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Performance evaluation of (D)APSK modulated coherent optical OFDM system
Optical Fiber Technology 19 (2013) 242–249
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Optical Fiber Technology www.elsevier.com/locate/yofte
Performance evaluation of (D)APSK modulated coherent optical OFDM system Hui Wang ⇑, Deming Kong, Yan Li, Jian Wu, Jintong Lin State Key Laboratory of Information Photonics & Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
a r t i c l e
i n f o
Article history: Received 26 September 2012 Revised 5 February 2013 Available online 6 March 2013 Keywords: Orthogonal frequency-division multiplexing (OFDM) Amplitude and phase shift keying (APSK) Quadrature amplitude modulation (QAM) Fiber nonlinearity
a b s t r a c t Performance of amplitude and phase shift keying (APSK) modulated coherent optical orthogonal frequency division multiplexing (CO-OFDM) with and without differential encoding is investigated. Numerical simulations based on 40 Gbit/s single-channel and 5 40 Gbit/s wavelength division multiplexing transmission are performed, and the impacts of amplified spontaneous emission noise, laser linewidth, chromatic dispersion, and fiber nonlinearity on the system performance are analyzed. The results show that compared with conventional 16 quadrature amplitude modulation (QAM) modulated optical OFDM signal, although 16(D)APSK modulated optical OFDM signal has a lower tolerance towards amplified spontaneous emission (ASE) noise, it has a higher tolerance towards fiber nonlinearity such as self-phase modulation (SPM) and cross-phase modulation (XPM): the optimal launch power and the corresponding Q2 factor of 16(D)APSK modulated OFDM signal are respectively 2 dB and 0.5 dB higher than 16QAM modulated optical OFDM signal after 640 km transmission, both in single-channel and WDM CO-OFDM systems. Although the accumulated CD decreases the peak-to-average power ratio (PAPR) during transmission, 16(D)APSK modulated OFDM signal will still remain an advantage compared with 16QAM modulated OFDM signal up to 1000 km single-channel transmission, meanwhile relaxing the needs for training symbols and pilot subcarriers and consequently increase the spectral efficiency. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Coherent optical orthogonal frequency division multiplexing (CO-OFDM) system [1–3] has found widespread applications due to its high spectral efficiency and ability to overcome transmission impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD). Most CO-OFDM signals utilize quadrature amplitude modulation (QAM) formats such as 16QAM [4–6] and 32QAM [7,8] nowadays. However, fiber nonlinearity greatly limits the performance of OFDM signals [9–11] due to large peak-to-average power ratio (PAPR). In order to improve the tolerance towards fiber nonlinearity, extensive researches have been carried out, such as compensation algorithms at the receiver [12], pre-process at the transmitter [13], and radio frequency pilot (RFP) insertion [14], which to some extent makes the transceiver complex and costly. Besides these techniques, modulation format with decreased PAPR – amplitude and phase shift keying (APSK) – is proposed in Ref. [15], to increase fiber nonlinearity tolerance of OFDM signal, while keeping the overall complexity and cost. But such modulation format, like QAM, is memoryless, so apriori knowledge such as training symbols and pilot subcarriers is required to realize channel estimation and channel equalization at the receiver. However, training symbols would decrease the bitrate and pilot subcarriers ⇑ Corresponding author. Fax: +86 10 62282303. E-mail address: [email protected] (H. Wang). 1068-5200/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2013.02.003
would occupy extra spectrum resources. As a result, a modification in the generation of OFDM signal with decreased PAPR and reduced overhead is of significance for future OFDM system. In this paper, differential APSK (DAPSK) is introduced in CO-OFDM system. DAPSK is first proposed in Ref. [16] for digital terrestrial video broadcasting (DTVB) applications and has already found applications in single-channel optical communication system [17], but to the best of the authors’ knowledge, it has not been employed in optical OFDM system yet. In this paper, we extend theoretical investigation on the origin of the advantage of APSK modulated OFDM signal and induce differential relation into APSK modulated OFDM signal. We thoroughly investigate differentially modulated APSK CO-OFDM systems (differential encoding/decoding in both the time domain and the frequency domain) and compare them with conventional QAM modulated CO-OFDM under the influences of different systems penalties including amplified spontaneous emission (ASE), laser linewidth, CD and fiber nonlinearity. Since 16QAM has been widely used in CO-OFDM system, a comparison with 16DAPSK is carried out through simulation. Various results indicate that 16DAPSK modulated OFDM signal (d-OFDM) inherits the low PAPR of 16APSK modulated OFDM signal (a-OFDM), thus performs higher nonlinearity tolerance than 16QAM modulated OFDM signal (q-OFDM). The optimal launch power and corresponding Q2 factor of a/d-OFDM are respectively 2 dB and 0.5 dB higher than q-OFDM after 640 km transmission, both in single-polarization, single-channel and
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... ...
...
...
...
2. Generation principles of 16QAM and 16(D)APSK
...
In either 16QAM or 16APSK modulation, one symbol represents four bits (b0, b1, b2, b3). In this paper, as shown in Table 1, for 16QAM modulation, the first two bits are used for the generation of in-phase component (I) and the last two are used for the generation of quadrature component (Q), the generated symbol is I + jQ; while for APSK modulation, the first three bits are used for the generation of phase component (u) and the last one is used for the generation of amplitude component (A), the generated symbol is Aeju. The corresponding constellations of 16QAM and 16APSK are shown in Fig. 1. Differential encoding is done after APSK modulation. Since differential encoding can be applied either in time domain or in frequency domain, two types of d-OFDM can be generated. If differential encoding is processed on the same subcarrier of adjacent OFDM symbols, the d-OFDM is termed as t-OFDM (‘t’ represents time domain); if differential encoding is processed on different subcarriers of the same OFDM symbol, the d-OFDM is termed as f-OFDM (‘f’ represents frequency domain). After APSK modulation, complex value Bi;k ¼ Ai;k expðjui;k Þ can be obtained, which represent the symbol on the ith interval at the kth subcarrier. Then, the complex value after differential encoding Si;k ¼ V i;k expðjhi;k Þ can be described as follows:
Si;k ¼ Bi;k Si1;k
for t OFDM
ð1Þ
Si;k ¼ Bi;k Si;k1
for f OFDM
ð2Þ
The operator ‘‘.’’ represents the differential calculation. Fig. 2 illustrates differential directions of t-OFDM and f-OFDM. The differential encoding is carried out for the amplitude component and phase
Table 1 Generation principles of 16QAM (left) and 16APSK (right). b0b1
I
b2b3
Q
b0b1b2
u
b3
A
10
+3
10
+3
000 001
0
0
1
1
2
p/4
11
+1
11
+1
011 010
p/2 3p/4
01
1
01
1
110 111
5p/4
101 100
3p/2 7p/4
00
3
00
3
p
...
Frequency
Direction of t-OFDM Symbol-to-be-discarded
OFDM Subcarrier Interval
Frequency
Fig. 1. Constellations of 16QAM (left) and 16APSK (right).
OFDM Subcarrier Interval
single-polarization, 5-channel wavelength-division-multiplexing (WDM) CO-OFDM systems. It is also found that along with an increased transmission distance, the advantage is slightly neutralized due to accumulated CD which leads to a reduced PAPR difference between a/d-OFDM and q-OFDM. However, the Q2 factor of a/dOFDM signal will still remain an advantage up to 1000 km transmission, making them promising candidate for metro network applications. Besides, as no apriori knowledge is needed for d-OFDM, the spectral efficiency is increased by at least 20% and the net bitrate is increased by at least 2% with reduced computation complexity in this paper. These advantages make d-OFDM not only an attractive technique in CO-OFDM system but also helpful in direct detection system such as passive optical network. The rest of this paper is organized as follows: the generation principles of 16QAM, 16APSK modulation formats and the differential encoding process are given in Section 2. Two kinds of d-OFDM are discussed. In Section 3, we provide the analysis of PAPR of different modulation formats modulated OFDM signal and the origin of low PAPR of (D)APSK modulated OFDM signal. The simulation setup and impairments influence on different OFDM signals are discussed in Section 4 before the conclusion is drawn in Section 5.
