QAM accommodated double-side band fast OFDM based on IDCT

In this paper, we theoretically and experimentally prove that sub-carriers in double-side band fast orthogonal frequency division multiplexing (DSB-FOFDM) are orthogonal over a symbol interval independent of the signal phase and amplitude. Therefore, the commonly utilized DSB-FOFDM is quadrature amplitude modulation (QAM) accommodated; while previously DSB-FOFDM was usually modulated by amplitude shift keying (ASK) or binary phase shift keying (BPSK). In our proof-of-concept experiments, bit error ratio (BER) performance of 10 Gb/s quadrature phase shift keying (QPSK) modulated DSB-FOFDM was equivalent to that of 10 Gb/s QPSK modulated OFDM after 500 km standard single mode fiber (SSMF) transmission. 10 Gb/s QPSK modulated DSB-FOFDM largely outperformed the commonly utilized 4-ASK modulated DSB-FOFDM in BER performance. Additionally, BER performance of 10 Gb/s 16-QAM modulated DSB-FOFDM was equivalent to that of 10 Gb/s 16-QAM modulated OFDM after 500 km SSMF transmission. © 2013 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2330) Fiber optics communications; (060.4230) Multiplexing. References and links 1. J. Armstrong, “OFDM for optical communications,” J. Lightw.Technol., 27(3), 189-204 (2009). 2. W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Exp., 15(16), 9936-9947 (2007). 3. Lenin Mehedy, Masuduzzaman Bakaul, and Ampalavanapillai Nirmalathas, “Frequency interleaving towards spectrally efficient directly detected optical OFDM for next-generation optical access networks,” Opt. Exp., 18(22), 23161-23172 (2010). 4. Chih-Yun Wang, Chia-Chien Wei, Chun-Ting Lin, and Sien Chi, “Direct-detection polarization division multiplexed orthogonal frequency-division multiplexing transmission systems without polarization tracking,” Opt. Lett., 37(24), 5070-5072 (2012). 5. S. Alireza Nezamalhosseini, Lawrence R. Chen, Qunbi Zhuge, Mahdi Malekiha, Farokh Marvasti, and David V. Plant, “Theoretical and experimental investigation of direct detection optical OFDM transmission using beat interference cancellation receiver,” Opt. Exp., 21(13), 15237-15246 (2013). 6. Liang B. Du and Arthur J. Lowery, “Pilot-based cross-phase modulation compensation for coherent optical orthogonal frequency division multiplexing long-haul optical communications systems,” Opt. Lett., 36(9), 16471649 (2011). 7. J. Zhao and A.D. Ellis, “A Novel Optical Fast OFDM with Reduced Channel Spacing Equal to Half of the Symbol Rate Per Carrier,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMR1. 8. S. K. Ibrahim, J. Zhao, D. Rafique, J. A. O’Dowd, and A. D. Ellis, “Demonstration of world-first experimental optical fast OFDM system at 7.174 Gbit/s and 14.348 Gbit/s,” in European Conference and Exhibition on Optical Communication (ECOC), 2010, paper PD3.4. #200145 $15.00 USD Received 24 Oct 2013; revised 24 Nov 2013; accepted 8 Dec 2013; published 20 Dec 2013 (C) 2013 OSA 30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032441 | OPTICS EXPRESS 32441 9. C. Lei, H. Chen, M. Chen, and S. Xie, “A high spectral efficiency optical OFDM scheme based on interleaved multiplexing,” Opt. Exp., 18(25), 26149-26154 (2010). 10. J. Zhao, and A. D. Ellis, “Discrete-Fourier transform based implementation for optical fast OFDM,” Optical Communication (ECOC), 36th European Conference and Exhibition on, Tu.4.A.3, 19-23 Sept. 2010. 11. E. Giacoumidis, I. Tomkos, and J. Tang, “Performance of optical fast-OFDM in MMF-based links,” in Optical Fiber Communication Conference, paper OWU3, (2011). 12. Jian Zhao and Andrew Ellis, “Advantage of Optical Fast OFDM Over OFDM in Residual Frequency Offset Compensation,” IEEE Photon. Technol. Lett., 24(24), 2284-2287 (2012). 13. Y. Yeh and S. Chen, “Efficient channel estimation based on discrete cosine transform,” in Proc. Int. Conf. Acoust. Speech Signal Process, 676C679 (2003). 14. X. Ouyang, J. Jin, G. Jin, Z. Wang, and Y. Park, “Interleaved Multiplexing Optical Fast OFDM Without the Interference Between Subchannels,” IEEE Photon. Technol. Lett., 25(4), 378-381 (2013). 15. E. Giacoumidis, S.K. Ibrahim, J. Zhao, J.M. Tang, I. Tomkos, and A.D. Ellis, “Experimental demonstration of cost-effective intensity-modulation and direct-detection optical Fast-OFDM over 40 km SMF transmission,” Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2012 and the National Fiber Optic Engineers Conference, JW2A.65 (2012). 16. C. Lei, H. Chen, Minghua Chen, and S. Xie, “16× 10Gb/s symmetric WDM-FOFDM-PON realization with colorless ONUs,” Opt. Exp., 19(16), 15275-15280 (2011). 17. J. Zhao, S.K. Ibrahim, D. Rafique, P. Gunning, and A.D. Ellis, “A Novel Method for Precise Symbol Synchronization in Double-Side Band Optical Fast OFDM,” in Optical Fiber Communication Conference, paper JWA23, (2011). 18. E. Giacoumidis, S. K. Ibrahim, J. Zhao, J. M. Tang, A. D. Ellis, and I. Tomkos, “Experimental and theoretical investigations of intensity-modulation and direct-detection optical fast-OFDM over MMF-links,” IEEE Photon. Technol. Lett., 24(1), 52-54 (2012). 19. W. L. Chin, “Maximization of Effective Signal Power in DCT Window for Symbol Time Synchronization in Optical Fast OFDM,” J. Lightw. Technol., 31(5), 740-748 (2013). 20. J. Zhao, and A. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photon. Technol. Lett., 24(1), 34-36 (2012). 21. J. Zhao, S.K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol Synchronization Exploiting the Symmetric Property in Optical Fast OFDM,” IEEE Photon. Technol. Lett., 23(9), 594-596 (2011). 22. J. Zhao and H. Shams, “Fast dispersion estimation in coherent optical 16QAM fast OFDM systems,” Opt. Exp., 21(2), 2500-2505 (2013).


