Download - Impact of Nonlinear LED Transfer Function on Discrete Multitone Modulation: Analytical Approach

4970 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 22, NOVEMBER 15, 2009

Impact of Nonlinear LED Transfer Function onDiscrete Multitone Modulation: Analytical Approach

Ioannis Neokosmidis, Thomas Kamalakis, Member, IEEE, Joachim W. Walewski, Beril Inan, andThomas Sphicopoulos, Member, IEEE

Abstract—Light-emitting diodes constitute a low-cost choice foroptical transmitters in medium-bit-rate optical links. An examplefor the latter is local-area networks. However, one of the disadvan-tageous properties of light-emitting diodes is their nonlinear char-acteristic, which may limit the data transmission performance ofthe system, especially in the case of multiple subcarrier modula-tion, which is starting to attract attention in various applications,such as visible-light communications and data transmission overpolymer optical fibers. In this paper, the influence of the nonlineartransfer function of the light-emitting diodes on discrete multitonemodulation is studied. The transfer function describes the depen-dence of the emitted optical power on the driving current. Analyt-ical expressions for an idealized link were derived, and these equa-tions allow the estimation of the power of the noise-like, nonlinearcrosstalk between the orthogonal subcarriers. The crosstalk com-ponents of the quadrature and in-phase subcarrier componentswere found to be independent and approximately normally dis-tributed. Using these results, the influence of light-emitting-diodenonlinearity on the performance of the system was investigated.The main finding was that systems using a small number of sub-carriers and/or high QAM level exhibit a large signal-to-noise-ratiopenalty due to the nonlinear crosstalk. The model was applied tosystems with white and resonant-cavity light-emitting diodes. It isshown that the nonlinearity may severely limit the performance ofthe system, particularly in the case of resonant-cavity light-emit-ting diodes, which exhibit a strong nonlinear behavior.

Index Terms—Discrete multitone (DMT) modulation, light-emit-ting diode (LED), nonlinear distortion, optical communication.

I. INTRODUCTION

I N recent years, there has occurred a rapid development ofoptical communication systems that can provide Tbit/s con-

nectivity in core and metropolitan-area networks [1]. As opticaltechnologies begin to migrate into the access- and home-net-work area, which are characterized by a much higher sensitivity

Manuscript received January 08, 2009; revised June 04, 2009 and July 07,2009. First published July 31, 2009; current version published September 10,2009. This work was supported in part by the European Community’s SeventhFramework Program FP7/2007-2013 under Grant 213311, also referred to asOMEGA.

I. Neokosmidis and T. Sphicopoulos are with the Department of Informaticsand Telecommunications, University of Athens, Athens GR-15784, Greece(e-mail: [email protected]; [email protected]).

T. Kamalakis is with the Department of Informatics and Telematics,Harokopio University, Harokopou 89, Athens, GR17671, Greece (e-mail:[email protected]).

J. W. Walewski is with the Siemens AG, Corporate Technology, Informationand Communications, Munich, Germany (e-mail: [email protected]).

B. Inan is with the Technische Universitaet Muenchen (TUM), Munich, Ger-many (e-mail: [email protected]).

Digital Object Identifier 10.1109/JLT.2009.2028903

to the initial capital expenditure, the cost of optical componentsand their ease of use becomes a critical factor for their deploy-ment and their future prospects. Light-emitting diodes (LEDs)can be used in low-cost, medium-bit-rate transmitters, and reso-nant-cavity LEDs (RC-LEDs) are capable of providing bit ratesup to 1 Gbit/s in local-area networks, where the link distancesare limited to less than 5 km [2]. LEDs also provide a cost-effec-tive solution for optical-wireless transmitters in both indoor andoutdoor systems [3], [4]. In the infrared range, such systems pro-vide wireless local-area-network connectivity in the order of 50Mbit/s and above, in both line of sight and the diffuse regime [5],[6]. It is also possible to modulate the light emitted by lightingLEDs, hence providing illumination and wireless connectivityat the same time. These systems are usually referred to as vis-ible-light communication (VLC) systems [7], [8].