Direction of f-OFDM Symbol-to-be-discarded
... ...
...
...
... ... Time
Time
OFDM Symbol Interval
...
OFDM Symbol Interval
Fig. 2. Differential directions and positions of discarded symbols for t-OFDM (left) and f-OFDM (right).
component independently. The constellation remains the same after differential encoding. Take 16DAPSK of t-OFDM for example, the phase component after differential encoding is
hi;k ¼ modðui;k þ hi1;k ; 2pÞ
ð3Þ
where mod(x, y) is to get the remainder after x is divided by y. And the amplitude component after differential encoding is
if Ai;k – V i1;k ; V i;k ¼ 2;
else V i;k ¼ 1:
ð4Þ
Since an additional differential encoding process is required, the modulation of DAPSK is a little more complicated than that of QAM or APSK. However, the demodulation of DAPSK is comparatively easy:
Ri;k Si;k Hi;k Hi;k ¼ ¼ Bi:k Ri1;k Si1;k Hi1;k Hi1;k Ri;k Si;k Hi;k Hi;k ¼ ¼ ¼ Bi:k Ri;k1 Si;k1 Hi;k1 Hi;k1
Di;k ¼
for t OFDM
ð5Þ
Di;k
for f OFDM
ð6Þ
where H, R and D represent the channel transfer coefficient, the received signal, and the differential demodulated signal, respectively. As a result, for t-OFDM, if the channel is quasi-stationary during two symbols, then Hi,k = Hi1,k; and for f-OFDM, if the channel is quasistationary during two subcarriers, then Hi,k = Hi,k1. In either case, Di,k = Bi,k is obtained, so that ideal demodulation can be realized. Obviously, correlation induced by differential encoding between successive symbols or subcarriers can greatly simplify the demodulation process. As a result, neither explicit knowledge about channel properties nor a separate channel estimation procedure is necessary at the receiver, which reduces the computation complexity to a large extent. However, although no apriori knowledge is needed for d-OFDM, there is redundant information due to the differential demodulation: the first OFDM symbol should be discarded for t-OFDM and the data symbol carried on the first subcarrier of the first OFDM symbol should be discarded for f-OFDM, as shown in Fig. 2.
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The difference D between PAPRq-OFDM and PAPRa-OFDM is
D ¼ 10 log10
The PAPR of OFDM signal s(t) is defined as
PAPR ¼
maxfjsðtÞj2 g
ð7Þ
EfjsðtÞj2 g
According to Ref. [18], cumulative distribution function (CDF) Pc is used to characterize PAPR, which represents the probability that the PAPR is more than a certain value x.
Pc ¼ PrfPAPR > xg
ð8Þ
3.1. Theoretical analysis of PAPR of q-OFDM and a-OFDM As is well known, the average power of a signal over T time interval could be expressed as
8 2 9 = N <1 Z T X P av e ¼ E ðai;k cosðxk tÞ þ bi;k sinðxk tÞÞ dt ; :T 0 i¼1 ( ) N 1X 2 a2i;k þ bi;k ¼E 2 i¼1
ð9Þ
where ai,k, bi,k represent the ith in-phase and quadrature data carried on the kth subcarrier respectively and xk represents the angular frequency of the kth subcarrier, N is the total number of subcarriers that carry data. Then the average power of q-OFDM and a-OFDM are
1 1 Pav e 16QAM ¼ N P0 16QAM þ ð3Þ2 P0 16QAM 2 2 1 ¼ 5NP0 16QAM þN P 0 16QAM þ ð3Þ2 P0 16QAM 2 P av e
( ) N 1X 2 ¼E r 2 i¼1 i;k 1 1 ¼ N P0 2 2
16APSK
¼ 5NP0 where P 0
16QAM
16APSK
þ ð2Þ2 P0
16APSK
ð11Þ
16APSK =4
and P 0
APSK
ð10Þ
The baseband OFDM signal is generated by a MATLAB program from a 215 1 pseudorandom binary sequence (PRBS) unless otherwise stated. The IFFT size is 256, from which 165 subcarriers are used for useful data transmission. The signal structure of q-OFDM and a-OFDM before IFFT is shown in Fig. 3. Details of pilot subcarriers and training symbols used for q-OFDM and a-OFDM are shown in Table 2. There are 63 (for q-OFDM and a-OFDM)/91 (for d-OFDM) virtual subcarriers located in the outer part of the spectrum for zero padding. The signal is oversampled four times to sufficiently evaluate the PAPR. About 500 OFDM symbols have been evaluated per measurement point. The theoretical maximum PAPR and calculated maximum PAPR is shown in Table 3. Numbers in brackets represent the interval of pilot subcarriers and training overhead used for qOFDM and a-OFDM. In the analyses of Part A, Pmax is calculated under the condition that all symbols are the same constellation point with the largest amplitude. But in fact, the symbols are randomly distributed, so the actual Pmax is much lower than the theoretical value, which in turn makes the calculated maximum PAPR much lower than the theoretical maximum PAPR. This could be seen from Fig. 4a, where the CDFs of PAPR for different OFDM signals with PAPR length of 215 1 is shown. If the PRBS length is increased to 223 1, as shown in Table 3, the calculated PAPR value after four times oversampling is more approached to the theoretical value. However, the differences between the maximum PAPR of q-OFDM and a-OFDM or d-OFDM remain the same: about 2 dB larger. As there are only two amplitude values in the 16APSK constellation, the probability of the constellation points with large amplitude values (8/16) is lower than that of 16QAM (12/16), so the actual Pmax of a-OFDM drops more than that of q-OFDM. And this is why there is 1.5 dB difference between the calculated PAPR difference and the theoretical PAPR difference in Eq. (17). As the modulation formats are the same for a-OFDM, t-OFDM and f-OFDM, they are supposed to have the similar PAPR, which
represent the power of the signal with qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 a2i;k þ bi;k is the
Pmax
16QAM
16APSK
¼ ð3NÞ2 P0
16QAM
þ ð3NÞ2 P0
16QAM
8 2 9 = N <X ¼ ð2NÞ2 P0 ¼ max ðr i;k Þ ; : i¼1 ¼ 4N2 P0
16APSK
¼ 18N2 P 0
16QAM
ð13Þ
16APSK
ð14Þ
As a result, the theoretical maximum PAPR of q-OFDM and a-OFDM are respectively:
PAPRq-OFDM ¼
Pmax 16QAM 18 ¼ N 5 P av e 16QAM
ð15Þ
PAPRa-OFDM ¼
Pmax 16APSK 16 ¼ N 5 Pav e 16APSK
ð16Þ
OFDM Subcarrier Interval
Pmax
IFFT size
Then the maximum power of q-OFDM and a-OFDM are
Virtual subcarriers
ð12Þ
Pilot subcarrier interval
amplitude of the symbol carried on the kth subcarrier. The maximum power of a signal is expressed as
Pmax
ð17Þ
3.2. Parameters settings
the smallest amplitude in the constellation, r i;k ¼
8 2 9 <X N = ¼ max a cosðxk tÞ þ bi;k sinðxk tÞ ; : i¼1 i;k
PAPRq-OFDM ¼ 0:5 dB PAPRa-OFDM
Frequency
3. PAPR analysis
Data Symbol
Training Symbol Pilot Subcarrier
...
...
...
...
...
...
...
...
...
...
...
...
2 training symbols
Zero Subcarrier ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
...
...
Time
OFDM Symbol Interval 50 OFDM symbols
Fig. 3. Signal structure of q-OFDM and a-OFDM before IFFT.
