Impact of Channel Spacing on the Design of a Mixed-Line-RateOptical Network

Avishek Nag and Massimo TornatoreUniversity of California, Davis, USA

Email: {anag, mtornatore}@ucdavis.edu

Abstract-Due to the increasing heterogeneity and the growingvolume of traffic, telecom backbone networks are going throughnew innovations and paradigm shift. The wavelength-divisionmultiplexed (WDM) optical networks may cost-effectively sup­port the growing heterogeneity of traffic demands by havingmixed line rates (MLR) over different wavelength channels.

The coexistence of wavelength channels with different linerates in the same fiber brings up the important issue of the choiceof the channel spacing that one can have in these MLR networks.The channel spacing affects the signal quality in terms of bit­error rate (BER), and hence affects the maximum reach of theIightpaths, which is a function of line rates. Various approachesto set an opportunistic width of the channel spacing can beconsidered: i) on a practical side, one may choose uniform fixedchannel spacing specified by the ITU-T grid (typically 50 GHz);ii) alternatively, to optimize the usage of the fiber spectrum, onecan explore different channel spacing for different line rates, alsoreferred to as the "one-size-does-not-fit-all" approach; iii) elsean optimal value of channel spacing that leads to minimum costcan be sought.

In this work, we investigate the third case by evaluating thecost of a MLR network for different channel spacings. Our resultsshow that, even under the assumption of uniform channel spacingfor a MLR network, it is possible to identify optimal values ofchannel spacing for a minimum-cost MLR network design.

Index Terms-Optical Network, WDM, Network Design,Mixed Line Rate, Maximum Transmission Range, Bit-Error Rate,Channel Spacing.

I. INTRODUCTION

Today's backbone telecom networks employing opticalwavelength-division multiplexing (WDM) technology are onthe verge of a paradigm shift. Increasing heterogeneity inthe traffic, and the ever-increasing need for bandwidth, maymake it convenient to set up lightpaths on these networks withmultiple line rates. Such networks can be termed as mixed­line-rate (MLR) optical networks: in [1], [2] it has been shownthat MLR networks are more cost-effective than a single-line­rate (SLR) network and design methods for MLR networkshave been presented. Other related works on this topic [3], [4],[5], focus on how to upgrade the network by putting higher linerates, e.g., 40-Gbps and 100-Gbps line rates, over an existing10-Gbps SLR network.

In MLR networks, different wavelength channels can havedifferent capacities. So, the WDM channel spacing is animportant issue. Most works consider the coexistence ofmultiple line rates on the same fiber, assuming a fixed channelspacing of 50 GHz, which is an ITU-T specification. InMLR networks that support line rates up to 40 Gbps, thischannel spacing is compatible with comparatively simple mod­ulation techniques such as on-off keying, optical duobinary,etc. But, if we want to fit a 100-Gbps signal into a 50-

GHz grid, then the role of modulation formats becomesvery important, because their spectral efficiency needs tobe very high to support high bit rates over narrow channelspacing. For instance, in [4], [5], the authors propose advancedmodulation formats, such as differential quadrature phase­shift keying (DQPSK), polarization-multiplexed DQPSK, andoptical orthogonal frequency-division multiplexing (OOFDM),to fit-in 40/100 Gbps over an existing 10-Gbps infrastructure.Therefore, if a network operator wants to preserve a fixedchannel spacing of 50 GHz, then it can only resort to advancedmodulation formats to support multiple line rates.

The choice of channel spacing is significant in a MLRscenario, especially if one needs to have a uniform modulationformat throughout the network'. On one hand, small channelspacing may bandlimit the high-bit-rate signals and degradetheir BER and, hence, the maximum optical reach becomeslimited. On the other hand, if the channel spacing is high, thelow-bit-rate signals may have poor BER because more opticalnoise (amplified spontaneous emission (ASE) noise from theoptical amplifiers) will be added (more discussion in SectionII). Thus, having a fixed channel spacing in a MLR networkleads to penalties, at least for a subset of the line rates. So,the question is: what should be the optimum channel spacingso that these penalties are minimized?

So, how the channel spacing affects the MLR networkdesign is an important problem. In earlier works [1], [2], wehave shown how the different set of available lightpaths overdifferent line rates significantly affects the total network costin terms of transponders (based on the fixed threshold BER,different line rates will have different maximal reach). Now,the set of available lightpaths will also be a function of thechannel spacing. Therefore, in this paper, we solve variousinstances of the MLR network-design problem for differentvalues of fixed channel spacing and investigate if there is anyoptimum value of channel spacing for a minimum-cost MLRnetwork design.

