Telecommun Syst (2014) 55:461–470DOI 10.1007/s11235-013-9801-3

Optimum link distance determination for a constant signalto noise ratio in M-ary PSK modulated coherent optical OFDMsystems

Ayhan Yazgan · I. Hakki Cavdar

Published online: 17 August 2013© Springer Science+Business Media New York 2013

Abstract In this paper 40 Gb/s and 100 Gb/s Coherentoptical Orthogonal Frequency Division Multiplexing (CO-OFDM) systems are studied to obtain the relation betweenthe bit error rate (BER) and transmission link distance for aconstant signal to noise ratio (SNR). Utilizing Dense Wave-length Division Multiplexing (DWDM) with 192 opticalchannels in C and L bands (1528.77 nm–1612.65 nm), datarates can theoretically reach up to 19 Tb/s (192 ∗ 100 Gb/s)using only one optical fiber core. In this research, we se-lected the same data rates with the IEEE standards publishedby IEEE Computer Society in 2010 and 2011. Results showthe performance of the CO-OFDM system at different datarates and distances for one RF carrier and one optical carrierinstead of 4 optical carriers used in IEEE 802.3ba.

Keywords Radio over Fiber · Optical link design · Opticalnetworks · Fiber optical communication · OFDMmodulation

1 Introduction

Thanks to the many advantages already known in wirelesscommunications, OFDM is a convenient solution to resistRF microwave multipath fading. The most important pointto be focused on is that OFDM separates a high speed datablock into a number of low speed data blocks which aretransmitted simultaneously over a transmission channel [1].Therefore OFDM is to be employed in the forthcoming 4G

A. Yazgan (B) · I.H. CavdarDepartment of Electrical-Electronics Engineering, KaradenizTechnical University, 61080 Trabzon, Turkeye-mail: ayhanyazgan@ktu.edu.tr

wireless cellular standards such as Worldwide Interoperabil-ity for Microwave Access (WiMAX), Long Term Evolution(LTE) and high speed WLAN standards. From the point ofview of a transmission channel, optical communication isthe key to reaching long distances with high data rates espe-cially for modern communication systems. The advantagesmentioned above are the trigger points that made researchersbring out this new technique called CO-OFDM [1, 2]. Onthis basis, CO-OFDM has been suggested as an effectivetechnique for long haul fiber optic transmission systems toeliminate the inter-symbol interference (ISI) effect causedby intra modal dispersion [2]. A subject that requires care-ful consideration for CO-OFDM systems is the phase noise.Generally, phase noise is compensated for using a preamblearray or estimating the local oscillator offset using the guardinterval of OFDM symbol [3]. The negative effect of thephase noise of the system can be reduced by utilizing OFDMpilot subcarriers. Although this method has been proposedfor the compensation of phase noise, we show here the per-formance of this method with different channel parametersand data rates.

The first CO-OFDM transmission was reported in 2006[1, 2]. Since then, CO-OFDM transmission experimentshave rapidly gained attention for standard single mode fiber(SSMF) transmission [4, 5]. In parallel, Arthur James Low-ery and Jean Armstrong published their study presentingchromatic dispersion compensating aspects of OFDM inan optical channel [6]. They also made a comparison be-tween OFDM and classical NRZ system, and figured outthat OFDM had a 0.5 dB power sensitivity advantage overthe NRZ system [6]. Besides the effect of chromatic dis-persion, Polarization Mode Dispersion (PMD) has also beeninvestigated with some benefits to the fiber nonlinearity [7].

In this study, we focused on the optimum link distancedetermination for a constant signal to noise ratio in CO-

462 A. Yazgan, I.H. Cavdar

OFDM systems. The effect of the fiber cable has also beentaken into account by choosing different dispersion param-eters of SSMF. Erbium Doped Fiber Amplifiers (EDFA)with suitable pump power and cable length have been in-cluded in the system to achieve the minimum nonlinear-ity as the light must be amplified. The phase shift keyingwas chosen for the mapping. Quadrature Phase Shift Key-ing (QPSK) and 16PSK digital modulation formats wereselected to reach 40 Gb/s and 100 Gb/s, respectively. Itis well known that raising the level of digital modula-tion gives rise to throughput increase. However, multilevelmodulation techniques are very sensitive to ISI in wire-less or fiber optic communication systems [8]. This infor-mation has also been supported by our previous research[9–13]. Hence, its further investigation is omitted here. Weselected the DWDM wavelengths compatible with Inter-national Telecommunication Union (ITU) standards [14].Here, we used the SSMF as a communication channel, nev-ertheless CO-OFDM is also suitable for wireless multi-Gb/ssystems beyond 60 GHz [15].

