crosstalk noise in wdm-based optical networks-on-chip: a ... · device parameters, we present a...

2552 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 11, NOVEMBER 2015

Crosstalk Noise in WDM-Based Optical Networks-on-Chip: A Formal Study and Comparison

Mahdi Nikdast, Member, IEEE, Jiang Xu, Member, IEEE, Luan Huu Kinh Duong,Xiaowen Wu, Student Member, IEEE, Xuan Wang, Student Member, IEEE,

Zhehui Wang, Zhe Wang, Peng Yang, Yaoyao Ye, and Qinfen Hao

Abstract— Optical networks-on-chip (ONoCs) usingwavelength-division multiplexing (WDM) technology haveprogressively attracted more and more attention for their use intackling the high-power consumption and low bandwidth issuesin growing metallic interconnection networks in multiprocessorsystems-on-chip. However, the basic optical devices employed toconstruct WDM-based ONoCs are imperfect and suffer frominevitable power loss and crosstalk noise. Furthermore, whenemploying WDM, optical signals of various wavelengths caninterfere with each other through different optical switchingelements within the network, creating crosstalk noise. As aresult, the crosstalk noise in large-scale WDM-based ONoCsaccumulates and causes severe performance degradation,restricts the network scalability, and considerably attenuates thesignal-to-noise ratio (SNR). In this paper, we systematically studyand compare the worst case as well as the average crosstalk noiseand SNR in three well-known optical interconnect architectures,mesh-based, folded-torus-based, and fat-tree-based ONoCsusing WDM. The analytical models for the worst case and theaverage crosstalk noise and SNR in the different architecturesare presented. Furthermore, the proposed analytical modelsare integrated into a newly developed crosstalk noise and lossanalysis platform (CLAP) to analyze the crosstalk noise andSNR in WDM-based ONoCs of any network size using anarbitrary optical router. Utilizing CLAP, we compare the worstcase as well as the average crosstalk noise and SNR in differentWDM-based ONoC architectures. Furthermore, we indicatehow the SNR changes in respect to variations in the numberof optical wavelengths in use, the free-spectral range, and themicroresonators Q factor. The analyses’ results demonstratethat the crosstalk noise is of critical concern to WDM-basedONoCs: in the worst case, the crosstalk noise power exceeds thesignal power in all three WDM-based ONoC architectures, evenwhen the number of processor cores is small, e.g., 64.

Index Terms— Optical crosstalk noise, optical interconnects,optical losses, signal-to-noise ratio (SNR), wavelength-divisionmultiplexing (WDM).

I. INTRODUCTION

ON-CHIP communication in multiprocessor systems-on-chip (MPSoCs) is rapidly growing due to the

Manuscript received April 1, 2014; revised August 18, 2014; acceptedOctober 21, 2014. Date of publication December 5, 2014; date of currentversion October 21, 2015. This work was supported by Huawei TechnologiesCompany, Ltd.

M. Nikdast, J. Xu, L. H. K. Duong, X. Wu, X. Wang, Z. Wang,Z. Wang, and P. Yang are with the Department of Electronic andComputer Engineering, Hong Kong University of Science and Technology,Hong Kong (e-mail: [email protected]; [email protected]).

Y. Ye and Q. Hao are with Huawei Technologies Company, Ltd.,Shenzhen 518129, China.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVLSI.2014.2370892

integration of many processor cores on a single die.Networks-on-chip (NoCs) can bring better scalability andperformance to the traditional communication infrastructurein MPSoCs. However, as the technology continues to scaledown and allows integration of an even larger number ofprocessor cores, the metallic interconnects’ power dissipationin NoCs will progressively increase to a considerable portionof the system power budget, becoming a bottleneck. On-chip optical communication and integration technologies, how-ever, present an appealing solution for outperforming the lowbandwidth, high latency, and high-power dissipating metal-lic interconnects in MPSoCs. Furthermore, the employmentof wavelength-division multiplexing (WDM) technology inoptical NoCs (ONoCs) can further boost the bandwidth in opti-cal interconnects through concurrent transmission of multipleoptical signals on a single waveguide.

Several optical NoCs employing WDM with high-capacityand low-power consumption have been proposed basedon mesh, torus, and fat-tree topologies, in which opticalwaveguides and microresonators (MRs) are extensivelyused [2]–[4]. These basic photonic devices, however, sufferfrom inevitable crosstalk noise and power loss. Some com-ponents in WDM-based ONoCs, such as filters, wavelengthmultiplexers/demultiplexers, switches, and semiconductoroptical amplifiers, introduce interchannel and intrachannelcrosstalk noise. Interchannel crosstalk noise occurs when thecrosstalk signal is at a wavelength different from the desiredsignal’s wavelength, while intrachannel crosstalk noise occurswhen the crosstalk signal is at the same wavelength as thatof the desired signal or sufficiently close to it. Intrachan-nel crosstalk effects can be much more severe than thoseof interchannel crosstalk since they cannot be removed byfiltering [5]. In this paper, we focus on analyzing first-orderincoherent interchannel and intrachannel crosstalk noise, andfor convenience, we use crosstalk noise when referring to thetwo types in the rest of this paper. In large-scale WDM-basedONoCs, the crosstalk noise from the basic photonic devicesin the optical switching elements and from the interferencesamong the different wavelengths in the WDM-based networkaccumulates on the optical signal in question and eventuallydiminishes the signal-to-noise ratio (SNR) as well as imposesscalability constraints. The SNR determines the feasibilityof WDM-based ONoCs, and thus it is essential to find andanalyze the worst case and the average SNR in differentWDM-based ONoCs. In addition, the analysis of crosstalknoise and SNR is topology dependent and is different in

1063-8210 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

NIKDAST et al.: CROSSTALK NOISE IN WDM-BASED ONoCs 2553

various WDM-based ONoC architectures, necessitating thedevelopment of a unique approach for each architecture torealize the SNR analysis in that architecture.

The worst case crosstalk noise and SNR in arbitrary mesh-based, folded-torus-based, and fat-tree-based ONoCs wereanalyzed in [6]–[8]. The proposed formal analytical modelsat the device, router, and network levels in those works arebased on the consideration of a single wavelength only, andhence cannot consider the impact of the interchannel andintrachannel crosstalk noise existing in WDM-based networks.Moreover, they only consider the worst case crosstalk noiseand SNR analyses; however, the average analyses are also ofvital importance. In addition, Duong et al. [9] presented ananalysis of the worst case SNR specifically for a case studyof WDM-based ring-based ONoCs, the corona network.

The novel contribution of this paper is presentinga systematic study and comparison of the worst caseas well as the average crosstalk noise, power loss, andSNR in mesh-based, folded-torus-based, and fat-tree-basedONoCs using WDM. We present formal analyses for realcase studies of WDM-based mesh-based and WDM-basedfolded-torus-based ONoCs using the Crux optical router andWDM-based fat-tree-based ONoCs using the optical turn-around router (OTAR). Moreover, the newly developedcrosstalk and loss analysis platform (CLAP), presented in [7],has been upgraded by including the proposed formal analyticalmodels for the worst case and the average crosstalk noiseand SNR in arbitrary WDM-based ONoCs. The proposedanalytical models for modulators and photodectors as well asthe fat-tree topology are also included in CLAP. The analysesstart hierarchically from the basic photonic device level, to theoptical router level, and finally, to the network level. Therefore,the analytical models at the network level can be easilytranslated into the initial device level models for validation.The analytical models proposed for the basic optical elementscan be applied to any WDM-based ONoC. Utilizing theproposed analyses, CLAP, and considering recent photonicdevice parameters, we present a detailed study and comparisonof the worst case and the average crosstalk noise power,signal power, and SNR in WDM-based mesh-based, folded-torus-based, and fat-tree-based ONoCs. The quantitative sim-ulation results signify the severe effect of crosstalk noise inWDM-based ONoCs: the worst case and the averageSNR decrease exponentially in WDM-based ONoCs as thenetwork scales. Furthermore, the SNR in WDM-based ONoCsis reversely related to the number of employed optical wave-lengths in the network: the SNR drops quickly as the numberof optical wavelengths in use increases over a fixedfree-spectral range (FSR).