Introduction
Multiple sub-carriers technology has gained much attention in recent years as it provides a relatively straightforward way to accommodate high data rate link.Orthogonal frequency division multiplexing (OFDM) is a typical multiple sub-carriers modulation format [1][2][3].It enjoys a much higher spectrum efficiency (SE) than many other multiple sub-carriers technologies as a result of overlapped orthogonal sub-carriers.Additionally, it can be easily implemented by inverse fast Fourier transform (IFFT) and FFT.These merits make OFDM widely used and investigated in optical fiber communications [4][5][6].
To address this problem, in 2013, A. D. Ellis presented a 16-QAM FOFDM scheme implemented by an optical I/Q modulator [22].In each branch of the optical I/Q modulator, 4-ASK modulated FOFDM was utilized.After the optical I/Q modulator, 16-QAM modulated FOFDM was generated.However, in this scheme, each branch was still 4-ASK modulated, two inverse DCT (IDCT) and two DCT modules were required, and this scheme did not improve SE of each branch in essence.Thus, this scheme did not well address the problem [7-9, 11-13, 17] pointed out that FOFDM can only be ASK or BPSK modulated actually.
In this paper, we theoretically and experimentally prove that orthogonality of sub-carriers in the widely utilized double-side band FOFDM (DSB-FOFDM) is independent of the signal amplitude and phase during a symbol interval in fact.Therefore, DSB-FOFDM is QAM accommodated, and thus its SE can be further improved.Moreover, sub-carrier spacing of QAM modulated DSB-FOFDM is just half of that of OFDM, identical to that of the ASK or BPSK modulated DSB-FOFDM.
In our proof-of-concept experiment, 10 Gb/s QPSK modulated DSB-FOFDM and 16-QAM modulated DSB-FOFDM were successfully transported over 500 km standard single mode fiber (SSMF).Bit error ratio (BER) performance of the QPSK modulated DSB-FOFDM and OFDM was equivalent.QPSK modulated DSB-FOFDM largely outperformed 4-ASK modulated DSB-FOFDM, the commonly utilized modulation format in DSB-FOFDM, in BER performance after 500 km SSMF transmission.In addition, BER performance of 16-QAM modulated DSB-FOFDM was equivalent to that of 16-QAM modulated OFDM.