There are several properties of LEDs that can affect the per-formance of a communication system. One of them is the non-linearity of their transfer function, i.e., the dependence of theemitted optical power on the driving current. Due to interfer-ence from fluorescent lighting of up to several hundreds of kHzit is beneficial to encrypt the data in VLC on subcarriers. Byapplying multilevel QAM modulation on discrete multitones(DMT) [9], Grubor et al. demonstrated data transmission ratesin excess of 100 Mbit/s [10]. Although existing DMT chips witha similar modulation bandwidth make this approach very at-tractive [11], it also comes with a potential drawback, since theabove nonlinearity causes subcarrier interaction, and the datastream from other subcarriers increases the noise floor undereach subcarrier [9].

The interrogation into the impacts of nonlinearity on OFDMand DSL can be divided into two main areas of activities:clipping of otherwise linear transfer functions and nonlineartransfer functions exhibiting continuous gradients. Clipping inOFDM and DMT is the practice of putting a symmetric upperand lower bound on the AC-portion of the signal. The impetusbehind this is to limit the potentially very large crest factorof these signals and, thus, to increase the channel throughput.However, while increasing the power submitted, clipping alsoentails noise, whose characteristics have been widely studied[12]–[14]. Since, due to the discontinuity of their gradientsand their otherwise linear behavior, the considered transferfunctions essentially differ from nonlinear transfer functions ofLEDs, the findings of these publications are of limited valueto us. Concerning studies considering continuous-gradienttransfer function, one has to divide them in those addressingOFDM and those addressing DMT. Studies addressing OFDMare of limited value for us, since the OFDM signal by its natureis bipolar, it is inherently point symmetric and the respectivetransfer function can be described by Taylor series containing

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NEOKOSMIDIS et al.: IMPACT OF NONLINEAR LED TRANSFER FUNCTION ON DISCRETE MULTITONE MODULATION 4971

Fig. 1. Experimental setup for measuring the nonlinear transfer function of asingle-chip white LED.

only odd-powered elements [15]. Also, due to its bandpasscharacteristics, many of the interference terms lie out of band[15]. Examples of such studies are those of Tang et al. [16],Chorti et al. [17] and O’Droma et al. [18]. Baseband multicar-rier is also used in analogue video transmission, and they comeclosest to the issue studied in our work. Example works arethose of Frigo et al. [13], [19]. While the former only addressesclipping effects, the latter presents a general approach based onprobability-density transfer functions describing the deteriora-tion of individual subcarriers. However, even in this case, onlyclipping is considered.

In contrast, we investigate the impact of continuous-gradientnonlinear LED transfer functions on the overall performance ofa DMT transmitter system. Based on a measured static transferfunction of a white LED, a quadratic polynomial is used as theparameter-free model of the transfer function. This polynomialapproximation has been widely used in the past to model thenonlinearity of LEDs or laser diodes [20]. In this paper, it isused as a starting point to obtain closed-form expressions forthe intercarrier crosstalk power and the study of the statisticalproperties of this crosstalk noise. The analytical formulas can beused to study of the impact of LED nonlinearity on the perfor-mance of DMT without the need for time-consuming numericalsimulations.

The remainder of this paper is organized as follows. InSection II, the measured nonlinear transfer function of a whitesingle-chip LED is presented and polynomial fitting is usedto obtain a second-order parameter-free model of the transferfunction. In Section III, the DMT system is described in detailand analytical formula for the power of the intersubcarriercrosstalk are derived. Also, the model is extended in orderto include additive white Gaussian noise (AWGN) in theflat-frequency-response channel, as described elsewhere inthe literature [6], [21]. In Section IV, our model is used tostudy various aspects of the DMT system, for instance, thedependence of the nonlinear crosstalk on the total numberof subcarriers and the modulation level for both white andRC-LEDs. Conclusions are provided in Section V.

