Abstract

In this paper we present the intensive theoretical laborcarried out to describe optical communication systemswhich employ orthogonal frequency division multi-plexing (OFDM), and, more concretely, those systemswhich use direct laser intensity modulation and directdetection. Firstly, we propose an analytical model tostudy in detail the main phenomena which affect thesignal information detected at the receiver. Moreover,the analytical model is complemented with a study ofsignal clipping at the transmitter and the filtering ef-fects affecting the signal through the communicationsystem. With the analytical model reported we can des -cribe in a rather comprehensive way the main phenom-ena as well as exploring and optimizing the final systemperformance of OOFDM systems with direct modula-tion and detection.

By taking advantage of the analytical model derived, wepropose a pre-distortion technique which improves themodulation efficiency, making possible to increase the sig-nal information term without increasing the nonlinear dis-tortion at the receiver, improving in this way the systemperformance obtained. An alternative technique for thesystem performance improvement based on optical filte -ring is also mathematically studied in order to understandexactly its working principle, the improvement obtained,as well as its potentiality. The derived mathematical ex-pressions allows us to systematically explore the differenteffects involved in the final performance obtained, thestudy of OOFDM systems with different optical filteringstructures, as well as the possibility of optimization in aquick and efficient manner different optical filtering struc-tures.

1. Introduction

OFDM is a multi-carrier format widespread used in wire-less communications and DSL applications [1,2]. Since2005 optical OFDM has also attracted lots of attentionfor a great variety of optical communication scenarios,from long-reach to short-reach optical links, or commu-nications systems based on single mode, multimode andplastic optical fiber [3-5]. In the context of access net-works, passive optical networks have emerged as a coste -fficient architecture to provide advanced and speed ratedemanding communications applications. In this cost-sensitive scenario, OOFDM is a promising format/multi-plexing technique, what has led to a high number ofresearch results published by several investigation groups[6,7]. Besides its versatility, the potentials of OOFDM havecontributed as well to this interest: it can offer high spec-tral efficiencies by using high quadrature-amplitude mod-ulation formats, robustness to frequency roll-off oftransceiver electronics, dispersion equalization complexityeasily scalable with transmission rate or subcarrier granu -larity. The proposed transceiver architecture varies foreach scenario depending on the required trade-off be-tween system performance/cost. When the optical inten-sity is used for information transmission, a simple pinphotodetector is appropriate for the opto-electronic con-version to recover the transmitted information, what iscalled intensity modulated/directly detected (IM/DD) sys-tem. This variant is more appropriate for medium andshort reach applications where the cost is of great con-cern, such as metro and access optical networks. The di-rect modulation of a laser in the OFDM transmitter bringsadditional advantages in terms of cost reduction, com-pactness, low power consumption and high optical out-put power.

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Theoretical analysis of directly modulated optical OFDM signals over an IM/DD fiber linkChristian Sánchez Costa, Beatriz Ortega Tamarit and José Capmany Francoy

Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universitat Politècnica de València, 8G Building - access D - Camino de Vera s/n - 46022 Valencia (Spain) Corresponding author: bortega@iteam.upv.es

Nevertheless, its performance is severely limited by dis-tortions arising from the laser and photodetector non-linearities and the propagation of the chirped signalthrough the dispersive link connecting the central officeand the optical network unit. Analytical models whichenlighten the physics behind the performance of directlymodulated/detected (DM/DD) OOFDM systems can beof great help for their design and the proposal of tech-niques aimed to increase the performance obtained. Pre-vious published analytical models focus on the influenceof the transceiver electronics design parameters but noton the direct modulation process and fiber transmissioneffects [8], or are based on not general mathematical as-sumptions [9,10]. In this sense, we present a theoreticalanalysis using a detailed mathematical treatment tostudy the effects of the laser nonlinearity and the globalimpact of the laser chirp and chromatic dispersion withregard to the system performance. Moreover, a compre-hensive framework for the quick, systematic and effi-cient evaluation of DM/DD OOFDM systems is proposedafter i) simplifying the expressions describing the lineareffects and the second order intermodulation distortionin DM/DD OOFDM systems, ii) the study of the effectsof linear filtering through the communication systemcausing inter-carrier and inter-symbol interferences (ISIand ICI), and iii) the study of the effects of signal clippingat the transmitter.