We analyze mesh-based and folded-torus-based ONoCs ofa hybrid structure consisting of a packet-switched electronicnetwork, for controlling the photonic network and routingcontrol packets, and a circuit-switched photonic network,which is responsible for transmitting the payload data. Thefat-tree-based ONoC is a hierarchical, multistage networkin which payload data and network control data are bothbeing transmitted on the same optical network. An off-chipvertical cavity surface emitting laser (VCSEL) is considered

as the laser source. Dimension-ordered routing is used inthe mesh-based and folded-torus-based networks, while theoptical turnaround routing algorithm is considered in the fat-tree-based networks. Analyses of dynamic variations in opticaldevices, such as laser and thermal noise, as well as fabricationvariations are not considered in this paper.

The rest of this paper is organized as follows. Section IIsummarizes some of the related works. Section III describesdetailed analyses of the basic optical elements and opticalrouters used in WDM-based ONoCs. We present the worstcase as well as the average crosstalk noise and SNR analysesat the network level in Section IV. Section V presents thequantitative simulation results and comparisons. Finally, theconclusion is drawn in Section VI.

II. RELATED WORKS

Although there are several works that have tackled thecrosstalk noise issue at the device level [10]–[12], only afew works have explored it at the network level in ONoCs.Xie et al. [13] studied the worst case crosstalk noise and SNRin mesh-based ONoCs using an optimized optical crossbarrouter. In the same work, it was proved that the worst caseSNR link is not always the longest optical link, which suffersfrom the highest power loss in the network. Moreover,a compact high-SNR optical router, called the Crux opticalrouter, was proposed to improve the SNR of ONoCs. The samegroup systematically analyzed the worst case crosstalk noiseand SNR in general mesh-based ONoCs using an arbitraryoptical router in [6]. In addition, Nikdast et al. [7], [8]proposed formal analytical approaches to analyze the worstcase crosstalk noise and SNR in folded-torus-based andfat-tree-based ONoCs using arbitrary optical routers. TheONoC considered in all the aforementioned works utilizesa single-wavelength approach.

Chan et al. [14] proposed a methodology to characterize andmodel basic photonic blocks, which can form full photonicnetwork architectures, and used a physical-layer simulatorto assess the physical-layer and system-level performance ofa photonic network. Vaez and Lea [15] indicated that thecrosstalk noise is an intrinsic, serious issue in directional-coupler-based optical networks, and Lin and Lea [16] devel-oped an analytical model to characterize the crosstalk noiselevel in a microring-based optical interconnection network.The fundamental limits for the number of WDM channels andpower per channel when using building blocks that includesilicon waveguides, silicon microring modulators, and filterswere described in [17].

III. BASIC OPTICAL ELEMENTS AND OPTICAL

ROUTERS IN WDM-BASED ONOCS

Almost every component in WDM-based ONoCs introducescrosstalk noise. Among these components, those presented andstudied in this paper have the highest impact on the worst caseand the average SNR in WDM-based ONOCs. Waveguidesand MRs are the two fundamental optical elements employedto construct basic optical switching elements (BOSEs) andoptical routers. Optical routers consist of BOSEs, waveguide


Fig. 1. Basic optical elements and BOSEs: (a) Waveguide crossing, (b) PSE in ON and OFF states, (c) Optical terminator, and (d) CSE in ON and OFF states.

Fig. 2. (a) Optical modulator, and (b) photodetector models as a part of theE-O and O-E interfaces.

crossings, waveguide bendings, and optical terminators. Thewaveguide crossing, shown in Fig. 1(a), is a structure consist-ing of two crossed orthogonal waveguides. Two types of basic1 × 2 optical switching elements are the parallel switchingelement (PSE) and the crossing switching element (CSE).The PSE consists of an MR located between two parallelwaveguides, as shown in Fig. 1(b). The optical terminator,shown in Fig. 1(c), is responsible for absorbing the opticalsignal at the input port and then avoiding it reflecting backonto the input port. The structure shown in Fig. 1(d), consistingof an MR adjacently positioned next to a waveguide crossingintersection, is the CSE.

WDM-based ONoCs also include optical modulators andphotodetectors in their electronic-optical (E-O) and optical-electronic (O-E) interfaces. The optical modulator as a partof the E-O interface is responsible for modulating the opticalsignal by an information data signal at the very beginning ofany on-chip optical communication. In this paper, we considerexternal modulation, in which the optical signal is modulatedafter its generation at the laser source. The optical photode-tector as a part of the O-E interface is employed to detect

TABLE I

POWER LOSS VALUES, CROSSTALK NOISE,

AND REFLECTANCE COEFFICIENTS

the modulated optical signal at the end of the communicationline at the receiver. Fig. 2 shows the optical modulators andphotodetectors in WDM-based ONoCs. We consider an activeMR-based switching technique, in which the MRs can bepowered ON (the ON state) or OFF (the OFF state) by applyingan electrical voltage to the p-n contacts surrounding thering.

We analyze and model the power loss and crosstalknoise in basic optical devices and later in optical routersin WDM-based ONoCs in this section. Table I lists thenotations and their recent values considered for power loss,crosstalk noise, and reflectance coefficients in basic opti-cal elements [11], [14], [18]–[20]. It is worth mentioningthat the proposed analytical models in this paper are basedon the defined notations, and hence the power loss andcoefficient values listed in Table I are used only as anexample.

A. Analytical Models for Basic Elements

Considering the waveguide crossing in Fig. 1(a), the inputoptical signal of the wavelength λn passes the crossingintersection with some insertion loss at the out1 output port,


while there is a portion of the signal power which goes tothe out2 and out3 output ports and also reflects back on theinput port. Given Pλn

in as the power of the optical signal atthe input port, (1) calculates the output powers at the out1,out2, and out3 output ports, Pλn

out1, Pλnout2, and Pλn

out3, as well asthe reflected power, Pλn

Rc , on the input port in the waveguidecrossing. In (1) and also the rest of the equations in this paper,n is the number of the optical wavelength under study andn ∈ [1,W], where W is the total number of wavelengths con-sidered in the network. In addition, λn indicates the wavelengthnumber and is not an exponent

PλnOut1 = Lc Pλn

in (1a)

PλnOut2 = P

λn

Out3 = Kc Pλnin (1b)

PλnRc = Kr Pλn

in . (1c)

The main function of an optical terminator is to absorb theinput light and prevent it from reflecting back onto the inputport. A recent approach for terminating waveguides, consid-ered in this paper, is through deeply etched gratings [20].When an optical signal of the wavelength λn and with theoptical power Pλn

in enters an optical terminator, as shownin Fig. 1(c), the reflected power on the input port of the opticalterminator can be defined as

PλnR = Kt Pλn

in . (2)

Prior to studying the power loss and crosstalk noise in thePSE and CSE, we present an analytical model to characterizethe interchannel and intrachannel crosstalk noise (see ourdiscussion in Section I) in MR-based photonic switchingelements. MRs have a lorentzian power transfer function,which is peaked at the resonant wavelength λMR. For opticalsignals carried on wavelength λn , the power transferred tothe drop port can be expressed as (3a) [21]. In this equation,κ2

e and κ2e are the fraction of the optical power that the lower

waveguide and the upper waveguide couple into or out of theMR, respectively [Fig. 1(b)]. Moreover, κ2

p is the fraction ofthe intrinsic power losses per round trip in the MR. Whenκ2

d + κ2e � κ2

p , nearly full power transfer can be achievedat the peak resonance point, and the MR will exhibit a lowinsertion loss. Without loss of generality, we suppose thatκ2

d + κ2e � κ2

p and κd = κe. As a result, the coefficient beforeψ(n, λMR m) in (3a) is equal to one

Pλndrop

Pλnin

=(

2κeκd

κ2e + κ2

d + κ2p

)2

· ψ(n, λMRm) (3a)

where

ψ(n, λMR m) = δ2

(λn − λMRm)2 + δ2 . (3b)

In (3b), 2δ is the 3-dB bandwidth of the MR and it can bedefined as Q = (λMR/2δ), in which Q is the quality factorof the MR. When an optical signal of the wavelength λn

passes the MR m with the resonant wavelength λMRm(λn �= λMRm), a portion of the optical signal carried on λn

couples into the ring and is directed to the drop port [Fig. 1(b)],generating crosstalk noise. According to (3b), the amount of

this crosstalk noise is determined by the spacing betweenλn and λMRm and the 3-dB bandwidth of the MR. In thispaper, we suppose equal spacing among different opticalwavelengths that cover a whole FSR. As a result, the spacingbetween the two consecutive wavelengths λn and λn+1, whenthe total number of wavelengths is W, equals (FSR/W).Therefore, for the optical signal of the wavelength λn , we haveλn = λ0 + ((n − 1)FSR/W). Similarly, for the MRm , one cannote that λMRm = λMR0+((m − 1)FSR/W). In the former andlatter equations, λ0 and λMR0 can be decided by the systemdesigner and we assume that λ0 = λMR0.