II. NONLINEAR CHARACTERISTIC OF THE LED

Fig. 1 shows the experimental setup that was used for mea-suring the static transfer function of a phosphorescent single-chip LED (NICHIA, NSPW500CS). The DC impedance of theLED was matched to 50 with a serial resistor, and the DCvoltage was supplied by a commercial power source (Agilent,E3620A). The emitted light was directed onto an amplified pho-todiode (Thorlabs, PDA10A-EC). Both the applied voltage andthe current through the diode are measured with multimeters(Voltcraft, VC220). The output power, , of the LED is mea-sured with the photo detector. The latter is measured as a func-tion of the DC driving current. The choice of an optimum de-gree for a polynomial representing the LED transfer functionhas been discussed in detail by Walewski [22], who showed that

Fig. 2. Three measurement sets of the LED optical output power as a functionof the DC driving current obtained for a single-chip white LED. The setup inFig. 1 was used. Markers: measurement data; solid line: second-order polyno-mial fit to the data.

albeit polynomial orders of as high as five are needed to realis-tically model measured transfer functions, a second-order poly-nomial already provides a fair description, as is demonstrated inFig. 2. The polynomial function in question is

(1)

where mA. The coefficients , , and are theDC term, the linear gain, and the second-order nonlinearity co-efficient, respectively.

The polynomial expansion in (1) is the model used in the fol-lowing derivation of analytical expressions for the intercarrierdistortion in DMT as a result of transfer-function nonlinearity.It should be noted that the proposed model is only valid for mod-ulation frequencies well below the LED 3-dB bandwidth, since(1) is actually the static transfer function of the LED. A morecomplete description would require the use of a dynamic modelbased on the solution of the active region carrier density rateequation [23]. Deriving closed form formulas for the intercarriercrosstalk power is much more involved in this case, however.

III. ANALYTICAL EXPRESSIONS FOR

INTERCARRIER DISTORTION

In this section, the DMT waveform distortion due to the LEDnonlinearity is investigated. It is shown that the nonlinearity ofthe LED transfer function adds a nonlinear crosstalk componentto each subcarrier, and closed-form formulas are obtained forthe power of this distortion. It will also be numerically shownthat this crosstalk noise is approximately normally distributed,and that the in-phase and quadrature noise components are ap-proximately independent. The model is also extended to includethe contribution of AWGN stemming from thermal noise at thereceiver and/or ambient light noise.

A. DMT Waveform Distortion

In order to simplify the analysis, cyclic prefixes are ignored.In this case, the current signal driving the LED can be written as

(2)

where is the bias current, is the subcarrier number,is the total number of subcarriers, is the sent symbol on sub-carrier , is the subcarrier frequency, is the complex con-


jugate, and is the duration of a DMT symbol. The subcarrierfrequencies are given by . Notice that the DC carrieris not modulated [10]. In (2), is a current amplitude, whichis chosen to keep the current inside a given operationalrange .The modulation index MIis defined as

(3)

In our calculations, we have chosen mA(i.e., ) and the operational range is, thus, [0 61mA].We do not consider clipping of the driving current. The DMTsymbols are obtained from a QAM symbol constellation

(4)

where is the symbol value and and are the in-phaseand the quadrature components, respectively. For aQAM modulation ( bits per symbol, i.e., for quadraticconstellations), one can use the following equation for thein-phase and the quadrature components of the symbols:

(5)

Using (5) as well as the fact that is maximized whenboth and are maximized, that is when ,one can easily show that the AC component of the current, i.e.,

, is bounded by

(6)

Another approach to calculate the maximum value of the ACcurrent has been proposed by Mestdagh [14]. In this model,the current is maximized if one chooses a suitable combina-tion of QAM symbols from the corners of the constellation di-agram such that for odd values of and

for even values of . In this case themaximum amplitude of the current is obtained by replacing the

with the factor .Although, will never take the value of (6), it is close

enough to the actual maximum. Furthermore, it helps to in-crease the channel throughput avoiding the clipping noise. Onthe other hand, Mestdagh’s maximum is only valid for highQAM levels and number of sub-carriers. On the contrary, it un-derestimates the amplitude of the DMT signal for few QAMsymbols and few carriers .Therefore, Mestdagh et al.’s approach fails in always providingan unclipped DMT signal and was not further pursued in ourinvestigation

(7)

Inserting (2) into (1), one can easily derive the optical outputpower as a function of the DMT driving current

(8)