In order to overcome the underlying limiting system per-formance in IM/DD OOFDM systems, such as the non-linear distortion, several solutions have been proposedin order to overcome it (e.g., [11,12]). Our proposal isbased on the employment of pre-distortion at the trans-

mitter and in the frequency domain (before the trans-mitter inverse Fourier transform), and makes use of theanalytical model previously reported for the reconstruc-tion of the interference. Unlike previous referencesabout digital pre-distortion, the technique here pro-posed aims to mitigate the nonlinear distortion with anend-to-end perspective, rather than only that originatedby the optical modulator.

The employment of an optical filter to improve the sys-tem performance by suitable conversion of the inherentfrequency modulation at the laser transmitter output intoadditional intensity modulation at the end of the link hasbeen studied for traditional modulation formats [13], andrecent results showed considerable power budget im-provements for DM/DD OOFDM systems [14]. Neverthe-less, this approach is only qualitatively understood inprevious literature and further work is necessary to graspthe theoretical foundations which can provide the designcriteria for optimum operation. By extending the previ-ously presented theory, we provide an end-to-end ana-lytical model to describe the operation of a DM/DDOOFDM system when an arbitrary optical filter is insertedin the dispersive link.

2. Analytical modelling

2.1. System descriptionThe optical OFDM communication system is basicallycomposed of an OFDM transmitter, the directly modu-lated laser (DML), the dispersive fiber link, a photode-tection stage, and, finally, the OFDM receiver, asdepicted in Fig. 1.

In the OOFDM system, the information binary data ismapped into M-QAM complex symbols and a block ofthe resulting complex symbols is fed to an Inverse FastFourier Transform (IFFT) processor with a size equals to FS.

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The direct modulation of a laser in the OFDM transmitterbrings additional advantages in terms of cost reduction,compactness, low power consumption and high opticaloutput power.

Figure 1. Schematic illustration of the DM/DD OOFDM system.

(1)

In order to obtain a real-valued signal x[n] at the output,the original information complex symbols and their co -rresponding conjugate values are arranged with Hermi -tian symmetry at the IFFT input. The obtained real-valueddiscrete signal is composed of N subcarriers, each ofthem modulated by an information complex symbol.Note that some symbols Xk at highest frequencies maybe set to zero in order to introduce oversampling. Afterparallel-to-serial conversion, a cyclic pre/post-fix is addedto each OFDM symbol in order to combat ISI and ICI ef-fects, and hard clipping in the digital domain is appliedin order to limit the amplitude swing of the OFDM signal.Finally, the signal is interpolated and low-pass filtered.The OFDM symbol starting at t=0 and with duration Tcan be expressed as:

(2)

where Xk=|Xk |�exp( j��Xk ) are the information com-plex symbols, �k is the angular frequency of the is thekth OFDM subcarrier, and htrx(t) is the impulse responseof the transmitter. The value of the discrete frequency �kis given by k·Δ�, where Δ� is the spacing angular fre-quency between consecutive subcarriers. The spacing an-gular frequency Δ� is given by 1/T, where T=FS·fsamand fsam is the sampling rate. The analog OFDM signalis then scaled by a factor to yield a certain value of peakcurrent and a dc value is added to operate the opticalsource. The input current to the laser is then given by:

(3)

where i0 represents the dc-offset added just before thelaser, m is the scaling factor determined by the electricalattenuation to operate the laser within a certain region(|im(t)|

where P0 is the optical intensity due to the steady drivingcurrent value i0, P1(t) is the linear optical intensity term(function of Hp1(k)), whilst P2(t) and P11(t) representthe harmonic and intermodulation distortion of the op-tical intensity modulation (functions of Hp2(k) andHp11(k, 1), respectively). Finally, the optical modula-tion frequency indices mk exp ( j��mk ) in Eq. (7) includeboth linear and nonlinear effects in the optical phasemodulation.