Considering Fig. 1(b) and when the PSE is in the ON state,the input optical signal of the wavelength λn couples into theMR n, whose resonant wavelength is equal to λn (λn = λMRn),and makes a turn to the drop port, while a portion of the powergoes to the through port as crosstalk noise. Please note thatwe only consider the first-order incoherent crosstalk noise inthis paper, and hence when the PSE is in the ON state, thecrosstalk noise from different wavelengths on the drop portis not considered. In addition, the two optical signals shownin Fig. 1(b) and (d) have the same optical wavelength of λn ,but are from different power sources and hence incoherent.When an optical signal of the wavelength λn passes a PSEin the ON state, the output powers at the through, PT , anddrop, PD , ports of the PSE are calculated in

PTλnpse,ON = K p1 LW−1

p0 Pλnin (4a)

PDλnpse,ON = L2(n−1)

p0 L p1 Pλnin . (4b)

According to Fig. 1(b), when the PSE is in the OFF state,the optical signal carried on the wavelength λn travels fromthe input port to the through port, while a portion of thesignal (crosstalk noise) couples into the ring n, whose resonantwavelength is now shifted to the OFF state at λ

′MRn = λMRn+ε

and ε < (FSR/W), and goes to the drop port. Furthermore,portions of the optical signals on the other wavelengthsthan λn , say λm where m ∈ [1,W ] and n �= m, also coupleinto the ring n, creating crosstalk noise. When the PSE is inthe OFF state, (5) calculates the output powers at the throughand drop ports. As can be seen in this equation, for theoptical signal of the wavelength λn passing the MR n in theOFF state, the crosstalk coefficient is assumed to be K p0, aslisted in Table I, since λn is the closest wavelength to λ

′MRn .

However, (3b) helps calculate the crosstalk coefficient forthe same optical signal passing other MRs than the ring n,whose resonant wavelengths are farther from λn . A similarassumption is considered in (4a) for using K p1 when thePSE is in the ON state. In addition, to simplify the analyticalmodels, we assume the use of average passing and droplosses in the PSEs, L p0 and L p1 listed in Table I, for opticalsignals of different wavelengths and under different values ofFSR and Q

PTλnpse,OFF = LW

p0 Pλnin (5a)

PDλnpse,OFF = K p0 L2(n−1)

p0 Pλnin

+W∑

j=1, j �=n

(L2( j−1)

p0 ψ(n, λ

′MR j

))Pλn

in . (5b)


The CSE is composed of a waveguide crossing anda PSE. Leveraging the analytical models of the PSE and thewaveguide crossing, we model the power loss and crosstalknoise in the CSE. Regarding Fig. 1(d), when the CSE is inthe ON state, the output powers at the through and drop portsfor an input optical signal of the wavelength λn are defined in

PTλncse,ON = K p1 LW−1

p0 Lc Pλnin (6a)

PDλncse,ON = L2(n−1)

p0 L p1 Pλnin . (6b)

Considering the CSE in the OFF state, the output powers atthe through, drop, and add ports for an input optical signalcarried on the wavelength λn is calculated in (7). As can beseen from (6) and (7), the analytical models for the CSE arebased on the analyses of the PSE and waveguide crossing. Forexample, the output power at the through port of the CSE inthe ON state is associated with the passing loss of the PSEin the ON state, PT pse,ON defined in (4a), and the crossingloss in the waveguide crossing, POut1 calculated in (1a). It isworth mentioning that PAcse,ON = PR cse,ON = PRcse,OFF = 0since the first-order incoherent crosstalk noise is considered.In addition, for simplification, the bending loss between theadd and drop ports is not considered

PTλncse,OFF = LW

p0 Lc Pλnin (7a)

PDλncse,OFF = K p0 L2(n−1)

p0 Pλnin

+W∑

j=1, j �=n

(L2( j−1)

p0 ψ(n, λ

′MR j

))Pλn

in +LWp0Kc Pλn

in (7b)

PAλncse,OFF = LW

p0 Kc Pλnin . (7c)

The optical modulator structure, as a part of theE-O interface, is shown in Fig. 2(a) in which it is assumedthat no crossing exists between the waveguides transmittingpower and the one carrying data. We carefully studied differentpossible modulation structures, and the one shown in Fig. 2resulted in low crosstalk noise by separating different opticalwavelengths at the modulation and switching stages before theout port. The optical signal of the wavelength λn is generatedat its corresponding VCSEL, VCSEL λn , then is modulated atthe modulator Mn , and finally is directed to the communicationline toward the out port through the MR n. The power of theoptical signal carried on the wavelength λn at the out portin the optical modulator is calculated in (8). In this equation,Pv is the optical signal power at the VCSEL and Lm is theaverage modulation loss at the modulator. In this paper, weassume that Lm = L p0

PλnMsignal = Lm LW−n

p0 L2b L p1 Pλn

v . (8)

Fig. 2(b) shows the photodetector structure as a part of theO-E interface. The optical signal of the wavelength λn couplesinto the MR n and then is directed to the photodetec-tor n, P Dn . When the power of the optical signal onthe wavelength λn at the input port of the photodetectorequals Pλn

in , (9a) defines the signal power received at thephotodetector n, Pλn

Dsignal, while (9b) calculates the crosstalknoise from the optical signals on the other wavelengths

Fig. 3. (a) Crux optical router and (b) OTAR designed for WDM-basedONoCs using W optical wavelengths.

received at that photodetector, PλnDnoise. It is worth mentioning

that different from Fig. 1(b), this crosstalk noise is incoherent

PλnDsignal = Ln−1

p0 L p1 Pλnin (9a)

PλnDnoise = L(n−1)

p0

⎛⎝ W∑

j=n+1

ψ( j, λMRn)

⎞⎠ Pλn

in . (9b)

B. Crosstalk Noise in WDM-Based Optical Routers

Optical routers are the key components in ONoCs sincethey transmit information between a source and a destinationprocessor. Different optical routers have been proposed formesh-based, folded-torus-based, and fat-tree-based ONoCs.Fig. 3 shows the Crux optical router, which is used in mesh-based and folded-torus-based ONoCs using WDM, and theOTAR, which is designed for fat-tree-based ONoCs usingWDM. Both optical routers can route optical signals onW different wavelengths. The Crux optical router has fiveinput and five output ports. Each port is assigned with anumber and can be shown as Ii , where i equals 0 for theinjection/ejection, 1 for the North, 2 for the East, 3 for theSouth, and 4 for the West. However, the OTAR has four inputand four output ports, including the upper left, upper right,lower right, and lower left ports. The numbers assigned tothese ports are i = 0 for the upper left, i = 1 for the upperright, i = 2 for the lower right, and i = 3 for the lower left.The numbers assigned to the different ports in both opticalrouters are shown in Fig. 3. The Crux optical router is basedon the dimension-ordered routing algorithm, also known as


the XY routing algorithm, while the OTAR uses the opticalturnaround routing technique proposed in [4]. In the analyticalequations in this paper, the subscript a is used when the Cruxoptical router is employed and b is considered when the OTARis used. Furthermore, the abbreviations M, Ft, Ftr, Wtc, andAvg are used for convenience while referring to mesh, folded-torus, fat-tree, worst case, and average, respectively. It is worthmentioning that the proposed analytical models for the Cruxoptical router (OTAR) can be applied to any other 5×5 (4×4)optical router