The rest of this paper is organized as follows; Sect. 2 con-cisely presents the theory of Coherent Optical OFDM sys-tems, the channel model is also given in Sect. 2; Sect. 3gives the 40 Gb/s and 100 Gb/s results that we obtainedbefore and after laser phase noise fixing process compara-tively. Section 4 discusses how the nonlinearity affects thecommunication performance and when it must be takeninto account by giving the most important contributionsand solutions in this field. Section 5 concludes the pa-per.

2 Principle of CO-OFDM

Before explaining the details of the CO-OFDM systems,general outlines of OFDM should be given here. An impor-tant advantage of using OFDM systems over classical multicarrier modulation (MCM) systems is the bandwidth effi-ciency [16, 17]. Second advantage is the ability of electronicdispersion compensation (EDC) due to the flat channel prop-erty of each subcarrier. Some dynamic subcarrier allocationalgorithms can also be applied for OFDM systems to obtainvarious data rates [18, 19]. f0 = 0, NSC is the number ofsubcarrier, Ts is the sampling period, ϕn is the phase term ofthe nth subcarrier and k = 0,1,2, . . . ,NSC − 1; an OFDMsymbol is given by (1) [20].

Ss(kTs) =(

1

NSC

)NSC−1∑n=0

cne(j2πn)( k

NSC)e(jϕn) (1)

To build a CO-OFDM system, the classical OFDM the-ory defined for wireless communication [16, 17] is imple-mented in an optical channel. Actually CO-OFDM uses the

advantages of OFDM in the optical channel. The basic CO-OFDM system block diagram is given in Fig. 1. In this sys-tem, data is first sent to the OFDM transmitter. Then, it isup-converted to a desired RF signal. After the conversionfrom RF to optical signal, the data packet is sent to thefiber optic channel. Depending on the link distance, sev-eral EDFA’s may be used during the transmission. At thereceiver side, for the down conversion from optical to RF, alaser diode and photo diode pairs are used. Using the localoscillator at the receiver side the base band OFDM signal isobtained. Then the phase noise of the laser is eliminated bythe OFDM pilot subcarriers. At the end of each process theBER and SNR are calculated for different channel param-eters, link distances and M-ary PSK modulations. In orderto satisfy the minimum nonlinearity condition for all pro-cesses, the amplifiers, input power and link distances needto be determined meticulously. It has been proposed and an-alyzed that by biasing the Mach-Zehnder modulator (MZM)at null point, a linear conversion between the RF and opticalsignal can be achieved [21–25]. Thanks to coherent detec-tion, a linear transformation from the optical to RF signalmay also be obtained [1–5]. Neglecting the digital modu-lation and pulse waveform, the received optical signal forone OFDM symbol is given in (2, 3). Here ϕD(n) is theeffect of chromatic dispersion for the phase component ofnth OFDM subcarrier as given in (4). β2 is the group veloc-ity dispersion parameter that indicates how much the opti-cal signal will broaden as given in (5). Substituting (5) into(4), the equation (6) is obtained. In these equations, fLD1

is the optical carrier frequency, L is the link distance andfn is the related subcarrier frequency of the optical OFDMsymbol. Figure 2 shows the optical channel model. Equa-tions (7) and (8) explain the channel model mathematicallywhere cmn and c′

mn are transmitted and received signals, re-spectively, ϕm is the phase drift of the mth OFDM symboldue to the laser phase noise and nmn is the optical noise ofthe related subcarrier. In this model, the transfer function ofnth subcarrier including the effect of group velocity delay isindicated as hn which consists of a constant term ϕ0, a linearterm which is related to the first subcarrier latency τ0, and aquadrature term related to the fiber chromatic dispersion inthe unit of ps/(nm km). Within one OFDM frame, the trans-fer functions of subcarriers in optical fibers are considered tobe static. The phase drift within one OFDM symbol can beregarded as constant and common to all subcarriers [2, 3, 12,25, 26].

Es = LL ·NSC−1∑

n=0

cne(j2π.fnt)e(jϕD(n)) (2)

LL = e(j (2π(fLD1+fLO1)t+ϕLD1)) (3)

ϕD(n) = 1

2β2ω

2nL (4)

Optimum link distance determination for a constant signal to noise ratio in M-ary PSK modulated coherent 463

Fig. 1 CO-OFDM blockdiagram

Fig. 2 Optical channel model for a single mode fiber cable

β2 = λLD12

2πvDt (5)

ϕD(n) = v · πfLD1

2Dtfn

2L (6)

After single symbol duration, the phase drift was recalcu-lated and compensated. A 20 kHz linewidth was chosen foreach laser diode close to the value achieved commercially.In order to compensate for ISI which causes the orthogonal-ity between the subcarriers in CO-OFDM system to disap-pear, a cyclic prefix is added to the beginning of the data

subcarriers. If a cyclic prefix has an extension longer thanthe channel delay spread and is added as a prefix of the CO-OFDM symbol, then the delay spread which comes from theeffect of the chromatic dispersion cannot create ISI as givenin (9) where v is the light velocity in the fiber cable; Dt

is the chromatic dispersion parameter; Δf is the subcarrierspacing and ΔG is the guard interval length.