Getting rid of the square root by approximating01+x≈1+x/2-x2/8, the fiber transfer function in Eq.(5) can be applied in the frequency domain, and the sig-nal at the fiber output can be determined by calculatingits inverse Fourier transform. Neglecting some higherorder terms, and using the Graf’s theorem for the sumof Bessel functions, one can arrive at the following ex-pression for the photocurrent:

(8)

T0 and T1 contain the information component, whichcan be extracted by setting one of the indices n1, n2,...nNto 1, and the rest to 0, as well as nonlinear distortion dueto the laser chirp, the expressions of which are obtainedby particularizing the indices n1, n2,...nN such that

. T2, T3, T4 and T5 are essentially termsdue to nonlinear distortion which stem from the lasernonlinearities (T2 and T3) and the imbalance caused

by the chromatic dispersion on the optical field (T4 andT5).

In Fig. 2 the received 32-QAM complex symbols beforeequalization obtained through the evaluation of with dif-ferent nonlinear gain coefficient and fiber dispersionvalu es and through the simulation of the IM/DD OOFDMsystem are shown. We have chosen to show the complexsymbols before equalization to demonstrate how accu-rately the analytical model can follow the physics behindthe whole process of transmission and direct detectionof directly modulated OOFDM signals.

Although the derived expression for the photocurrent inEq. (7) offers us a very accurate description of the physicalprocesses which govern the optical transmission, propaga-tion and detection of OOFDM signals in DM/DD systems,we need to derive more intuitive and computationally easyexpressions of the linear and nonlinear effects. Such sim-plification can be carried out by approximating the Besselfunctions involved in the photocurrent expression Eq. (8):

(9)

and retaining only the intermodulation distortion productsup to the second order. The expression characterizing thelinear effects is then reduced to the following equation

(10)

Moreover, the evaluation of the nonlinear distortion is ratherdirect and still accurate for typical parameter values em-ployed in DM/DD OOFDM systems in short/medium haullinks. The resulting nonlinear distortion expressions are:

90

The analytical model follows accurately the physics be-hind the whole process of transmission and direct detec-tion of directly modulated OOFDM signals.

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Figure 2. Constellation diagrams obtained through the simulation of the DM/DD OOFDM system and the evaluationof Eq. (7). fsam=11GHz, FS=128, N=55, L=60km, (a) the nonlinear gain coefficient is equal to 3x10-24m3; (b) the nonlineargain coefficient is equal to 3x10-23m3; (c) same as (b) but the fiber dispersion is D=-7ps=(nm_km).

The total nonlinear distortion, I[k], is given by the sum ofthese terms: and the variance due to nonlinear distortionis calculated as .

2.2.2. ISI and ICI due to filteringIn order to avoid ISI from the adjacent OFDM symbols andmake the linear convolution behave as a circular convolu-tion, cyclic extensions are appended to the original OFDMsymbols [2]. Since the transmission information rate is re-duced because of the transmission of redundant samples,it is essential to evaluate the penalty due ISI & ICI effectsas a function of the number of these redundant samples.The theoretical expressions aimed to evaluate the penaltydue to ISI & ICI effects are deduced from similar analysisto those reported in [16,17], but we take into account thecorrelation between the discrete samples of the generated

OFDM signal and we employ the transfer function givenby Eq. (10) to include laser intensity and phase modula-tions as well as the propagation of the signal through thedispersive fiber.