Lλna,i, j =

⎧⎪⎨⎪⎩

Sλna,Li,0

LWλn

l i,0p , j = 0

Sλna,Li, j

LHM|Ft +Wλn

l i, jp , j �= 0

i, j Z ∈ {0, . . . , 4}. (10)

Utilizing the analytical models defined for the basic opticalelements, we start with analyzing the power loss in the Cruxoptical router. Lλn

a,i, j , as defined in (10), is the insertion lossfrom the ith input port to the jth output port in the Crux opticalrouter for an optical signal carried on the wavelength λn .In this equation, Sλn

a,Li, jindicates the switching loss

that accounts for losses from passing or coupling intoMRs (L p0 or L p1), passing waveguide crossings (Lc), andpassing waveguide bendings (Lb) in the optical router.Moreover, the propagation loss inside the optical router is cal-culated by considering the waveguide length travelled by theoptical signal λn between the ith input port and the jth outputport, Wλn

l i, j , and the propagation loss, L p (Table I). We inte-grate the propagation loss at the network level into our opticalrouter model: when the output port is not the ejection, j �= 0,we consider the propagation loss of the waveguide that con-nects the optical router to the next one, as shown in (10).HM |Ft is the hop length and can be calculated based onHM |Ft ∼= (S/M × N )1/2 in homogeneous symmetrical mesh-based and folded-torus-based ONoCs. S is the chip size incm2, and M × N is the network size

Lλnb,i, j =

⎧⎪⎨⎪⎩

Sλnb,L i, j

LWλn

l i, j +2HFtr

p , destination

Sλnb,L i, j

LWλn

l i, j +HFtr

p , otherwise

i, j ∈ {0, . . . , 3}. (11)

Similar to (10), the insertion loss imposed on the opticalsignal of the wavelength λn travelling from the ith input porttoward the jth output port in the OTAR is analyzed in (11).In this equation, the propagation loss of either L HFtr

p , whenthe current optical router is not the destination, or L2HFtr

p ,when the current router is the destination, is added to thepropagation loss analysis at the router level. HFtr is thehop length in optimized fat-tree-based ONoCs and can beapproximated using HFtr ∼= (S/R × C)1/2, where R and Care the number of processor cores located, respectively, in arow and a column of the optimized floorplan of fat-tree-basedONoCs [22]. According to (10) and (11), it is obvious thatLλn

a|b,i, j �= Lλea|b,i, j and when n �= e.

When an optical signal of the wavelength λn whose poweris Pλn

i enters the ith input port of the optical router, the power

of that optical signal at the jth output port of the opticalrouter, Pλn

i, j , is defined in (12). In this equation, Lλna|b,i, j is the

insertion loss from the optical router and it can be calculatedusing (10) and (11)

Pλni, j = Pλn

i Lλna|b,i, j . (12)

When an optical signal of the wavelength λn , which werefer to as the considered optical signal, and other opticalsignals from other power sources carried on the same opticalwavelength, which we refer to as interfering optical signals,simultaneously pass through a single optical router, crosstalknoise will be introduced to the considered optical signal fromthose interfering optical signals. nλn

i, j , as calculated in (13), isdefined as the crosstalk noise power added to the consideredoptical signal on the wavelength λn traveling from the ith inputport toward the jth output port in the optical router

nλni, j =

prt_num∑m=0

⎛⎝Pλn

m Lλnm, j Xλn

i, j,m +W∑

e=1,e �=n

(Pλn

m Lλnm, j Y

ei, j,m

)⎞⎠(13)

where

Y ei, j,m ≡ ψ(n, λMRe|λ′

MRe).

In this equation, Xλni, j,m is the crosstalk noise coefficient

introduced by the interfering optical signals of the wave-length λn , which are entering the optical router through theinput port m, to the considered optical signal through thewaveguide crossings and MRs associated with λn , i.e., MRn .Moreover, Y e

i, j,m , which is associated with ψ(n, λMRe|λ′MRe),

is the crosstalk noise coefficient from the interfering opticalsignals of the wavelength λn , but through MRs MRe ande �= n. Pm is the power of the interfering optical signal at theinput port m, and Lm, j is the insertion loss from the mth inputport to the jth output port excluding the loss of the element atwhich the interfering optical signal mixes with the consideredoptical signal. In this equation, prt_num = 4 when the Cruxoptical router is used and prt_num = 3 when the OTAR isconsidered

SNRλn = 10 log

(Pλn

S

PλnN

). (14)

The SNR of the optical signal carried on the wavelength λn isdefined as the ratio of the signal power to the power of thecrosstalk noise corrupting the signal, as described in (14),where Pλn

S is the optical signal power and PλnN is the crosstalk

noise power received at the photodetector PDn in the receiver.Utilizing the analytical models proposed in this section, we

present an example of the OTAR in Fig. 4 to indicate howto analyze the crosstalk noise and power loss at the opticalrouter level. We consider the use of two wavelengths (W = 2),λ1 and λ2, in this example, and we present the analysesfor the optical signal on the wavelength λ2. In the figure,the considered optical signals of the wavelengths λ1 and λ2(shown in red) are travelling from the upper right input porttoward the lower right output port, i = 1 and j = 2,while there are two other interfering optical signals carried


Fig. 4. Example of interference between two optical signals in the OTAR(W = 2).

Fig. 5. Abstract overview of an optical communication betweenprocessors c0 and c1 in WDM-based ONoCs.

on the same wavelengths (shown in blue) travelling from theupper left input port to the lower left output port, m = 0,and they mix with the considered optical signals through theCSE shown in the figure. There are other possible interferingoptical signals from other input ports, and those from theupper left to the lower left ports are indicated as an example.Employing (11) and (12), the signal power at the lower rightoutput port is Pλ2

1,2 = Pλ21 Lλ2

b,1,2 = Pλ21 L2

b L4p0 L2

c , in which Pλ21

is the power of the optical signal carried on the wavelength λ2at the upper right input port. Considering (13), the crosstalknoise power added to the considered optical signal on thewavelength λ2, nλ2

1,2, and received at the lower right outputport is defined in

nλ21,2 = Pλ2

0 Lλ2b,0,2

(Xλ2

1,2,0 + Y 11,2,0

)= Pλ2

0 L2b L2

p0 L2c

((Kc + L2

p0 L2c K p0

) + L2cψ

(2, λ

′MR1

)).

(15)

The SNR at the lower right output port can be calculated usingthe received signal power and the crosstalk noise power atthis port. Following the same approach defined in (15), wecan calculate the total crosstalk noise power from interferingoptical signals to a considered optical signal at each opticalrouter on the considered optical link in the network.

IV. SNR IN WDM-BASED OPTICAL NETWORKS-ON-CHIP

Leveraging the proposed analytical models for basic pho-tonic devices and optical routers, we present crosstalk noiseand SNR analyses at the network level for WDM-basedONoCs in this section. Fig. 5 shows an overview of an

on-chip optical communication in WDM-based ONoCs. Whenthe processor core c0 decides to communicate with anotherprocessor core c1, optical signals of different wavelengthswill be generated at off-chip VSCELs and then they willbe modulated at the modulators in the E-O interface of theprocessor c0. Those optical signals then pass through theoptical switching network and ultimately will be received atthe processor core c1 after being detected at the photodectorsin the O-E interface of that processor. All along this opticalpath, however, the optical signals on different wavelengthssuffer from power losses and crosstalk noise will also beaccumulated on them. When an optical signal carried on thewavelength λn travels from the processor core c0 toward thecore c1, the signal power received at the latter core can becalculated based on

PLλn(c0,c1)

= Pλnv Lλn

Mod Lλn(c0,c1)Net

LλnDet. (16)

In this equation, Pλnv is the optical power at the VCSEL n

generating an optical signal on the wavelength λn . Moreover,Lλn

Mod and LλnDet, can be calculated based on (8) and (9a),

and are, respectively, the modulation loss and detection lossimposed on the optical signal of the wavelength λn , whileLλn(c0,c1)Net

denotes the power loss from passing the opticalrouters in the optical switching network, and it can be calcu-lated using (10) and (11). The subscript Net varies based on theONoC architecture in use, and it can be M , Ft , or Ftr whenconsidering mesh-based, folded-torus-based, or fat-tree-basedONoCs, respectively. While Lλn

Mod and LλnDet are the same for

different WDM-based ONoCs in this paper, Lλn(c0,c1)Net

relies

on the topological properties of each ONoC architecture andhence is different in various WDM-based ONoCs.