hn = |hn| exp(j(ϕ0 + 2Πτ0fn + ϕD(n)

))(7)

c′mn = cmn · hn · exp(jϕm) + nmn (8)

v

fLD2|Dt |NSCΔf ≤ ΔG (9)

To receive data with low BER, laser phase drift must beestimated and compensated. For this purpose, pilot carriersof the OFDM signal can be used. This procedure is given in(10)–(12) where pa(cmn) is the known phase angle of therelated transmitted OFDM pilot subcarrier, pa(c′

mn) is thereceived phase angle of the related OFDM pilot subcarrier,ϕ̄m is the estimated total phase drift including laser phasenoise and ¯cmn is the obtained signal after phase noise com-

464 A. Yazgan, I.H. Cavdar

pensation.

ϕ̄m = 1

NSP

NSP −1∑n=0

[pa

(c′mn

) − pa(cmn)]

(10)

clpmn = c′

mn exp(−j ϕ̄m

)(11)

¯cmn = lpcmn

hn∗

|hn|2(12)

The known pilot carriers which are sent from the trans-mitter are received at the end of the optical channel. Ac-cording to our simulations, pilot carriers are affected dif-ferently by this transmission. However, the average of thedifferences between transmitted and received pilot subcar-rier phases gives us a phase value which is close to the ex-act phase shift. The laser phase noise fixing process is car-ried out just after this phase drift estimating process is com-pleted. Simulation results are in agreement with this pro-cess. Equations given in (10)–(12) mathematically explainthe procedure [9, 11–13].

3 Results

Some critical information to address this research should begiven here. First of all, it is crucial that the BER thresh-old of 10−2 is a sufficient level for advanced Forward ErrorCorrection (FEC) algorithm to obtain sufficient BER val-ues [1]. Secondly, due to the various DWDM design optionsor different configurations, results are given for one opticalwavelength instead of whole DWDM. We select 1549.32 nm(193.5 THz) in C band window. These results have been ob-tained for one fiber core, one optical carrier and one RF car-rier without using any optical dispersion compensation tech-nique.

The channel is modeled by taking basic optical chan-nel parameters into consideration such as phase compo-nent, chromatic dispersion, optical noise, and the attenua-tion. Since the link distance is not static in our simulation,the number of EDFA also changes dynamically. Therefore,the link distance determines the number of EDFA whichshould be used. In our simulation, for 1000 km link distance14 EDFA is placed through the fiber optic communicationschannel. Optical fiber and OFDM parameters are given inTable 1 and Table 2, respectively.

Comparing to pure silica, doping can change materialdispersion parameter. For example germanium-doped sil-ica has different material dispersion parameter dependingon the percentage of the germanium used [27]. This prop-erty is taken into account by selecting different dispersionparameters for the same wavelength. In this manner, threekinds of chromatic dispersion parameters 6 ps/(nm km),10 ps/(nm km) and 17 ps/(nm km) are used for the designed

Table 1 Basic Optical Fiber Parameters

Parameter Value

Wavelength 1549.32 nm

Velocity of light in fiber cable 200000 km/s

Fiber optical cable length 100–3000 km

Chromatic Dispersion Parameter 6, 10, 17 ps/(nm km)

Table 2 Basic OFDM Parameters for 40 Gb/s

Parameter Value

Modulation QPSK

Data Rate (Gb/s) 40

Sampling frequency (fs) 20 GHz

Sampling Period (Ts) Ts = 50 ps

Useful symbol duration (Tu) 25.6 ns

Cycling prefix duration (Tcp) 3.2 ns, 6.4 ns

Symbol duration (Tsym = Tu + Tcp) 28.8 ns, 32 ns

Data subcarrier number (NSD) 448

Pilot subcarrier number (NSP ) 32 or 64

Total subcarrier number (NSC ) 512

Monte Carlo simulation in order to determine the opticalfiber cable effects. Results also give us information abouthow the CO-OFDM system is affected with the increasingthe data rate from 40 Gb/s to 100 Gb/s.

Several noise sources exist in optical communication sys-tems such as shot noise, thermal noise which is the ef-fect of the electronic devices, dark current comes from ran-dom generation of electron-hole pairs and laser phase noisewhich broadens the spectrum from a single spectral line toa Lorentzian line shape. Some of these can be modeled asPoisson distribution and some can be described as a Gaus-sian distribution. Another important phase noise source thatmust be taken into account is EDFA which causes bothamplitude and phase changes called amplified spontaneous-emission (ASE) [28].