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H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249 Table 2 Details of pilot subcarriers and training symbols. Name
Place
Function
Number
Modulation formats
Pilot subcarriers
Periodically inserted At the beginning
Common phase error compensation Channel estimation (time domain averaging algorithm)
Pilot interval (the number of subcarriers between adjacent pilot subcarriers) is 7, so the number of pilot subcarrier is 28 Training overhead (the ratio between training symbol number and data symbol number) is 4%
Same modulation formats with the data symbol
Training symbols
Table 3 PAPR values of different signals. Kinds of signal
Theoretical maximum PAPR (dB)
q-OFDM (7, 4%) a-OFDM (7, 4%) t-OFDM f-OFDM
Calculated maximum PAPR (dB)
28.4 27.9 27.2
(a) 1.0
(b)
PRBS length: 223 1
14 12
24.8 22.8
1 0.9
0.9 0.8
Probability, X <=x
Probability, X <= x
PRBS length: 215 1
1.00
0.7 0.6
0.98
0.5 0.4
0.96
0.3
10
0.2
12
14
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
0.1 0.0 6
7
8
9
10
0.8 0.7 0.6
q-OFDM(7,4%)
0.5
a-OFDM(7,4%)
0.4
t-OFDM
0.3
f-OFDM
0.2 0.1 0
11
12
13
14
15
PAPR, x dB
13
14
15
16
17
18
19
20
21
22
23
24
25
PAPR, x dB
Fig. 4. CDFs of PAPR of different signals with PRBS length 215 1 (a) and 223 1 (b).
could be further confirmed in Fig. 5a. The figure shows the PAPR distribution of all the symbols of the four signals. Distribution of PAPR over 50 symbols (one frame) is shown in Fig. 5b, which indicates the PAPR of (D)APSK modulated OFDM signal is much lower than q-OFDM. PAPR distribution over one symbol for long PAPR length of 223 1 is shown in Fig. 5c, showing similar phenomena with short PAPR length. 4. Simulations, results and discussion VPI Transmission Maker™ is used to evaluate the performance of different OFDM signals. The simulation setup is shown in Fig. 6, where the differences among the generation of t-OFDM, f-OFDM, a-OFDM and q-OFDM could be found. The length of cyclic prefix (CP) for every OFDM symbol is 10 samples. The sampling rate of DAC is set to 10 GS/s, so the total bitrate (including zero subcarriers and all the other information) is 40 Gb/s. The sampling rate of ADC is the same as DAC. System parameters are calculated in Table 4. It should be noted that as 50 OFDM symbols are simulated each time, the ‘‘differential overhead’’ for t-OFDM is regarded as 2% (1/50), while the ‘‘differential overhead’’ for f-OFDM is regarded as 0.01% (1/(50 165 1)). The baseband OFDM signal is processed by a square root raised cosine filter with a roll-off factor 0.18 in order to remove aliasing products and then transformed to optical domain using an I/Q modulator. Only one polarization is considered. The linewidth of lasers is assumed to be 0 unless otherwise stated. The transmission
link includes a power controlled EDFA and a recirculating loop. The loop has an 80 km standard single mode fiber (SSMF) and a gain controlled EDFA. The fiber parameters are: DSSMF = 17 ps/nm/km, aSSMF = 0.2 dB/km, cSSMF = 1.3 W1 km1. The gain controlled EDFA with a noise figure of 4.5 dB is used to compensate the fiber loss. At the receiver, a 2nd order Gaussian-shaped optical band-pass filter (OBPF) with a bandwidth of 20 GHz is used to filter out ASE noise. The coherent detector consists of a local oscillator (LO), a 90° hybrid, and two balanced detectors. Then the electrical signal is filtered out and processed with a MATLAB program. 4.1. Performance evaluation under ASE noise Fig. 7 depicts the Q2 factor against the optical signal-to-noise ratio (OSNR) of the four received OFDM signals under back-to-back (B2B) configuration. The OSNR is defined with the common 0.1-nm noise bandwidth. To achieve a Q2 factor of 9.8 dB (BER = 1 103), the required OSNR values for q-OFDM, a-OFDM, t-OFDM and f-OFDM signals are 14 dB, 15.3 dB, 15.2 dB, 15.2 dB respectively. The corresponding constellations are shown in the insets of Fig. 7. The scattering effect of q-OFDM and a-OFDM is due to the one-tap equalization, which could found in Ref. [19]. Theoretical SNR of 16QAM, 16APSK and 16DAPSK modulated system could be calculated according to Refs. [20–22] respectively. The converted theoretical OSNR requirements of 40 Gbit/s optical system are 12.5 dB (q-OFDM), 13.8 dB (a-OFDM) and 14 dB (d-OFDM), respectively. The difference b etween simulation results and
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H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249
(a)
(b) 15
15 14
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
12
14
PAPR (dB)
PAPR (dB)
13
11 10 9
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
13 12 11
8
10
7 6
9 0
100
200
300
400
500
1
2
3
4
(c)
5
6
7
8
9
10
Frame Index
Symbol Index 25 24
PAPR (dB)
23 22 21 q-OFDM(7,4%)
20
a-OFDM(7,4%) t-OFDM
19
f-OFDM
18 0
2000
4000
6000
8000
10000
12000
Symbol Index Fig. 5. PAPR distribution of different signals over one OFDM symbol with PRBS length 215 1 (a), PAPR distribution of different signals over one OFDM frame with PRBS length 215 1 (b) and PAPR distribution of different signals over one OFDM symbol with PRBS length 223 1 (c).
S/P
ModuDifferential lation encoding ModuDifferential lation encoding ModuAdd Training lation Symbol
DAC LPF P/S Add CP IFFT
S/P
Data
S/P
I/Q Modulator EDFA
DAC LPF
P/S
Data
P/S
S/P Remove CP FFT
P/S
DemoduDifferential lation decoding DemoduDifferential lation decoding DemoduChannel lation Estimation
ADC LPF
Balanced PIN
EDFA
Recirculation loop
For q/a-OFDM
Fiber
For f-OFDM For t-OFDM
Laser
OBPF 90° Hybrid
LO
Balanced ADC LPF PIN
Fig. 6. Simulation setup.
Table 4 System parameters. Kinds of Signal
q/a-OFDM[14]
t-OFDM
f-OFDM
Bitrate (Gbit/s) Net bitrate (Gbit/s) (7% FEC overhead)
30.2 22.3
10 log2(16) (165/256) = 25.8 25.8 (256/266)/(1 + 2%)/(1 + 7%) = 22.8
25.8 (256/266) (1 + 0.01%)/(1 + 7%) = 23.2
Optical bandwidth (GHz) Spectral efficiency (bit/s/Hz)
7.5 22.3/7.5 = 2.97
10 165/256 = 6.4 22.8/6.4 = 3.56
23.2/6.4 = 3.63
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H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249
f-OFDM t-OFDM
-0.2 -0.2
0
0 I
0.2
10 -0.2 -0.2
0 I
q-OFDM
0.2
5
9
Q
a-OFDM
-5
Q
8
0
t-OFDM
2
f-OFDM
1
2
2 1 0 -1 -2
q-OFDM(7,4%) a-OFDM(7,4%)
0
0.2
Q
Q 2 Factor (dB)
Q
f-OFDM
11
q-OFDM(7,4%) a-OFDM(7,4%) a-OFDM(0,0)
Q Factor Penalty (dB)
t-OFDM 0.2
12
-5
0 I
5
0 -2 -1 0 1 2 I
7 12
13
14
15
8500
16
theoretical OSNR is the joint results of the CP length, virtual carriers and overheads. The number of pilot subcarriers for data is fixed throughout this paper. Given a fixed net rate and no phase noise, a-OFDM (7, 4%) with additional pilot subcarriers requires more average power to achieve the same performance as a-OFDM (0, 0) (a-OFDM without pilot subcarriers and training symbols), resulting in high OSNR at a certain Q2 factor. There is about 2.2 dB differential encoding induced penalty for d-OFDM compared with a-OFDM (0, 0) (@BER = 1 103). The Q2 factor advantage of q-OFDM is mainly due to the maximized average Euclidean distance (AED) between each constellation point.
