
On each iteration i, the estimated PDF of Y is stored in the variables Pi
k
A sample of Y is calculated by randomly selecting zi using the Metropolis algorithm
Multicanonical Sampling
14COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
At the end of the iteration the values of Pki
are updated according to the MCMC recurrence relations
Pki are normalized such that their sum with
respect to k is equal to unityThe process is repeated until the PDF
reaches sufficiently low values
Multicanonical Sampling
15COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
System Parameters
Symbol Quantity Values
nonlinear coefficient 2.4 (Watt×km)-1
c speed of light in vacuum 3×108 m/sec
λ Wavelength 1.55μm
D fiber chromatic dispersion coefficient
2 ps/km/nm
Δf channel spacing 50GHz
α The fiber loss coefficient 0.2 dB/km
L total fiber length 80 km
Leff effective length 21.169 km
R receiver responsivity 1.28 A/W
N number of channels 16
M number of interferers 10
c02 # of photoelectrons in the signal
at the receiver100
16COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
For the case of the crosstalk noise, the Gaussian model does not provide an accurate estimate of the BER especially for small values of the traffic load
The error is much more pronounced in the case of FWM noise.
The Gaussian approximation cannot predict the maximum power that the system can tolerate. 0,2 0,4 0,6 0,8 1,0
4
6
8
10
12
14
16
18
20
4
6
8
10
12
14
16
18
20
SXR
(dB)
Pin (
dBm
)
Traffic load
BER=10-9
FWM-MCMC FWM-Gaussian approximation Crosstalk-MCMC Crosstalk-Gaussian approximation
(b)
0,2 0,4 0,6 0,8 1,010-16
10-14
10-12
10-10
10-8
10-6
10-4
10-2
BE
R
Traffic load
FWM Pin=8dBm
MCMC Gaussian approximation
In-band crosstalk SXR=12dB MCMC Gaussian approximation
(a)
Are the noises Gaussian?
17COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
As the traffic becomes heavier, the average power at each wavelength is increased
An increment of the traffic load leads to a broadening of the PDFs
-30 -20 -10 0 10 20 3010
-14
10-12
10-10
10-8
10-6
10-4
10-2
1
Im
= 0.2 = 0.4 = 0.6 = 0.8 = 1
(a)
0 100 200 300 40010-12
10-10
10-8
10-6
10-4
10-2
1
Is
= 0.2 = 0.4 = 0.6 = 0.8 = 1
(b)
Calculation of the FWM PDF
18COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
The pdf of the decision variable is strongly dependent on the value of ρ
As the traffic becomes lighter, smaller BER values are obtained for the same SXR
For light traffic, more nodes can be concatenated in the network
There is a strong dependence between the system performance and the SXR
0 50 100 150 200 250 30010-12
10-10
10-8
10-6
10-4
10-2
1
bs=1
pdf (
phot
oele
ctro
ns-1
)
S (photoelectrons)
= 0.2 = 0.4 = 0.6 = 0.8 = 1
bs=0
(a)
10 11 12 13 14 15 1610-12
10-10
10-8
10-6
10-4
10-2
1
BE
R
SXR (dB)
= 0.2 = 0.4 = 0.6 = 0.8 = 1
(b)
Inband Crosstalk PDF
19COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
The performance of the higher layers can be quantified in terms of the packet error rate
PER=1‑(1‑BER)k k=256bytes=2048bits (short
packets) and k=1500bytes=12000bits (long packets)
The PER has almost the same behaviour as the BER (PERkBER)
The PER is higher for longer packets (segmentation)
Erroneous receptions could cause packet retransmissions and/or loss of quality of service
Inaccuracy of the Gaussian model, especially in the case of FWM noise
0,2 0,4 0,6 0,8 1,010-14
10-12
10-10
10-8
10-6
10-4
10-2
1
PE
R
Traffic load
FWM, Pin=8dBm
MCMC, Short Packets MCMC, Long Packets Gaussian, Short Packets Gaussian, Long Packets
(b)
0,2 0,4 0,6 0,8 1,010-14
10-12
10-10
10-8
10-6
10-4
10-2
1
PE
R
Traffic load
In-band crosstalk SXR=12dB MCMC, Short Packets MCMC, Long Packets Gaussian, Short Packets Gaussian, Long Packets
(a)
Packet Error Rates
20COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Channel Traffic Load Distribution
0 2 4 6 8 10 12 14 16 1810-16
10-14
10-12
10-10
10-8
10-6
BE
R
Channel Number
FWM, Pin=7.6dBm
=0.6 mean()=0.6
(c)
0 2 4 6 8 10 12 14 16 180,0
0,2
0,4
0,6
0,8
1,0
1,2
Traf
fic lo
ad
Channels (a)
21COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
The MCMC method is used to study the statistical behavior of FWM and inband crosstalk taking into account the impact of traffic burstiness in an IP over MPλS‑based WDM network
The MCMC method is proved to be more efficient (faster) and accurate
The performance of such systems is very sensitive to the traffic load
The Gaussian approximation does not yield accurate results
Careful traffic engineering can improve the system performance in terms of the BER
Conclusions
22COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006
Thank you!
Email: [email protected]