II. PROBLEM DESCRIPTION

In MLR network design, as discussed in [1], [2], the BERof the lightpaths sets the feasibility of a particular line ratefor a given source-destination (s-d) pair. The BER modelconsisted of physical impairments such as switch crosstalk,optical amplifier noise (ASE noise), dispersion, laser center

1This assumption appears to be more practical because optical switcheswith uniform filters are cheaper and easier to operate and design. Anotheralternative can be to use different channel spacings on the same network. In[6], the authors propose different channel spacings for different line rates.

V (i ,j)

V (i ,j) (3)

V (m, n), V >. (4)

if s = jif d = jotherwise

L L X ijk>. . CXijk>. S; 1i, j EP",n k

L L rk . X ijk>. . CXijk>' ~ L f&dx k s,d

(5)The solution to this ILP is a set of lightpaths between the

s-d pairs over different line rates and wavelengths, which carryall the demands. These set of lightpaths in the global solutionis a subset of a pre-computed set of feasible lightpaths ; thefeasibility depends on whether the BER of the paths are belowa certain threshold. With variation in channel spacing, this pre­computed set of lightpaths changes and we obtain a differentsolution. In the next section, we present our results.

III. RESULTS AND DISCUSSION

We present our results in the form of total network cost(total cost of transponders) for different values of channelspacing and different traffic volumes. The example networkis the 14-node topology shown in Fig. 2; and the nonuniformtraffic matrix is given in Table I. It represents a total trafficof 1 Tbps, which is multiplied by different factors (e.g., 1,5, 10, 20) to represent a range of loads. The costs of 10­Gbps, 40-Gbps, and 100-Gbps transponders are, respectively,

of the MLR network gains an added dimension if we considerthe channel spacing as a parameter.

The design problem formulation thus remains mostly similaras in [I] . The problem turns out to be an integer linear program(ILP), which minimizes the overall network cost in terms oftransponders. For completeness, the formulation is providedbelow.Input Parameters:G(V,E): Physical topology of the network with V nodes andE links; T = [Asd]: Traffic matrix with aggregate demandsAsd in Gbps between a s-d pair; R = {rl ' r2, . . . , rk} :Set of available channel rates; Di: Cost of a transponderwith rate n: L ij : Length of the lightpath between a s­d pair (in km); lmn : Physical link between nodes m-n;W : Maximum number of wavelengths supported on a link,>. E {I, 2, . , . ,W}; B: Threshold BER: a lightpath witha higher BER will be rejected; BERijk>.: BER for thelightpath between a s-d pair ij at rate rk and wavelength >.;

_{I if BERijk>. S; B V(' ')k >..CXijk>' - 0 otherwise 2, J , , ,

Pmn: Set of lightpaths passing through link lmn.Variables:X ijk>.: Number of lightpaths at rate rk and wavelength >.between nodes ij; ftl Traffic from source s to destinationd routed on lightpath ij .Problem Formulation:

Minimize : L L L X ijk>. . o, (2)such that x ij k

1 0'~'-0 ------'40'--------'SO-.....LaO- --1...1OO- --L120- j-'--40-j-LSO-1.L..aO----'200OplicalChannel Spacingin GHz

Fig. I. HER vs. optical channel spacing for 40-Gbps DQPSK system witha lightpath length of 1000 km.

Now, this variability of BER with B; will be line-rate­sensitive. Thus, with different values of B o, the set of admis­sible lightpaths over different line rates will change and thiswill result in different optimum cost for the network . Thus,the capacity-vs.-reach tradeoff which affects the overall cost

frequency offset, and optical filter misalignment. The crosstalkand ASE noise generate beat noise terms in the receiver. Boththe beat noises' power and the received signal power arestrong functions of the optical filter bandwidth Bo , i.e., of thechannel spacing. Therefore, the BER, which is a function ofthe signal-to-noise ratio (see Eqn. (1) below), is also a functionof the channel spacing . The formula for the BER and the noisepowers are reported below for reference :

1 IT lsI - ITBER = -4 [erfc( M ) + er fc ( M )] (1)

y2aO y2al

where IT = O"oI!I+o)I,o and I and I are the sig-0"0+0"1' s l sO

nal current due to " I" and "0" reception, respectively; andafi = a;h + a;hO + a;p_sp + a;_ x + a ;_sp; ar = a;h +2+2 +2 +2 +2 +2.2a sh 1 a sp- sp a x-x ax-s~ a s 1-x a s1-sp' a t h

is the thermal-noise variance; a shO is the shot-noise vari­ance for "0" reception; a;hl is the shot-noise variance for"I" tion: 2 2 2 2 d 2recep ion; a sp- sp' a x- x' a x- sp' a sl- x' an a s1-sp arethe spontaneous-spontaneous, crosstalk-crosstalk, crosstalk­spontaneous, signal-crosstalk, and signal-spontaneous beat­noise variances, respectively.

