978-1-4244-7173-7/10/$26.00©2010 IEEE

CROSSTALK AWARE WAVELENGTH ASSIGNMENT IN STATIC WAVELENGTH ROUTING

Suvarna S. Patil#1 , Bharat S. Chaudhari* #Bharati Vidyapeeth University, Pune – 411043, India

*International Institute of Information Technology, Pune – 411057, India 1sschorage@gmail.com

Abstract-- The transparent WDM optical networks in absence of electrical regenerators reduce the overall network cost. The Quality of Service (QoS) in such networks can be guaranteed if and only if the Bit Error Rate (BER) and the crosstalk induced power penalty is significantly reduced. In this paper we have studied the wavelength assignment mechanism based on BER blocking probability and power penalty blocking probability. The blocking probability is found to be the function of node count and wavelength count as well while considering the scalability of optical crossconnect (OXC). A wavelength assignment strategy is analyzed based on knowledge of crosstalk component, BER and power penalty at each node.

Index Terms-- WDM, physical impairments, power penalty, BER, Blocking probability, QoS.

I. INTRODUCTION

The transparent WDM optical network with tremendous capacity of carrying huge data is the best possible solution for the backbone networks. The wavelengths in such networks are spaced very close to each other. However, the implementation of such dense WDM networks requires taking into account physical impairment information for effective lightpath setup. It is also necessary to establish the path only if the required optical signal quality is ensured [1]. This helps in improving QoS for the given system. In optical networks the QoS mainly depends on the BER and blocking probability. The major BER and blocking probability affecting impairments that are found in optical networks include ASE (Amplified Spontaneous Emission) noise from pre or post detection amplifiers, linear crosstalk introduced due to OXC node, as well as attenuation, dispersion and nonlinear effects from the optical fibers. With the growing demand for the data traffic it is necessary to accommodate more number of channels in the existing WDM networks. So the requirements of better BER to maintain good QoS increases. For a transmitted channel, the BER at its destination node is dependent on the number and the intensity of the inband crosstalk accumulated throughout the optical path introduced due to the neighboring channels. The inband crosstalk is defined as the power leakage from other channels, at the same nominal wavelength as that of the desired signal

channel. The effect of the inband crosstalk is severe as it cannot be removed with the optical filter as well [2]. The other impairment such as dispersion, can be eliminated using dispersion compensated fibers and attenuation, which can be compensated using optical amplifiers to provide sufficient gain. The nonlinear effects are not under consideration in this paper. If the crosstalk power increases, then it also leads to increase in the power penalty. The increase in signal power required to maintain a defined level of bit error rate of a system in the presence of crosstalk (or any other signal impairment) is referred to as power penalty. Each wavelength channel transmitted in the optical network is tested for the required BER i.e. 910− and the minimum power penalty criteria as 1 dB. If the wavelength channel satisfies the given conditions then only the path is established otherwise the input wavelength channel will be blocked. We have extended our work for calculating the blocking probability in the optical network based on BER & power penalty criteria in a optical network without wavelength converters.

The analysis is carried out for the available path for the transmitted channel. The path is established only if the

( )910−≤ thBERBER as well as ( )dBpppenaltypower th 1≤ . We have studied the wavelength assignment mechanism which will calculate BER and power penalty at the source node itself. Without any wavelength converters, the transmission uses the same wavelength while switching from one node to the other. If the optical network uses the wavelength converters then there will be more flexibility to utilize the available wavelengths and a smaller blocking probability as well [3]. We have analyzed the blocking probability as a function of wavelength count and node count which can route the wavelength very efficiently throughout the WDM network.

The paper is organized as follows. The OXC crosstalk model, power penalty, BER and blocking probability estimation are discussed in Section II. The wavelength assignment (WA) strategy is studied in Section III. Section IV presents the numerical results on the network blocking probabilities and our conclusions are discussed in Section V.

