Signal restoration in intensity-modulatedoptical OFDM access systems

Evgeny VaninNetwork and Transmission Laboratory, Acreo AB, Electrum 236, SE-16440, Kista, Sweden (evgeny.vanin@acreo.se)

Received July 1, 2011; revised August 24, 2011; accepted September 23, 2011;posted October 3, 2011 (Doc. ID 150375); published November 10, 2011

It is well known that deliberate signal clipping in an intensity-modulated (IM) laser transmitter helps to overcomethe optical orthogonal frequency division multiplexing (OFDM) system performance limitation that is related to thesignal high peak-to-average power ratio. The amplitude of a clipped OFDM signal has to be optimized in order tominimize the optical power that is required to achieve a specified system performance. However, the signal clippingintroduces nonlinear distortion (so-called clipping noise) and leads to a system performance penalty. In this Letter,the performance of the IM optical OFDM system with digital baseband clipping distortion in the transmitter andclipping noise compensation by means of signal restoration in the digital signal processing unit of the system re-ceiver is analytically evaluated. It is demonstrated that the system bit-error ratio can be reduced by more than anorder of magnitude, from 10−3 to 3:5 × 10−5, by applying only the first iteration of the signal restoration algorithmproposed in this Letter. The results of the analytical analysis are verified with brute-force numerical simulationsbased on direct error counting. © 2011 Optical Society of AmericaOCIS codes: 060.2330, 060.4080, 060.4230.

Orthogonal frequency division multiplexing (OFDM) [1]has been extensively exploited in broadband wired andwireless radio applications for a decade [2,3]. Today, thismodulation technique constitutes a hot research topic inthe field of optical fiber communications. Distinctive fea-tures of OFDM, such as high spectral efficiency, superiorflexibility due to dynamic bandwidth allocation and adap-tive bit rate, and high tolerance to multipath interferenceas well as to modal and chromatic fiber dispersion, madethis modulation format attractive for applications in thewhole spectrum of optical communication systems, fromhome and access networks to long-haul transmissionlines [4–11]. In this Letter, the OFDM system for low-costapplications, mainly in the access segment of optical fi-ber network, employing intensity-modulated (IM) lasertransmitter and optical power receiver is considered.The performance of optical IM OFDM system, with the

outline shown in Fig. 1 (excluding the signal restorationunit), has been analytically evaluated in [12]. In the digitalsignal processing (DSP) unit of the system transmitter, asequence of data is mapped to subcarriers by using quad-rature amplitude modulation (QAM) and processed inparallel by using the inverse fast Fourier transform(IFFT). The DSP unit generates a real valued multileveldigital signal. This signal is symmetrically clipped (seeinset A in Fig. 1.), and then converted into an analog elec-trical waveform in the digital-to-analog converter (DAC).The analog waveform is biased with dc, and then appliedto drive a laser source (see inset B in Fig. 1.). The gen-erated optical signal is transmitted over the optical fibernetwork and detected by the optical power receiver. Thereceived signal is sampled in the analog-to-digital conver-ter (ADC) and processed in the DSP unit in order to re-cover the transmitted data.The conclusionmade in [12] is that the IMoptical OFDM

system is characterized by reduced power sensitivity andrequires about 3 dB higher optical power at the front endof the receiver in comparison to a system based on multi-level amplitude shift keying. The reason for reducedpower sensitivity is related to the well-known drawbackof OFDM systems, the high peak-to-average power ratio

(PAPR). The issue of high PAPR has been previously ad-dressed in a number of reports, e.g., [13,14]. Applying de-liberate clipping of the signal in the system transmitter, asproposed in [12], constitutes a simple and effective meth-od for reducing PAPR and minimizing the optical powerthat is required for achieving a specified system perfor-mance. However, the performance of such a system is lim-ited by both the additive noise in the receiver as well as bythe nonlinear signal distortion—the so-called clippingnoise—introduced in the transmitter. In this Letter, an ad-vanced modification of the system shown in Fig. 1 is pro-posed: a signal restoration unit in the DSP part of thereceiver is introduced in order to reduce the effect of clip-ping noise and improve the system performance.