We first present 40 Gb/s results using the parametersgiven in Table 1 and Table 2. In this part, the effect of linkdistance on the communication performance is presented asgiven SNR-BER and BER-Distance variations in Fig. 3 andFig. 4, respectively. This result is taken under the conditionof 0.2 dB/km fiber attenuation and 17 ps/(nm km) chromaticdispersion parameter. It is known that the most importantnoise component in coherent systems is phase noise. If it isnot compensated or fixed, we can easily see how it affectsthe system performance in Fig. 3, where pl and flpn indi-cate the results in the presence of laser phase noise and fixedlaser phase noise, respectively. According to the results, athigh data rates, demodulation is nearly impossible withoutcarrying out a laser phase noise fixing algorithm. Even if

Optimum link distance determination for a constant signal to noise ratio in M-ary PSK modulated coherent 465

we increase the SNR up to 27 dB, it is not possible to seesignificant change in BER, as the maximum error floor hasbeen observed. On the other hand, fixing phase noise de-creases the BER dramatically. Compared with our previouswork, small differences can be observed for QPSK modu-lated CO-OFDM signals [12, 13]. There are various differ-ent reasonable causes to obtain these differences. The firstone is that the number of simulated channels are not same.In this improved simulation, we send our data packet over

Fig. 3 40 Gb/s QPSK SNR-BER performance, L: 100–300 km,Dt: 17 ps/(nm km)

1000 different optical channels and take the average of thesebefore sketching the variations. Theoretically, to reach theexact same results for each simulation, the number of chan-nels must go on to infinity. Therefore, increasing the numberof channels also increases the accuracy of the results. Thepossible second reason is that, in previous work, we normal-ized the amplitude of the QPSK signals to one. This normal-ization created some changes compared to the previous re-sults. Now, we do not normalize the amplitude of the QPSKmodulated signal. This is also shown in Fig. 5 where the

Fig. 4 40 Gb/s QPSK BER-Distance variations, L: 0–3000 km

Fig. 5 QPSK Constellation diagrams at different SNR values, L: 200 km, 40 Gb/s data rate, Dt: 17 ps/(nm km)

466 A. Yazgan, I.H. Cavdar

Fig. 6 40 Gb/s QPSK BER-Distance variations, SNR: 10 dB,L: 0–800 km

total clustering is around the value of 1√2

. Different opticalcarriers and OFDM subcarriers may also force the systemperformance to fluctuate around the expected value.

In Fig. 3, considering 100 km link distance with 16 dBSNR value, BER reaches below 10−7. This result is alsosupported by the constellation diagrams which show the rateof correctly demodulated signal variations with increasingSNR given in Fig. 5. Figure 3 also gives information aboutthe link distance. Assuming that BER is 10−3, we need only2.5 dB SNR improvement to increase the link distance from100 km to 200 km. However, to increase the link distancefrom 200 km to 300 km for the same BER we need morethan 11 dB SNR advance. This result supports the theorythat chromatic dispersion is more effective in higher datarates and longer distances.

According to the communication standard, the optimumcondition can be determined considering the tradeoff be-tween BER and link distance which is the main purpose ofthis work. Results given in Fig. 4 explain this phenomenonfor 40 Gb/s up to 3000 km with two different SNR val-ues. Figure 6 and Fig. 7 also give BER-optical link distancevariations to observe a more detailed view for 10 dB and20 dB SNR values, respectively. Optimum values that havebeen selected from simulation results are given here: Con-sidering SNR: 10 dB, BER: 10−2, the optical link distancecan reach up to 590 km, 365 km and 212 km for the chro-matic dispersion parameter: 6 ps/(nm km), 10 ps/(nm km)and 17 ps/(nm km), respectively without FEC. If we increaseSNR up to 20 dB, BER: 10−3, the optical link distance canreach up to 800 km, 483 km and 282 km for the chro-matic dispersion parameter: 6 ps/(nm km), 10 ps/(nm km)and 17 ps/(nm km), respectively without FEC.

Another solution to having a better BER value is SNR:20 dB, BER: 10−5, in this case, the optical link distancecan reach up to 610 km, 367 km and 217 km for the chro-

Fig. 7 40 Gb/s QPSK BER-Distance variations, SNR: 20 dB,L: 0–800 km

Fig. 8 100 Gb/s 16PSK SNR-BER performance, L: 10–100 km,Dt: 17 ps/(nm km)

matic dispersion parameter: 6 ps/(nm km), 10 ps/(nm km)and 17 ps/(nm km), respectively without FEC.

In the second part of the results section, the data rate isswitched from 40 Gb/s to 100 Gb/s. We present the tradeoffbetween BER and optical link distance for 100 Gb/s whichis the ultimate data rate coming from the last IEEE standardfor information technology, telecommunications and infor-mation exchange between systems and local and metropoli-tan area networks published 2011 by IEEE Computer So-ciety called IEEE 802.3bg. The selected OFDM parametersfor 100 Gb/s in our simulations are given in Table 3.

