IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 13, JULY 1, 2013 1199

Optimal 16-Ary APSK Encoded Coherent OpticalOFDM for Long-Haul Transmission

Sujie Fan, Hui Wang, Yan Li, Wentao Du, Xin Zhang, Jian Wu, and Jintong Lin

Abstract— In this letter, an optimal 4 + 12 amplitude andphase shift keying (APSK) modulated coherent optical orthogonalfrequency-division-multiplexing (CO-OFDM) system is proposed(the numbers 4 and 12 represent the constellation points locatedin the inner ring and the outer ring, respectively). Although the4 + 12APSK modulation format has smaller average Euclideandistance than 16 quadrature amplitude modulation (QAM),the 4 + 12APSK modulated CO-OFDM system has the besttransmission performance, with increased tolerance towards bothamplified spontaneous emission noise and fiber nonlinearitiescompared with 16QAM and 8 + 8APSK modulated OFDMsystems. The maximum reach at Q factor = 8.2 dB (whenbit-error rate (BER) equals 5 × 10−3) is evaluated to assess thesystem performance based on a single-channel and five-channelwavelength division multiplexing (WDM) CO-OFDM system,and illustrates that the transmission performance of 4 + 12APSKmodulated OFDM outperforms 8 + 8APSK modulated OFDMand 16QAM modulated OFDM by approximately 10.5%, and inthe WDM system, it surpasses 8 + 8APSK modulated OFDM byapproximately 5.6% and 16QAM modulated OFDM by 18.75%.

Index Terms— Amplitude and phase-shift keying (APSK),fiber nonlinearities, orthogonal frequency-division-multiplexing(OFDM), quadrature amplitude modulation (QAM).

I. INTRODUCTION

RECENTLY, coherent optical orthogonal frequencydivision multiplexing (CO-OFDM) has attracted consid-

erable interest in large capacity and long haul transmissionsystems due to its high spectral efficiency [1]. However,an OFDM signal has a large PAPR, which leads to badnonlinear performance [2]. Traditionally, approaches such aspre-processing at the transmitter or discrete Fourier transformspread (DFT-S) [3], have been carried out to reduce thePAPR or to compensate the nonlinearities directly. In Ref. [4],the 16APSK modulated OFDM signal has been proposedto reduce the PAPR effectively, thus improving the sys-tem performance towards fiber nonlinearities compared with16QAM modulated OFDM systems. However, its transmissionperformance is limited due to its lower average Euclidean

Manuscript received March 31, 2013; revised April 25, 2013 and May 2,2013; accepted May 3, 2013. Date of publication May 31, 2013; date ofcurrent version June 13, 2013. This work was supported in part by NSFCprogram under Grants 60932004, 61001121, 61006041, and 61205031, inpart by 863 program under Grant 2012AA011303, in part by 973 programunder Grant 2011CB301702, and in part by the Fundamental Research Fundsfor the Central Universities.

The authors are with State Key Laboratory of InformationPhotonics and Optical Communication, Beijing University of Posts andTelecommunications, Beijing 100876, China (e-mail: vansujie@gmail.com;wanghui0805@126.com; liyan1980@bupt.edu.cn; 294527994@qq.com;zhangxin0701@126.com; jianwu@bupt.edu.cn; jtl@bupt.edu.cn).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LPT.2013.2262042

Fig. 1. Constellation of 4 + 12 APSK.

distance (AED). So one the way to improve the AED whilemaintain the advantage should be concerned. 4 + 12APSK [6]which was first proposed in satellites communication againstnonlinearities produced by high power amplifiers, can beapplied in optical communications.

In this letter, the 4 + 12APSK modulation format is intro-duced into CO-OFDM system for the first time. Various simu-lation results indicate that even though 4 + 12APSK encodedCO-OFDM has smaller AED when compared with 16QAM,its transmission performance is the best.

