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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 18 — Aug. 31, 2009
  • pp: 15614–15622
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A simple peak-to-average power ratio reduction scheme for all optical orthogonal frequency division multiplexing systems with intensity modulation and direct detection

Xiaojun Liang, Wei Li, Weidong Ma, and Kai Wang  »View Author Affiliations


Optics Express, Vol. 17, Issue 18, pp. 15614-15622 (2009)
http://dx.doi.org/10.1364/OE.17.015614


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Abstract

This paper fundamentally investigates the peak-to-average power ratio (PAPR) theory in all optical orthogonal frequency division multiplexing (OFDM) systems which employ intensity modulation-direct detection (IM-DD) scheme. We propose a low-complexity PAPR reduction scheme based on phase pre-emphasis. Simulations show that the proposed scheme brings about a 3.74 dB PAPR reduction and better nonlinear impairment tolerance in a 16×10Gb/s IM-DD all optical OFDM system.

© 2009 Optical Society of America

1. Introduction

Optical OFDM has become a promising technique in long-haul and high-speed optical transmission systems, for its high spectral efficiency, relatively low bit rate and advanced robustness against chromatic dispersion and polarization mode dispersion [1

1. J. Armstrong, “OFDM for Optical Communications,” J. Lightwave. Technol. 27, 189–204 (2009). [CrossRef]

3

3. J. Armstrong, “OFDM: From Copper and Wireless to Optical,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM1.

]. Conventional optical OFDM systems utilize electronic fast Fourier transform (FFT) circuits and complicated digital to analog (D/A) converters to generate OFDM symbols, bringing about limited processing speed as well as high system cost. In order to eliminate these defects, many research studies [4

4. K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16, 4023–4028 (2008). [CrossRef] [PubMed]

7

7. K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, “Optical OFDM Demultiplexer Using Silica PLC Based Optical FFT Circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWO3.

] have been focused on optical implementation of Fourier transformation and constructing all optical OFDM systems. An optical discrete Fourier transformer (ODFT) was proposed for a 4×25Gb/s all optical OFDM system, eliminating requirements of 100Gb/s bandwidth for OFDM electronics of D/A converter and digital signal processors (DSP) [4

4. K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16, 4023–4028 (2008). [CrossRef] [PubMed]

]. 50×88.8Gb/s all optical OFDM transmission was demonstrated using a photonic integrated circuit [5

5. E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori1, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, “Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1Tb/s (50×88.8-Gb/s) DWDM Link over 800 km SMF Including 50-GHz Spaced ROADM Nodes,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP8.

]. 100Gb/s all optical OFDM transmission was demonstrated employing optical FFT elements based on coupler interferometry [6

6. Y. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-Polarization 2×2 IFFT/FFT Optical Signal Processing for 100-Gb/s QPSK-PDM All-Optical OFDM,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuM4.

]. 4×10Gb/s all optical OFDM demultiplexer was successfully demonstrated using silica planar lightwave circuit (PLC) based optical FFT circuits [7

7. K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, “Optical OFDM Demultiplexer Using Silica PLC Based Optical FFT Circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWO3.

]. Similar to conventional optical OFDM systems [8

8. Y. Tang, K. P. Ho, and W. Shieh, “Coherent Optical OFDM Transmitter Design Employing Predistortion,” IEEE Photon. Tech. Lett. 20,954–956 (2008). [CrossRef]

,9

9. J. Armstrong, “New OFDM peak-to-average power reduction scheme,” in Proceedings of IEEE on Vehicular Technology , (IEEE, 2001), pp 756–760.

], high PAPR is a serious intrinsic cause of penalty in all optical OFDM systems as well. Moreover, it deteriorates nonlinear impairment in optical fibers. However, hardly any investigations are centered on the PAPR characteristics in all optical OFDM systems.

This paper studies the fundamental PAPR theory in all optical OFDM systems and illustrates the differences of PAPR characteristics between conventional optical OFDM systems and IM-DD all optical OFDM systems for the first time. It’s well-known that intensity modulation (IM) is a very simple and cost-effective modulation technology. Ref [4

4. K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16, 4023–4028 (2008). [CrossRef] [PubMed]

] demonstrated the transmission efficiency of a 4×25Gb/s IM-DD all optical OFDM system. For simplicity, this paper will be confined to IM-DD all optical OFDM systems. Our scheme is based on phase pre-emphasis and requires hardly any additional system or device complexity. Simulations show a 3.74 dB PAPR reduction and better nonlinear impairment tolerance in a 16×10Gb/s all optical OFDM system.