Npre = ηpre·FS and Npreos = ηpos·FS samples are usedas pre- and post-fix for each OFDM symbol. We considera channel impulse response with a positive tail extendingto Tsam·L+ and a negative tail extending to -Tsam·L- (L+and L- represent a certain number of samples, and Tsamis the sampling period), and we assume that ISI occursonly due to the adjacent OFDM symbols. Apart from ISI,ICI also occurs due to the loss of orthogonality betweensubcarriers, and the variance characterizing this processhas the same value as that due to ISI. The total variancedue to ISI & ICI on the k-th subcarrier is given by:

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(11)

(12)

(13)

(14)

(15)

(16)

(16)

2.2.3. Clipping of the OFDM signalAfter arranging the QAM symbols X1, X2,...Xn with Her-mitian symmetry at the IFFT input, the signal at the inputof the clipping device is given by:

(17)

As the central limit theorem, for a sufficiently high valueof N, x[n] follows a Gaussian distribution with zero meanand variance equal to . This meansthat high peak values of amplitude occur with a smallprobability and the OFDM signal presents a high peak-to-average power ratio, which is its main drawback.

A simple technique used to limit the random amplitudeof the generated OFDM signal is to deliberately clip it, asshown in Fig. 3.

The value of Aclip is an important system parameter in op-tical OOFDM systems: the smaller its value, the smaller theamplitude excursion of the electrical OFDM signal, andtherefore less stringent conditions on the design of elec-tronics in the transceiver and higher optical modulation ef-ficiency, but the higher the distortion introduced by suchnonlinear operation. Aclip is usually defined in relation tothe clipping level CL, given by CL= .

Recalling the Bussgang’s theorem [18], the clipping ope -ration ouput signal can be expressed as the sum of anundistorted signal part and a noisy term:

(18)

where χ=1-erfcCL/2), and np-,clip[n] is the clipping noise,whose expressions for the autocorrelation and the powerspectral density can be found in [19]. In Fig. 4 we com-pare the normalized power spectral density of the clip-ping noise for different values of CL and N = 60, beingFS = 256.

As expected, the smaller the value of CL, higher is theclipping noise introduced, and its spectral density rangesfrom values around -40dB/Hz for CL = 10dB to valuesaround -20dB/Hz for CL = 5dB. We observe from Fig. 4.4that comparisons between the PSDs obtained throughtheory and the simulations are in good agreement.

The noise variance on the kth subcarrier at the receivercan be calculated as:

(19)

where H (e jΩk) is the transfer function from the trans-mitter IFFT to the receiver FFT, and np-,clip(e jΩk) is thepower spectral density of np-,clip[n].

The spectral estimation of the clipping noise np-,clip(ejΩk)involves a statistical averaging and the clipping noise isassumed to be uniformly distributed with time. However,CL is usually set to a high value and, thus, clipping is arare event [20]. In order to get a better approach in thesesituations, we propose to divide the whole clippingprocess into a finite number of processes, which aregiven by the union of the OFDM symbols with the samenumber of clips. Once obtained the power spectral den-sity of the clipping noise with a certain clipping rate i/FS,with i=0,1,..imax, that is, ni,clip(e

jΩk) , the variance is of

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Figure 3. Clipping operation.

Figure 4. Power spectral density of the clipped signal and the clipping noise for FS = 256 and N = 60.

the kth subcarrier at the receiver can be calculated as:

(20)

which can be used in a more refined expression of theerror probability:

(21)

This approach has demonstrated to provide a more ac-curate evaluation of the clipping effects than the tradi-tional one based on the direct computation of the powerspectral density of the clipping noise [21].

3. Performance evaluation

Due to the unique algorithm used to demultiplex the re-ceived OFDM signal through the use of a FFT, the diffe -rent impairment effects which add to the received complexsymbol, H[k]·X[k], can be approximated to a Gaussian dis-tribution [2] provided a sufficiently high number of datasubcarriers N is used. Thus, the system performance evalu -ation can be accomplished through a simple figure ofmerit which accounts for the power of the undistortedpart of the received information signal and the variance ofthe impairment effects on each subcarrier [8]. In order tocalculate the BER of each subcarrier (BER[k]), due to theanalytical treatment to study the clipping noise explainedin the subsection 2.2.3, a signal-to-noise ratio conditionedto the number of clips i is calculated

(19)

Once determined SNRi,clips[k], BER[k] with k = 1,…,N iseasily determined with the help of BER evaluation for-mulas [21] and making use of Eq. (21).