The third term in the sum of (8) represents intermodulationproducts at frequencies and , which give rise tononlinear crosstalk noise, since for randomly distributed inputdata, the terms in the third term are uncorrelated to the datastream purveyed by term two. To estimate the impact of thisnoise on the performance of the system, one needs to calculatethe decoded symbols. In a matched receiver, the decoded symbolof carrier is

(9)

(10)

Inserting (8) into (9) and (10), one obtains the following equa-tion for the symbol estimates at the receiver:

(11)

(12)

where

(13)

(14)

Here, the sets and are given by

and (15)

and (16)

B. Analytical Formulas for the Variation of the IntercarrierCrosstalk

The conditions posed in the sums of (13) and (14) stem fromthe condition that the frequency of the interference has to coin-cide with a subcarrier in order to contribute to the detected noise.Using (13) and (14), one can estimate the variances and

of the quadrature and in-phase component of the inter-carrier crosstalk. As stated above, our approach is only valid foran even number of bits per symbol . Fortuitously, for exactlythis case both variances can be written in a closed form. For this,one invokes the assumption that symbols of different subcarriersare statistically independent, viz. for

. After some mathematical manipulation and exploitingthat , as provided in the literature[24], one obtains for even subcarrier numbers

(17)

(18)


Fig. 3. Crosstalk ratios �� [see equations (20) and (21)] as a function ofsubcarrier number� for 4 QAM and 64 QAM modulation for (a) the real partand (b) the imaginary part of the received symbols. The total number of subcar-riers is 7.

while for odd subcarrier numbers , the variances are given by

(19)Equations (17)–(19) are very useful since they allow the esti-

mation of the noise variances without the need for numericalsimulations. When the number of bits per symbol is odd,it is more difficult to derive a closed form expression for thecrosstalk variances and one can resort to numerical approacheslike Monte Carlo (MC) simulation in order to calculate them.To assess the validity of (17)to (19) we compared them againstresults obtained from Monte Carlo (MC) simulations based on(13) and (14). Convenient figures of merit for the comparison ofintercarrier crosstalk are the ratio of the crosstalk variance andthe symbol distance, viz.

(20)

(21)

where and are the in-phase and quadra-ture crosstalk ratios for subcarrier , respectively, and is theminimum distance between QAM symbols. For the QAM con-stellation defined in (5), one finds that [24]. It is alsouseful to define the average signal-to-crosstalk ratio for subcar-rier , given by

(22)

In Fig. 3(a) and (b), and obtained from MCsimulations are compared to the analytical formulas and for var-ious subcarrier numbers in a DMT system with seven totalsubcarriers and 4-QAM and 64-QAM modulation, respectively.We conducted similar comparisons for various total numbers ofsubcarriers and yielded a similar excellent agreement. Note thatthe value is not included in the figures, since the DCcomponent does not carry any signal.

It is also interesting to note that one could include a cubic termin the polynomial expansion in (1). A series of Monte Carlo sim-ulations were performed in order to estimate the influence of thecubic term and it was concluded that its influence is negligible.For example in the case of and the obtained

value is only 0.0014 dB lower when the cubic term isincluded.

Fig. 4. PDFs of the of nonlinear intercarrier crosstalk obtained by Monte Carlosimulation (dots) of (a) the in-phase component [equation (13)] and (b) theout-of-phase component [equation (14)] of the received symbol for a DMT mod-ulation with seven subcarriers and � � �� QAM states per subcarrier. ThePDF of a Gaussian random variable with the same variance is also shown (solidline).

Fig. 5. PDFs of the of nonlinear intercarrier crosstalk obtained by Monte Carlosimulation (dots) of for (a) the in-phase component [equation (13)] and (b) theout-phase component [equation (14)] of the received symbol for a DMT modu-lation with 255 subcarriers and� � �� QAM states per subcarrier. The PDFof a Gaussian random variable with the same variance is also shown (solid line).

C. Statistical Nature of the Nonlinear Crosstalk Noise

Next, we consider the distribution function of the intercar-rier crosstalk. In Fig. 4(a) and (b), the probability density func-tions (PDFs) of and , respectively [see (13) and (14)],are illustrated for the first channel , in the case ofa DMT system with seven subcarriers and QAMlevels. Also plotted is the PDF of a zero-mean Gaussian randomvariable with the same variance. The results indicate that thePDFs of the intercarrier crosstalk can be roughly approximatedby a Gaussian PDF. The approximation becomes better as thenumber of carriers is increased. This is illustrated in Fig. 5,where similar PDFs are plotted for 255 subcarriers andQAM levels. Similar results are obtained for other subcarrierindices.