34000
2
Fig. 8. Q factor penalty versus accumulated CD. (OSNR = 15 dB/0.1 nm).
12
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM
11
Q 2 Factor (dB)
Fig. 7. Q factor versus receiver OSNR in back-to-back case.
25500
CD Tolarence (ps/nm)
OSNR (dB/0.1nm) 2
17000
f-OFDM
10
9
8
4.2. Performance evaluation under CD effect 7
The tolerance of three kinds of modulation formats to accumulated CD is evaluated by transmitting optical OFDM signals over fiber with only CD effect. Q2 factor penalty is defined as the difference of Q2 factor without and with CD effect at OSNR = 15 dB/ 0.1 nm. Fig. 8 shows that when the accumulated CD equals to 34,000 ps/nm, the Q2 factor penalty of f-OFDM is about 0.5 dB larger than q-OFDM, while penalty difference between t-OFDM and q-OFDM is less than 0.1 dB. The reason is that for f-OFDM the differential encoding among adjacent subcarriers makes it more sensitive to the phase differences induced by accumulated CD. The minor advantage of q-OFDM over t-OFDM and a-OFDM is due to the maximized AED.
Launch Power (dBm) Fig. 9. Q2 factor versus launch power after 640 km, 720 km, 800 km transmission.
the launch power keeps increasing. This is also due to the limited AED between each constellation point of APSK format. Still, a/dOFDM outperforms q-OFDM in the nonlinearity dominated range, showing higher tolerance towards SPM (self-phase modulation) and XPM (cross-phase modulation) effect. In addition, as neither pilot subcarrier nor training symbol is used, the spectral efficiency
4.3. Performance evaluation under SPM and XPM effect 12
11
Q 2 Factor (dB)
Fig. 9 shows the intra-channel nonlinearity tolerance of four kinds of signals over 640 km, 720 km, 800 km transmission. The results of the center channel from 5-channel 50-GHz spaced WDM system are shown in Fig. 10. Except different transmitted data, all the five channels are with the same signal parameters and same state of polarization. It could be seen that the performance of d-OFDM is similar to a-OFDM, which proves the advantage comes from the low PAPR of APSK format, so the curves of a-OFDM (7, 4%) and f-OFDM are thin for clear comprehension. After 640 km transmission, the optimal launch power and the corresponding Q2 factor of a/d-OFDM are 2 dB and 0.5 dB higher than q-OFDM respectively in both single-channel condition and WDM condition. When the launch power is low where ASE noise is dominated, the performance of q-OFDM is better than a/d-OFDM, as illustrated in Fig. 7. When the launch power is high where the nonlinear effect dominates, the performance of q-OFDM declines. However, the performance of a/d-OFDM degrades faster than q-OFDM when
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
10
9
8
7
Launch Power per Channel (dBm) Fig. 10. Q2 factor of the center channel versus launch power per channel after 640 km, 720 km, 800 km transmission.
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H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249
of t-OFDM and f-OFDM is increased by 20% [(3.56 2.97)/2.97, as shown in Table 4] and 22% [(3.63 2.97)/2.97], while the net bitrate is increased by 2% [(22.8 22.3)/22.3] and 4% [(23.2 22.3)/22.3]respectively. The accumulated CD, which increases with the transmission distance and the bitrate, will decrease the peak power of the signal, thus the advantage of a/d-OFDM – low PAPR – will be reduced. As the Q2 factor benefit of a/d-OFDM depends on the trade-off between the low PAPR and limited AED, there are appropriate ranges of launch power and bit rate for a/d-OFDM. Further simulation results show the Q2 factor advantage of a/d-OFDM over q-OFDM is 0.5 dB, 0.4 dB, 0.3 dB, 0.2 dB, 0.15 dB and 0.06 dB respectively after 640 km, 720 km, 800 km, 880 km, 960 km and 1040 km single-channel transmission.
Table 5 Q2 factor penalty compared with a-OFDM (@linewidth = 100 kHz). Kinds of signal
Q2 factor penalty in the back-to-back case (no ASE)
Q2 factor penalty after 800 km transmission (launch power is 9 dB m)
t-OFDM f-OFDM
1.3 0.3
0.6 0.3
symbols in [25]. The training symbols could be used for synchronization, frequency offset estimation and polarization demultiplexing. In this way, the advantage of no need for apriori knowledge disappears, but the training symbol or the pilot subcarrier overhead still could be reduced due to the differential relation. Future work will focus on the solutions in the PDM system.
4.4. Performance comparison under laser linewidth 5. Conclusions The Q2 factor versus linewidth of lasers in the transmitter and the receiver of a/d-OFDM is shown in Fig. 11. The calculated Q2 factor penalties of t-OFDM and f-OFDM compared with a-OFDM, when the linewidth of laser in the transmitter and the receiver are both 100 kHz, are shown in Table 5. As could be seen from Fig. 11, t-OFDM and f-OFDM can relax the needs for pilot subcarriers, so the whole comparison in the paper is carried out between a-OFDM (7, 4%) (rather than a-OFDM (0, 0)) and d-OFDM.As can be seen from Eq. (5), t-OFDM is suitable if the channel changes little between two adjacent OFDM symbols. The first OFDM symbol performs like a training symbol, so the CD effect has little influence on t-OFDM. Although the laser linewidth will induce extra penalty, this penalty is only 0.6 dB after 800 km transmission. On the other hand f-OFDM is suitable if the channel changes little between two adjacent OFDM subcarriers. The first subcarrier is similar to a pilot subcarrier, so the laser phase noise has little influence on f-OFDM. Although the CD effect could decrease its performance, f-OFDM still performs well after transmission (as shown in Figs. 9 and 10). In practical system, synchronization and frequency offset compensation are needed, but this could be accomplished through blind estimation using cyclic prefix or zero virtual subcarriers [23,24], making the d-OFDM free from apriori knowledge like training symbols and pilot subcarriers. Besides, as RF pilot insertion method [14] is independent of the OFDM signal generation process, it is anticipated that the tolerance of DAPSK modulated OFDM signals towards fiber nonlinearity will be further increased with this method. t-OFDM and f-OFDM could be used in polarization division multiplexing (PDM) system using the training
11 a-OFDM(7,4%)
10
a-OFDM(165,4%)
Q 2 Factor (dB)
t-OFDM
9
f-OFDM
8 7 6 5 4 100
150
200
250
300
350
400
Linewidth (kHz) Fig. 11. Q2 factor versus laser linewidth of a/d-OFDM in back-to-back case and 800 km transmission.
Differential encoding has been introduced to APSK modulated CO-OFDM system to increase the tolerance towards fiber nonlinearity and release the need for channel estimation. Two kinds of DAPSK modulated OFDM signals can be generated according to different differential directions. Simulations are based on singlepolarization system. The results indicate that 16DAPSK modulated OFDM signal could achieve similar performance to 16APSK modulated OFDM signal towards fiber nonlinearity. The optimal launch power and the corresponding Q2 factor of 16(D)APSK modulated OFDM signal are respectively 2 dB and 0.5 dB higher than that of 16QAM modulated OFDM signal after 640 km transmission in both single-channel and WDM condition These advantages stem from the APSK modulation format, but DAPSK modulated OFDM signal relaxes the needs for training symbols and pilot subcarriers and consequently increases the spectral efficiency. This differential technique will also be helpful in direct detection system such as passive optical network. Acknowledgments This work was partly supported by NSFC Program 60932004, 61001121, 61006041, 973 Program 2011CB301702, 863 Program 2012AA011303, the Fundamental Research Funds for the Central Universities, China Scholarship Council. References [1] W. Shieh, H. Bao, Y. Tang, Coherent optical OFDM: theory and design, Opt. Express 16 (2008) 841–859. [2] J. Zhao, A. Ellis, Transmission of 4-ASK Optical fast OFDM with chromatic dispersion compensation, Photon. Technol. Lett. 24 (2012) 34–36. [3] J. Zhao, S.K. Ibrahim, D. Rafique, P. Gunning, A.D. Ellis, Symbol synchronization exploiting the symmetric property in optical fast OFDM, Photon. Technol. Lett. 23 (2011) 594–596. [4] P. Wei-Ren, T. Koki, M. Itsuro, T. Hidenori, T. Hideaki, Scattered pilot channel tracking method for PDM-CO-OFDM transmissions using polar-based intrasymbol frequency-domain average, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OWE6. [5] Q. Yang, H. Zhixue, L. Wu, Y. Zhu, Y. Shaohua, W. Shieh, I.B. Djordjevic, 1-Tb/s large girth LDPC-coded coherent optical OFDM transmission over 1040-km standard single-mode fiber, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference, 2011, p. JThA35. [6] C.T. Lin, C. Jyehong, W. Jiang Jr., H. Li-Ying Wang, S. Po-Tsung, H. Chun-Hung, C. Sien, Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and adaptive OFDM formats, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OThJ6. [7] D. Qian, F. Shu-Hao, N. Cvijetic, J. Hu, T. Wang, 64/32/16QAM-OFDM using direct-detection for 40G-OFDMA-PON downstream, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OMG4. [8] X. Liu, Q. Yang, S. Chandrasekhar, W. Shieh, Transmission of 44-Gb/s coherent optical OFDM signal with trellis-coded 32-QAM subcarrier modulation, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2010, p. OMR3.