Principle
To investigate the minimum sub-carrier spacing for crosstalk-free operation, sub-carrier orthogonality should be considered firstly.Generally, a sub-carrier can be written as, where ω c denotes the sub-carrier frequency, a(t) and b(t) are the input complex signal data.Then, where [t 0 ,t 0 + T ] is a symbol interval, s k (t) represents the k-th sub-carrier, s * l (t) denotes conjugation of the l-th sub-carrier.In crosstalk-free operation, we have ξ (t) = 0.For QAM modulated a k , a l , b k and b l , they are constant complex during [t 0 ,t 0 + T ].Therefore, to make ξ (t) = 0 for arbitrary a k , a l , b k and b l , we have , where m and n are positive integers and t 0 determines the initial phase of sub-carriers.Furthermore, to make this solution correct for arbitrary k and l, we have ω c = mπ/T with t 0 = (2n + 1)T /(2m).Then, we have the minimum sub-carrier spacing T } is the only solution of Eq. ( 3) and t 0 is arbitrary in this case.Therefore, we have a minimum sub-carrier spacing Δω = 2π/T for arbitrary integers k and l.This is the standard OFDM with Δω = 2π/T .Note that in Eq. ( 3), t 0 can only determine whether equation contains the signal data is true is not determined by t 0 .Therefore, t 0 can only determine the initial sub-carrier phase, not the signal data phase.Moreover, this indicates that the orthogonality of these sub-carriers is independent of the signal phase and amplitude.
Therefore, according to the solutions to Eq. ( 3), to achieve DSB-FOFDM with Δω = π/T , identical to half of that of standard OFDM, we must have In addition, sub-carriers a k cos(kω c t) + b k sin(kω c t) and a l cos(lω c t) + b l sin(lω c t) should have the same form.Therefore, combined with Eq. ( 4), we have a k =0 and a l = 0 or b k = 0 and b l = 0 to achieve the DSB-FOFDM scheme with a halved minimum sub-carrier spacing Δω = π/T .This indicates that the sub-carrier spacing can be reduced if only cosine or sine sub-carriers are utilized instead of the exponential sub-carriers in the standard OFDM.Furthermore, in our derivations, a k , a l , b k , and b l are constant complex signal during a symbol interval.Thus, DSB-FOFDM is QAM accommodated actually while previously it was only ASK or BPSK modulated [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].
Moreover, the QAM modulated DSB-FOFDM can be implemented by IDCT with s(t) = a(t) cos(ω c t) when b(t) = 0 or inverse discrete sine transform (IDST) with s(t) = b(t) sin(ω c t) when a(t) = 0. We can denote a DSB-FOFDM symbol as follows, where a k and b k are constant complex during a DSB-FOFDM interval.[12,13,21,22].

