A simple peak-to-average power ratio reduction

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,1 Wei Li,1,* Weidong Ma,2 Kai Wang1
1
Wuhan National Lab for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074,
P.R.China.
2
Accelink Technologies Co., Ltd, Wuhan, 430074, P.R.China.
*weilee@hust.edu.cn，weilee020116@yahoo.com.cn
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
OCIS codes: (060.0060) Fiber optics and optical communications; (060.2330) Fiber optics and
optical communication: Fiber optics communications; (070.7145) Fourier optics and signal
processing: Ultrafast processing; (190.4370) Nonlinear optics, fibers; (999.9999) Orthogonal
frequency division multiplexing.
References and links
J. Armstrong, “OFDM for Optical Communications,” J. Lightwave. Technol. 27, 189-204 (2009).
W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Exp. 16, 841-859
(2006).
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).
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).
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).
1.
2.
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15614
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).
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 [1-3]. 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 [4-7] 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].
50×88.8Gb/s all optical OFDM transmission was demonstrated using a photonic integrated
circuit [5]. 100Gb/s all optical OFDM transmission was demonstrated employing optical FFT
elements based on coupler interferometry [6]. 4×10Gb/s all optical OFDM demultiplexer was
successfully demonstrated using silica planar lightwave circuit (PLC) based optical FFT
circuits [7]. Similar to conventional optical OFDM systems [8,9], 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]
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.
There are mainly two kinds of feasible ODFTs and OIDFTs. One is based on a phase
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
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shifter array and an optical delay line array, proposed by Kyusang Lee [4]. The main idea of
this scheme is to divide the overall discrete Fourier transformation (DFT) into multiple
phase-shifting and optical delay operations. In this kind of ODFT, the phase-shiftings are
implemented by phase shifters and the optical delays are implemented by delay lines. The
other is based on silica PLC technology [7,10]. This scheme is proposed on the basis of the
similarity of transfer functions between 2×2 DFT and 2×2 directional couplers. For example,
Fig.2 depicts a PLC-based OIDFT with 4 sub-carriers, owing to the page layout limitation.
The OIDFT with 16 sub-carriers can be constructed in the same way [10]. Figure 2 depicts the
core layer of the OIDFT circuit. It consists of four directional couplers and nine phase shifters
(in yellow). The phase-shifting value of every phase shifter is п/2. In Fig. 2, α0, α1, α2, α3 are
the amplitudes of four parallel input lights, and β0, β1, β2, β3 are the DFT of α0, α1, α2, α3. The
light beams of β0, β1, β2, β3 are coupled together after different time delays. The lengths of
delay lines (dL, 2dL, 3dL) are determined by bit rate of every sub-carrier [7]. It is worth
mentioning that the two phase-shifters (in red) is only related with PAPR reduction, not
necessary in the latter scheme. The PLC-based OIDFT is easy to achieve using current silica
PLC technology.
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.
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
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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 { X k } =
1
∑
N −1
X k exp( j
2π
nk )
N
(n = 0,1,..., N − 1)
(1)
where N is the number of sub-carriers, and X k denotes the kth modulated phase shift keying
(PSK) or quadrature amplitude modulation (QAM) symbol. X k can be written as
X k = ak + jbk , where ak and bk indicate the real component and imaginary component
of X k , 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)
N
k =0
D {ak } = D {bk } = σ 2
(3)
where E and D are expectation operator and variation operator, respectively. σ 2 is the
variation of ak and bk . Setting xn = xn,I + jxn,Q , xn , I and xn ,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], the probability distributions of xn , I and xn ,Q follow
the Gaussian distribution. Therefore, the complementary cumulative distribution function
(CCDF) of PAPR can be written as Eq.(4) [12].
P( PAPR > PAPR0) = 1 − (1 − e− PAPR0 ) 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, X k follows
0-1 distribution. Consequently, Eq.(2) and (3) should be modified to Eq. (5) and (6).
E {ak } = 1/ 2, E {bk } = 0
(5)
D {ak } = 1/ 4,
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]. Unfortunately, xn , I and xn ,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
High PAPR is a major drawback in optical OFDM systems. It deteriorates nonlinear
impairment in optical fibers. Many research studies have been focused on PAPR reduction
schemes [8,9]. Most of them are related with those optical OFDM systems which utilize
electronic FFT circuits. However, they may be ineffective or unfeasible in all optical OFDM
systems. Hardly any reports are centered on PAPR reduction scheme in all optical OFDM
systems. Between conventional optical OFDM systems and IM-DD all optical OFDM
systems, the differences of PAPR characteristics are notable. We propose a novel PAPR
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15617
reduction scheme for the latter based on phase pre-emphasis, which requires hardly any
additional system or device complexity.