H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249 [9] Y. Tang, W. Shieh, B.S. Krongold, Fiber nonlinearity mitigation in 428-Gb/s multiband coherent optical OFDM systems, in: OFC, 2010, p. JThA6. [10] Y. London, D. Sadot, Nonlinear effects mitigation in coherent optical OFDM system in presence of high peak power, J. Lightw. Technol. 29 (2011) 3275– 3281. [11] P. Jie, C. Chi-Hao, Nonlinear electrical compensation for the coherent optical OFDM system, J. Lightw. Technol. 29 (2011) 215–221. [12] X. Liu, F. Buchali, Improved nonlinear tolerance of 112-Gb/s PDM-OFDM in dispersion-uncompensated transmission with efficient channel estimation, in: European Conference on Optical Communication (ECOC), 2008, p. Mo.3.E.2. [13] L.B. Du, A.J. Lowery, Improved nonlinearity precompensation for long-haul high-data-rate transmission using coherent optical OFDM, Opt. Express 16 (2008) 19920–19925. [14] S.L. Jansen, I. Morita, T.C.W. Schenk, N. Takeda, H. Tanaka, Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF, J. Lightw. Technol. 26 (2008) 6–15. [15] H. Wang, Y. Li, X. Yi, D. Kong, J. Wu, J. Lin, APSK modulated CO-OFDM system with increased tolerance towards fiber nonlinearity, Photon. Technol. Lett. 24 (13) (2012) 1085–1087. [16] H. Rohling, V. Engels, Differential amplitude phase shift keying (DAPSK) – a new modulation method for DTVB, in: Roadcasting Convention International, 1995, pp. 102–108.
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[17] T. Ekawit, K. Magnus, A. Erik, A. Peter, Performance comparison between 120 Gbit/s RZ-DQP-ASK and RZ-D8PSK over a 480 km link, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OMI5. [18] R.D.J.V. Nee, R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, 2000. [19] J.E. Mitchell, Performance of OFDM at 5.8 GHz using radio over fibre link, Electron. Lett. 40 (2004) 1353. [20] J.G. Proakis, Digital Communications, 2000. [21] D. Xiaodai, N.C. Beaulieu, P.H. Wittke, Error probabilities of two-dimensional M-ary signaling in fading, IEEE Trans. Commun. 47 (1999) 352–355. [22] B. Eitel, J. Speidel, Speed-optimized soft-decision demodulation of multilevel DAPSK, in: International Conference on Consumer Electronics, 2006. ICCE ’06, 2006 Digest of Technical Papers, 2006, pp. 469–470. [23] J.J. van de Beek, M. Sandell, P.O. Borjesson, ML estimation of time and frequency offset in OFDM systems, IEEE Trans. Signal Process. 45 (1997) 1800– 1805. [24] Y. Qiao, Z. Wang, Y. Ji, Blind frequency offset estimation based on cyclic prefix and virtual subcarriers in CO-OFDM system, Chin. Opt. Lett. 8 (2010) 888–893. [25] S.L. Jansen, I. Morita, T.C.W. Schenk, H. Tanaka, Long-haul transmission of 16 52.5 Gbits/s polarization-division-multiplexed OFDM enabled by MIMO processing (invited), J. Opt. Netw. 7 (2008) 173–182.
Contents lists available at SciVerse ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Performance evaluation of (D)APSK modulated coherent optical OFDM system Hui Wang ⇑, Deming Kong, Yan Li, Jian Wu, Jintong Lin State Key Laboratory of Information Photonics & Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
a r t i c l e
i n f o
Article history: Received 26 September 2012 Revised 5 February 2013 Available online 6 March 2013 Keywords: Orthogonal frequency-division multiplexing (OFDM) Amplitude and phase shift keying (APSK) Quadrature amplitude modulation (QAM) Fiber nonlinearity
a b s t r a c t Performance of amplitude and phase shift keying (APSK) modulated coherent optical orthogonal frequency division multiplexing (CO-OFDM) with and without differential encoding is investigated. Numerical simulations based on 40 Gbit/s single-channel and 5 40 Gbit/s wavelength division multiplexing transmission are performed, and the impacts of amplified spontaneous emission noise, laser linewidth, chromatic dispersion, and fiber nonlinearity on the system performance are analyzed. The results show that compared with conventional 16 quadrature amplitude modulation (QAM) modulated optical OFDM signal, although 16(D)APSK modulated optical OFDM signal has a lower tolerance towards amplified spontaneous emission (ASE) noise, it has a higher tolerance towards fiber nonlinearity such as self-phase modulation (SPM) and cross-phase modulation (XPM): the optimal launch power and the corresponding Q2 factor of 16(D)APSK modulated OFDM signal are respectively 2 dB and 0.5 dB higher than 16QAM modulated optical OFDM signal after 640 km transmission, both in single-channel and WDM CO-OFDM systems. Although the accumulated CD decreases the peak-to-average power ratio (PAPR) during transmission, 16(D)APSK modulated OFDM signal will still remain an advantage compared with 16QAM modulated OFDM signal up to 1000 km single-channel transmission, meanwhile relaxing the needs for training symbols and pilot subcarriers and consequently increase the spectral efficiency. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Coherent optical orthogonal frequency division multiplexing (CO-OFDM) system [1–3] has found widespread applications due to its high spectral efficiency and ability to overcome transmission impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD). Most CO-OFDM signals utilize quadrature amplitude modulation (QAM) formats such as 16QAM [4–6] and 32QAM [7,8] nowadays. However, fiber nonlinearity greatly limits the performance of OFDM signals [9–11] due to large peak-to-average power ratio (PAPR). In order to improve the tolerance towards fiber nonlinearity, extensive researches have been carried out, such as compensation algorithms at the receiver [12], pre-process at the transmitter [13], and radio frequency pilot (RFP) insertion [14], which to some extent makes the transceiver complex and costly. Besides these techniques, modulation format with decreased PAPR – amplitude and phase shift keying (APSK) – is proposed in Ref. [15], to increase fiber nonlinearity tolerance of OFDM signal, while keeping the overall complexity and cost. But such modulation format, like QAM, is memoryless, so apriori knowledge such as training symbols and pilot subcarriers is required to realize channel estimation and channel equalization at the receiver. However, training symbols would decrease the bitrate and pilot subcarriers ⇑ Corresponding author. Fax: +86 10 62282303. E-mail address: [email protected] (H. Wang). 1068-5200/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2013.02.003
would occupy extra spectrum resources. As a result, a modification in the generation of OFDM signal with decreased PAPR and reduced overhead is of significance for future OFDM system. In this paper, differential APSK (DAPSK) is introduced in CO-OFDM system. DAPSK is first proposed in Ref. [16] for digital terrestrial video broadcasting (DTVB) applications and has already found applications in single-channel optical communication system [17], but to the best of the authors’ knowledge, it has not been employed in optical OFDM system yet. In this paper, we extend theoretical investigation on the origin of the advantage of APSK modulated OFDM signal and induce differential relation into APSK modulated OFDM signal. We thoroughly investigate differentially modulated APSK CO-OFDM systems (differential encoding/decoding in both the time domain and the frequency domain) and compare them with conventional QAM modulated CO-OFDM under the influences of different systems penalties including amplified spontaneous emission (ASE), laser linewidth, CD and fiber nonlinearity. Since 16QAM has been widely used in CO-OFDM system, a comparison with 16DAPSK is carried out through simulation. Various results indicate that 16DAPSK modulated OFDM signal (d-OFDM) inherits the low PAPR of 16APSK modulated OFDM signal (a-OFDM), thus performs higher nonlinearity tolerance than 16QAM modulated OFDM signal (q-OFDM). The optimal launch power and corresponding Q2 factor of a/d-OFDM are respectively 2 dB and 0.5 dB higher than q-OFDM after 640 km transmission, both in single-polarization, single-channel and
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... ...
