Coherent And Incoherent Crosstalk In WDM

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 5, MAY 1999

759

Coherent and Incoherent Crosstalk in WDM Optical Networks Yunfeng Shen, Kejie Lu, and Wanyi Gu, Member, IEEE

Abstract— The impact of coherent and incoherent crosstalk on an optical signal passing through optical cross-connect nodes (OXC’s) in wavelength division multiplexing (WDM) optical networks is studied, and the analytical expressions are given. Such crosstalk will be generated when the optical propagation delay differences of optical paths in an OXC do not exceed the coherent time of the lasers. While causing fluctuation of signal power, coherent crosstalk may cause noise or not, depending on the relationship between the optical propagation delay differences and the time duration of one bit of the signal. Incoherent crosstalk may cause very high noise power, because it can be a coherent combination of crosstalk contributions. The statistical impact of all crosstalk contributions on signal is studied by simulation, and the concept of quantile is proposed to relax the crosstalk specification requirement for components. The crosstalk specification requirements are then obtained for components used in WDM optical networks with different scales. Index Terms—Coherent crosstalk, incoherent crosstalk, optical cross-connect, optical networks, wavelength division multiplexing (WDM).

I. INTRODUCTION

W

AVELENGTH division multiplexing (WDM) optical networks are attracting more and more attention because of their ability to provide increased capacity and flexibility [1]. Optical cross-connect node (OXC) is an essential network element in WDM optical networks [2]. While crossconnecting wavelengths from input to output fibers, OXC introduces homodyne crosstalk which has the same wavelength as the signal and degrades the transmission performance seriously [3]–[6]. Homodyne crosstalk can be divided into coherent crosstalk, whose phase is correlated with the signal considered, and incoherent crosstalk, whose phase is not correlated with the signal considered. Coherent crosstalk is believed not to cause noise but cause fluctuation of signal power [6]. This is true only under the condition that the optical propagation delay differences are much less than the time duration of one bit of the signal. In this paper, we show that coherent crosstalk also causes noise when this condition is not satisfied. The impact of incoherent crosstalk on signal transmission performance has been studied in [3]–[5], but the details of incoherent crosstalk have not been analyzed, as we will show that such crosstalk may also be a coherent combination of crosstalk contributions and then cause much higher noise power.

Manuscript received August 10, 1998; revised January 8, 1999. The authors are with the Optical Communication Center, Beijing University of Posts and Telecommunications, Beijing, China. Publisher Item Identifier S 0733-8724(99)03809-8.

Fig. 1. Typical structure of an OXC and the introduced crosstalk contributions.

When an optical signal passes through an OXC, many crosstalk contributions are combined with the signal. The number of contributions leaked from each signal with the same wavelength as the signal considered is in random depending on the cross-connecting state of the OXC. The optical propagation delay differences and polarization states of the crosstalk contributions are also in random and drift with respect to one another due to thermal and mechanical fluctuations in minutes on timescale. Therefore, the transmission performance also varies from time to time. We studied the statistical impact of coherent and incoherent crosstalk in an OXC and in optical networks and then proposed the concept of quantile to relax the crosstalk specification requirement for components such as wavelength demultiplexer, multiplexer, and optical switch. II. COHERENT AND INCOHERENT CROSSTALK IN AN OXC A typical structure of OXC is shown in Fig. 1. The OXC optical demultiplexers, optical consists of a total of multiplexers. Each of the input fibers to switches, and different wavelengths. an optical demultiplexer contains The optical demultiplexer spatially separates the incoming paths. Each of these paths passes through wavelengths into an optical switch before they are combined with the outputs optical switches. from the other Assuming the OXC is fully loaded, each signal passing homodyne through the OXC will be interfered by of which are leaked by the crosstalk contributions, are leaked by the optical switch, and the other demultiplexer/multiplexer pair. For facilitating the description,