2. All optical OFDM system configuration

Configuration analysis of the all optical OFDM system is necessary for PAPR investigation. Fig. 1 depicts a 16×10Gb/s IM-DD all optical OFDM system, as an example. At the transmitter, a 160Gb/s serial data stream is converted into sixteen 10Gb/s parallel data streams by the serial to parallel convertor (S/P). Driven by a 10GHz clock signal, an electro-absorption modulator (EAM) generates a 10GHz phase-locked optical pulse train, with a duty cycle of 1/16, using the input continuous-wave (CW) laser. The optical pulse train is then split into 16 identical pulse trains, which are modulated by sixteen 10Gb/s parallel data streams by IM, respectively. The optical inverse discrete Fourier transformer (OIDFT) implements the optical inverse Fourier transformation to generate all optical OFDM symbols. After transmission, the ODFT rebuilds optical signals in 16 sub-carriers at the receiver. 16 photodetectors (PDs) demodulate data in every sub-carrier after EAM sampling. The parallel to serial processor (P/S) combines sixteen 10Gb/s parallel electronic data streams into a 160Gb/s serial data stream. Because all optical OFDM systems need no electronic FFT or D/A circuits, the limitation of processing speed and high cost of electronic circuits are eliminated.

Fig. 1. Configuration of a 16×10Gb/s IM-DD all optical OFDM system
Fig. 2. A PLC-based OIDFT

3. PAPR theory in IM-DD all optical OFDM systems

In this section, a review of PAPR theory in conventional optical OFDM systems will be given. After that, the differences in IM-DD all optical OFDM systems will be illuminated.

In conventional optical OFDM systems, the base band equivalent time-domain signal xn can be expressed by Eq. (1).

xn=IFFT{Xk}=1Nk=0N1Xkexp(j2πNnk)(n=0,1,,N1)
(1)

where N is the number of sub-carriers, and Xk denotes the kth modulated phase shift keying (PSK) or quadrature amplitude modulation (QAM) symbol. Xk can be written as Xk=ak+jbk, where ak and bk indicate the real component and imaginary component of Xk, respectively. Assuming that ak and bk are independent with each other, the statistical characteristics of ak and bk are given in Eq. (2) and Eq. (3).

E{ak}=E{bk}=0
(2)
D{ak}=D{bk}=σ2
(3)

where E and D are expectation operator and variation operator, respectively. σ2 is the variation of ak and bk. Setting xn=x n,I+jx n,Q, x n,I and x n,Q respectively indicate the real component and imaginary component of xn. Calculating Eq. (1)~(3) and applying the central limit theorem for large N [11

11. N. Shiryaev, Probability (New York, springer-verlag, 1996).

], the probability distributions of x n,I and x n,Q follow the Gaussian distribution. Therefore, the complementary cumulative distribution function (CCDF) of PAPR can be written as Eq.(4) [12

12. S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” Wireless Communications IEEE 12(2), 56–65 (2005).

].

P(PAPR>PAPR0)=1(1ePAPR0)N
(4)

Nevertheless, Eq. (4) is only applicable to conventional optical OFDM systems with PSK or QAM mapping, because Eq.(3) will be unestablished in IM-DD all optical OFDM systems.

In the IM-DD all optical OFDM system shown in Fig.1, no PSK or QAM are employed. It is clear that 16 incident lights of the OIDFT have identical initial phase, because they originates from a same phase-locked pulse train. It should be noticed that there will be initial phase differences between the 16 incident lights, owing to the different transmission lengths from the EAM to the OIDFT. However, these initial phase differences are time-invariant and are available for PAPR investigation once the system is set up. For simplicity, the initial phases of the 16 incident lights are set zero. Under this condition of IM scheme, Xk follows 0–1 distribution. Consequently, Eq.(2) and (3) should be modified to Eq. (5) and (6).

E{ak}=12,E{bk}=0
(5)
D{ak}=14,D{bk}=0
(6)

According to probability theorem, summations of independent non-identical distributed random variables have analytical probability distribution functions only if they satisfy the Lindeberg condition [11

11. N. Shiryaev, Probability (New York, springer-verlag, 1996).

]. Unfortunately, x n,I and x n,Q don’t satisfy the Linderberg condition any more. So they have no analytical probability distribution functions. Consequently, Eq. (4) is not suitable for IM-DD all optical OFDM systems. Numerical simulation is the only way to investigate PAPR characteristics under this condition.