Next, it is of interest whether the distortion terms andare uncorrelated. To this end we investigated into the cor-

relation coefficient of these terms, i.e.,

(23)

for which we assume that the expectation of both distortionterms is zero, which has already been shown to be supportedby simulation. The correlation coefficient was estimated fromrepeated Monte Carlo runs. After 50 runs the correlation coef-ficient was estimated by aid of (23) and the procedure repeatedfor a total of 20 000 times. The resulting histograms of the cor-relation coefficient were found to be centered on zero, which


Fig. 6. Histograms of � for the first subcarrier. The quantity � is the transformedvalue of the correlation coefficient between � and � [see equation (24)],as compared with the student � distribution (solid line) for four sets of QAMlevel and total number of subcarriers (‘sub’).

supports our hypothesis, that the distortion terms indeed are un-correlated. If one instead of the correlation coefficient plots thedistribution of

(24)

one expects a student distribution in case both distortions arenormally distributed [25]. In Fig. 6, we show the histogram ofthe correlation coefficients for four cases and compare themwith the theoretical distribution. For low sub-carrier numbersthe historgram of is indeed symmetrical but is close dis-tributed around zero than the theoretical distribution. This devi-ation can be attributed to a non-normal distribution of the inter-ferences themselves. While the histogram supports the assump-tion that the correlation coefficient is zero we cannot test thishypothesis, since the distribution function of is unknown.As discussed before, for an increasing number of total subcar-riers the distribution of the interferences becomes more normal,and, as can be seen in Fig. 6, the distribution of [see (24)] ismuch closer to the theoretical one. For these cases, we can applyhypothesis testing based on the student distribution, and for allthe subcarrier and QAM-level combinations addressed in thiswork the hypothesis that the correlation coefficient is not dis-tributed according to the student distribution could be rejectedwith an alpha of 0.05 for all simulations with QAM level higherthan 4 and more than seven subcarriers. Therefore, the hypoth-esis of the correlation coefficient being unequal zero can alsobe rejected. Since two uncorrelated normally distributed enti-ties are statistically independent this is, hence, also the case forthe in- and quadrature intercarrier interferences and .

D. Inclusion of Additive White Gaussian Noise

The model presented above can be generalized by includingAWGN, which may originate from thermal noise at the receiver

TABLE IBIT RATES FOR A SYMBOL RATE OF 24.2 MHz AND

VARIOUS QAM MODULATION LEVELS

and/or ambient light noise. This can be done in a straight for-ward manner by adding an AWGN term in (8). The symbolestimates in (11) will, thus, contain additional Gaussian noisecomponents and , i.e.,

(25)

(26)

The noise components and are independent andidentically distributed, with zero mean and the variance is

(27)

with the double-sided power spectral density of the noise.To characterize the influence of the AWGN one figure of

merit is the signal-to-noise ratio per bit, defined as, where is the average energy per bit. Assuming a

DMT waveform [see (2)], ignoring the intercarrier crosstalknoise, relying on the fact that ,and that inside a DMT symbol period there are QAMsymbols or bits, it is straightforward to showthat

(28)

IV. SIMULATION RESULTS AND DISCUSSION

A. System Bitrate

The analytical model described in Section III is used tofurther analyze the impact of the nonlinear LED transferfunction on the performance of a point-to-point DMT system.Since the DC subcarrier is not modulated, the symbol rate

of the system is . Hence,does not depend on and . The bit rate of the signal is

and varies with . It is already noted thatthe proposed model is only valid for modulation frequencieswell below the LED 3 dB bandwidth. Since the frequency ofthe last subcarrier, and, hence, the maximum allowable signalbandwidth cannot be determined, the data rates are normalizedassuming that the signal at the maximum data rate (e.g., for1024 QAM levels) utilizes the whole allowable bandwidth.Table I summarizes the values of the normalized bit rates forseveral values of used in this paper.