As expected, increasing the data rate with same opticallink distance brings high SNR necessity. If we deal withFig. 8, it can be seen that the system performance neverreaches 10−3 BER value for 100 km optical link distancewithout FEC. It can also be seen that, compared with 50 kmoptical link distance; there is no large difference between

Optimum link distance determination for a constant signal to noise ratio in M-ary PSK modulated coherent 467

Fig. 9 100 Gb/s 16PSK BER-Distance variations, L: 0–800 km

Table 3 Basic OFDM Parameters for 100 Gb/s

Parameter Value

Modulation 16PSK

Data Rate (Gb/s) 100

Sampling frequency (fs) 30 GHz

Sampling Period (Ts) Ts = 33.3 ps

Useful symbol duration (Tu) 17 ns,

Cycling prefix duration (Tcp) 2.1 ns, 4.2 ns

Symbol duration (Tsym = Tu + Tcp) 19.1 ns, 21.2 ns

Data subcarrier number (NSD) 448

Pilot subcarrier number (NSP ) 32 or 64

Total subcarrier number (NSC ) 512

10 km and 25 km optical link distances. Considering thatat 50 km link distance, there is 10−3 BER floor which cannot be overcome without a FEC algorithm. For the 100 Gb/sdata rate, there is an inevitable truth that we need to eitherdecrease the optical link distance or increase the SNR to ob-tain same BER as can be seen in Fig. 9 and Fig. 10. Constel-lation diagrams for 100 Gb/s given in Fig. 11 support thisfinding. Figure 10 gives the same result with more detailscompared to the result given in Fig. 9. Some results underthe constant SNR condition are given below.

SNR: 20 dB, BER: 10−2, the optical link distance goesto 100 km, 60 km and 35 km for the chromatic dispersionparameter: 6 ps/(nm km), 10 ps/(nm km) and 17 ps/(nm km),respectively without FEC.

SNR: 30 dB, BER: 10−5, the optical link distance fluc-tuates between 85–100 km, 50–60 km and 30–35 kmfor the chromatic dispersion parameter: 6 ps/(nm km),10 ps/(nm km) and 17 ps/(nm km), respectively withoutFEC.

In our previous work, we recognized that switching thedispersion parameter from 6 to 17 ps/(nm km), under thecondition of 10 dB signal to noise ratio for BPSK modu-

Fig. 10 100 Gb/s 16PSK BER-Distance variations, L: 0–300 km

lated CO-OFDM systems, constellation diagrams changedtheir shape from a circle to an ellipsoid [9, 11–13]. We cansee a similar result for 40 Gb/s results in Fig. 5-f. This re-sult is also directly related to the chromatic dispersion effectwhich causes extra imaginary part and comes out as a phaseshift in constellation diagrams.

4 Discussion

The optimum link distance for an optical communicationsystem depends on the SNR, BER, FEC and the fulfillmentof the minimum nonlinearity condition. These parameters,determined by the designers, in combination give the opti-mum link distance. Results given for 40 Gb/s and 100 Gb/sare good references for designers. However these results canbe applied to an optical communication link as long as theminimum nonlinearity conditions are satisfied. The discus-sion so far has been limited to a launch power of −8 dBmin which the nonlinearity is insignificant. Furthermore, non-linearity due to the high launch power can be partially mit-igated by the digital signal processing either in transmitteror receiver. The improvements on the topic of the nonlineareffect in CO-OFDM systems are summarized in this section.

To address our study, the effect of the nonlinearity for theCO-OFDM systems should be discussed here. Fiber nonlin-earity compensation was first proposed in 1996 using neg-ative nonlinear coefficient materials [29]. Due to the diffi-culty of implementation of this method, EDC method wasdeveloped by producing a pre-distortion signal [30, 31]. In2007 Arthur James Lowery figured out that the nonlinearpower limit of optical links where optical OFDM is uti-lized for dispersion compensation can be significantly im-proved by a simple and computationally efficient nonlinear-ity pre-compensation technique [32]. He and his researchgroup also examined the effect of fiber nonlinearity on thetransmission performance using different fibers and WDM

468 A. Yazgan, I.H. Cavdar

Fig. 11 16PSK Constellation diagrams at different SNR values, L: 50 km, 100 Gb/s data rate Dt: 17 ps/(nm km)