Experiment setup
Proof-of-concept experiments on QPSK modulated DSB-FOFDM were carried out.Figure 2 shows the experiment setup for 10 Gb/s QPSK modulated DSB-FOFDM coherent optical communication system.At transmitter, the initial binary sequence was firstly distributed to 256 sub-carriers by a serial to parallel (S/P) module.Then time-domain QPSK modulated DSB-FOFDM signal was generated through QPSK modulation and IDCT modules.8 sub-carriers were utilized as pilot sub-carriers.7  The generated time-domain QPSK modulated DSB-FOFDM signal was then uploaded into an arbitrary waveform generator (Tektronix AWG7122C) operating at 5 GSa/s to generate analog signals.As SE of QPSK is 2 bit/s/Hz, the overall link rate was about 10 Gb/s and the data rate in our experiment was approximately 8.5 Gb/s determined by the ratio of the data subcarriers to the total sub-carriers and the overall link rate((256 − 7 − 8)/256 × 15/16 × 62/64 × 10 Gb/s ≈ 8.5 Gb/s).
The optical source in our experiment was a commercially available external cavity laser (ECL) operating at a wavelength of 1550.05 nm with a line-width of about 100 kHz.To fix polarization state of signal light, a polarization controller (PC) was utilized following ECL but before optical I/Q modulator.Subsequently, the generated analog waveforms were amplified by SHF 100 AP with a maximum response bandwidth of 25 GHz.Then, the amplified analog waveforms were fed into an integrated dual-parallel dual-electrodes MZM (FUJITSU FTM7920EX) worked as an optical I/Q modulator to up-convert the baseband signal.3-dB bandwidth of this MZM is about 40 GHz.The typical V π of our integrated dual-parallel dualelectrodes MZM (FUJITSU FTM7920EX) is 3.5 V. Optical insertion loss is about 9.0 dB.In our experiment, the two sub-MZMs worked at the null-bias point; the main-MZM worked at the quadrature-bias point.
The typical noise figure of our utilized Opeak EDFAs is about 5.5 dB.The input optical power into the SSMF fiber is about −2.0 dBm in our experiment.Fiber chromatic dispersion is about 17 ps/nm/km, attenuation loss is about 0.2 dB/km.Before the coherent receiver, a variable optical attenuator (VOA) was utilized to regulate the received optical power.Single-polarization coherent receiver was utilized in our experiment and its 3-dB bandwidth is about 43 GHz.The input local oscillator (LO) power is about 5 dBm.LO utilized in the coherent receiver is the output of a 1 × 2 optical power splitter following PC at the transmitter.Our balanced coherent receiver is based on the u 2 t photodiodes BPDV2150R.The maximum photodiodes bias voltage of PD1 and PD2 are +3.5 V and −3.5 V, respectively.Their typical 3 dB cut-off frequency is about 42 GHz.The coherent received signal was subsequently fed into a digital phosphor oscilloscope (Tektronix DPO72004C) operating at 50 GSa/s after amplification to implement A/D conversion.Then we downloaded the digital signal into Matlab, separated the training symbols and data symbols and removed CP.Subsequently, this digital signal was fed into a DCT module.Channel estimation was implemented by the simple least square (LS) algorithm.Phase estimation was implemented by the commonly utilized pilot-aided algorithm.At last, the equalized signal was then fed into a QPSK demodulation module.
In our experiments, the data processing algorithms were all the same as that utilized in the standard OFDM optical communication systems to fairly compare their performance.Performance of DSB-FOFDM and its advantages have been widely investigated in the previous works [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], so this paper mainly focuses on whether DSB-FOFDM is QAM accommodated to further improve its SE. Figure 3 shows the experiment constellations of the proposed 10 Gb/s QPSK modulated DSB-FOFDM after 500 km SSMF transmission at different received optical power.These con-stellations experimentally prove that DSB-FOFDM is QPSK accommodated indeed.Figure 5 clearly shows that 10 Gb/s QPSK modulated DSB-FOFDM largely outperforms 10 Gb/s 4-ASK modulated DSB-FOFDM after 500 km SSMF transmission in BER performance.10 Gb/s QPSK modulated DSB-FOFDM can achieve a BER of 10 −3 when the average received optical power was about −38 dBm while 10 Gb/s 4-ASK modulated DSB-FOFDM can achieve a BER of 10 −3 when the average received power was about −36 dBm after 500 km SSMF transmission.And also, the difference in BER performance of 10 Gb/s QPSK modulated DSB-FOFDM and 10 Gb/s 4-ASK modulated DSB-FOFDM after 500 km transmission is in proportion to the average received optical power shown in Fig. 5.To investigate performance of the high-order QAM modulated DSB-FOFDM and verify that DSB-FOFDM is also the higher-order QAM accommodated, 16-QAM modulated DSB-FOFDM was also carried out in our proof-of-concept experiments.Its experiment setup is the same as that shown in Fig. 2. The AWG operated at 2.5 GSa/s to generate the 10 Gb/s 16-QAM DSB-FOFDM signal.Parameters including the total sub-carriers, data sub-carriers, CP length were also set the same as that in the 10 Gb/s QPSK DSB-FOFDM experiments.