B. Nonlinear Degradation

Fig. 7 illustrates the values of the average signal-to-crosstalkratio obtained for various DMT parameter settings. Theresults are based on (17)to (21). There are several interestingfeatures that can be drawn from this figure. First, the lowestsubcarrier is always the subcarrier with the worstdistortion. This is consistent with (17)to (19), which show that


Fig. 7. Average signal-to-crosstalk ratio �� as a function of the subcarriernumber� for various QAM modulation levels and total number of subcarriers.

the power of the crosstalk noise decreases as increases. It isalso interesting to note that the lowest subcarrier has about 3 dBlower SXR than the highest subcarrier. Another point that canbe drawn from Fig. 7 is the fact that the generally tendsto improve as the number of QAM levels is reduced. As shownin the figure, there is about 20-dB degradation of when

QAM instead of QAM is used. In mostcases, there is a 4 to 5 dB decrease in increasing the modu-lation level from to QAM. The degrada-tion with increasing is not surprising. Although the distancebetween neighboring symbols in the original QAM constella-tion does not depend on , the average power at the transmittermust be kept constant, and, hence, the actual distance betweenthe symbols in the scaled waveform (2) is decreased, renderingthe signal more susceptible to the crosstalk noise, whose statis-tical properties vary little upon a change of .

It is also interesting to mention that, as the number of subcar-riers is increased, is improved, and, hence, an LED-basedoptical wireless multiple subcarrier system exhibits differentbehavior than its wired, Four-Wave-Mixing limted counterpart[26]. The improvement becomes even more obvious in Fig. 8,where the is plotted as a function of the total number ofsubcarriers for (a) the first and (b) the central subcarrier, re-spectively. The explanation of this behavior can be found inthe fact that according to (7), the parameter in (17)to (19)decreases as . This decrease is much faster than the in-crease of the possible combinations satisfying the conditions

and , the number of which is equal to. From another point of view, the use of more subcarriers

will result in the original DMT waveform having largespikes while still remaining inside a given operational range

. As the number of subcarriersis increased, these spikes will become sharper and sharper, fol-lowed by longer periods of time, where will possess asmall amplitude. Since the influence of nonlinearity grows withan increase in , only high-current spikes will be affectedby the LED nonlinear characteristic, while the distortion for therest of the signal will be small. Thus, the occurrence of nonlinear

Fig. 8. Estimation of SXR for (a) the first subcarrier and (b) the central subcar-rier �� as a function of the number of subcarriers.

Fig. 9. Bit-error ratio �� of the first subcarrier as a function of thesignal-to-noise ratio per bit �� for various QAM modulation levels andfor (a) three subcarriers and (b) 255 subcarriers.

distortion, and, hence, its impact on the overall signal integrity,decreases with an increase in the total number of subcarriers.There is one point to note, however: The linear signal-to-noiseration as defined in (28) decreases with an increase in thenumber of subcarriers since is inversely proportional to .This means that, as increases, obtaining the same re-quires a lower . Since is due to both ambient light noiseand thermal noise, in practice, it is not possible to reducebeyond a certain minimum value leading to an upper bound forthe achievable .

C. Power Penalty

The influence of the LED nonlinearity on the performanceof a system degraded by AWGN is illustrated in Fig. 9, wherethe bit-error ratio (BER) is plotted as a function of the[see (28)]. Note that takes only the AWGN into ac-count, not the intercarrier crosstalk. The values of the BER arethen calculated with and without the nonlinear crosstalk (dottedand solid lines, respectively). Fig. 9(a) and (b) corresponds tothe case with three and 255 subcarriers, respectively. The BER


Fig. 10. Bit-error ratio (BER) as a function of the signal-to-noise ratio per bitfor various QAM modulation levels and for (a) three subcarriers and (b) 255subcarriers (RC-LED).

was calculated for the first subcarrier (worst case scenario) andthe intercarrier crosstalk is assumed to follow Gaussian statis-tics (see Section III-C). In a system with three subcarriers, theperformance is severely degraded compared to the linear casefor a QAM constellation with 64 symbols and above. For 64QAM symbols and dB, the BER is increased from

to 0.0013, almost three orders of magnitude. Onthe other hand, the performance of a system with fewer QAMsymbols or with larger number of subcarriers is less severely af-fected. It is, therefore, understood that depending on the systemparameters the intercarrier cross talk due to LED nonlinearitymay drastically influence the performance of a system with asmall number of subcarriers.