The arrows in Fig. 5 indicate at which point the maximumvalue of transmission information rate is achieved, being27.63Gbits/s for i0=46mA, α = 4 and εnl = 1.7×10-23m3, and26.606Gbits/s for i0=78mA, α = 7 and εnl = 1.7×10-23m3.From Fig. 5(a) we can observe that the system performanceis clearly limited by the laser chirp and the informationtransmission rate decreases with α, whereas for i0 = 78mA,a higher value of α is beneficial because of the linear con-tribution due to the laser chirp, as expressed in Eq. (10).The variation of the achievable information transmissionrate with εnl is due to two counteracting factors: at smallvalues, frequency dips may appear as result of the oppositephases between the two terms in Eq. (10), and at highervalues, laser nonlinearity becomes more significant.

4. Applications for system performance enhancement

4.1. Pre-distortion techniqueThe principle is rather simple and is based on the recons -truction of the interference I[k] with k = 1,2...N andproper substraction at the transmitter. It is assumed thatthe channel varies at a sufficiently slow speed such thatthe transmitter is able to track the changes of I[k], withk = 1,2...N, through appropriate feedback informationfrom the receiver, which is a reasonable assumption forshort/medium IM/DD links. The reconstruction of the in-terfering term I[k] with k = 1,2...N is based on the ana-

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Figure 5. Information transmission rate for a) i0 = 46mA and b) i0 = 78mA.

Figure 6. Constellation diagrams of the 62th to 110th subcarriers for L = 40km. a) Conventional DM/DD OOFDM sys-tem (128-QAM), b) DM/DD OOFDM system without pre-distortion technique (512-QAM), and c) DM/DD OOFDM systemwith pre-distortion technique (512-QAM).

a) b) c)

lytical model reported in section 2.2.1. Apart from thefeedback provided by the receiver, another feedback pathis employed at the transmitter in order to identify othermagnitudes needed for the reconstruction of I[k], whatis done by splitting the laser output signal into two sig-nals by means of an optical power divider.

Denoting as Irec[k] the interference reconstructed at thetransmitter, it is divided by the linear transfer functionH[k], k = 1,2...N. The information complex symbols withthe proposed technique turn into:

(19)

As result of the transmission of Xprd[k] instead of X[k], k= 1,2, ...N, we have at the output of the communicationsystem:

(20)

where χ[k] is a difference term due to the transmissionof Xprd[k] instead ofX[k], k = 1,2, ...N through the non-linear communication system. With this technique, thesystem performance increases provided that the recons -tructed interference Irec[k] is sufficiently close to the ac-tual interference I[k] and the magnitude of the additionalnonlinear term χ[k] is smaller thanI[k], which is a rea-sonable assumption in a communication system usinghigh order QAM modulation formats and the symbolsmust be weakly impaired in order to assure a certain per-formance (e.g., BERT < 10-4).

In Fig. 6 we show the constellation diagrams of the 62th-110th subcarriers in order to get a visual impression ofthe improvement achieved by means of the proposedpre-distortion technique.

The conventional DM/DD OOFDM system employs 128-QAM in the subcarriers ranging from 62 to 110, and thereceived symbols after equalization are shown in Fig. 6(a).Using this modulation format guarantees that the ob-tained BER does not exceed considerably the objectiveBERT = 10

-4, situation which would occur if the modu-lation format order is increased to 512-QAM. The aim ofthe constellation diagrams Figs. 6(b) and (c) is to showthe effects of the proposed pre-distortion technique.Both of them show the constellation diagram for thesame subcarriers (62 to 110), using 512-QAM as modu-lation format, but in Fig. 6(b) the pre-distortion techniqueis not used at all. It is clear that the quality of the receivedsignal is ruined and it would lead to an unacceptablevalue of BERT. The use of the pre-distortion technique,Fig. 6(c), offers us a much clearer constellation diagram,and, similarly to Fig. 6(a), an appropriate quality of the

received symbols is achieved and the value of the ob-tained BERT does not increase significantly.