The signal restoration algorithm is based on the well-known Bussgang decomposition [15,16] applied to theOFDM signal that is nonlinearly distorted in the systemtransmitter: y ¼ QðxÞ ¼ αxþ d, where the function QðxÞrepresents the deliberate clipping of the OFDM signal x,and α is an attenuation factor of the undistorted signalcomponent. The factor α is computed by assuming thatthe distortion noise d is statistically independent ofthe signal x [see Eqs. (3), (6), and (12) in [12]]. Usingthe Bussgang decomposition, as well as assuming that

DAC

Optical fiber

DATADSP

DC bias

Laser source

PD ADC DSPDATA

Drive current

Op

tic

al p

ow

er

DC bias

Inset B: Laser source modulation

Inset A: Digital baseband distortiondue to signal clipping

)(tx

)(ty0x

0x−

)(xQ

Signal restoration

0P

Fig. 1. Schematic of IM optical OFDM system with digitalbaseband distortion. Advanced configuration with signalrestoration unit is shown in dashed lines.

4338 OPTICS LETTERS / Vol. 36, No. 22 / November 15, 2011

0146-9592/11/224338-03$15.00/0 © 2011 Optical Society of America

the modulation characteristic of the laser transmitter islinear and the receiver is matched, the time-domain digi-tal signal samples at the output of ADC in the systemreceiver can be expressed in the following form:z ¼ ρP0ð1þ y=xDCÞ þ n, where ρ is the optical receiverresponsivity given in units of A/W, P0 is the received aver-age optical power, xDC ¼ IDC − Ith is the difference be-tween dc bias and the transmitter laser thresholdcurrent, and n is the additive noise. In the optical trans-mission part of the system, the signal loss only is takeninto consideration. The transmitted signal is restored inthe receiver by applying the following algorithm:

X ðjþ1Þ ¼ K̂

�FFT

�xDC

z − zDCαρP0

−

dðjÞ

α

��; ð1Þ

dðjÞ ¼ QðxðjÞÞ − αxðjÞ; ðxðjÞ ¼ IFFTðX ðjÞÞÞ; ð2Þwhere j is an iteration index, X ðjÞ and xðjÞ are arrays ofdimension NFFT representing FFT and IFFT of the re-stored signal in one OFDM symbol, NFFT is the FFT sizethat is equal to the total number of OFDM subcarriers,zDC is dc (zero-frequency) component of the received sig-nal, and K̂ is the operator performing decoding. The out-put of the operator K̂ is a point (complex amplitude) inQAM constellation that is closest to the input argument.In the step specified by Eq. (1), the restored signal is eval-uated by using the received signal and the distortionnoise estimate that has been computed in the previousiteration. The distortion noise estimate is computed ac-cording to Eq. (2) by applying the known clipping func-tion to the updated version of the restored time-domainsignal samples. The attenuation factor α is evaluated in astraightforward way [12] by using the amplitude ofclipped signal x0 and the signal amplitude mean squareσ2x ¼ hx2i because the clipping of the signal is deliberateand the clipping function is known.The first version of the restored signal, which seeds

the algorithm, is computed by neglecting the distortionnoise contribution in Eq. (1): dð0Þ ¼ 0. This step is equiva-lent to the well-known signal equalization and data recov-ery in a standard OFDM system. The equalization isbased on the estimation of transmission channel transferfunction hω ¼ αρP0=xDC (accounting for electrical-optical-electrical signal conversion in an optical IMOFDM system) that is performed by using training se-quences (pilot tones). The obtained estimate of the signalX ð1Þ is transformed with IFFT and employed to evaluatethe clipping noise contribution dð1Þ in the first iteration byusing Eq. (2). The evaluated clipping noise contributiondð1Þ is then used in Eq. (1) to compute the restored signalX ð2Þ. The process of signal restoration can be continuedby applying the next iteration(s).The performance of the system with the signal restora-

tion can be analytically evaluated in a simple way by in-troducing an effective signal-to-noise ratio (SNR) [12]:

SNReff ¼S0α2

ðRþ S0σ2d=σ2xÞ; ð3Þ

where S0 ¼ ðx0=xDCÞ2ðρP0Þ2=ððS2th þ 2qρP0ÞΔf Þ, R ¼

x20=σ2x is the clipping ratio, σ2d is the variance of clipping

noise, Sth is the thermal noise density given in units ofA=

ffiffiffiffiffiffiHz

p, Δf is the receiver bandwidth, and q is the elec-

tron charge. Please note that the parameter S0 is equal tothe conventionally defined SNR (i.e., the ratio betweenaverage received signal power and the additive noisepower at the output of photo receiver) reduced withthe factor ðx0=xDCÞ2 related to the clipping amplitudeand dc bias. The attenuation factor α and clipping noisevariance σ2d are both dependent on the clipping ratio R.

Equation (3) reflects the following behavior in the sys-tem performance: at very large clipping ratios, the mod-ulation index of the optical signal is too small, whereas,at small clipping ratios, the clipping noise (nonlinear sig-nal distortion) is too large. Both limits result in a reducedvalue of SNReff and are not favorable for the system op-eration. The optimized operation of the system isachieved when the nonlinear distortion due to signal clip-ping is of the order of the additive noise and SNReff is atthe maximum.

This behavior of SNReff on the clipping ratio at differ-ent values of parameter S0 is displayed in Fig. 2 by solidcurves. Figure 2 also shows SNReff at the optimum clip-ping ratio by dashed curves. The case when the signalrestoration is not applied in the system is indicated inFig. 2 by solid and dashed curves in black. When the sig-nal restoration is applied, the contribution of the clippingnoise is reduced and therefore the optimum operationpoint of the system shifts toward smaller values of theclipping ratio. This behavior is illustrated in Fig. 2, whereSNReff for the system with signal restoration using thefirst iteration of the algorithm specified by Eqs. (1)and (2) is plotted versus clipping ratio in blue. Theseresults quantify the improvement of the system perfor-mance in terms of enhanced SNReff or reduced averageoptical power (parameter S0) that is required to achieve aspecified bit-error ratio (BER). The system performanceat various QAM constellation size is evaluated by usingSNReff and the well-known expression for BER, e.g.,see Eq. (11) in [12].

0 2 4 6 8 10 12 14

Clipping ratio, dB

0

10

20

30

40

50

SN

Ref

f,dB

10dB

15dB

20dB

25dB

30dB

35dB

40dB

45dB

50dB

55dB

S0

No signal restoration

First iteration of signal restoration

Fig. 2. Analytically evaluated effective SNR versus clipping ra-tio at parameter S0 set to 10 to 55dB with 5 dB step is shown insolid curves. Dashed curves indicate effective SNR at optimumclipping ratio. The case of signal restoration by applying Eqs. (1)and (2) in the first iteration is shown in blue. The case of nosignal restoration analyzed in [12] is shown for comparisonby black solid and dashed curves.

November 15, 2011 / Vol. 36, No. 22 / OPTICS LETTERS 4339

Figure 3 shows the analytically evaluated system BERversus clipping ratio (solid curves) in the case when16-QAM is applied to all OFDM subcarriers. In order toexemplify the system performance improvement due tosignal restoration in terms of reduced BER as well as therequired optical power (parameter S0), three cases areshown: no signal restoration when S0 ¼ 25 dB andS0 ¼ 27:7 dB, and the case of signal restoration in the firstiteration when S0 ¼ 25dB. These results demonstratethat the system BER is reduced from 10−3 to 3:5 × 10−4

due to signal restoration by applying only the first itera-tion of the algorithm specified by Eqs. (1) and (2).Figure 3 also shows the results of brute-force numer-

ical simulations with direct error counting for the case ofsignal restoration specified by Eqs. (1) and (2). The caseof signal restoration in the first iteration is shown by dotsin green, blue, and red when NFFT is set to 32, 128, and512, respectively. The numerical results shown in Fig. 3verify the analytically estimated BER when the clippingratio is larger than 5 to 6 dB. The results also indicate thatthe efficiency of the signal recovery algorithm is im-proved at increased FFT size. Indeed, at NFFT ¼ 512, alower level of BER at a smaller optimum clipping ratiothat is very close to the analytically calculated value isachieved. This behavior is related to the fact that theBussgang decomposition (on which the restoration algo-rithms is based) has improved accuracy when NFFT islarge. In this case, the central limit theorem applies andthe statistics of the undistorted OFDM signal x is closerto Gaussian. However, even if the FFT size is large, thereis a disagreement between the analytical and numericalresults in Fig. 3 when the clipping ratio is smaller than 5