0733–8724/99$10.00  1999 IEEE

760


we now consider the signal with wavelength 1 in input fiber or the main signal, in the rest of this paper. 1, noted as is also true for other signals. The following analysis for will be interfered by crosstalk The main signal signals with wavelength contributions leaked from the input fibers, , , when 1 in the other passing through the optical switch 1 because of the nonideal crosstalk crosstalk specification of optical switches. The contributions can be treated as generated by different lasers , and with each and then are phase incorrelated with other. Similarly, when each signal with wavelength 1 is demultiplexed to one path, there will be a fraction of it outputs of the corresponding in each of the other demultiplexer because of the nonideal crosstalk specification of optical demultiplexers. Passed through the optical switches, signals with the main signal is multiplexed with crosstalk different wavelengths. At the same time, the paths are contributions of wavelength 1 in these combined with the main signal though isolated again by the crosstalk contributions can optical multiplexer. These be leaked from any signal with wavelength 1 in all the input fibers. Note that some of them can be leaked from , i.e., the main signal itself. The number of contributions leaked , depending from each signal is in random, from 0 to as the on the cross-connecting state of the OXC. Defining in a given state of number of contributions leaked from the OXC, we have

noises of the lasers, respectively; is the unit magnitude , and , are the polarization vector of the signal; , propagation delay differences and unit magnitude polarization vectors of the contributions, respectively; is the optical power ratio of each crosstalk contribution to the signal, and for simplicity, we assume all the crosstalk contributions have the are treated as time-invariant here same power. , , and as they change rather slowly compared to the bit period. The first term of the right part of (4) is the field of the main signal, the second term is of the crosstalk contributions leaked from the main signal itself and the third term is of the contributions leaked from the other signals with the same wavelength. and : If the optical propagation 1) If delay differences in an OXC exceed the coherent time of the ) , is incorrelated with laser, i.e., ( and , and are also incorrelated with each crosstalk other for different . Therefore, all the contributions (incoherent with each other) are incoherent with the signal. In this case, the field of the main signal and all the crosstalk contributions can be generally expressed as

(1)

, , , and are the binary data sequence, where center frequency, phase noise, and unit magnitude polarization is vector of the th crosstalk contribution, respectively. even for the contributions leaked from incorrelated with the main signal itself because is long enough and they are not synchronous. Assuming all the signals with wavelength , when 1 have exact the same center frequency, i.e., , the normalized photocurrent caused by the signal and crosstalk is

Defining leaked from account the 1, we have

as the number of contributions in the same state of the OXC, taking into contributions leaked by the optical switch (2)

and

(5)

(3) The field of the main signal and all the contributions can be expressed as

crosstalk

(4) is the signal field amplitude which is assumed to where and be unchanged as the leaked power is rather low; are the binary data sequences with values and , respectively, , of 0 or 1 in a bit period of , and , are the center frequencies and phase

(6) in which the subscript 1 states for the case discussed in this section. Similarly, the subscripts 2, 2a, and 2b in the following equations state for the case discussed in Section II-A and B, respectively. The second term of the right part of (6) is the signal-crosstalk beat noise and is a result of the laser relative intensity noise (RIN). The terms of high orders of are neglected because is rather low. By calculating the autocovariance of the beat noise and making Fourier transformation, the noise power can be expressed as [4], [5] (7) (8) where

is the polarization angle difference between the th

SHEN et al.: COHERENT/INCOHERENT CROSSTALK IN WDM OPTICAL NETWORKS

crosstalk contribution and the signal. Here we assume the case for high-speed systems whose receiver bandwidths are wider than the signal-crosstalk beat noise spectrum. Because is not synchronous with , we take the average of the in bit periods to be 0.5. When integrations of and the lasers have ideal extinction radio, there is no noise. With the fixed decision-threshold setting, the power penalty is given by [5, eq. (7)], [7, eq. (22)] dB for BER

where Max

761

(11) are coherent with the main signal. On the other hand, the composite crosstalks in the third term are incoherent crosstalk, while each of them is a coherent combination of a random number of crosstalk contributions. After they are received by a photodetector whose response factor is one, the normalized photocurrent is given by

(9) 10

9

. The maxim of

is

Max (12)