...
...
...
2. Generation principles of 16QAM and 16(D)APSK
...
In either 16QAM or 16APSK modulation, one symbol represents four bits (b0, b1, b2, b3). In this paper, as shown in Table 1, for 16QAM modulation, the first two bits are used for the generation of in-phase component (I) and the last two are used for the generation of quadrature component (Q), the generated symbol is I + jQ; while for APSK modulation, the first three bits are used for the generation of phase component (u) and the last one is used for the generation of amplitude component (A), the generated symbol is Aeju. The corresponding constellations of 16QAM and 16APSK are shown in Fig. 1. Differential encoding is done after APSK modulation. Since differential encoding can be applied either in time domain or in frequency domain, two types of d-OFDM can be generated. If differential encoding is processed on the same subcarrier of adjacent OFDM symbols, the d-OFDM is termed as t-OFDM (‘t’ represents time domain); if differential encoding is processed on different subcarriers of the same OFDM symbol, the d-OFDM is termed as f-OFDM (‘f’ represents frequency domain). After APSK modulation, complex value Bi;k ¼ Ai;k expðjui;k Þ can be obtained, which represent the symbol on the ith interval at the kth subcarrier. Then, the complex value after differential encoding Si;k ¼ V i;k expðjhi;k Þ can be described as follows:
Si;k ¼ Bi;k Si1;k
for t OFDM
ð1Þ
Si;k ¼ Bi;k Si;k1
for f OFDM
ð2Þ
The operator ‘‘.’’ represents the differential calculation. Fig. 2 illustrates differential directions of t-OFDM and f-OFDM. The differential encoding is carried out for the amplitude component and phase
Table 1 Generation principles of 16QAM (left) and 16APSK (right). b0b1
I
b2b3
Q
b0b1b2
u
b3
A
10
+3
10
+3
000 001
0
0
1
1
2
p/4
11
+1
11
+1
011 010
p/2 3p/4
01
1
01
1
110 111
5p/4
101 100
3p/2 7p/4
00
3
00
3
p
...
Frequency
Direction of t-OFDM Symbol-to-be-discarded
OFDM Subcarrier Interval
Frequency
Fig. 1. Constellations of 16QAM (left) and 16APSK (right).
OFDM Subcarrier Interval
single-polarization, 5-channel wavelength-division-multiplexing (WDM) CO-OFDM systems. It is also found that along with an increased transmission distance, the advantage is slightly neutralized due to accumulated CD which leads to a reduced PAPR difference between a/d-OFDM and q-OFDM. However, the Q2 factor of a/dOFDM signal will still remain an advantage up to 1000 km transmission, making them promising candidate for metro network applications. Besides, as no apriori knowledge is needed for d-OFDM, the spectral efficiency is increased by at least 20% and the net bitrate is increased by at least 2% with reduced computation complexity in this paper. These advantages make d-OFDM not only an attractive technique in CO-OFDM system but also helpful in direct detection system such as passive optical network. The rest of this paper is organized as follows: the generation principles of 16QAM, 16APSK modulation formats and the differential encoding process are given in Section 2. Two kinds of d-OFDM are discussed. In Section 3, we provide the analysis of PAPR of different modulation formats modulated OFDM signal and the origin of low PAPR of (D)APSK modulated OFDM signal. The simulation setup and impairments influence on different OFDM signals are discussed in Section 4 before the conclusion is drawn in Section 5.
Direction of f-OFDM Symbol-to-be-discarded
... ...
...
...
... ... Time
Time
OFDM Symbol Interval
...
OFDM Symbol Interval
Fig. 2. Differential directions and positions of discarded symbols for t-OFDM (left) and f-OFDM (right).
component independently. The constellation remains the same after differential encoding. Take 16DAPSK of t-OFDM for example, the phase component after differential encoding is
hi;k ¼ modðui;k þ hi1;k ; 2pÞ
ð3Þ
where mod(x, y) is to get the remainder after x is divided by y. And the amplitude component after differential encoding is
if Ai;k – V i1;k ; V i;k ¼ 2;
else V i;k ¼ 1:
ð4Þ
Since an additional differential encoding process is required, the modulation of DAPSK is a little more complicated than that of QAM or APSK. However, the demodulation of DAPSK is comparatively easy:
Ri;k Si;k Hi;k Hi;k ¼ ¼ Bi:k Ri1;k Si1;k Hi1;k Hi1;k Ri;k Si;k Hi;k Hi;k ¼ ¼ ¼ Bi:k Ri;k1 Si;k1 Hi;k1 Hi;k1
Di;k ¼
for t OFDM
ð5Þ
Di;k
for f OFDM
ð6Þ
where H, R and D represent the channel transfer coefficient, the received signal, and the differential demodulated signal, respectively. As a result, for t-OFDM, if the channel is quasi-stationary during two symbols, then Hi,k = Hi1,k; and for f-OFDM, if the channel is quasistationary during two subcarriers, then Hi,k = Hi,k1. In either case, Di,k = Bi,k is obtained, so that ideal demodulation can be realized. Obviously, correlation induced by differential encoding between successive symbols or subcarriers can greatly simplify the demodulation process. As a result, neither explicit knowledge about channel properties nor a separate channel estimation procedure is necessary at the receiver, which reduces the computation complexity to a large extent. However, although no apriori knowledge is needed for d-OFDM, there is redundant information due to the differential demodulation: the first OFDM symbol should be discarded for t-OFDM and the data symbol carried on the first subcarrier of the first OFDM symbol should be discarded for f-OFDM, as shown in Fig. 2.
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H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249
The difference D between PAPRq-OFDM and PAPRa-OFDM is
D ¼ 10 log10
The PAPR of OFDM signal s(t) is defined as
PAPR ¼
maxfjsðtÞj2 g
ð7Þ
EfjsðtÞj2 g
According to Ref. [18], cumulative distribution function (CDF) Pc is used to characterize PAPR, which represents the probability that the PAPR is more than a certain value x.