Equation (1) implies that every OFDM symbol contains N components ( x0 , x1 ,..., xN −1 ),
lining up
in time domain. Because X k follows 0-1 distribution, it’s clear that
1 inN −sequence
1
| xn |≤
Xk
∑
k =0
and
| xn | reaches a maximum when n=0. This means that X k
N
(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 X k ' =
1
N
∑
N −1
k =0
X k exp( jϕ k ) exp( j
'
X k = X k exp( jϕk )
where
2π
nk )
N
( n = 0,1,..., N − 1)
(7)
(k = 0,1,..., N − 1)
(8)
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.
Simulation proves the effectiveness of the proposed PAPR reduction scheme. In order to
get suitable values for ϕk , a simulation tool is developed using the Matlab package. The
simulation is related with an ODFT that is based on a phase shifter array and an optical delay
line array. Fig.3 depicts the diagram of PAPR simulation. Random inputs ( x0 , x1 ,..., x15 ) are
multiplexed by phase pre-emphasis values ( ϕ0 , ϕ1 ,..., ϕ15 ). After ODFT, PAPR values are
calculated for different chooses of ϕk The optimized values for
.
PAPR
ϕ = [0, −
is
π
16
,
the
minimal.
The
ϕk are obtained when the
optimized
ϕk
3π
π 3π
π 7π
π
9π
π
11π
π
π
π
13π
π
, − ,
, − ,
, −
,
, −
,
, −
,
, −
,
, −
]
32
48 32
80 96
112 128
144 160
176 16
208 224
240
is
. 65000
points are used in the simulation. Fig.4 depicts the comparison of the probability distributions
of PAPR between IM-DD all optical OFDM systems with and without phase pre-emphasis,
where X-axis represents the PAPR value and Y-axis represents the corresponding possibility.
Without phase pre-condition, the probability of PAPR as high as 10dB is larger than 0.02, and
the most possible PAPR is 9dB. The remarkable characteristics are that the PAPR in IM-DD
all optical OFDM systems can only be discrete values. The underlying cause is implied in Eq.
(1). As aforementioned, | xn | reaches the maximum when n=0, and X k follows 0-1
distribution. Consequently, the maximum of | xn | can only be an integral number, varying
from 1 to 16. Moreover, the expectation of | xn | is determined by X k , so that the average
power of all optical OFDM symbols changes slightly. Therefore, PAPR can only be discrete
values. Since the PAPR distribution here differs greatly from those in conventional optical
OFDM systems, they cannot have similar probability distribution functions ， which is
theoretically proved in section 3. What is more, Fig.4 shows that PAPR characteristics
improve significantly when appropriate phase pre-emphasis is applied. Fig.4 illustrates
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15618
evidently that the possibility of PAPR larger than 7dB is almost zero, and the most possible
PAPR is less than 5dB. Under this condition, PAPR changes continuously. This is because
| xn | doesn’t always reach the maximum when n=0, owing to the influence of phase
pre-emphasis.
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
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
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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 TransmissionMakerTM 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)
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Figure 8 depicts the bit error rate (BER) performance versus average transmitted power, under
three different conditions: transmission without phase pre-emphasis, transmission with phase
pre-emphasis and linear transmission. The related simulation parameters are given in table 1. In
Fig.8, X-axis represents the average optical signal power transmitted into fibers. Y-axis represents
lg(BER). It is obvious that the proposed PAPR reduction scheme brings high tolerance of nonlinear
impairment in fibers. If the required BER is 1×10-9, the maximum transmitted power is enhanced by
0.9mW, which is an increase of 39%. If the required BER is 1×10-12, the maximum transmitted
power is enhanced by 0.75mW, which is an increase of 42%. The frequency space between
sub-channels is typically as low as tens of GHz in all optical OFDM systems. This will result in
serious cross phase modulation (XPM) and four wave mixing (FWM) effects in optical fibers.
Further studies are needed to reduce XPM and FWM effects, in order to enhance system
performance.
Fig. 8. BER performance versus transmitted power
Table 1. Simulation parameters
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Dispersion(G.655)
4.6651 ps/(nm·km)
Dispersion slop(G.655)
0.0114 ps/(nm2·km)
Fiber length(G.655)
80 km
Dispersion(DCF)
-90.0 ps/(nm·km)
Fiber length(DCF)
4.15 km
Nonlinear index(DCF)
4e-20 m2/W
Nonlinear index(G.655)
2.6e-20 m2/W
Total bit rate
160Gb/s
Number of sub-carriers
16
Bit rate of sub-carrier
10 Gb/s
Transmission distance
400km
Central frequency
193.1THz
Simulation time window
1.28e-7 s
Sample rate
640 GHz
Pseudo-random binary sequence
2e7-1
Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15621
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).
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Received 5 Jun 2009; revised 8 Jul 2009; accepted 22 Jul 2009; published 19 Aug 2009
31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15622