# Optimum link distance determination for a constant signal to noise ratio in M-ary PSK modulated coherent optical OFDM systems

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<ul><li><p>Telecommun Syst (2014) 55:461470DOI 10.1007/s11235-013-9801-3</p><p>Optimum link distance determination for a constant signalto noise ratio in M-ary PSK modulated coherent optical OFDMsystems</p><p>Ayhan Yazgan I. Hakki Cavdar</p><p>Published online: 17 August 2013 Springer Science+Business Media New York 2013</p><p>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 nm1612.65 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.</p><p>Keywords Radio over Fiber Optical link design Opticalnetworks Fiber optical communication OFDMmodulation</p><p>1 Introduction</p><p>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</p><p>A. Yazgan (B) I.H. CavdarDepartment of Electrical-Electronics Engineering, KaradenizTechnical University, 61080 Trabzon, Turkeye-mail: ayhanyazgan@ktu.edu.tr</p><p>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.</p><p>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].</p><p>In this study, we focused on the optimum link distancedetermination for a constant signal to noise ratio in CO-</p><p>mailto:ayhanyazgan@ktu.edu.tr</p></li><li><p>462 A. Yazgan, I.H. Cavdar</p><p>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[913]. 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].</p><p>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.</p><p>2 Principle of CO-OFDM</p><p>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, n is the phase term ofthe nth subcarrier and k = 0,1,2, . . . ,NSC 1; an OFDMsymbol is given by (1) [20].</p><p>Ss(kTs)=(</p><p>1</p><p>NSC</p><p>)NSC1n=0</p><p>cne(j2n)( k</p><p>NSC)e(jn) (1)</p><p>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</p><p>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 EDFAs 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 [2125]. Thanks to coherent detec-tion, a linear transformation from the optical to RF signalmay also be obtained [15]. Neglecting the digital modu-lation and pulse waveform, the received optical signal forone OFDM symbol is given in (2, 3). Here D(n) is theeffect of chromatic dispersion for the phase component ofnth OFDM subcarrier as given in (4). 2 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, fLD1is 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 cmn are transmitted and received signals, re-spectively, m 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 0, a linearterm which is related to the first subcarrier latency 0, 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].</p><p>Es = LL NSC1n=0</p><p>cne(j2.fnt)e(jD(n)) (2)</p><p>LL= e(j (2(fLD1+fLO1)t+LD1)) (3)D(n)= 1</p><p>22</p><p>2nL (4)</p></li><li><p>Optimum link distance determination for a constant signal to noise ratio in M-ary PSK modulated coherent 463</p><p>Fig. 1 CO-OFDM blockdiagram</p><p>Fig. 2 Optical channel model for a single mode fiber cable</p><p>2 = LD12</p><p>2vDt (5)</p><p>D(n)= v fLD1</p><p>2Dtfn</p><p>2L (6)</p><p>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</p><p>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; Dtis the chromatic dispersion parameter; f is the subcarrierspacing and G is the guard interval length.</p><p>hn = |hn| exp(j(0 + 20fn + D(n)</p><p>))(7)</p><p>cmn = cmn hn exp(jm)+ nmn (8)v</p><p>fLD2|Dt |NSCf G (9)</p><p>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(cmn) is thereceived phase angle of the related OFDM pilot subcarrier,m is the estimated total phase drift including laser phasenoise and cmn is the obtained signal after phase noise com-</p></li><li><p>464 A. Yazgan, I.H. Cavdar</p><p>pensation.</p><p>m = 1NSP</p><p>NSP1n=0</p><p>[pa</p><p>(cmn</p><p>) pa(cmn)] (10)</p><p>clpmn = cmn exp</p><p>(j m) (11)cmn = lpcmn hn</p><p>|hn|2(12)</p><p>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, 1113].</p><p>3 Results</p><p>Some critical information to address this research should begiven here. First of all, it is crucial that the BER thresh-old of 102 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.</p><p>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.</p><p>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</p><p>Table 1 Basic Optical Fiber Parameters</p><p>Parameter Value</p><p>Wavelength 1549.32 nm</p><p>Velocity of light in fiber cable 200000 km/s</p><p>Fiber optical cable length 1003000 km</p><p>Chromatic Dispersion Parameter 6, 10, 17 ps/(nm km)</p><p>Table 2 Basic OFDM Parameters for 40 Gb/s</p><p>Parameter Value</p><p>Modulation QPSK</p><p>Data Rate (Gb/s) 40</p><p>Sampling frequency (fs) 20 GHz</p><p>Sampling Period (Ts) Ts = 50 psUseful symbol duration (Tu) 25.6 ns</p><p>Cycling prefix duration (Tcp) 3.2 ns, 6.4 ns</p><p>Symbol duration (Tsym = Tu + Tcp) 28.8 ns, 32 nsData subcarrier number (NSD) 448</p><p>Pilot subcarrier number (NSP ) 32 or 64</p><p>Total subcarrier number (NSC ) 512</p><p>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.</p><p>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].</p><p>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 im...</p></li></ul>

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