The crosstalk noise from the interfering optical signals accu-mulated on the considered optical signal of the wavelength λn

while it is travelling from the processor core c0 toward thecore c1 is calculated in

Nλn(c0,c1)

= NλnMod + Nλn

(c0,c1)Net+ Nλn

Det . (17)

In this equation, NλnMod and Nλn

Det , defined in (9b), showthe crosstalk noise power from the modulator and detector,respectively. Furthermore, Nλn

(c0,c1)Netis the crosstalk noise

introduced to the optical signal on the wavelength λn throughthe optical routers inside the optical switching network.We assume that NMod ∼= 0 since the amount of crosstalk noisefrom the modulators at the receiver side is negligible. Nλn

Det isthe same in different WDM-based ONoCs, but analyzingNλn(c0,c1)Net

depends on each ONoC architecture. In this section,an effort is made to systematically analyze the worst case aswell as the average Lλn

(c0,c1)Netand Nλn

(c0,c1)Netin the three well-

known ONoC architectures, mesh-based, folded-torus-based,and fat-tree-based ONoCs using WDM.

Figs. 6 and 7, respectively, show M × N WDM-basedmesh-based and folded-torus-based ONoCs, and the opti-mized WDM-based fat-tree-based ONoC comprises k proces-sor cores. In these figures, the optical signals of differentwavelengths are shown using a single optical signal for con-venience. As Fig. 7 shows, when the number of processor


Fig. 6. (a) and (c) Worst case and (b) and (d) average SNR optical linksin M × N WDM-based mesh-based and folded-torus-based ONoCs using theCrux optical router and W wavelengths.

cores is equal to k, there are a total number of log2 k − 1levels in the fat tree. Each level is assigned with a number,and we assume that the processor cores are located at level 0and are connected to the optical routers at level 1. Opticalrouters at different levels are illustrated in different colors forconvenience. The diverse architectural properties of the threeONoC architectures result in different worst case and averageanalyses, as we will show in this section.

The worst case SNR link simultaneously suffers fromhigh-power loss and crosstalk noise. Compared with theworst case SNR link, the average SNR link passes througha smaller number of optical routers, the average hop lengthin this case, and suffers from less crosstalk noise comparedwith the worst case link. In the following, we systematicallyanalyze the worst case and the average crosstalk noise andSNR in WDM-based ONoCs. In this paper, M and N aresupposed to be even numbers.

A. Worst Case Analyses

Worst case SNR analyses in mesh-based, folded-torus-based, and fat-tree-based ONoCs using the single-wavelengthapproach were proposed in [6]–[8]. Based on the analyses’results from those previous works, we have analyzed differentoptical links among the longest in WDM-based ONoCs andhave found that the worst case SNR optical links, i.e., therouting paths inside the optical switching network, in mesh-based, folded-torus-based, and fat-tree-based ONoCs usingWDM are similar to those demonstrated in those previous

Fig. 7. (a) Worst case and (b) average SNR optical links in WDM-basedfat-tree-based ONoCs using the OTAR and W wavelengths.

works. Considering (16) and (17), one can note that thepower loss and crosstalk noise caused by the modulation anddetection are unique among different optical links (routingpaths). However, the power loss and crosstalk noise fromthe optical switching network depend on the routing pathas well as the ONoC architecture under study, as also dis-cussed above (Fig. 5). Therefore, the worst case routing pathand the communication pattern that introduces the highestcrosstalk noise to the worst case SNR link inside the opticalswitching network in each WDM-based ONoC architectureremain the same as those in a single-wavelength-based ONoC.Nevertheless, when using the WDM, the analyses and results


are different due to the presence of different optical wave-lengths. In this subsection, we present the worst case crosstalknoise and SNR analyses for WDM-based folded-torus-basedONoCs. The worst case SNR analysis for the other two WDM-based ONoC architectures, shown in Figs. 6(a) and 7(a),is based on the worst case SNR analyses in [6] and [8]and follows the same analytical approach proposed forWDM-based folded-torus-based ONoCs.

We previously demonstrated that the worst case SNR linkin folded-torus-based ONoCs using the single-wavelengthapproach and an arbitrary 5 × 5 optical router should beamong the first, second, third, and fourth longest opticallinks [7]. We have analyzed the SNR of those optical links inWDM-based folded-torus-based ONoCs using the Crux opticalrouter to find the worst case SNR link. The analyses’ resultsindicate that when the Crux optical router is employed theoptical link from the processor core (1, 1) toward thecore (M, N), as shown in Fig. 6(c), has the worst caseSNR. Considering all the possible traffic patterns and dynamicworkloads in the network, the communication pattern, shownas dotted-green lines in Figs. 6 and 7, is considered in sucha way as to guarantee that the worst case (average) crosstalknoise be received at the destination of the optical signal whileanalyzing the worst case (average) SNR in each architecture.According to Fig. 6(c) and (16), the power of the opticalsignal of the wavelength λn on the worst case SNR link inWDM-based folded-torus-based ONoCs using the Crux opticalrouter is calculated in (18a), and the worst case power lossfrom the optical switching network, WtcLλn

((1,1),(M,N))Ft, is

defined in (18b). The seven terms on the right-hand side of thelatter equation represent the insertion losses from the opticalrouters on the path (first five terms), the crossing loss fromthe waveguide crossings at the network level, and the bendinglosses. The first subscript, a, indicates the use of the Cruxoptical router, while the second and third subscripts represent,respectively, the input and output port numbers in the opticalrouter (Fig. 3)

WtcP Lλn((1,1),(M,N)) = Pλn

v LλnModWtcLλn

((1,1),(M,N))FtLλn

Det

(18a)

where

WtcLλn((1,1),(M,N))Ft

= Lλna,0,2 L

λn

(N2 −1

)a,4,2 Lλn

a,2,3Lλn

(M2 −1

)a,1,3 Lλn

a,3,0L3M+3N−4c L2

b. (18b)

In (18b), the insertion losses imposed by passing an opticalrouter can be calculated based on (10). By way of example,according to the Crux optical router structure in Fig. 3(a) andusing (10), Lλn

a,0,2, i.e., the insertion loss from the injectionport toward the East output port for the optical signal on thewavelength λn , equals L5W−2n

p0 L p1L4b L3

c .Considering the worst case SNR link shown in Fig. 6(c), the

worst case crosstalk noise power accumulated on the opticalsignal carried on the wavelength λn on that link is calculatedin

WtcNλn((1,1),(M,N)) = WtcNλn

((1,1),(M,N))Ft+Nλn

Det (19a)

where

WtcNλn((1,1),(M,N))Ft

=nλna,0,2+

(N

2− 1

)nλn

a,4,2

+ nλna,2,3+

(M

2− 1

)nλn

a,1,3+nλna,3,0. (19b)

In this equation, WtcNλn((1,1),(M,N))Ft

is the worst casecrosstalk noise power accumulated on the optical signal λn

on the worst case SNR link through the optical switchingnetwork, and it is defined in (19b). In this equation, nλn

i, j , asdefined in (13), is the crosstalk noise power added to theconsidered optical signal of the wavelength λn . Differentnλn

i, j can be defined similarly to the crosstalk noise powercalculation in (15) proposed for the example shown in Fig. 4.The power of the interfering optical signals at each Cruxoptical router on the worst case SNR link can be calculatedbased on the communication pattern shown in Fig. 6(c). Forinstance, considering the first Crux optical router on the worstcase SNR link indicated in this figure, the considered opticalsignal traveling from the injection port toward the East outputport is mixed with the interfering optical signals through theNorth, South, and West input ports. The crosstalk noise poweraccumulated on the considered optical signal through theseinput ports can be calculated using nλn

a,0,2, in which the powerof the interfering optical signal, for example, at the Northinput port, Pλn

1 in (13), equals Pλnv Lλn

Mod Lλn((2,1),(1,1))Ft

, where

Lλn((2,1),(1,1))Ft

= Lλna,0,1 Lb L2

c [Fig. 6(c) and (16)]. Similarly,the power of the interfering optical signals at the Southinput port, Pλn

3 , and at the West input port, Pλn4 , can be

calculated.The worst case SNR in WDM-based folded-torus-based

ONoCs using the Crux optical router for the optical signalof the wavelength λn is calculated in

WtcSNRλn((1,1),(M,N)) = 10 log

(WtcP Lλn

((1,1),(M,N))

WtcNλn((1,1),(M,N))

).