II. PRINCIPLE

For 16QAM and 16APSK, one symbol represents 4 bits.In 16QAM modulation, the first two bits are used for in-phasecomponent and the last two are for quadrature component.While 16 APSK is composed of two concentric rings, eachof which consists of uniformly spaced PSK points. The signalconstellation points can be modeled as a set S [6]:

S ={

r1ej ( 2π

n1i+θ1)

, i = 0, . . . , n1 − 1(ring1)

r2ej ( 2π

n2i+θ2)

, i = 0, . . . , n2 − 1(ring2)

where ni , θi , ri (i = 1, 2) are defined as the numberof points, relative phase and radius of ring i . We code4 + 12APSK as Gray mapping (Fig. 1). For simplicity,we define the ring radius in relative terms so that the radius

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1200 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 13, JULY 1, 2013

Fig. 2. PAPR CDF of three kinds of modulation formats.

Fig. 3. Simulation setup for CO-OFDM system.

of ring 1 is noted as “1”, and that of the ring 2 can bewritten as radius ratio ρ2 = r2/r1 = r2. In this letter,ρ2 is 2.0 for 8 + 8APSK and ρ2 is 2.7 (referred to Ref. [6])for 4 + 12APSK. In the same way, θ1−θ2 = 0 for 8 + 8APSKand θ1 − θ2 = π/6 for 4 + 12APSK.

The PAPR property is characterized by cumulative distrib-ution function (CDF) Pc, which is defined as the probabilitythat the PAPR value is no more than a certain value:

Pc = Pr {P AP R ≤ x}The CDF curves are depicted in Fig. 2, which indicates that thetolerance towards nonlinearities of 16APSK modulated OFDMoutperforms 16QAM modulated OFDM.

III. SIMULATION SETUP

Our simulation tool is VPI Transmission Maker. Fig. 3shows the simulation setup for 40Gbit/s coherent opticalOFDM system [4]. At the transmitter, 215 − 1 pseudorandombinary sequence (PRBS) is modulated with different formatsonto 165 subcarriers. The IFFT size is 256. 4% trainingoverhead and 22 pilots are inserted for channel estimation.Residual subcarriers are used for zero padding. The length ofcyclic prefix for every OFDM symbol is 10. The sampling rateof the DAC is 10 GS/s, so that the time duration of one OFDMsymbol is 26.6ns. The bitrate of the OFDM signal is 29.2Gbit/s(10 × log2(16) × [(165 + 22)/256]) occupying a bandwidth

Fig. 4. Q Factor versus OSNR in back-to-back case.

of about 7.3GHz(10 × [(165 + 28)/256]). The net bitrate is23.9Gbit/s (29.2×(165/187)×(256/266)/(1+ 4%)). The base-band OFDM signal is processed by a square-root-raised-cosine-filter with a roll-off factor of 0.18 in order to removealiasing products and then transformed to optical domain usingan I/Q modulator. To eliminate the influence of the linewidth oflasers, we set the value to be 0. Then the signal is launched intoa re-circulating loop. One loop consists of an 80km standardSSMF, parameters of which are as follows: D = 17ps/nm · km,α = 0.2dB/km, rSS M F = 1.3 W−1km−1, and a gain controlledEDFA with 5dB of noise figure. At the receiver, a 2ndorder Gaussian-shaped optical band-pass filter (OBPF) witha bandwidth of 20GHz is used to filter out ASE noise. Thecoherent detector consists of a local oscillator (LO), a 90°hybrid, and two balanced detectors. At last, the electrical signalis filtered out and processed by MATLAB.

IV. RESULTS AND DISCUSSIONS

The performance of back-to-back Q factor, which is derivedfrom BER and calculated as 20 × log10 (

√2 × erfcinv

(2 × BER)), against optical signal-to-noise ratio (OSNR) isdepicted in Fig. 4. The corresponding constellations are shownin the insets. To achieve a Q factor of 9.8dB (when BER =1 × 10−3), the required OSNR value for 16QAM modulatedOFDM is about 13.3dB, and for 4 + 12APSK modulatedOFDM is 13.6dB. 8 + 8APSK modulated OFDM is about14.6dB. The advantage of 16QAM and 4 + 12APSK over8 + 8APSK at lower OSNR is mainly due to their similarmaximized AED between each constellation point.