channel spacing [33]. In the same year, William Shieh andhis group experimentally demonstrated the nonlinear phasenoise reduction by running a receiver digital signal process-ing method for CO-OFDM transmission and had 2-dB Qimprovement at high launch powers [34]. During the trans-mission throughout the fiber, because of the Kerr effect,four-wave mixing (FWM) products occur between OFDMsubcarriers. The effect of these FWM components dependson the Peak to average ratio (PAPR) of the signal. ArthurJames Lowery and his group developed a simple formula toestimate the effect of FWM on the received signal qualityin CO-OFDM systems. This formula shows that the non-linear limit is substantially independent to the number ofOFDM subcarriers [35]. They showed that a 1-dB decreasein transmission power leads to a 2-dB raise in quality. It wasalso demonstrated that an optimum combination of pre andpost compensation had advantage of 2-dB increase in launchpower for 2000 km SSMF [36]. Already available PAPR re-duction techniques could be used to nonlinearity compen-sation in optical fiber cables [37]. Several researchers pro-posed different schemes for reducing PAPR in the presenceof nonlinear power amplifier [38, 39]. Interleaving effectwas also proposed by Sabbir Ahmed and Makoto Kawai toreduce the PAPR effect [40]. By including the nonlinearityeffect to the transmission, Moshe Nazarathy and his researchgroup studied the analytic models [41]. In 2009, Bernhard

Goebel and his group made a review of the most prominentPAPR reduction techniques [42]. Yang Tang and his group,in 2010, claimed that the PAPR reduction on sub-band ba-sis was more effective than that across the whole OFDMspectrum. Their method had each sub band filled with adiscrete-Fourier-transform-spread OFDM (DFT-S OFDM)signal that reduces the PAPR within each sub band. Thistechnique improved the overall nonlinearity transmissionperformance [43]. In 2011 it was experimentally verified byLiang Du and Arthur James Lowery that Pilot-based nonlin-earity compensation (PB-NLC) was an effective method formitigating Cross Phase Modulation (XPM) in CO-OFDMsystems [44].

These results reveal the importance of nonlinear compen-sation in optical systems for higher input powers. Consid-ering any transmission system, there is an optimal launchpower beyond which the system SNR starts to decrease asthe input power increases. To reach the minimum nonlin-earity values, excellent power optimization issues shouldalso be carried out especially for higher input powers. How-ever this effect can be effectively mitigated using the ex-isting PAPR reduction techniques [37]. Besides, for lowerinput powers, the nonlinearity is not enough of an issue tobe a priority [1–3, 13]. In this study we used OFDM pilotsubcarriers to compensate for phase noise. It was discov-ered by Sander Lars Jansen and his group that the RF-pilot

Optimum link distance determination for a constant signal to noise ratio in M-ary PSK modulated coherent 469

tone based phase noise compensation scheme could be im-plemented as well to increase the nonlinear tolerance [45].Their study showed an improvement in nonlinear toleranceof 0.5 dB for higher launch powers.

Due to the presence of considerable gain fluctuations inC and L band, the gain spectrum of an EDFA should also beoptimized, in order to achieve a flat output power.

The effect of using the wireless relay stations in the net-work was proposed in [46]. The obtained results showedan improvement of the system performance. These stationscould be reorganized using Radio over Fiber (RoF) systemssince the results of our paper support these types of applica-tions.

From the point of view of dispersion compensation, weused EDC by choosing OFDM that turns each dispersivechannel into a flat channel itself as discussed in Sect. 2.

5 Conclusion

Optimum link distance determination of the CO-OFDM sys-tems is examined and simulated for 40 Gb/s and 100 Gb/s.Different optical channel parameters are taken into account.In this study, it is important to know that results are givenfor one optical channel (such as 1549.32 nm) instead of thewhole DWDM in order to support different DWDM config-urations. According to the simulation results, the optimumlink distance can be determined for different channel pa-rameters and data rates. For the long haul communicationsystems, compared to the attenuation, our findings supportthe theory that the main obstacle is the dispersion. It is clearthat the laser phase noise fixing is a significant process es-pecially for higher data rates in high dispersive channels.From the implementation point of view, one of the most im-portant points is the real time operation. Algorithms used forchannel modeling, phase noise compensation and demodu-lation must meet the real time conditions. In order to ob-tain higher data rates in long haul transmission systems, ob-viously, DWDM should be combined with the CO-OFDMsystem. Using DWDM and still one RF carrier, this systemcapacity may go beyond 19 Tb/s theoretically if the mini-mum nonlinear condition is satisfied.

References

1. Djordjevic, I. B., & Vasic, B. (2006). Orthogonal frequency divi-sion multiplexing for high-speed optical transmission. Optics Ex-press, 14, 3767–3775.

2. Shieh, W., & Athaudage, C. (2006). Coherent optical orthogonalfrequency division multiplexing. Electronics Letters, 42, 5–589.

3. Xingwen, Y., Shieh, W., & Tang, Y. (2007). Phase estimation forcoherent optical OFDM. IEEE Photonics Technology Letters, 13,919–921.

4. Jansen, S. L., Morita, I., Takeda, N., & Tanaka, H. (2007). 20-Gb/sOFDM transmission over 4,160 km SSMF enabled by RF-pilottone phase noise compensation. In Optical fiber communicationconference OFC07.

5. Lowery, A. J., Liang, D., & Armstrong, J. (2006). Orthogonal fre-quency division multiplexing for adaptive dispersion compensa-tion in long haul WDM systems. In Optical fiber communicationconference OFC06.