Pc ¼ PrfPAPR > xg
ð8Þ
3.1. Theoretical analysis of PAPR of q-OFDM and a-OFDM As is well known, the average power of a signal over T time interval could be expressed as
8 2 9 = N <1 Z T X P av e ¼ E ðai;k cosðxk tÞ þ bi;k sinðxk tÞÞ dt ; :T 0 i¼1 ( ) N 1X 2 a2i;k þ bi;k ¼E 2 i¼1
ð9Þ
where ai,k, bi,k represent the ith in-phase and quadrature data carried on the kth subcarrier respectively and xk represents the angular frequency of the kth subcarrier, N is the total number of subcarriers that carry data. Then the average power of q-OFDM and a-OFDM are
1 1 Pav e 16QAM ¼ N P0 16QAM þ ð3Þ2 P0 16QAM 2 2 1 ¼ 5NP0 16QAM þN P 0 16QAM þ ð3Þ2 P0 16QAM 2 P av e
( ) N 1X 2 ¼E r 2 i¼1 i;k 1 1 ¼ N P0 2 2
16APSK
¼ 5NP0 where P 0
16QAM
16APSK
þ ð2Þ2 P0
16APSK
ð11Þ
16APSK =4
and P 0
APSK
ð10Þ
The baseband OFDM signal is generated by a MATLAB program from a 215 1 pseudorandom binary sequence (PRBS) unless otherwise stated. The IFFT size is 256, from which 165 subcarriers are used for useful data transmission. The signal structure of q-OFDM and a-OFDM before IFFT is shown in Fig. 3. Details of pilot subcarriers and training symbols used for q-OFDM and a-OFDM are shown in Table 2. There are 63 (for q-OFDM and a-OFDM)/91 (for d-OFDM) virtual subcarriers located in the outer part of the spectrum for zero padding. The signal is oversampled four times to sufficiently evaluate the PAPR. About 500 OFDM symbols have been evaluated per measurement point. The theoretical maximum PAPR and calculated maximum PAPR is shown in Table 3. Numbers in brackets represent the interval of pilot subcarriers and training overhead used for qOFDM and a-OFDM. In the analyses of Part A, Pmax is calculated under the condition that all symbols are the same constellation point with the largest amplitude. But in fact, the symbols are randomly distributed, so the actual Pmax is much lower than the theoretical value, which in turn makes the calculated maximum PAPR much lower than the theoretical maximum PAPR. This could be seen from Fig. 4a, where the CDFs of PAPR for different OFDM signals with PAPR length of 215 1 is shown. If the PRBS length is increased to 223 1, as shown in Table 3, the calculated PAPR value after four times oversampling is more approached to the theoretical value. However, the differences between the maximum PAPR of q-OFDM and a-OFDM or d-OFDM remain the same: about 2 dB larger. As there are only two amplitude values in the 16APSK constellation, the probability of the constellation points with large amplitude values (8/16) is lower than that of 16QAM (12/16), so the actual Pmax of a-OFDM drops more than that of q-OFDM. And this is why there is 1.5 dB difference between the calculated PAPR difference and the theoretical PAPR difference in Eq. (17). As the modulation formats are the same for a-OFDM, t-OFDM and f-OFDM, they are supposed to have the similar PAPR, which
represent the power of the signal with qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 a2i;k þ bi;k is the
Pmax
16QAM
16APSK
¼ ð3NÞ2 P0
16QAM
þ ð3NÞ2 P0
16QAM
8 2 9 = N <X ¼ ð2NÞ2 P0 ¼ max ðr i;k Þ ; : i¼1 ¼ 4N2 P0
16APSK
¼ 18N2 P 0
16QAM
ð13Þ
16APSK
ð14Þ
As a result, the theoretical maximum PAPR of q-OFDM and a-OFDM are respectively:
PAPRq-OFDM ¼
Pmax 16QAM 18 ¼ N 5 P av e 16QAM
ð15Þ
PAPRa-OFDM ¼
Pmax 16APSK 16 ¼ N 5 Pav e 16APSK
ð16Þ
OFDM Subcarrier Interval
Pmax
IFFT size
Then the maximum power of q-OFDM and a-OFDM are
Virtual subcarriers
ð12Þ
Pilot subcarrier interval
amplitude of the symbol carried on the kth subcarrier. The maximum power of a signal is expressed as
Pmax
ð17Þ
3.2. Parameters settings
the smallest amplitude in the constellation, r i;k ¼
8 2 9 <X N = ¼ max a cosðxk tÞ þ bi;k sinðxk tÞ ; : i¼1 i;k
PAPRq-OFDM ¼ 0:5 dB PAPRa-OFDM
Frequency
3. PAPR analysis
Data Symbol
Training Symbol Pilot Subcarrier
...
...
...
...
...
...
...
...
...
...
...
...
2 training symbols
Zero Subcarrier ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
...
...
Time
OFDM Symbol Interval 50 OFDM symbols
Fig. 3. Signal structure of q-OFDM and a-OFDM before IFFT.
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H. Wang et al. / Optical Fiber Technology 19 (2013) 242–249 Table 2 Details of pilot subcarriers and training symbols. Name
Place
Function
Number
Modulation formats
Pilot subcarriers
Periodically inserted At the beginning
Common phase error compensation Channel estimation (time domain averaging algorithm)
Pilot interval (the number of subcarriers between adjacent pilot subcarriers) is 7, so the number of pilot subcarrier is 28 Training overhead (the ratio between training symbol number and data symbol number) is 4%
Same modulation formats with the data symbol
Training symbols
Table 3 PAPR values of different signals. Kinds of signal
Theoretical maximum PAPR (dB)
q-OFDM (7, 4%) a-OFDM (7, 4%) t-OFDM f-OFDM
Calculated maximum PAPR (dB)
28.4 27.9 27.2
(a) 1.0
(b)
PRBS length: 223 1
14 12
24.8 22.8
1 0.9
0.9 0.8
Probability, X <=x
Probability, X <= x
PRBS length: 215 1
1.00
0.7 0.6
0.98
0.5 0.4
0.96
0.3
10
0.2
12
14
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
0.1 0.0 6
7
8
9
10
0.8 0.7 0.6
q-OFDM(7,4%)
0.5
a-OFDM(7,4%)
0.4
t-OFDM
0.3
f-OFDM
0.2 0.1 0
11
12
13
14
15
PAPR, x dB
13
14
15
16
17
18
19
20
21
22
23
24
25
PAPR, x dB
Fig. 4. CDFs of PAPR of different signals with PRBS length 215 1 (a) and 223 1 (b).
could be further confirmed in Fig. 5a. The figure shows the PAPR distribution of all the symbols of the four signals. Distribution of PAPR over 50 symbols (one frame) is shown in Fig. 5b, which indicates the PAPR of (D)APSK modulated OFDM signal is much lower than q-OFDM. PAPR distribution over one symbol for long PAPR length of 223 1 is shown in Fig. 5c, showing similar phenomena with short PAPR length. 4. Simulations, results and discussion VPI Transmission Maker™ is used to evaluate the performance of different OFDM signals. The simulation setup is shown in Fig. 6, where the differences among the generation of t-OFDM, f-OFDM, a-OFDM and q-OFDM could be found. The length of cyclic prefix (CP) for every OFDM symbol is 10 samples. The sampling rate of DAC is set to 10 GS/s, so the total bitrate (including zero subcarriers and all the other information) is 40 Gb/s. The sampling rate of ADC is the same as DAC. System parameters are calculated in Table 4. It should be noted that as 50 OFDM symbols are simulated each time, the ‘‘differential overhead’’ for t-OFDM is regarded as 2% (1/50), while the ‘‘differential overhead’’ for f-OFDM is regarded as 0.01% (1/(50 165 1)). The baseband OFDM signal is processed by a square root raised cosine filter with a roll-off factor 0.18 in order to remove aliasing products and then transformed to optical domain using an I/Q modulator. Only one polarization is considered. The linewidth of lasers is assumed to be 0 unless otherwise stated. The transmission
link includes a power controlled EDFA and a recirculating loop. The loop has an 80 km standard single mode fiber (SSMF) and a gain controlled EDFA. The fiber parameters are: DSSMF = 17 ps/nm/km, aSSMF = 0.2 dB/km, cSSMF = 1.3 W1 km1. The gain controlled EDFA with a noise figure of 4.5 dB is used to compensate the fiber loss. At the receiver, a 2nd order Gaussian-shaped optical band-pass filter (OBPF) with a bandwidth of 20 GHz is used to filter out ASE noise. The coherent detector consists of a local oscillator (LO), a 90° hybrid, and two balanced detectors. Then the electrical signal is filtered out and processed with a MATLAB program. 4.1. Performance evaluation under ASE noise Fig. 7 depicts the Q2 factor against the optical signal-to-noise ratio (OSNR) of the four received OFDM signals under back-to-back (B2B) configuration. The OSNR is defined with the common 0.1-nm noise bandwidth. To achieve a Q2 factor of 9.8 dB (BER = 1 103), the required OSNR values for q-OFDM, a-OFDM, t-OFDM and f-OFDM signals are 14 dB, 15.3 dB, 15.2 dB, 15.2 dB respectively. The corresponding constellations are shown in the insets of Fig. 7. The scattering effect of q-OFDM and a-OFDM is due to the one-tap equalization, which could found in Ref. [19]. Theoretical SNR of 16QAM, 16APSK and 16DAPSK modulated system could be calculated according to Refs. [20–22] respectively. The converted theoretical OSNR requirements of 40 Gbit/s optical system are 12.5 dB (q-OFDM), 13.8 dB (a-OFDM) and 14 dB (d-OFDM), respectively. The difference b etween simulation results and
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(a)
(b) 15
15 14
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
12
14
PAPR (dB)
PAPR (dB)
13
11 10 9
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
13 12 11
8
10
7 6
9 0
100
200
300
400
500
1
2
3
4
(c)
5
6
7
8
9
10
Frame Index
Symbol Index 25 24
PAPR (dB)
23 22 21 q-OFDM(7,4%)
20
a-OFDM(7,4%) t-OFDM
19
f-OFDM
18 0
2000
4000
6000
8000
10000
12000
Symbol Index Fig. 5. PAPR distribution of different signals over one OFDM symbol with PRBS length 215 1 (a), PAPR distribution of different signals over one OFDM frame with PRBS length 215 1 (b) and PAPR distribution of different signals over one OFDM symbol with PRBS length 223 1 (c).