In Fig. 7 we compare the BER obtained through error-counting simulations of the conventional systems, thesystem with the proposed pre-distortion technique, andthe system with the non-linear equalizer proposed in[10].

We observe from Fig. 7 that the obtained BER values areclose to the objective BER = 10-4. As predicted by thesimulations with the simplified model, the achieved trans-mission information rates when the pre-distortion tech-nique is used are considerably higher. With the nonlinearequalizer at the receiver, the transmission informationrates are equal to 33.08Gbits/s and 14.49Gbits/s forL=40km and L=100km, respectively. Though the valuesobtained with the nonlinear equalizer at the receiver arenot the result of a so exhaustive system parameter opti-mization, the values presented in Fig. 5.10 show an in-tuitively clear issue: a nonlinear equalization at thereceiver can improve the quality of the detected signal,but, since the interference reconstruction depend on de-cisions about the received information signal, the ob-tained performance will eventually depend on the signalquality of the conventional DM/DD OOFDM system.

4.2. Optical filteringThe optically filtered DM/DD OOFDM system is very simi -lar to that shown in Fig. 1, but with an optical filter in-serted into the optical fibre link. The effects of the opticalfiltering onto the optical signal can be easily taken intoaccount using the well-known digital filtering theory. Theimpulse response and corresponding transfer function ofthe optical filter are given by:

(21)

where Ord is the order of the filter. The field at its outputis calculated as

(22)

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Novel predistortion and optical filtering approaches havebeen proposed to improve the OOFDM system perfor-mance with successful results.

Figure 7. Comparison of BER values obtained througherror-counting simulations.

In Fig. 8 an optical superGaussian filter of order 2 and 3-dB bandwidth of 10GHz is used to observe the influenceof the central frequency shift with respect to the opticalcarrier of the information signal.

As Eq. (24) points out, in the case some asymmetry is in-troduced, information components that otherwise wouldbe counteracted, start to spring up, increasing thus thesignal information detected at the receiver and the sys-tem, as it is observed in Fig. 8(a) and (b): the increase ofthe central frequency implies a stronger filtering of thelower sideband, and such asymmetry leads to the in-crease of the system transfer function plotted in Fig. 8(b).

Using the signal-to-noise ratio figure defined in Eq. (19),we can study the expected performance of an opticallyfiltered OOFDM system with different optical filtering ar-

chitectures. In Fig. 9(b) we show the obtained signal-to-noise ratio obtained for different values of the delay τMZIand the phase shift ϕupp of a Mach-Zehnder interferom-eter filter, shown in Fig. 9(a).

We can see in Fig. 9(b) that with a simple MZI we havebeen able to get an effective SNR around 19dB, whichis obtained when ϕupp=π/2. This value for the phase shiftentails a tradeoff point of the system, mainly determinedby the optical carrier attenuation and the degree of im-balance introduced. When the value for ϕupp is changedto π/4 or 3π/4 the effective SNR gets worse as a result ofa decrease of the system transfer function (Eq. (24)).Wecan also observe that for ϕupp=π/2, the delay τMZI canbe varied over a broad range and good values of signal-to-noise ratio are still obtained.

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Finally, the photocurrent is calculated as the squaredmodulus of the field. After a lengthy mathematical ma-nipulation, Iph(t') can be expressed as eq. (23).

From Eq. (23), we can observe that the different spectracomponents are weighted by the product of the filter co-efficients hκ·hε* and are also affected by the average

phase delay (τκ+τε)2. Because of the complexity of theexpressions obtained, we have proceeded as in the sec-tion 2.2.1 and we have obtained a simplified versionwhich gives reasonable good results. With these simpli-fications and making use of the transfer function of theoptical filter Eq. (21) the expression for the signal infor-mation component can be expressed as:

(23)

(24)

Figure 8. (a) Optical filter transfer function, (b) OOFDM system transfer function with q = 2, ΔΩ3dB/(2π) = 10GHz (0.08nm).