(20)

In this equation, WtcP Lλn((1,1),(M,N)) is the detected optical

signal power carried on the wavelength λn on the worst caseSNR link and is defined in (18a), while WtcNλn

((1,1),(M,N)),defined in (19a), denotes the worst case crosstalk noise powerreceived at the photodetector PDn associated with the opticalsignal λn in the receiver.

B. Average Analyses

The signal power loss is associated with the hop lengthof the signal, and hence the average hop length needs to beconsidered to analyze the average signal power loss in eachONoC architecture. Moreover, the crosstalk noise introducedby the average SNR link and the other interfering opticallinks should result in the average crosstalk noise power beingreceived at the destination of the average SNR link. While thepower loss and crosstalk noise analyses for the modulationand detection are the same as those proposed for the worstcase analyses, the average power loss and crosstalk noisepower from the optical switching network in the average case


is different. Given the network size is M × N , (21a) indi-cates the average hop length in mesh-based ONoCs, HAvgM

,while the average hop length in folded-torus-based ONoCs,HAvgFt

, when M and N are even numbers, is calculatedin (21b) [23]. In addition, the average hop length in opti-mized fat-tree-based ONoCs consisting of k processor cores isdefined in (21c)

HAvgM=

⌊M + N

3

⌋(21a)

HAvgFt=

⌊(M2 + 2M)(N + 1)+ (N2 + 2N)(M + 1)

4(M N + M + N)

⌋(21b)

HAvgFtr=

⎡⎢⎢⎢

log2 k−1∑i=2

(1

2i−1 (log2 k − i − 1)

)+ log2 k − 1

2

⎤⎥⎥⎥.

(21c)

We have analyzed different optical links with the averagehop length in WDM-based mesh-based and folded-torus-basedONoCs using the Crux optical router as well as in WDM-basedfat-tree-based ONoCs using the OTAR, and we have found thatthe optical links shown in Figs. 6(b) and (d), and 7(b) are theaverage SNR links in those ONoC architectures, respectively.

The average SNR link in WDM-based mesh-based ONoCsusing the Crux optical router is the one that starts from theprocessor core c0 = (2, 2), passes through α1 = �N/3 − 1routers on the X-section, turns to the Y -section, passes throughα2 = �M/3−1+(�M + N/3mod2) routers on the Y -section,and finally is received at its destination core, c1, as shownin Fig. 6(b). Using (21a) and (16), the power loss imposedon the optical signal of the wavelength λn on this link iscalculated in (22a). Since the average SNR link is diversefor different network sizes, we use c1 to indicate the des-tination of the average SNR link in each ONoC. For eachnetwork size, c1 can be determined by considering the coor-dinates of the source processor core, the optical path shownin Figs. 6(b) and (d), and 7(b), and is based on the averagehop length for each ONoC architecture

AvgP Lλn((2,2),c1)

= Pλnv Lλn

ModAvgLλn((2,2),c1)M

LλnDet (22a)

where

AvgLλn((2,2),c1)M

= Lλna,0,2Lλn(α1)

a,4,2 Lλna,4,3Lλn(α2)

a,1,3 Lλna,1,0. (22b)

In (22a), AvgLλn((2,2),c1)M

is the power loss imposed on theaverage SNR link through the optical switching network,as defined in (22b). Considering the communication patternshown in Fig. 6(b), the average crosstalk noise power intro-duced by the interfering optical signals to the consideredoptical signal of the wavelength λn on the average SNR linkis calculated in

AvgNλn((2,2),c1)

= AvgNλn((2,2),c1)M

+ NλnDet (23a)

where

Nλn((2,2),c1)M

= nλna,0,2 + α1nλn

a,4,2 + nλna,4,3 + α2nλn

a,1,3 + nλna,1,0.

(23b)

Considering the average signal power, defined in (22a), andthe average crosstalk noise power, calculated in (23a), theaverage SNR at the destination of the optical signal onthe wavelength λn in WDM-based mesh-based ONoCs usingthe Crux optical router can be calculated using

AvgSNRλn((2,2),c1)

= 10 log

(AvgP Lλn

((2,2),c1)

AvgNλn((2,2),c1)

). (24)

Fig. 6(d) shows the average SNR link in WDM-basedfolded-torus-based ONoCs using the Crux optical router.Similar to the average analyses proposed for WDM-basedmesh-based ONoCs, the average signal power, crosstalk noisepower, and SNR in WDM-based folded-torus-based ONoCsusing the Crux optical router are calculated in

PLλn((3,1),c1)

= Pλnv Lλn

ModAvgLλn((3,1),c1)Ft

LλnDet (25a)

where

AvgLλn((3,1),c1)Ft

= Lλna,0,2L

λn(� N+12 −1)

a,4,2 Lλna,2,0 L

6� N+12 −2

c Lb

(25b)

AvgNλn((3,1,),c1)

= AvgNλn((3,1),c1)Ft

+ NλnDet (26a)

where

AvgNλn((3,1),c1)Ft

= nλna,0,2 +

(⌊N + 1

2

⌋− 1

)nλn

a,4,2 + nλna,2,0

(26b)

AvgSNRλn((3,1),c1)

= 10 log

(AvgPLλn

((3,1),c1)

AvgNλn((3,1),c1)

). (27)

Moreover, the average signal power, crosstalk noise power, andSNR in WDM-based fat-tree-based ONoCs using the OTAR,shown in Fig. 7(b), can be calculated based on

AvgPLλn(k,c1)

= Pλnv Lλn

ModAvgLλn(k,c1)Ftr

LλnDet (28a)

where

AvgLλn(k,c1)Ftr

= Lλn(2)b,3,1 L

λn (log2 k−5)b,2,1 Lb,2,3L

λn(log2 k−5)b,1,2 Lλn

b,1,3Lα3b Lα4

c (28b)

AvgNλn(k,c1)

= AvgNλn(k,c1)Ftr

+ NλnDet (29a)

where

AvgNλn(k,c1)Ftr

= 2nλnb,3,1 + (log2 k − 5)nλn

b,2,1 + nb,2,3

+(log2 k − 5)nλnb,1,2 + nλn

b,1,3 (29b)

AvgSNRλn(k,c1)

= 10 log

(AvgPLλn

(k,c1)

AvgNλn(k,c1)

). (30)

In these equations, α3 = 4 log2 k −10 and α4 = 2(log2 k−3)−2.In addition, the subscript k represents the source processorcore’s number.


Fig. 8. Worst case signal power, crosstalk noise power, and SNR in an8 × 8 WDM-based mesh-based ONoC using the Crux optical router (W = 8,FSR = 6 nm, and Q = 9000).

V. QUANTITATIVE SIMULATIONS

The proposed analytical models for the worst case aswell as the average crosstalk noise and SNR in differentWDM-based ONoC architectures have been included in ournewly developed CLAP [7], [24]. Using CLAP and applyingrecent fabricated device parameters, as listed in Table I, wepresent and compare the quantitative simulation results of theworst case as well as the average signal power, crosstalknoise power, and SNR in real case studies of WDM-basedmesh-based, folded-torus-based, and fat-tree-based ONoCsusing the Crux optical router and the OTAR. It is assumedthat the injection laser power, Pv , at the different VCSELs isthe same and is equal to 0 dBm. It is worth mentioning thatthe output power at the E-O interface depends on the powerloss imposed on the optical path. Moreover, a waveguide witha size of 450 nm × 200 nm and an MR with a diameter of10 μm are considered.