Experiment results
Figure 6 demonstrates BER performance of 10 Gb/s 16-QAM modulated DSB-FOFDM and 10 Gb/s 16-QAM modulated OFDM after 500 km SSMF transmission versus the average received optical power.Constellation of the 16-QAM modulated DSB-FOFDM is also inserted in Fig. 6.It clearly shows that DSB-FOFDM is high-order QAM accommodated as OFDM does.And also, BER performance of 10 Gb/s 16-QAM modulated DSB-FOFDM and 10 Gb/s 16-QAM modulated OFDM was equivalent.They can achieve a BER of 10 −3 when the average received optical power was about −28 dBm as demonstrated in Fig. 6.

Conclusion
In this paper, we theoretically and experimentally prove that DSB-FOFDM is QAM accommodated while previously DSB-FOFDM was usually modulated by ASK or BPSK.Therefore, SE of DSB-FOFDM can be further improved with the introduction of high-order QAM.In addi-tion, the QAM modulated DSB-FOFDM halves the sub-carrier spacing of the standard OFDM as the conventional ASK or BPSK modulated DSB-FOFDM does.In our proof-of-concept experiment, 10 Gb/s QPSK modulated DSB-FOFDM and 10 Gb/s 16-QAM modulated DSB-FOFDM were successfully transported over 500 km SSMF, respectively.Experiment results show that BER performance of 10 Gb/s QPSK modulated DSB-FOFDM was equivalent to that of 10 Gb/s QPSK modulated OFDM after 500 km SSMF transmission.10 Gb/s QPSK modulated DSB-FOFDM largely outperformed 10 Gb/s 4-ASK modulated DSB-FOFDM, the commonly utilized modulation format in DSB-FOFDM, in BER performance after 500 km SSMF transmission.Also, BER performance of 10 Gb/s 16-QAM modulated DSB-FOFDM was equivalent to that of 10 Gb/s 16-QAM modulated OFDM.

Figure 1
Figure 1 depicts the spectrum of DSB-FOFDM and the standard OFDM.It demonstrates that the minimum sub-carrier spacing of DSB-FOFDM is just half of that of the standard OFDM.

Figure 4 shows
Figure4shows BERs of 10 Gb/s QPSK modulated OFDM and DSB-FOFDM versus the average received optical power after back-to-back (B2B) and 500 km SSMF transmission, respectively.After B2B transmission, BER of 10 −3 can be achieved when the received optical power was about −40 dBm.After 500 km transmission, BER of 10 −3 can be achieved when the received optical power was about −38 dBm.Also, as Fig.4demonstrated, BER performance of QPSK modulated DSB-FOFDM and OFDM was equivalent after B2B transmission and 500 km SSMF transmission, respectively.

Figure 5
Figure 5 demonstrates that BERs of 10 Gb/s 4-ASK modulated DSB-FOFDM and 10 Gb/s QPSK modulated OFDM after 500 km SSMF transmission versus the average received optical power.Constellations of the 4-ASK modulated DSB-FOFDM and the QPSK modulated DSB-FOFDM are also inserted in Fig. 5.Figure5clearly shows that 10 Gb/s QPSK modulated DSB-FOFDM largely outperforms 10 Gb/s 4-ASK modulated DSB-FOFDM after 500 km SSMF transmission in BER performance.10 Gb/s QPSK modulated DSB-FOFDM can achieve a BER of 10 −3 when the average received optical power was about −38 dBm while 10 Gb/s 4-ASK modulated DSB-FOFDM can achieve a BER of 10 −3 when the average received power was about −36 dBm after 500 km SSMF transmission.And also, the difference in BER performance of 10 Gb/s QPSK modulated DSB-FOFDM and 10 Gb/s 4-ASK modulated DSB-FOFDM after 500 km transmission is in proportion to the average received optical power shown in Fig.5.
sub-carriers around DC were left empty.1/16 cyclic prefix samples were employed.For every 64 DSB-FOFDM symbols, 2 training symbols were transmitted.