Finally, the performance improvement provided by theoptical filtering is quantified in terms of power budget.In Fig. 9 we show the BER obtained for different valuesof the received average optical power. Based on the pre-vious results, we set τMZI to 136ps and ϕupp=π/2. Giventhe importance of the clipping ratio used at the transmi -tter on the system performance, curves with differentvalu es of clipping ratio have been also plotted.

The performance improvement obtained by inserting theoptical filter in the OOFDM system is highly dependenton the clipping ratio: when no optical filter is used, asignifi cant power budget improvement can be obtainedby reducing the clipping ratio, whilst this reduction resultsin a more limited improvement in the distortion-limitedpower budget when an optical filter is used. When no op-tical filter is used, a received power equals to -15.2dBm isneeded to achieve a BER equals to 10-3 whenCL=13.8dB, whilst a received power equals to -17.6dBmis needed for CL=8dB. When a MZI is used, for which areceived power equals to -20.9dBm is needed to obtain aBER equals to 10-3 when CL=13.8dB, whilst it is reducedto -22.1dBm when CL=10dB, as it can be observed in Fig.9(b). Thus, with a MZI as optical filter, we are able to getan improvement equals to 4.5dB compared to the non-optically filtered system.

5. Conclusions

The proposed mathematical treatment has allowed us toinclude the main signal generation, transmission and de-tection effects, as well as providing us with a great ver-satility. After proper validation by comparing the resultswith those obtained with simulation commercial soft-ware, the analytical model has offered us a mathematicaldescription of the linear information signal term and thenonlinear distortion at the receiver-end side, determiningjointly to a great extent the obtained system performanceof DM/DD OOFDM systems. To the best of our knowle d ge,

the proposed model represents the most accurate modelup to the present day for the accounting of the main ef-fects in DM/DD OOFDM systems. Furthermore, despiteof its complexity, it can be conveniently simplified to pro-vide a much more simple description accordingly to theneeds of the particular system. A more complete descrip-tion of real DM/DD OOFDM systems with the considera-tion of important transceiver design parameters, such asthe clipping level, the length of the cyclic extensions andthe laser modulation index, has been also derived.

In order to deal with the underlying problem of nonlineardistortion in DM/DD OOFDM system, a novel pre-distor-tion technique has been proposed based on the previo -usly proposed analytical model. In the proposed scheme,a dedicated receiver extracts and tracks some of thenece ssary parameters needed to reconstruct the interfe -rence terms of the system. Together with the feedback-path from the receiver to the transmitter, the proposedtechnique is able to achieve great nonlinear distortion re-duction ratio values.

Transmission information rates equal to 40Gbits/s and18.5Gbits/s have been obtained for L=40km andL=100km, respectively, with a BER in the order of 10-4.The employment of QAM modulation formats of higherorder to those used in the conventional DM/DD OOFDMsystem has allowed us to obtain transmission informationrate improvements equal to 9Gbits/s and 8.5Gbits/s forL=40km and L=100km, respectively. Furthermore, com-parisons of the pre-distortion technique with a previouslyreported nonlinear mitigation technique based on non-linear equalization at the receiver-end side have been alsocarried out, showing that our proposed techniqueachieves a higher nonlinear distortion cancellation effi-ciency. As result, our proposed technique outperformsnonlinear equalization at the receiver by several Gbits/s.

Through the development of the corresponding analyti-cal model, we have been able to grasp the foundation

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Figure 9. (a) Schematic of the Mach-Zehnder interferometer filter, (b) Signal to noise ratio for different values of the delayand phase shift.

for the improvement obtained when an optical filter isused in a DM/DD OOFDM system. Results obtained haveconfirmed that optical filtering may be a suitable tech-nique for the improvement of power budget in DM/DDOOFDM systems by a few dBs (4.5dB with a MZI). Theanalytical formulation obtained for the description of op-tically filtered DM/DD OOFDM systems has demonstratedto be an useful tool to characterize the system perform-ance through the calculation of the effective signal-to-noise ratio. Its computation has allowed us to exploreoptimized values for a MZI filter.