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II. OXC CROSSTALK MODEL

Optical in-band crosstalk occurs when a signal and interferers have close value wavelengths. As a consequence, the signal and interferers are within the pass band of practical optical filter. Generally such filter is located at the front end of the receiver and interference causes a serious degradation in the system performance. As the interference is not mitigated, optical in-band crosstalk will propagate with the DWDM channels. The destructive effect of this type of crosstalk accumulates in the optical nodes. In such case, the desired signal and the leak signal have an identical wavelength. We have considered the same laser source for all the channels. At the output of the cross-connect, the multiplexers collect all wavelength channels together and the resulting output channels suffer from the crosstalk caused due to the demultiplexer and the space switch located at the output multiplexer. The destructive impact on the desired channels is enhanced by the fact that both the signals have almost same wavelength and the resulting beat terms are spectrally located within the receiver bandwidth. If several cross-connects are connected in a cascaded configuration in the network then the in-band crosstalk grows dramatically causing more serious degradation in system performance. Further, the coherent nature of the crosstalk degrades the performance. When crosstalk interferers and the desired signal are generated from different laser sources or from the same source but delayed by much longer period than the laser coherence length, the beating product will have incoherent nature. Optical out-band crosstalk arises from inadequately suppressed neighboring wavelength channels in the de-multiplexers, which also contributes to the crosstalk.

As shown in Fig. 1. The OXC is implemented by connecting the outputs of a WDM de-multiplexer to the inputs of a WDM multiplexer through crossbar switches. A specified wavelength channel can be passed to a desired output by activating the switch either in cross or in bar-state. The fraction of interfering signals gets leaked into the other space switches. For M wavelengths per fiber for N such fibers, interference with the desired signal can be written as 211 −+=−+− NMNM . These contributions can be coherent or incoherent depending upon whether they combine with the desired signal within the coherence time of the source or not. We have categorized the OXC generated crosstalk as coherent and incoherent crosstalk and considered the coherent contributions only.

A. Crosstalk estimation

Let an optical signal of peak power Ps is fed into an optical fiber with power levels, ONP and OFFP depending upon logical ONE’s and ZERO’s present in the input data sequence. The power levels can be related to the average output power avP , and nonzero extinction ratio r [4], as

Input Fibers

Output

Fibers

Optical Space Optical

Demultiplexer Switch Multiplexer

Fig.1. Structure of an Optical crossconnect (OXC) node. The dotted line shows the crosstalk signal leak.

"0";1

2

"1";1

2

forPr

forPr

rP

av

avs

+=

+=

(1)

The optical field of the desired signal in the fiber corresponding to the laser source will be described as the complex form [5],

])(exp[)( ssssss titiPrtE θφω ++= (2)

where sr expresses the state of polarization, sω the optical

angular frequency, )(tsφ the instantaneous optical phase and

sθ is the initial phase of the laser where ‘s’ denotes the desired signal. This desired signal could be interfered by k crosstalk contributions from k-transmitted signals. The total interfering field )(txE can be written as

( )dkkx tEtE τ−∑=)( (3)

where, )(tEk is the field corresponding to interfering signals

and dτ denotes the propagation delay. The total optical field, comprising the desired and the interfering fields ( 2−+ NM contributions), incident upon a photodetector is given as

1

2

3

4

λ1....λM

λ1... λM

λ1....λM

λ1....λM

978-1-4244-7173-7/10/$26.00©2010 IEEE

jljljljjlN

j

X

ljjljlj

kskksksksX

kks

ssssss

xshp

rtititbPPc

rtititbPcP

tititbPr

tEtEtE

])()(exp[)(2

])()(exp[)(

])(exp[)(

)()()(

2 1

2

1

θτφτωτ

θτφτωτ

θφω

Δ+−+−∑ ∑ −+

Δ+−+−−∑+

++=

+=

= =

=

(4)

where, c is the crosstalk parameter, given by the ratio of crosstalk power kP to the input power sP . )(tbs and

)(tb j are the binary data sequences with the bit interval T of

the desired signal and crosstalk signal respectively. jP and

lP are the crosstalk contributions from other wavelength channels of same nominal wavelength and other input fibers respectively. kr and jlr are the state of polarization for the

contributions. [ ]1,0 −∈ MX is the number of crosstalk signals leaked from the desired signal through the M space switches. These contributions are generally treated as the delayed version of the main signal while propagating through the crossconnect. skθΔ and jlθΔ are the phase differences between the signal with its delayed contribution and the number of beating terms respectively. kτ and jlτ are the propagation delay differences of the interfering signals and the beating signals respectively. Equation (4) has mainly three terms, first term to the right part indicates the desired signal, the second term indicates the crosstalk contributions due to the desired signal itself as a delayed one, and the third term is the interfering signal leaked from other signals at the same wavelength.