So far, we have only discussed the impact of transfer functionnonlinearity for a white LED. As it turns out, there are LEDsexhibiting an even stronger nonlinearity. One example is a redRC-LED from AVAGO (HFBR-1521Z). We recorded the statictransfer function of this LED and the parameters of the polyno-mial fitting were found to be , mAand mA . In our simulations, the DC currentwas set to 20 mA, while . Fig. 10 depicts thewith and without the intercarrier crosstalk as a function of thesignal-to-noise ratio per bit for the RC-LED. A system usingthe RC-LED exhibits the same behavior as the one with thewhite LED. For example, the performance is improved whenless QAM states per subcarrier are used and/or more subcarriersare included in the system. It is obvious that the performance ofthe system incorporating the RC-LED is worse compared to theone with the white LED, which is caused by the stronger non-linearity of its transfer function. It is interesting to note that forthree subcarriers, a floor higher than is observed formore than 16 QAM symbols.

Fig. 11. Signal-to-noise-ratio penalty of the first subcarrier as a function of theQAM level for achieving �� (white LED).

Fig. 12. Signal-to-noise ratio penalty of the first subcarrier as a function of theQAM level for achieving �� (red RC-LED).

To further illustrate the effect of nonlinear intercarriercrosstalk, the penalty was evaluated for various QAMlevels and numbers of subcarriers. The penalty is definedas the difference between the required for achievinga specific with and without the nonlinear crosstalk. InFig. 11, the penalty of the first subcarrier (worst case) fora BER equal to is plotted versus the QAM level.

Once again it is apparent that the noise stemming from in-tercarrier crosstalk is more pronounced for few subcarriers orhigher QAM level. For three subcarriers, the penalty is0.9 dB and 3.8 dB for and QAM symbols,respectively. For seven subcarriers and 64 QAM symbols, thedifference in the required approaches 1.7 dB.

In the case of the RC-LED the SNR penalty values are higher,as illustrated in Fig. 12. This is again due to the stronger non-linearity of the transfer function. Notice that the SNR penalty iscalculated for , which corresponds to the BERfloor of the system with more than 16 QAM symbols. Noticealso difference in maximum QAM level in Figs. 11 and 12.

It seems, therefore, that in both cases (white and RC-LED),the intersubcarrier crosstalk noise noticeably affects the perfor-mance of the system. Also, the nonlinear crosstalk becomes oneof the limiting factors in an optical communication system es-pecially in the case of few subcarriers and high number of QAMlevels.

V. CONCLUSION

In this paper, the impact of the nonlinear transfer functionof LEDs on the performance of a QAM-DMT data transmis-sion system was analyzed. Analytical formulas were derived,


which allow the estimation of the nonlinear crosstalk on eachsubcarrier when the total number of subcarrier channels andthe number of quadrature-amplitude levels is known. It wasshown that the crosstalk components of the quadrature and thein-phase components are independent and approximately nor-mally distributed. The model was extended to incorporate the in-fluence of an AWGN component, which may originate from thethermal noise at the receiver and/or ambient light noise. Usingthis model, the influence of the nonlinear LED transfer func-tion was investigated, and it was shown that for an unclippedsignal, the system performance is degraded as the number ofsubcarriers is reduced or higher QAM modulation is used. Themodel was applied to evaluate the performance degradation inthe case of a white LED (previously used in a VLC system) and aRC-LED transmitter (commonly used in polymeric optical fibertransmission systems). Stricter performance limits are posedfor the RC-LED due to its stronger nonlinearity. Increasing thenumber of subcarriers or reducing the number of QAM symbolsmay alleviate the effect of nonlinearity, thus improving the per-formance of the system.

ACKNOWLEDGMENT

The authors would like to thank their colleagues for their con-tributions. This information reflects the consortiums view; theCommunity is not liable for any use that may be made of any ofthe information contained therein.