Considering the advantage on fiber nonlinearities and tol-erance towards ASE noise together, 4 + 12APSK modulatedOFDM can be assumed to perform best.

Fig. 5 shows the Q factor versus launch power in singlechannel after 1040km, 1200km and 1360km transmission,and the Q factor performance of the center channel in5-channel 12.5-GHz spaced WDM system are shown inFig. 6. Obviously, the Q performance of 4 + 12APSK isthe best. For instance, in Fig. 5, after 1040km transmission,the optimal launch power of 4 + 12APSK OFDM is 2dBlarger than that of 16QAM and the corresponding Q factorof 4 + 12APSK OFDM is 2.3dB higher than 16QAM insingle channel system, while the optimal launch power of

FAN et al.: OPTIMAL 16-ARY APSK ENCODED CO-OFDM FOR LONG-HAUL TRANSMISSION 1201

Fig. 5. Q factor versus launch power in single channel after 1040km, 1200km,1360km transmission.

Fig. 6. Q factor versus launch power in WDM system after 880km, 1040km,1200km transmission.

8 + 8APSK OFDM is 2dB larger than that of 16QAM andthe corresponding Q factor of 4 + 12APSK OFDM is only0.9dB higher than 16QAM. In WDM system, we obtain thesimilar results.

In either single-channel system or WDM system, whenlaunch power is low and transmission distance is small whereASE noise is dominated, 8 + 8APSK performs worse than16QAM and 4 + 12APSK because of its limited AED, whilewhen launch power becomes higher where nonlinear effectdominates, the advantage of 16APSK towards fiber nonlinear-ities is obvious. As the transmission distance increases, theaccumulated ASE makes the advantage of 16QAM towardsASE noise more obvious, resulting in a decreased Q differencebetween 16QAM and 16APSK modulated OFDM. We assessthe system performance by evaluating the maximum reachat Q = 8.2dB (FEC threshold is assumed to be 5 × 10−3)when increasing the launched power, which is shown in Fig. 7for single channel and Fig. 8 for WDM system. In singlechannel system, the performance of 4 + 12APSK modulatedOFDM surpasses 8 + 8APSK and 16QAM by approximately10.5%. And in WDM system, it surpasses 8 + 8APSK byapproximately 5.6% and 16QAM by 18.75% respectively,illustrating that the transmission performance of 4 + 12APSKis best. In addition, we discuss the transmission performance

Fig. 7. Maximum reach of three modulation in single channel condition atdifferent Q threshold.

Fig. 8. Maximum reach of three modulation formats in WDM system atdifferent Q threshold.

at different Q threshold (see in Fig. 7 and Fig. 8). As thefigures show, when the Q factor is larger (BER threshold isset lower), the number of the re-circulation loops becomessmaller, then the advantage of 16APSK on nonlinearities ismore obvious. For instance, when Q threshold increases to9.0dB, 4 + 12APSK modulated OFDM surpasses 16QAM by18.75% in single channel system and 23.07% in WDM system.

V. CONCLUSION

We have proposed 4 + 12APSK encoded coherent opticalOFDM for the first time. Investigation on the PAPR propertyshows that the PAPR of 16APSK is lower than that of 16QAMso that the nonlinearity tolerance is enhanced. Simulationresults in back-to-back configuration indicate that 16QAMand 4 + 12APSK have similar OSNR requirement. The systemperformance is assessed by evaluating the maximum reach atQ = 8.2dB. The simulation results illustrate that 4 + 12APSKsurpasses 8 + 8APSK and 16QAM by approximately 10.5%,and in WDM system, it surpasses 8 + 8APSK by approxi-mately 5.6% and 16QAM by 18.75%. Based on results above,4 + 12 APSK modulation format is a competitive techniquefor coherent optical OFDM in long haul transmission.

1202 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 13, JULY 1, 2013

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