B. Power penalty estimation

The power penalty calculation at any intermediate OXC node can be done on the basis of minimum received power at that node and the noise components at the receiver itself. Perfect dispersion compensation is considered, so that the signal distortions due to dispersion are negligible. We assume IM/DD (Intensity Modulation/Direct Detection) system using OOK (On-Off Keying) with symbols transmitted with nonzero extinction ratio. The photocurrent at the output of the photodetector for the OXC node is given by

22)()()()( tEtERtERti xsphph +== (5)

where R )e/(hνη= is the photodetector responsitivity. While detecting this combined signal at the receiver the dominant noise terms involved are the signal crosstalk beat noise, shot noise, thermal noise. Therefore the total noise power in the receiver bandwidth, eB is given as in [6]

∫++=−

Be

BeNFRshotN fSRtt )()()( 2222 σσσ (6)

where, 2Nσ is noise power at the output of the receiver, is the

summation of quantum or shot noise, thermal noise, input amplifier noise current source and the input amplifier noise voltage source. This noise power decides the minimum detectable signal power at the receiver. The third term in (6)

)( fS N is the two-sided noise spectral density including the signal induced shot noise and amplified spontaneous emission (ASE) noise of the photodetector current.

The power penalty is calculated by taking the logarithmic ratio of the minimum received signal level to achieve specific BER with the crosstalk contributions to that of the minimum detected power to achieve the same BER without crosstalk contributions,

s

REC

PRP

dBpenaltyPower210log)( = (7)

RECP is the minimum detected signal along with the crosstalk terms [7].

C. BER and blocking probability estimation The −Q factor is calculated at the receiver, which is related to the BER ( )eP being the error probability. It is given by

OFFON

OFFON IIQσσ +

−=

=⎟⎠⎞⎜

⎝⎛ ++⎟

⎠⎞⎜

⎝⎛ +

+−

CTKOFFOFFCTKONON

avPrr

,22,22112

σσσσ (8)

CTKONON ,,σσ and CTKOFFOFF ,,σσ are signal and noise powers corresponding to ON state and OFF state respectively. Signal power fed in the desired signal is ONP considering all ONE’s. We have considered the unequal powered case of interferes [8].

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=

−

QPBER

Q

e

2

2

exp21)(π

(9)

The wavelength blocking probability in circuit switched networks can be calculated by considering M available wavelengths over H OXC nodes. If the optical network is said to have no wavelength converters at OXC nodes then considering the wavelength channel request arrives as a Poisson process with arrival rate α and the holding time of every wavelength channel is considered to be exponential

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distribution with parameter δ then the traffic behavior is modeled based on birth-death process, where jα is the birth

rate and jδ is the death rate for the respective wavelength

channel j . The steady state probability of the birth-death process is given as [9], [10]

( ) Myy

yoP

ymYP ……1,0,!

'

)( =⎟⎠⎞

⎜⎝⎛=

δα (10)

where, ( )ymYP )( denotes the PDF of the simultaneously

transmitting channels and 'oP is evaluated using the

normalization condition ( ) 1=∑ yYP , therefore

( )∑=

=

∑=

⎟⎠⎞

⎜⎝⎛

=M

yys

yM

y

y

y

oP

0 !11

0 !1

1'

δα

(11)

where, δα=s is the traffic load carried by the transmitting

channels. As we are concern with the crosstalk contributions here, the wavelength channel will be blocked considering the detector error probability. The probability of having number of simultaneously transmitting wavelength channels and the probability of having error in those active channels are statistically independent processes. Therefore the wavelength assignment is based on BER and pp criterion. The

probability of blocking bP in terms of BER at the OXC node is given as ,

∑==

M

mmemYb PyPP

1)()( )( (12)

It can be seen from the results that if the crosstalk is minimized, it will reduce the terminal BER as well as the power penalty, causing more paths available for the routing. This in turn reduces the wavelength blocking and would minimize the congestion of links at the expense of more nodes to be traveled.