6. Lowery, A. J., & Armstrong, J. (2006). Orthogonal frequency divi-sion multiplexing for dispersion compensation of long haul opticalsystems. Optics Express, 14, 2079–2084.

7. Shieh, W. (2007). PMD supported coherent optical OFDM sys-tems. IEEE Photonics Technology Letters, 19, 134–136.

8. Xiang, L., Qi, Y., Chandrasekhar, S., & Shieh, W. (2010). Trans-mission of 44-Gb/s coherent optical OFDM signal with trellis-coded 32-QAM subcarrier modulation. In 15th opto electronicsand communications conference OECC.

9. Yazgan, A. (2008). OFDM based chromatic dispersion compensa-tion in fiber optic media. M.Sc. thesis, Karadeniz Technical Uni-versity Department of Electrical-Electronics Engineering, Trab-zon, Turkey.

10. Yazgan, A., Aydemir, O., Tugcu, E., & Simsek, C. (2009). Per-formance analysis of OFDM systems on AWGN channels. InAkademik Bilisim, Turkey.

11. Yazgan, A. (2011). Performance analysis and link design of long-haul coherent optical OFDM systems. M.Sc. thesis in electricalengineering. Halmstad, Sweden: Halmstad University Microelec-tronics and Phonics program.

12. Yazgan, A. (2011). The tradeoff between BER and link distancefor a constant signal to noise ratio in coherent optical OFDM sys-tems. In 34 international conference on telecommunications andsignal processing, TSP 2011, Budapest, Hungary (pp. 126–130).

13. Yazgan, A., & Cavdar, I. H. (2011). Examination of the effect offixing laser phase noise in coherent optical OFDM systems withdifferent channel parameters. In 34 international conference ontelecommunications and signal processing, TSP 2011, Budapest,Hungary (pp. 121–125).

14. Laude, J. P. (2002). DWDM fundamentals, components and appli-cations. London: Artech house.

15. Stallo, C., Cianca, E., Mukherjee, S., Rossi, T., Sanctis, M.D., & Ruggieri, M. (2011). UWB for multi-gigabit/s com-munications beyond 60 GHz. Telecommunications Systems.doi:10.1007/s11235-011-9500-x.

16. Li, Y., & Stüber, G. L. (2006). Orthogonal frequency division mul-tiplexing for wireless communications. Atlanta: Springer.

17. Soysal, B. (2004). High performance receiver design for OFDMbased wireless communication systems. Ph.D. thesis, KaradenizTechnical University Department of Electrical-Electronics Engi-neering, Trabzon, Turkey.

18. Byun, D. K., Ki, Y. M., & Kim, D. K. (2007). Channel state-awarejoint dynamic cell coordination scheme using adaptive modulationand variable reuse factor in OFDMA downlink. Telecommunica-tions Systems, 36, 85–96.

19. Liu, Y., Song, Q., Guo, L., & Wang, X. (2011). Efficient schedul-ing algorithms for mixed services in wireless OFDMA system.Telecommunications Systems. doi:10.1007/s11235-011-9476-6.

20. Broadband radio access HIPERLAN type 2; Physical layer.Sophia Antipolis Cedex (1999).

21. McClellan, J. H., Schafer, R. W., & Yoder, M. A. (2003). Signalprocessing first. New York: Prentice Hall.

22. Matthew, N., & Sadiku, O. (2002). Optical and wireless commu-nications next generation networks. Boca Raton: CRC Press.

23. Franz, J. H., & Jain, V. K. (2000). Optical communications com-ponents and systems. Oxford: Alpha Science.

24. Rajiv, R., & Kumar, N. S. (2002). Optical networks a practicalperspective. San Mateo: Morgan Kaufmann.

470 A. Yazgan, I.H. Cavdar

25. Shieh, W., Bao, H., & Tang, Y. (2008). Coherent optical OFDMtheory and design. Optics Express, 16, 841–859.

26. Bulow, H., Buchali, F., & Klekamp, A. (2008). Electronic disper-sion compensation. Journal of Lightwave Technology, 26, 158–167.

27. Mynbaev, D. K., & Scheiner, L. L. (2001). Fiber-optic communi-cations technology. New Jersey: Prentice Hall.

28. Goldflab, G. (2008). Digital signal processing techniques for co-herent optical communication. Ph.D. thesis, University of CentralOrlando, Florida, Department of Optics in the College of Opticsand Photonics, Florida.

29. Paré, C., Villeneuve, A., Bélanger, P. A., & Doran, N. J. (1996).Compensating for dispersion and the nonlinear Kerr effect withoutphase conjugation. Optics Letters, 21, 459–461.

30. Killey, R. (2005). Dispersion and nonlinearity compensation us-ing electronic predistortion techniques optical fibre. In The IEEseminar on communications and electronic signal processing.