4. A novel simple PAPR reduction scheme

Equation (1) implies that every OFDM symbol contains N components (x 0,x 1,…,x N-1), lining up in sequence in time domain. Because Xk follows 0–1 distribution, it’s clear that xn1Nk=0N1Xk and |xn| reaches a maximum when n=0. This means that Xk (k=0,1,…,N-1) are multiplexed by the same phase factor. Because the value of |xn| always reaches its maximum when n=0, PAPR will be reduced if the in-phase condition (when n=0) is eliminated. In our PAPR reduction scheme, different phase pre-emphasises are introduced and Eq. (1) is converted to Eq. (7) and (8).

xn=IFFT{XK}=1NK=0N1Xkexp(k)exp(j2πNnk)(n=0,1,,N1)
(7)
Xk=Xkexp(k)(k=0,1,,N1)
(8)

where φk is the kth phase pre-emphasis. Chosen suitable values for φk, the in-phase condition (when n=0) can be eliminated and PAPR will be reduced.

Fig. 3. Diagram of PAPR simulation

Figure 5 depicts the differences between CCDFs, where X-axis represents the PAPR0 value and Y-axis represents the possibility when PAPR is larger than PAPR0. In the blue curve, there are some components parallel to the X-axis. This indicates that the possibility of some PAPR0 is zero, consistent with the aforementioned discrete PAPR values. 3.74dB PAPR reduction is achieved when the possibility of PAPR larger than PAPR0 is 0.001. To sum up, the proposed PAPR reduction scheme is effective in IM-DD all optical OFDM systems.

Fig. 4. Probability distribution of PAPR
Fig. 5. The CCDF of PAPR

The implementation of the proposed PAPR reduction scheme in IM-DD all optical OFDM systems needs hardly any additional system or device complexity. In an IM-DD system, initial signal phases will not affect the detection, so no modification is necessary for the receiver. In all optical OFDM systems employing OIDFTs based on a phase shifter array and a delay line array, the only modification for PAPR reduction is to change the values of the phase shifter array according to the phase pre-emphasis, without any device complexity. In all optical OFDM systems using silica PLC-based FFTs, only a few phase shifters are needed for PAPR reduction. As shown in Fig.2, only two additional phase shifters (in red) are needed. Considering that the circuit already contains nine phase shifters, the additional two can be produced synchronously during fabrication, without obvious additional complexity. In all, the proposed PAPR reduction will introduce negligible device or system complexity.

5. 16×10Gb/s IM-DD all optical OFDM application

We utilize VPI TransmissionMaker V7.6 to simulate a 16×10Gb/s IM-DD all optical OFDM system, the configuration of which is shown in Fig.1. In this simulation, the ODFT and OIDFT are based on a phase shifter array and a delay line array. The optical signal eye diagrams transmitted into the fiber are given in Fig.6 and Fig.7. Under the condition of no phase pre-emphasis, the eye diagram shows a power peak at the central of an OFDM symbol, as shown in Fig.6. This is consistent with the aforementioned PAPR characteristics in IM-DD all optical OFDM systems. When phase pre-emphasis is applied, no obvious power peak appears in the eye diagram, as shown in Fig.7. This means that with phase pre-emphasis, the peak power is dispersed to the whole OFDM symbol cycle. As a result, the corresponding PAPR will be significantly lower.

Fig. 6. Eye diagram of transmitted OFDM symbols (without phase pre-emphasis)
Fig. 7. Eye diagram of transmitted OFDM symbols (with phase pre-emphasis)

Fig. 8. BER performance versus transmitted power

Table 1. Simulation parameters

table-icon
View This Table

6. Conclusions

All optical OFDM is a promising technique in long-haul and high-speed optical transmission systems. High PAPR is a serious intrinsic defect in all optical OFDM systems. This paper fundamentally investigates PAPR theory in IM-DD all optical OFDM systems. In IM-DD all optical OFDM systems, the number of subcarriers is relatively small, so that the analytical PARP model based on the central limit theorem is not applicable unlike conventional optical OFDM systems. As a result, numerical simulation is the only approach. An effective and low-complexity PAPR reduction scheme is proposed. Simulation shows a 3.74dB PAPR reduction. The proposed PAPR reduction scheme is applied in a 16×10Gb/s IM-DD all optical OFDM system. Simulation indicates that the maximal transmitted powers increase by 39% and 42%, when the BER requirements are 1×10-9 and1×10-12, respectively. Therefore, system tolerance of nonlinear impairment increases significantly, owing to the contribution of the proposed PAPR reduction scheme.