(10) where the maxim of noise power equals the sum of the optical powers of the contributions. In the process of deriving noise powers and power penalties, we assume both the beat noise and the receiver noise existing in the absence of crosstalk have Gaussian probability density distribution. Though the probability density distribution of beat noise is not Gaussian when there is only one crosstalk contribution [7], it is found experimentally that the distribution gradually becomes Gaussian as the number of crosstalk contributions increase [5]. This agrees with the central limit theorem. The condition we discussed is just with a large number of crosstalk contributions. The probability density distribution of noise at the receiver side in the absence of crosstalk is also not Gaussian when amplified spontaneous emission (ASE) of erbium doped fiber amplifiers (EDFA’s) dominates other noise sources [8]. For simplicity in the derivation of the analytic expression of the system power penalty caused by crosstalk, we still assume that the receiver noise has Gaussian probability density distribution. Though the derived power penalty may not be very accurate, such inaccuracy is of little significance for the conclusion we derived through the comparison between power penalties before and after introducing the concept of quantile. and : If , when two 2) If contributions are or more contributions in the fractions of a same signal, they would combine coherently and to form a composite crosstalk. In this case, can be treated as equaling to and , respectively. The magnitude of each composite crosstalk is determined by the phase relation among the contributions. Equation (4) can then be expressed as

(11) Crosstalk contributions in the second term of the right part of

, , , , , and represents the polarization angle differences between the crosstalk contributions and the signal. In . The three terms in (12) (12), we used the condition represent photocurrent generated by signal, beat part between signal and coherent crosstalk, and beat part between signal and incoherent crosstalk, respectively. and : If the optical propagation dea) If lay differences are much less than the time duration of one , equal to approximately. The bit, i.e., second term in (12) can be added to the signal as a random but time-invariant amount. Therefore, coherent crosstalk does not cause noise, but causes fluctuation of the signal power in this , the normalized signal photocurrent is case. When

where

(13) is incorThe third term in (12) is beat noise because . When , the noise power can be related with expressed by the same way as (7) as

(14) is incorrelated with and where we assume . From (14) we can see that this noise power may be is high and all much higher than that in (7) when any . its and : If the OXC is not an integrated b) If one but equipped with individual components, the optical path length differences may exceed the length of one bit period (approximately 0.08 m for 2.5 Gb/s systems and 0.02 m . In this case, for 10 Gb/s systems), i.e., become incorrelated completely with , because is a random sequence and they are not synchronous. When in a bit period , the amount of is in random with different and has a mean of 0.5. Therefore, if the receiver has a integration decision method, the second term in (12) is time-

762


variant and causes noise to the signal. This noise power caused by coherent crosstalk is (15) represents the second term in (12). We assume that are incorrelated with different , and so their noise power can be added directly. The normalized mean signal current in this case should be

where

(16) Fig. 2. The normalized histograms of pp1 ; pp2a , and pp2b (" =

The noise power caused by incoherent crosstalk is hard to express exactly. However, we can still use (14) since the beat noise is much more dominant. So, the noise power is

(17) Assuming both the beat noise and receiver noise have Gaussian probability density distribution, the bit error rate (BER) in case (2a) and (2b) can be expressed as BER

erfc

erfc (18)

, and could be BER BER , where BER , , and , respectively; is the denotes the receiver noise which exists decision-threshold; is fixed to 0.5, the power in the absence of crosstalk. If 10 9 is given by penalty at BER (19) where

could be , ; for BER , however, the power penalty is

10

9

. If

(20) Because fluctuates rather slowly and receiver should be able , (20) is used in the to adjust the decision-threshold to is not so high and is small enough, rest of this paper. If is always small compared to 1, the maxims of i.e., and take place when all the crosstalk both contributions introduced by the demultiplexer/multiplexer pair are coherent with each other but not with the main signal and are all “1” or “ 1.” It can be expressed as their Max

(21)

040 dB).