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Ioannis Neokosmidis was born in Athens, Greece, in 1977. He received theB.Sc. degree in physics, the M.Sc. degree in telecommunications, and the Ph.D.degree in transmission limitations due to nonlinear phenomena from the Uni-versity of Athens in 1999 and 2002, respectively.

He is currently a Research Associate for the Optical Communications Labo-ratory, University of Athens. His research interests include nonlinearities, WDMoptical networks and optical components, photonic crystals, and wireless opticalsystems.

Thomas Kamalakis (M’09) was born in Athens, Greece, in 1975. He receivedthe B.Sc. degree in informatics, the M.Sc. degree (with distinction) in telecom-munications, and the Ph.D. degree in the design and modeling of arrayed wave-guide grating devices from the University of Athens in 1997, 1999, and 2004,respectively.

He is a Lecturer at the Department of Informatics and Telematics, HarokopioUniversity of Athens, and a research associate in the Optical CommunicationsLaboratory, University of Athens. His research interests include photonic crystaldevices, coupled resonator optical waveguides, optical wireless, and nonlineareffects in optical fibers.

Dr . Kamalakis is a member of the Optical Society of America and IEEE.

Joachim W. Walewski graduated from the Christian Albrechts University, Ger-many, with a diploma degree in physics (Dipl.-Phys.) in 1995 and the Ph.D. de-gree from the Lund Institute of Technology, Sweden, in 2002 for his researchon applied laser spectroscopy.

From 1996 to 1997, he was a visiting scientist at the Tampere University ofTechnology, Finland, engaging in laser-assisted diagnostics of CVD diamond.From 2001 to 2003, he served as junior lecturer at the Lund Institute of Tech-nology, and from 2003 to 2006, he held positions as research associate and fi-nally as assistant scientist at the Engine Research Center of the University ofWisconsin-Madison. At the latter two institutions, his research was focused onthe development and application of laser-spectroscopic techniques for combus-tion research. In May 2006, he joined Siemens Corporate Technology, Infor-mation and Communications, Munich, Germany and has focused his efforts onR&D in the field of wireless optical communications and Green ICT.


Beril Inan was born in Ankara, Turkey, in 1983. She received the B.Sc. degreein electrical and electronics engineering at Middle East Technical University,Ankara, Turkey, in 2005, and the M.Sc. degree from the Eindhoven Universityof Technology, Eindhoven, The Netherlands, in 2008, in electrical engineering.She carried out her M.S. thesis project at Siemens Corporate Technology, Infor-mation and Communications, Munich, Germany, in the field of nonlinearity im-pact on optical communication. She is currently pursuing her Ph.D. at SiemensCorporate Technology, Information and Communications.

From 2005 to 2006, she worked at ASELSAN Electronic Industries Inc.,Ankara, Turkey, as a system engineer.

Thomas Sphicopoulos (M’87) received the degree in physics from Athens Uni-versity, Athens, Greece, in 1976, the D.E.A. degree and the Ph.D. degree in elec-tronics, both from the University of Paris VI, Paris, France, in 1977 and 1980,respectively, and the D.Sc. degree from the Ecole Polytechnique Federale deLausanne, Lausanne, Switzerland, in 1986.

From 1976 to 1977, he worked at Thomson CSF Central Research Labo-ratories on microwave oscillators. From 1977 to 1980, he was an AssociateResearcher in Thomson CSF Aeronautics Infrastructure Division. In 1980, hejoined the Electromagnetism Laboratory of the Ecole Polytechnique Federal deLausanne, where he carried out research on applied electromagnetism. Since1987, he has been with the University of Athens, engaged in research on broad-band communications systems. In 1990, he was elected as an Assistant Professorof communications in the Department of Informatics and Telecommunications,in 1993 as Associate Professor, and since 1998, he has been a Professor. Hismain scientific interests are optical communication systems and networks andtechno-economics. He has lead about 40 National and European research anddevelopment projects. He has more than 150 publications in scientific journalsand conference proceedings. Since 1999, he has been an advisor in several or-ganizations in the fields of fiber optics networks, spectrum management tech-niques, and technology convergence.

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