The BER decreases with increasing B; at lower valuesof B; and then attains a minimum at an optimum valueof B; (Fig. I). This is because , at lower values of Bo,

the received optical power gets bandlimited and so does thecrosstalk power, but the BER becomes high as signal is notstrong enough to combat the total noise power including allof its components (the summation of all the noise variances) .With increasing Bo, the signal loss decreases faster thanthe reduction in crosstalk power, as the signal-crosstalk beatnoise is distributed over a bandwidth wider than the electricalsignal components. This results in the improvement of BERwith increasing B; for small values of bandwidth. As thebandwidth increases beyond its optimum value, truncation insignal spectrum becomes negligible but signal-crosstalk beatcontinues to increase and so does the signal-spontaneous beat.This explains the increase of the BER beyond the optimumti:

10.3r--- - - - - - - - - - - - - ----,

Fig. 2. I4-node NSF network (link lengths in km).TABLE I

TRAFFIC MATRIX FORN SF N ETWORK (EACH ENTRY IS IN GBPS).

Node 1 2 3 4 5 6 7 8 9 10 11 12 13 141 0 2 I I 1 4 I 1 2 I I I I I2 2 0 2 I 8 2 I 5 3 5 I 5 I 43 1 2 0 2 3 2 11 20 5 2 I I I 24 1 I 2 0 1 1 2 1 2 2 I 2 I 25 1 8 3 I 0 3 3 7 3 3 I 5 2 56 4 2 2 I 3 0 2 1 2 2 I I I 27 I I II 2 3 2 0 9 4 20 I 8 I 48 I 5 20 I 7 1 9 0 27 7 2 3 2 49 2 3 5 2 3 2 4 27 0 75 2 9 3 I10 1 5 2 2 3 2 20 7 75 0 I 1 2 111 1 I 1 1 1 1 1 2 2 1 0 2 1 6112 1 5 I 2 5 1 8 3 9 I 2 0 I 8113 1 I I I 2 1 I 2 3 2 I I 0 214 I 4 2 2 5 2 4 4 I I 6 1 81 2 0

l x ,2 .5x and 3.75x as in [7]. Thus, higher-rate transpondersprovide volume discount. The modulation format is DQPSK,the threshold BER is 10-3, and other physical layer parametersare identical as in [8]. The number of available wavelengthsW on a fiber is chosen such that the total spectrum usage inthe C-band is 4 THz (e.g., for 50-GHz spacing, W =80; andfor 100-GHz spacing, W=40 .).

Figure 3 shows results for non-uniform (using the trafficmatrix in Table I) and uniform (i.e., equal traffic for all the s­d pairs) traffic demands. For nonuniform traffic, the total costfirst comes down as channel spacing increases. The cost isminimum at a channel spacing of 80 GHz and then the costrises up again slightly. This is because, for smaller channelspacing, the number of high-bit-rate paths is less due to

bandlimiting. So the volume discount is not fully exploited.Then, as the channel spacing increases, some higher-bit-ratepaths become feasible and the cost goes down because thevolume discount can be exploited in a better way. At the sametime, due to the increase in channel spacing, the number ofavailable wavelengths decreases as well as some ofthe low-bit­rate paths become infeasible (due to more noise as discussedin Section II). Both these factors have an increasing effect onthe cost.

If low-bit-rate paths are fewer compared to the high-bit­rate paths, then for some small demands there would havebeen over-provisioning of capacity which tends to increasethe cost. Similarly, if the number of wavelengths are less, thesolution space becomes constrained and the cost tends to gethigher.

Thus, the combined effect ofall these factors makes the totalcost a concave function of the channel spacing. This concavityis more pronounced at higher volumes of traffic.

For uniform traffic, the cost shows the same behavior withchannel spacing. Here, the concavity is more pronounced thanin case of nonuniform traffic. This is because, in case ofnonuniform traffic, most of the bulky demands are along shortdistances, in contrast to the uniform traffic case, where all s-dpairs have equal volume of traffic. Hence, the change in the setof feasible lightpaths with change in channel spacing affectsthe uniform traffic case more.

IV. CONCLUSION

We have investigated the effect of channel spacing on thedesign of a MLR network. We have shown that, as channelspacing increases, the network cost (in terms of transponders)comes down up to a certain optimum channel spacing, andbeyond the optimum channel spacing, the cost increases. Thebehavior of network cost with channel spacing may varywith network topologies. Larger topologies may exhibit moresensitivity of the cost with channel spacing. We plan to extendthis work, with different practical topologies, in future.

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