III. STATISTICAL IMPACT OF COHERENT AND INCOHERENT CROSSTALK The cross-connecting state of an OXC is changed continuously (though slowly) depending on the routing of optical and then change correspondingly. Furthermore, signals. is very sensitive to fluctuations of laser frequency and optical path length in OXC due to thermal or mechanical fluctuations because the frequency of optical signal is very also drifts because the polarization state of each high. crosstalk contribution changes slowly. Therefore, the exact impact of coherent and incoherent crosstalk on signal transmission performance changes in minutes on timescale. Because the probability that all the crosstalk contributions increase the noise power in the worst way is rather low, the statistical impact of them should be studied. Ten million iterations are generated to illustrate the nor, and in Fig. 2 when malized histograms of dB. Each iteration of the simulation generates and ), random cross-connecting state (corresponding to and random and which are uniformly distributed in the for each crosstalk contribution. and interval are assumed to be 8 and 4, respectively in the rest of this paper. Power penalties are then calculated using (9) and (20). is rather centralized and We find that the distribution of drops down quickly with increasing power penalty. On the and have long other hand, the distributions of and trails toward high power penalty, which means can be much higher than . We can also see that and overlap each other when the distributions of the power penalty is high. The reason is high power penalties crosstalk contributions leaked happen when most of the by multiplexer/demultiplexer pair are leaked from a same signals and are coherent with each signal of the other other, and so the number of crosstalk contributions that are coherent with the main signal is small. Thus, the difference between condition 2a and 2b caused by coherent crosstalk is small. To ensure the transmission performance, the crosstalk level of components must be low enough to ensure that the highest possible power penalty is not higher than a standard, 1 dB in most networks. The method which considers the worst cases is used in most published papers [3], [4]. This method is a good because even the worst power penalty is not too one for

SHEN et al.: COHERENT/INCOHERENT CROSSTALK IN WDM OPTICAL NETWORKS

763

Fig. 3. The power penalties versus crosstalk level " in one OXC for different cases (quantile = 10 6 ).

Fig. 4. The crosstalk specification requirement versus the number of nodes optical signal passing through (pp = 1 dB).

high (0.34 dB in Fig. 2) and can be limited to lower than 1 dB by components with normal crosstalk specification. For and , however, Max is so high (6.5 dB in Fig. 2) that very small is required to satisfy the standard. In order to relax the crosstalk specification requirement for components, the concept of quantile is proposed here. It is used to specify a probability of unacceptable high power penalty generated due to crosstalk. The power penalty corresponding to this probability is found and treated as the highest possible power penalty. The specified probability should be bigger than the probability that actual power penalty is higher than the found one, and it also should be considerably less than that of failure due to other reasons, such as cable breaks or deteriorating laser transmitters. 10 6 , a probability which corresponds to a failure time of around 30 s/yr, seems to be a good quantile. (The selection of the quantile is discussed in Section IV.) The highest possible power penalties with the quantile (10 6 ) and the maxim of power penalties of the three cases with different are calculated and shown in Fig. 3. We find increases much more quickly than Max that Max which means much more power penalty would be generated if . If dB is needed, has to be lower than 44 dB for Max and 36 dB for Max , respectively. When the quantile (10 6 ) is used, the crosstalk specification requirement for components reduces to 42 and 35.5 dB, and with the quantile respectively. The curves of overlap in Fig. 3, so we do not distinguish between them in the rest of this paper.

dB is needed. With the increase of the number of OXC signals passed, the crosstalk specification requirement and Max increases rather quickly because for Max the maxims of the noise powers increase linearly with . If is used in designing an optical network, crosstalk Max specification of components used in the network has to be lower than 57 dB when 20 is set as the highest number a signal can pass transparently. It is a strict requirement on components. Though the introduction of quantile (10 6 ) relaxes only 2 dB of the crosstalk specification in Section III, the effect improves when the number of nodes increase. The crosstalk specification requirement increases rather slowly and , i.e., 8 dB relaxation is obtained. is 49 dB when The crosstalk specification can be even lower than that of when is more than 20. The fluctuation in the Max curves with quantile arises from the random of the simulation. From the three curves with quantile of 10 4 , 10 5 , and 10 6 , we find that the crosstalk specification requirement increases with rather small steps. It can be anticipated that the crosstalk specification can be still much lower than that when a smaller quantile is used. There is also of Max when , though smaller than a 2 dB relaxation for . that of

0

IV. NETWORK SCALING If a signal passes OXC’s in a WDM optical network, crosstalk contributions with there would be the main signal when it is detected. The number of coherent crosstalk contributions in this case is the total of the number signals with the same in each OXC. All the other wavelength can be treated as generated by different lasers. So and in the equations above should be replaced the and . The in (7) should by . We simulate the variables be replaced by OXC’s and calculate the crosstalk specification in all the requirements for components with different in Fig. 4 when