III. WAVELENGTH ASSIGNMENT STRATEGY

To concentrate on crosstalk impairment effect, here we have neglected path loss and attenuation aspects. The WA strategy will estimate BER for predefined available path and will assign the wavelength only when it satisfies the performance criteria. We call the blocking probability to be BER blocking probability and power penalty blocking probability. Hence BER blocking probability is defined as the wavelength rejection when the BER estimation performed upon the given wavelength channel shows unsatisfactory

result, also power penalty blocking probability is defined as the wavelength blocking for greater than ppdB1 .

IV. RESULTS AND DISCUSSION

The crosstalk model helps in determining the amount of crosstalk component accumulated at each node. When the number of wavelengths increases, it causes more crosstalk thereby causing more power penalty. Blocking probability is less than 0.01 for the crosstalk level is – 30 dB and the channel population is 50 given in Fig.2. The channel blocking is negligible if crosstalk levels are considered at low levels. To show this the crosstalk level is assumed to be varying between – 55 dB to – 10 dB. The plots of power penalty as a function of crosstalk level for different wavelength count are given in Fig. 3. The result show that above – 20 dB level of crosstalk the power penalty is greater than the threshold value of 1 dB. Therefore the blocking probability will be high at that time.

Fig.2. Crosstalk versus blocking probability for number of wavelength channels 20, 40 and 50 from bottom to top in graph.

The BER blocking probability is plotted against crosstalk in Fig. 4. The blocking of channels is dependent on the code length and the amount of traffic carried. When considering 20 wavelength channels each having code length of 300 and traffic load as 300 with the crosstalk level of – 25 dB and for equal value of linewidth and receiver bandwidth, the blocking probability is approximately 0.01.

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Fig.3. Crosstalk Vs power penalty

Fig.4. Crosstalk versus blocking probability

Fig.5. Node count versus OSNR for different crosstalk level.

It can be seen from the results in Fig. 5, that the threshold value of OSNR can be set to 2 dB for 20 stages of OXCs even though the crosstalk level is – 20 dB. Better value of OSNR can be achieved for lesser crosstalk levels. OSNR of the

system defines the QoS for the given network. The results obtained will help in deciding the possible number of stages in a network to maintain better QoS. Linewidth of the laser source also contributes to the blocking probability in the network. We have analyzed the impact of ∆ν/BW, linewidth to bandwidth ratio on network performance. Figure 6 shows the plots for blocking probability as a function of ∆ν/BW ratio. The larger values of linewidth will reduce the blocking probability.

Fig.6. Blocking probability as a function of ∆ν/BW ratio for different crosstalk levels.

V. CONCLUSION

Allocation of wavelength in establishment of optical path from source to destination is one of the critical requirements. The assignment of wavelength controls the performance of the networks. In this paper, we have studied and discussed the impact of crosstalk on the wavelength assignment in static wavelength routing mechanism. With number of wavelength channels crosstalk components and in turn the blocking probability are also increases. We have studied a WA strategy which will be based on knowledge of crosstalk, power penalty as well as blocking probability. We have also analyzed the worst case where the number of wavelength channels are 20 with maximum traffic load of 600 and maximum code length of 600. Our result show that wavelength blocking can be below 0.04 for the worst case with the crosstalk level of – 25 dB. OSNR can be set to the threshold value of 2 dB for a network of 20 stages. The blocking probability of 0.01 can be obtained when the linewidth equals the receiver bandwidth for the – 25 dB crosstalk level. To increase number of hops in the network for required QoS one should ensure and limit the crosstalk and power penalty levels by choosing proper design parameters as discussed in the paper.

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