Acknowledgement

This work was supported by the National Basic Research Program of China (973 Program:2010CB328300), China National Science Foundation Project (under granted:60772013) and the 863 high technology plan(2009AA03Z408).

References and links

1.

J. Armstrong, “OFDM for Optical Communications,” J. Lightwave. Technol. 27, 189–204 (2009). [CrossRef]

2.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Exp. 16, 841–859 (2006). [CrossRef]

3.

J. Armstrong, “OFDM: From Copper and Wireless to Optical,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM1.

4.

K. Lee, T. T. Chan, and J. K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16, 4023–4028 (2008). [CrossRef] [PubMed]

5.

E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori1, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, “Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1Tb/s (50×88.8-Gb/s) DWDM Link over 800 km SMF Including 50-GHz Spaced ROADM Nodes,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP8.

6.

Y. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-Polarization 2×2 IFFT/FFT Optical Signal Processing for 100-Gb/s QPSK-PDM All-Optical OFDM,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuM4.

7.

K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, “Optical OFDM Demultiplexer Using Silica PLC Based Optical FFT Circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWO3.

8.

Y. Tang, K. P. Ho, and W. Shieh, “Coherent Optical OFDM Transmitter Design Employing Predistortion,” IEEE Photon. Tech. Lett. 20,954–956 (2008). [CrossRef]

9.

J. Armstrong, “New OFDM peak-to-average power reduction scheme,” in Proceedings of IEEE on Vehicular Technology , (IEEE, 2001), pp 756–760.

10.

K. Tanaka and S. Norimatsu, “Transmission Performance of WDM/OFDM Hybrid Systems over Optical Fibers,” Electronics and Communications in Japan , Part 1, 90, 14–24(2007). [CrossRef]

11.

N. Shiryaev, Probability (New York, springer-verlag, 1996).

12.

S. H. Han and J. H. Lee, “An overview of peak-to-average power ratio reduction techniques for multicarrier transmission,” Wireless Communications IEEE 12(2), 56–65 (2005).

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(070.7145) Fourier optics and signal processing : Ultrafast processing

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 5, 2009
Revised Manuscript: July 8, 2009
Manuscript Accepted: July 22, 2009
Published: August 19, 2009

Citation
Xiaojun Liang, Wei Li, Weidong Ma, and Kai Wang, "A simple peak-to-average power ratio reduction scheme for all optical orthogonal frequency division multiplexing systems with intensity modulation and direct detection," Opt. Express 17, 15614-15622 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-15614


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References

  1. J. Armstrong, "OFDM for Optical Communications," J. Lightwave. Technol. 27, 189-204 (2009). [CrossRef]
  2. W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt. Express 16, 841-859 (2006). [CrossRef]
  3. J. Armstrong, "OFDM: From Copper and Wireless to Optical," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OMM1.
  4. K. Lee, T. T. Chan and J. K. Rhee, "All optical discrete Fourier transform processor for 100 Gbps OFDM transmission," Opt. Express 16, 4023-4028 (2008). [CrossRef] [PubMed]
  5. E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori1, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, "Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1Tb/s (50 x 88.8-Gb/s) DWDM Link over 800 km SMF Including 50-GHz Spaced ROADM Nodes," in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDP8.
  6. Y. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, "Dual-Polarization 2x2 IFFT/FFT Optical Signal Processing for 100-Gb/s QPSK-PDM All-Optical OFDM," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuM4.
  7. K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, "Optical OFDM Demultiplexer Using Silica PLC Based Optical FFT Circuit," in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWO3.
  8. Y. Tang, K. P. Ho, and W. Shieh, "Coherent Optical OFDM Transmitter Design Employing Predistortion," IEEE Photon. Tech. Lett. 20, 954-956 (2008). [CrossRef]
  9. J. Armstrong, "New OFDM peak-to-average power reduction scheme," in Proceedings of IEEE on Vehicular Technology, (IEEE, 2001), pp 756-760.
  10. K. Tanaka and S. Norimatsu, "Transmission Performance of WDM/OFDM Hybrid Systems over Optical Fibers," Electron. Commun. Japan, Part 1,  90, 14-24(2007). [CrossRef]
  11. N. Shiryaev, Probability (New York, springer-verlag, 1996).
  12. S. H. Han and J. H. Lee, "An overview of peak-to-average power ratio reduction techniques for multicarrier transmission," Wireless Commun. IEEE 12(2), 56-65 (2005).

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