to 6 dB. At these values of the clipping ratio, the signaldistortion is so large that the assumption of Gaussian-distributed clipping noise [used in Eq. (3)] is not justified.Figure 3 also displays the numerical results obtained inthe case when signal restoration is performed with twoiterations (not analyzed analytically in this Letter) in or-der to demonstrate the feasibility of further improvementof the system performance with increased computationalefforts [specified by Eqs. (1) and (2)] in the DSP unit ofthe receiver.

In conclusion, by performing the analytical analysis aswell as numerical simulations with direct error counting,it is demonstrated that the performance of the IM opticalOFDM system can be significantly improved by applyingthe proposed signal restoration algorithm. The algorithmis based on the Bussgang decomposition of the clippedOFDM signal and demonstrates improved efficiency ata large number of subcarriers and increased numberof iterations.

References

1. R. W. Chang, “Orthogonal frequency division multiplexing,”U. S. patent 3,488,445 (1970).

2. A. R. Bahai and B. R. Saltzberg, Multi-Carrier Digital

Communications: Theory and Applications of OFDM

(Plenum, 1999).3. R. van Nee and R. Prasad, OFDM for Wireless Multimedia

Communications (Artech House, 2000).4. J. M. Tang and K. Alan, J. Lightwave Technol. 24, 2318

(2006).5. I. B. Djordjevic and B. Vasic, Opt. Express 14, 3767 (2006).6. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, Opt.

Express 14, 2079 (2006).7. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H.

Tanaka, J. Lightwave Technol. 26, 6 (2008).8. S. C. J. Lee, F. Breyer, S. Randel, R. Gaudino, G. Bosco, A.

Bluschke, M. Matthews, P. Rietzsch, R. Steglich, H. P. A. vanden Boom, and A. M. J. Koonen, J. Lightwave Technol. 27,1503 (2009).

9. T.-N. Duong, N. Genay, M. Ouzzif, J. L. Masson, B.Charbonnier, P. Chanclou, and J. C. Simon, IEEE Photon.Technol. Lett. 21, 790 (2009).

10. N. Cvijetic, D. Qian, and J. Hu, IEEE Commun. Mag. 48,70 (2010).

11. R. Schmogrow, M. Winter, D. Hillerkuss, B. Nebendahl, S.Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker,C. Koos, W. Freude, and J. Leuthold, Opt. Express 19,12740 (2011).

12. E. Vanin, Opt. Express 19, 4280 (2011).13. S. H. Han and J. H. Lee, IEEEWirel. Commun. 12, 56 (2005).14. J. Armstrong and A. J. Lowery, Electron. Lett. 42 (2006).15. J. J. Bussgang, Research Lab. Electron, Tech. Rep. 216

(Massachusetts Institute of Technology, 1952).16. J. Tellado, L. M. C. Hoo, and J. M. Cioffi, IEEE Trans.

Commun. 51, 218 (2003).

1st iteration:NFFT=32

NFFT=128

NFFT=512

0 4 8 12Clipping ratio, dB

1x10-6

1x10-5

1x10-4

1x10-3

1x10-2

1x10-1

BE

R

2nd iteration:NFFT=32

NFFT=128

NFFT=512

No signal restoration (S0=25dB)

1st iteration of signal restoration (S

0=25dB)

No signal restoration (S0=27.7dB)

Fig. 3. BER versus clipping ratio for IM optical OFDM systemwhen subcarriers are modulated with 16-QAM. Solid curvesshow the results of analytical evaluation. Symbols displaythe results of brute-force numerical simulations with directerror counting for NFFT equal to 32, 128, and 512. Dots, signalrestoration in the first iteration in Eqs. (1) and (2); crosses, sig-nal restoration in the second iteration.

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