Fig. 8 shows the worst case signal power, crosstalk noisepower, and SNR received at different photodetectors at thedestination of the worst case SNR link in an 8×8 mesh-basedONoC using the Crux optical router [Fig. 6(a)] when W, FSR,and Q equal 8, 6 nm, and 9000, respectively. As can be seen,while the signal power slightly decreases as the wavelength’snumber, n, increases, the crosstalk noise power rises whenn < (W/2), peaks at n = (W/2), and then moderately reducesfor n > (W/2). Accordingly, the SNR decreases at firstand then starts increasing for the last few wavelengths. Thebehavior of the crosstalk noise power can be described basedon (3b): when |λn − λMRm | is larger, the resulting crosstalknoise power will be lower, and as it declines, the crosstalknoise power will become higher. Since the results for differentwavelengths are not the same, we consider the worst case(average) values among different wavelengths when showingthe worst case (average) results in the rest of this paper.

The proposed analytical models for WDM-based ONoCsin Section IV are based on W, FSR, and Q. Understandingthe SNR variations based on employing different values forthose parameters, we analyze and compare the worst caseSNR in different ONoC architectures of the same networksize (M = N = 8 and k = 64) while considering differentvalues of W, FSR, and Q in CLAP. The analyses’ resultsfrom CLAP are shown in Fig. 9, in which we consider

Fig. 9. Worst case SNR in 8×8 (64-core) WDM-based mesh-based, folded-torus-based, and fat-tree-based ONoCs using the Crux optical router andOTAR while considering different values of W, FSR, and Q. (a) FSR = 32 nmand Q = 9000. (b) W = 32 and Q = 9000. (c) W = 16 and FSR = 32 nm.

using ε = (FSR/2W). It is worth mentioning that the MRsdiameter varies according to the employed values of Q andFSR in Fig. 9. As Fig. 9(a) shows, when the FSR and Qare, respectively, 32 nm and 9000 and W varies, the SNRdecreases with an increase in W. In other words, when Wincreases, a larger number of MRs is required, which imposesa higher power loss and crosstalk noise power, and hence alower SNR. In addition, as W increases over a fixed FSR,the spacing among different wavelengths becomes smaller,which results in a higher crosstalk noise power, and conse-quently lower SNR. Fig. 9(b) shows the SNR variations whenW = 32 and Q = 9000, but FSR varies from 2 to 128 nm.As the FSR increases, the spacing among different optical


Fig. 10. Signal power, crosstalk noise power, and SNR in WDM-based mesh-based and folded-torus-based ONoCs using the Crux optical router (W = 16,FSR = 32 nm, and Q = 9000). (a) Worst case signal and crosstalk noise power. (b) Average signal and crosstalk noise power. (c) Worst case SNR.(d) Average SNR.

wavelengths becomes larger, and thus the SNR improves[see (3b)]. Considering Fig. 9(a) and (b), one can notice thatwhen Q = 9000 and (FSR/W) > 1 nm, the resultant SNRis improved. However, (FSR/W) � 1 nm cannot consid-erably improve the SNR. Finally, Fig. 9(c) shows the SNRvariations under different values of Q and when W = 16 andFSR = 32 nm. The higher the value of Q, the better the SNRis. Furthermore, there is a slight improvement in the SNRwhen Q becomes very large.

Fig. 10 shows the worst case and the average signalpower, crosstalk noise power, and SNR comparison betweenWDM-based mesh-based and folded-torus-based ONoCs usingthe Crux optical router under different network sizes.We considered the use of 16 wavelengths, W = 16, withFSR = 32 nm and Q = 9000, and we found that whenM and N are equal, the resulting SNR is the best. Hence,in the simulation, as shown on the x-axis in Fig. 10, weconsidered M = N . As Fig. 10(a) and (b) shows, the worstcase and the average signal power decrease when the networksize increases, while the worst case and the average crosstalknoise power increase. Furthermore, WDM-based folded-torus-based ONoCs have higher worst case signal power and lowercrosstalk noise power compared with WDM-based mesh-basedONoCs. However, both the average signal power and crosstalknoise power in WDM-based mesh-based ONoCs are higherthan those in WDM-based folded-torus-based ONoCs underdifferent networks sizes. According to Fig. 10(c) and (d), theworst case and the average SNR exponentially reduce when

the network scales. In addition, the worst case and the averageSNR in WDM-based folded-torus-based ONoCs are higherthan those in WDM-based mesh-based ONoCs using the Cruxoptical router. Another important observation is that under allthe network sizes in both ONoC architectures, the worst casecrosstalk noise power is higher than the signal power, andhence the worst case SNR is smaller than 0 dB. Consider-ing the average case, however, the average crosstalk noisepower only exceeds the average signal power in WDM-basedmesh-based ONoCs larger than 16 × 16 and in folded-torus-based ONoCs larger than 20 × 20.

The worst case and the average signal power, crosstalk noisepower, and SNR in WDM-based fat-tree-based ONoCs usingthe OTAR and when W = 16, FSR = 32 nm, and Q = 9000are shown in Fig. 11. According to this figure, while there is arapid reduction in the worst case and the average signal powerwith an increase in the number of processor cores, the worstcase and the average crosstalk noise power are, respectively,almost equal to −10 and −14 dBm for different networkscales. This is because when the network scales, the worstcase and the average SNR link include more optical routersand this results in higher crosstalk noise accumulation and, atthe same time, higher power loss. However, the accumulatedcrosstalk noise through a larger number of optical routers issmall, and the imposed extra power loss is high enough toattenuate both the signal power and crosstalk noise power.This attenuation in signal power and the accumulated crosstalknoise power depends on the topological properties of the


TABLE II

WORST CASE AND AVERAGE SIGNAL POWER, CROSSTALK NOISE POWER, AND SNR COMPARISON (W = 16, FSR = 32 nm, AND Q = 9000)

Fig. 11. Signal power, crosstalk noise power, and SNR in WDM-based fat-tree-based ONoCs using the OTAR (W = 16, FSR = 32 nm, and Q = 9000).(a) Worst case results. (b) Average results.

ONoC architecture and the structure of the optical router.As Fig. 11(a) shows, the worst case signal power is smallerthan the worst case crosstalk noise power when the numberof processor cores is larger than 26. In addition, consideringFig. 11(b), the average crosstalk noise power exceeds theaverage signal power when the number of processor cores islarger than 29.

Table II compares the worst case as well as the averagesignal power, crosstalk noise power, and SNR among thethree ONoC architectures when the network size is 8 × 8(64 cores) and 16 × 16 (256 cores). According to thistable, WDM-based mesh-based ONoCs using the Crux opticalrouter have the lowest worst case and average SNR underboth network sizes. Using the same optical router and whenthe network size is small, WDM-based folded-torus-basedONoCs achieve the highest average SNR, while WDM-based

fat-tree-based ONoCs using the OTAR have the highest worstcase SNR under the same network size. As the network scales,however, the worst case SNR in WDM-based folded-torus-based ONoCs using the Crux optical router is the highest,while WDM-based fat-tree-based ONoCs using the OTARachieve the highest average SNR. The worst case crosstalknoise power exceeds the worst case signal power in all threearchitectures when the network size is 16 × 16. Comparingthe signal power efficiency, one can notice that WDM-basedmesh-based ONoCs using the Crux optical router have the bestworst case and average signal power when the network size issmall. As the network scales, WDM-based folded-torus-basedONoCs and WDM-based mesh-based ONoCs using the Cruxoptical router achieve the highest worst case and average signalpower, respectively.

VI. CONCLUSION

Crosstalk noise is a critical issue for the SNR performanceof WDM-based ONoCs. Evaluating the worst case as wellas the average crosstalk noise and SNR in different ONoCarchitectures helps choose a proper ONoC architecture thatcan efficiently satisfy certain performance and scalabilityrequirements. We present detailed systematical analyses andcomparisons of the worst case as well as the average signalpower, crosstalk noise power, and SNR in WDM-based mesh-based, folded-torus-based, and fat-tree-based ONoCs usingthe Crux optical router and the OTAR. The proposed ana-lytical models are integrated into a recently released CLAPto facilitate the analyses in arbitrary WDM-based ONoCs.Performing quantitative simulations in CLAP, we indicatethat different ONoC architectures result in different SNRperformances. Moreover, we demonstrate how the SNR varieswhen employing different numbers of optical wavelengthsand values of FSR and Q in WDM-based ONoCs. We alsofind that crosstalk noise considerably restricts the scalabilityof ONoCs; for example, in the worst case and consideringthe use of 16 optical wavelengths with FSR = 32 nm andQ = 9000, for network sizes larger than 6 ×6 in WDM-basedfolded-torus-based and WDM-based mesh-based ONoCs usingthe Crux optical router and larger than 64 processor coresin WDM-based fat-tree-based ONoCs using the OTAR, thecrosstalk noise power exceeds the signal power.