V. CONCLUSION Under the condition that the optical propagation delay differences of optical paths in an OXC are less than the coherent time of the lasers, coherent and incoherent crosstalk may generate much more power penalty than that of the case when this condition is not satisfied. Coherent crosstalk causes fluctuation of signal power, and it may cause noise or not, depending on the relationship of delay differences and the bit period of the signal. Incoherent crosstalk may generate much more noise power because its contributions are still coherent with each other. The introduction of quantile can relax the crosstalk specification requirement for components based on the statistic analysis of the impact of coherent and incoherent crosstalk. In the designing of OXC, the optical propagation delay differences should be set to be longer than the coherent time of the lasers in order to reduce the impact of crosstalk.

764


REFERENCES [1] G. R. Hill, P. J. Chidgey, F. Kaufhold, T. Lynch, O. Sahlen, M. Gustavsson, M. Janson, B. Lagerstrom, G. Grasso, F. Meli, S. Johansson, J. Ingers, L. Fernandez, S. Rotolo, A. Antonielli, S. Tebaldini, E. Vezzoni, R. Caddedu, N. Caponio, F. Testa, A. Scavennec, M. J. O’Mahony, J. Zhou, A. Yu, W. Sohler, U. Rust, and H. Herrmann, “A transport network layer based on optical network elements,” J. Lightwave Technol., vol. 11, pp. 667–679, May/June 1993. [2] E. Iannone and R. Sabella, “Optical path technologies: A comparison among different cross-connect architectures,” J. Lightwave Technol., vol. 14, pp. 2184–2196, Oct. 1996. [3] E. L. Goldstein, L. Eskildsen, and A. F. Elrefaie, “Performance implications of component crosstalk in transparent lightwave networks,” IEEE Photon. Technol. Lett., vol. 6, pp. 657–660, May 1994. [4] C. S. Li and F. Tong, “Crosstalk and interference penalty in all-optical networks using static wavelength routers,” J. Lightwave Technol., vol. 14, pp. 1120–1126, June 1996. [5] H. Takahashi, K. Oda, and H. Toba, “Impact of crosstalk in an arrayedoptical interconnection,” J. Lightwave waveguide multiplexer on Technol., vol. 14, pp. 1097–1105, June 1996. [6] S. D. Dods, J. P. R. Lacey, and R. S. Tucker, “Homodyne crosstalk in WDM ring and bus networks,” IEEE Photon. Technol. Lett., vol. 9, pp. 1285–1287, Sept. 1997. [7] J. L. Gimlett and N. K. Cheung, “Effects of phase-to-intensity noise conversion by multiple reflections on gigabit-per-second DFB laser transmission systems,” J. Lightwave Technol., vol. 7, pp. 888–895, June 1989. [8] D. Marcuse, “Derivation of analytical expression for the bit-error probability in lightwave systems with optical amplifiers,” J. Lightwave Technol., vol. 8, pp. 1816–1823, Dec. 1990.

N 2N

Yunfeng Shen was born in Henan Province, China, in November 1973. He received the Bachelor degree in telecommunication and control engineering from Northern Jia Tong University, China, and the Ph.D. degree in electromagnetic field and microwave technology from Beijing University of Posts and Telecommunications, Beijing, China, in 1994 and 1998, respectively. His research interests include optical crossconnect systems and WDM optical networks.

Kejie Lu was born in Fuzhou, China, in December 1973. He received the Bachelor degree in communications engineering and the Master degree in communications and electronic system from Beijing University of Posts and Telecommunications, Beijing, China, in 1994 and 1998, respectively. His interests include ATM network, optic ATM, flow control, and routing algorithm.

Wanyi Gu (M’95) received the B.S. degree in physics from Peking University, Peking, China, in 1970, and the M.S. degree in electromagnetic field and microwave technology from Beijing University of Posts and Telecommunications, Beijing, China, in 1982. She is presently a Professor and the Dean at the College of Telecommunication Engineering, Beijing University of Posts and Telecommunications. Her research interests include high-speed optical communication systems, broad-band subcarrier multiplexed lightwave systems, and WDM optical networks. She has authored more than 50 papers in the field of optical fiber communications. Prof. Gu was awarded the Science and Technology Progress Prize by the Chinese former Ministry of Posts and Telecommunications.