31. Roberts, K., Li, C., Strawczynski, L., O’Sullivan, M., & Hardcas-tle, I. (2006). Electronic precompensation of optical nonlinearity.IEEE Photonics Technology Letters, 18, 403–405.

32. Lowery, A. J. (2007). Fiber nonlinearity mitigation in optical linksthat use OFDM for dispersion compensation. IEEE PhotonicsTechnology Letters, 19, 1556–1558.

33. Lowery, A. J., Du, L. B. Y., & Armstrong, J. (2007). Perfor-mance of optical OFDM in ultralong-haul WDM lightwave sys-tems. Journal of Lightwave Technology, 25, 131–138.

34. Shieh, W., Yi, X., Ma, Y., & Tang, Y. (2007). Theoretical and ex-perimental study of PMD-supported transmission using polariza-tion diversity in coherent optical OFDM systems. Optics Express,15, 9936–9947.

35. Lowery, A. J., Wang, S., & Premaratne, M. (2007). Calculationof power limit due to fiber nonlinearity in optical OFDM systems.Optics Express, 15, 13282–13287.

36. Lowery, A. J. (2007). Fiber nonlinearity pre and post compen-sation for long optical links using OFDM. Optics Express, 15,12965–12970.

37. Goebel, B., Fesl, B., Coelho, L. D., & Hanik, N. (2008). On theeffect of FWM in coherent optical OFDM systems. In Nationalfiber optic engineers conference, NFOEC.

38. Shokair, M., & Sakran, H. (2011). Performance of SDM/COFDMsystem in the presence of nonlinear power amplifier. Telecommu-nication systems. doi:10.1007/s11235-010-9393-0.

39. Al-kamali, F. S., Dessouky, M. I., Sallam, B. M., Shawki,F., & Abd El-Samie, F. E. (2011). Impact of the power am-plifier on the performance of the single carrier frequencydivision multiple access system. Telecommunications Systemsdoi:10.1007/s11235-011-9439-y.

40. Ahmed, S., & Kawai, M. (2011). Interleaving effects on BER fair-ness and PAPR in OFDMA System. Telecommunication systems.doi:10.1007/s11235-011-9557-6.

41. Nazarathy, M., Khurgin, J., Weidenfeld, R., Meiman, Y., Cho, P.,Noe, R., Shpantzer, I., & Karagodsky, V. (2008). Phased-arraycancellation of nonlinear FWM in coherent OFDM dispersivemulti-span links. Optics Express, 16, 15777–15810.

42. Goebel, B., Hellerbrand, S., Haufe, N., & Hanik, N. (2009). PAPRreduction techniques for coherent optical OFDM transmission.

In International conference on transparent optical networks, IC-TON09.

43. Tang, Y., Shieh, W., & Krongold, B. S. (2010). Fiber nonlinear-ity mitigation in 428-Gb/s multiband coherent optical OFDM sys-tems. In National fiber optic engineers conference, NFOEC.

44. Du, L. B. Y., & Lowery, A. J. (2011). Pilot-based XPM nonlin-earity compensator for CO-OFDM systems. Optics Express, 19,B862–B867.

45. Inan, B., Randel, S., Jansen, S. L., Lobato, A., Adhikari, S., &Hanik, N. (2010). Pilot-tone-based nonlinearity compensation foroptical OFDM systems. In 36th European conference and exhibi-tion on optical communication.

46. Mach, P., Bestak, R., & Becvar, Z. (2011). Optimization of associ-ation procedure in WiMAX networks with relay stations. Telecom-munications Systems. doi:10.1007/s11235-011-9661-7.

Ayhan Yazgan received the B.Sc.and M.Sc. degree in Electrical-Electronics Engineering Depart-ment from the Karadeniz TechnicalUniversity, Trabzon, Turkey in 2005and 2008, respectively. He receivedsecond M.Sc. degree in the programof Microelectronics and Photonicsfrom Halmstad University, Swedenin 2011. He is currently a Ph.D. stu-dent at Karadeniz Technical Uni-versity. He is a student memberof Optical Society of America andIEEE. His current research interestsinclude advanced modulation and

coding schemes for optical communications, Coherent Optical OFDMsystems, Cognitive radio, RoF systems and fractal antennas.

I. Hakki Cavdar is a Professorof Electrical and Electronics En-gineering department at the Ka-radeniz Technical University, Tra-bzon, Turkey. He received the B.Sc.degree from the Gazi UniversityAnkara, Turkey in 1985, and theM.Sc. degree in electrical elec-tronic engineering from the Ka-radeniz Technical University, Tra-bzon, Turkey in 1988. He receivedthe Ph.D. degree from the Karad-eniz Technical University, Trabzon,Turkey in 1994. He is a member ofIEEE. His current research interests

are wireless communication systems and electronic circuit design. Heis the author or coauthor of more than 25 publications.