To sum up, DM/DD OOFDM systems are suitable optionto be employed in dynamical metro/access optical net-works, able to provide great spectral efficiencies and ver-satility. The cost of such systems is also one of its mainadvantages, compared to other architectures such as ex-ternally modulated/directly detected systems or coher-ently detected systems. The laser chirp impose limitationson the link reach and the achievable transmission infor-mation rate, but, as we have seen in this work, DSP andoptical signal processing techniques may make a valu-able contribution to mitigate their effects. Other disad-vantages arising from the nature of the informationtransmission (it must be conveyed in the optical intensitydomain), such as the loss of the information on thephase and polarization of the optical signal makeDM/DD systems unflatte ring compared to their morecomplex counterparts.

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Biographies

Dr. Christian Sánchez received theTelecommunication Engineer bache -lor's degree in 2008, the M.Sc. de-gree in 2010 and PhD in 2014 fromthe Universidad Politecnica de Va-lencia. Since March 2008, he wasworking toward the Ph.D. degree inthe Optical and Quantum Commu-nications Group. He has been in-

volved in the european project ALPHA and the nationalproject NETWON. In 2010, he was a Guest Researcher atthe Bangor University, under the supervision of Prof. J.Tang. He is currently at the Aston University, Birmingham,as post-doctoral research fellow, studying digital signalprocessing techniques to be employed in optical commu-nication systems with spatial division multiplexing. Hismain research interests include optical fiber communica-tions, advanced optical modulation formats and signalprocessing techniques. He serves as reviewer for jour-nals of his field, such as Photonics Technology Letters,Journal Lightwave of Technology, Optics Letters and Op-tics Express.

Dr. Beatriz Ortega was born inValencia, Spain, in 1972. She re-ceived the M.Sc. degree in physicsin 1995 from the Universidad deValencia, and the Ph.D. in Telecom-munications Engineering in 1999from the Universidad Politécnica deValencia. She joined the Departa-mento de Comunicaciones at the

Universidad Politécnica de Valencia in 1996, where shewas engaged to the Optical Communications Group andher research was mainly done in the field of fibre gra -tings. From 1997 to 1998, she joined the OptoelectronicsResearch Centre, at the University of Southampton(United Kingdom), where she was involved in severalprojects developing new add-drop filters or twin-corefibre-based filters. Since 1999 she is an Associate Lecturerat the Telecommunications Engineering Faculty in theUniversidad Politécnica de Valencia. She has publishedmore than 100 papers and conference contributions infibre Bragg gratings, microwave photonics and opticalnetworks. She has participated in the European Networksof Excellence IST-NEFERTITI, IST-EPIXNET, and IST-EPHO-TON/ONE and she has also been involved in several EUfunded projects such as IST-LABELS, IST-GLAMOROUS,IST-OFFSOHO and IST-ALPHA project. Currently she isleading the NEWTON national project, where her mainresearch is focused on advanced modulation techniquesin optical systems.

José Capmany obtained the M.Sc.degrees in Telecommunications En-gineering and Physics from Univer-sidad Politecnica de Madrid (UPM)and UNED respectively. He holds aPh.D. in Telecommunications Engi-neering from UPM and a Ph.D. inPhysics from the Universidad deVigo. In 1991 he moved to the Uni-

versidad Politecnica de Valencia (UPVLC) where he hasbeen a full Professor in Photonics and Optical Communi-cations since 1996. In 2002 he was appointed Directorof the Institute Of Telecommunications and Multimedia(iTEAM) at UPVLC. He has been engaged in many re-search areas within the field of photonics during the last25 years including Microwave Photonics, Integrated Op-tics, Fiber Bragg Grating design and fabrication, OpticalNetworks and, most recently Quantum Information sys-tems. He has published over 375 papers in scientific jour-nals and confererences. He is a Fellow of the Institute ofElectrical and Electronic Engineers (IEEE) and the OpticalSociety of America (OSA). In 2012, he was awarded withthe Rey Jaime I on New Technologies.

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