REFERENCES

[1] E. Bonetto, L. Chiaraviglio, D. Cuda, G. A. Gavilanes Castillo, andF. Neri, “Optical technologies can improve the energy efficiency ofnetworks,” in Proc. 35th Eur. Conf. Opt. Commun., Sep. 2009, pp. 1–4.


[2] M. J. Cianchetti, J. C. Kerekes, and D. H. Albonesi, “Phastlane:A rapid transit optical routing network,” in Proc. 36th Annu. ISCA, 2009,pp. 441–450.

[3] L. Zhang, E. E. Regentova, and X. Tan, “A 2D-torus based packetswitching optical network-on-chip architecture,” in Proc. SOPO, 2011,pp. 1–4.

[4] H. Gu, J. Xu, and W. Zhang, “A low-power fat tree-based opticalnetwork-on-chip for multiprocessor system-on-chip,” in Proc. DATE,2009, pp. 3–8.

[5] R. Ramaswami, K. Sivarajan, and G. Sasaki, Optical Networks:A Practical Perspective. San Mateo, CA, USA: Morgan Kaufmann,2009.

[6] Y. Xie et al., “Formal worst-case analysis of crosstalk noise inmesh-based optical networks-on-chip,” IEEE Trans. Very Large ScaleIntegr. (VLSI) Syst., vol. 21, no. 10, pp. 1823–1836, Oct. 2013.

[7] M. Nikdast et al., “Systematic analysis of crosstalk noise in folded-torus-based optical networks-on-chip,” IEEE Trans. Comput.-Aided DesignIntegr. Circuits Syst., vol. 33, no. 3, pp. 437–450, Mar. 2014.

[8] M. Nikdast et al., “Fat-tree-based optical interconnection networks undercrosstalk noise constraint,” IEEE Trans. Very Large Scale Integr. (VLSI)Syst., to be published.

[9] L. H. K. Duong et al., “A case study of signal-to-noise ratio in ring-based optical networks-on-chip,” IEEE Des. Test Comput., vol. 31, no. 5,pp. 55–65, Oct. 2014.

[10] F. Xu and A. W. Poon, “Silicon cross-connect filters using microringresonator coupled multimode-interference-based waveguide crossings,”Opt. Exp., vol. 16, no. 12, pp. 8649–8657, 2008.

[11] W. Ding, D. Tang, Y. Liu, L. Chen, and X. Sun, “Compact and lowcrosstalk waveguide crossing using impedance matched metamaterial,”Appl. Phys. Lett., vol. 96, no. 11, pp. 111114-1–111114-3, Mar. 2010.

[12] Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design anddemonstration of compact, wide bandwidth coupled-resonator filters on asilicon-on-insulator platform,” Opt. Exp., vol. 17, no. 4, pp. 2247–2254,2009.

[13] Y. Xie et al., “Crosstalk noise and bit error rate analysis for opti-cal network-on-chip,” in Proc. 47th ACM/IEEE DAC, Jun. 2010,pp. 657–660.

[14] J. Chan, G. Hendry, K. Bergman, and L. P. Carloni, “Physical-layermodeling and system-level design of chip-scale photonic interconnectionnetworks,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst.,vol. 30, no. 10, pp. 1507–1520, Oct. 2011.

[15] M. Mehdi Vaez and C.-T. Lea, “Strictly nonblocking directional-coupler-based switching networks under crosstalk constraint,” IEEE Trans.Commun., vol. 48, no. 2, pp. 316–323, Feb. 2000.

[16] B.-C. Lin and C.-T. Lea, “Crosstalk analysis for microring basedoptical interconnection networks,” J. Lightw. Technol., vol. 30, no. 15,pp. 2415–2420, Aug. 1, 2012.

[17] K. Preston, N. Sherwood-Droz, J. S. Levy, and M. Lipson, “Perfor-mance guidelines for WDM interconnects based on silicon microringresonators,” in Proc. Conf. Lasers Electro-Opt., May 2011, pp. 1–2.

[18] P. Dong et al., “Low loss silicon waveguides for application of opticalinterconnects,” in Proc. IEEE Photon. Soc. Summer Topical MeetingSer., Jul. 2010, pp. 191–192.

[19] F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on asilicon chip,” Nature Photon., vol. 1, no. 1, pp. 65–71, Jan. 2007.

[20] G.-R. Zhou, X. Li, and N.-N. Feng, “Design of deeply etched antireflec-tive waveguide terminators,” IEEE J. Quantum Electron., vol. 39, no. 2,pp. 384–391, Feb. 2003.

[21] S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Modeling and measurementof losses in silicon-on-insulator resonators and bends,” Opt. Exp., vol. 15,no. 17, pp. 10553–10561, Aug. 2007.

[22] Z. Wang et al., “Floorplan optimization of fat-tree-based networks-on-chip for chip multiprocessors,” IEEE Trans. Comput., vol. 63, no. 6,pp. 1446–1459, Jun. 2014.

[23] K. Feng, Y. Ye, and J. Xu, “A formal study on topology and floor-plan characteristics of mesh and torus-based optical networks-on-chip,”Microprocessors Microsyst., vol. 37, no. 8, pp. 941–952, Nov. 2013.

[24] (2013). Crosstalk and Loss Analysis Platform (CLAP). [Online]. Avail-able: http://www.ece.ust.hk/~eexu/,

Mahdi Nikdast (S’10–M’14) received the Ph.D. degree in electronic andcomputer engineering from the Hong Kong University of Science and Tech-nology, Hong Kong, in 2013.

He is currently a Post-Doctoral Fellow with the Department of Computerand Software Engineering, Polytechnique Montreal, Montreal, QC, Canada.He has authored and co-authored more than 40 papers in refereed journals andinternational conference publications. His current research interests includeembedded and computing systems, multiprocessor systems-on-chip, and opti-cal/photonic interconnects.

Jiang Xu (S’02–M’07) received the Ph.D. degree from Princeton University,Princeton, NJ, USA, in 2007.

He is currently an Associate Professor with the Hong Kong University ofScience and Technology, Hong Kong. He has authored and co-authored morethan 70 book chapters and papers in peer-reviewed journals and internationalconferences. His current research interests include embedded system, opticalinterconnects, and HW/SW codesign.

Luan H. K. Duong is currently pursuing the Ph.D. degree in electronicand computer engineering with the Hong Kong University of Science andTechnology, Hong Kong.

Xiaowen Wu (S’12) is currently a Visiting Scholar with the Mobile Comput-ing System Laboratory, Hong Kong University of Science and Technology,Hong Kong.

Xuan Wang (S’12) is currently pursuing the Ph.D. degree in electronicand computer engineering with the Hong Kong University of Science andTechnology, Hong Kong.

Zhehui Wang is currently pursuing the Ph.D. degree in electronic and com-puter engineering with the Hong Kong University of Science and Technology,Hong Kong.

Zhe Wang is currently pursuing the Ph.D. degree in electronic and computerengineering with the Hong Kong University of Science and Technology,Hong Kong.

Peng Yang is currently pursuing the Ph.D. degree in electronic and computerengineering with the Hong Kong University of Science and Technology,Hong Kong.

Yaoyao Ye is currently with the Shannon Laboratory, Huawei TechnologiesCompany, Ltd., Shenzhen, China. Her current research interests includeinterconnect networks, systems-on-a-chip, and embedded systems.

Qinfen Hao is currently with the Shannon Laboratorty, Huawei TechnologiesCompany, Ltd., Shenzhen, China. His current research interests include com-puter architectures, high-performance computers, and optical interconnects.

crosstalk noise in wdm-based optical networks-on-chip: a ... · device parameters, we present a...

Documents