S/P
ModuDifferential lation encoding ModuDifferential lation encoding ModuAdd Training lation Symbol
DAC LPF P/S Add CP IFFT
S/P
Data
S/P
I/Q Modulator EDFA
DAC LPF
P/S
Data
P/S
S/P Remove CP FFT
P/S
DemoduDifferential lation decoding DemoduDifferential lation decoding DemoduChannel lation Estimation
ADC LPF
Balanced PIN
EDFA
Recirculation loop
For q/a-OFDM
Fiber
For f-OFDM For t-OFDM
Laser
OBPF 90° Hybrid
LO
Balanced ADC LPF PIN
Fig. 6. Simulation setup.
Table 4 System parameters. Kinds of Signal
q/a-OFDM[14]
t-OFDM
f-OFDM
Bitrate (Gbit/s) Net bitrate (Gbit/s) (7% FEC overhead)
30.2 22.3
10 log2(16) (165/256) = 25.8 25.8 (256/266)/(1 + 2%)/(1 + 7%) = 22.8
25.8 (256/266) (1 + 0.01%)/(1 + 7%) = 23.2
Optical bandwidth (GHz) Spectral efficiency (bit/s/Hz)
7.5 22.3/7.5 = 2.97
10 165/256 = 6.4 22.8/6.4 = 3.56
23.2/6.4 = 3.63
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f-OFDM t-OFDM
-0.2 -0.2
0
0 I
0.2
10 -0.2 -0.2
0 I
q-OFDM
0.2
5
9
Q
a-OFDM
-5
Q
8
0
t-OFDM
2
f-OFDM
1
2
2 1 0 -1 -2
q-OFDM(7,4%) a-OFDM(7,4%)
0
0.2
Q
Q 2 Factor (dB)
Q
f-OFDM
11
q-OFDM(7,4%) a-OFDM(7,4%) a-OFDM(0,0)
Q Factor Penalty (dB)
t-OFDM 0.2
12
-5
0 I
5
0 -2 -1 0 1 2 I
7 12
13
14
15
8500
16
theoretical OSNR is the joint results of the CP length, virtual carriers and overheads. The number of pilot subcarriers for data is fixed throughout this paper. Given a fixed net rate and no phase noise, a-OFDM (7, 4%) with additional pilot subcarriers requires more average power to achieve the same performance as a-OFDM (0, 0) (a-OFDM without pilot subcarriers and training symbols), resulting in high OSNR at a certain Q2 factor. There is about 2.2 dB differential encoding induced penalty for d-OFDM compared with a-OFDM (0, 0) (@BER = 1 103). The Q2 factor advantage of q-OFDM is mainly due to the maximized average Euclidean distance (AED) between each constellation point.
34000
2
Fig. 8. Q factor penalty versus accumulated CD. (OSNR = 15 dB/0.1 nm).
12
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM
11
Q 2 Factor (dB)
Fig. 7. Q factor versus receiver OSNR in back-to-back case.
25500
CD Tolarence (ps/nm)
OSNR (dB/0.1nm) 2
17000
f-OFDM
10
9
8
4.2. Performance evaluation under CD effect 7
The tolerance of three kinds of modulation formats to accumulated CD is evaluated by transmitting optical OFDM signals over fiber with only CD effect. Q2 factor penalty is defined as the difference of Q2 factor without and with CD effect at OSNR = 15 dB/ 0.1 nm. Fig. 8 shows that when the accumulated CD equals to 34,000 ps/nm, the Q2 factor penalty of f-OFDM is about 0.5 dB larger than q-OFDM, while penalty difference between t-OFDM and q-OFDM is less than 0.1 dB. The reason is that for f-OFDM the differential encoding among adjacent subcarriers makes it more sensitive to the phase differences induced by accumulated CD. The minor advantage of q-OFDM over t-OFDM and a-OFDM is due to the maximized AED.
Launch Power (dBm) Fig. 9. Q2 factor versus launch power after 640 km, 720 km, 800 km transmission.
the launch power keeps increasing. This is also due to the limited AED between each constellation point of APSK format. Still, a/dOFDM outperforms q-OFDM in the nonlinearity dominated range, showing higher tolerance towards SPM (self-phase modulation) and XPM (cross-phase modulation) effect. In addition, as neither pilot subcarrier nor training symbol is used, the spectral efficiency
4.3. Performance evaluation under SPM and XPM effect 12
11
Q 2 Factor (dB)
Fig. 9 shows the intra-channel nonlinearity tolerance of four kinds of signals over 640 km, 720 km, 800 km transmission. The results of the center channel from 5-channel 50-GHz spaced WDM system are shown in Fig. 10. Except different transmitted data, all the five channels are with the same signal parameters and same state of polarization. It could be seen that the performance of d-OFDM is similar to a-OFDM, which proves the advantage comes from the low PAPR of APSK format, so the curves of a-OFDM (7, 4%) and f-OFDM are thin for clear comprehension. After 640 km transmission, the optimal launch power and the corresponding Q2 factor of a/d-OFDM are 2 dB and 0.5 dB higher than q-OFDM respectively in both single-channel condition and WDM condition. When the launch power is low where ASE noise is dominated, the performance of q-OFDM is better than a/d-OFDM, as illustrated in Fig. 7. When the launch power is high where the nonlinear effect dominates, the performance of q-OFDM declines. However, the performance of a/d-OFDM degrades faster than q-OFDM when
q-OFDM(7,4%) a-OFDM(7,4%) t-OFDM f-OFDM
10
9
8
7
Launch Power per Channel (dBm) Fig. 10. Q2 factor of the center channel versus launch power per channel after 640 km, 720 km, 800 km transmission.
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of t-OFDM and f-OFDM is increased by 20% [(3.56 2.97)/2.97, as shown in Table 4] and 22% [(3.63 2.97)/2.97], while the net bitrate is increased by 2% [(22.8 22.3)/22.3] and 4% [(23.2 22.3)/22.3]respectively. The accumulated CD, which increases with the transmission distance and the bitrate, will decrease the peak power of the signal, thus the advantage of a/d-OFDM – low PAPR – will be reduced. As the Q2 factor benefit of a/d-OFDM depends on the trade-off between the low PAPR and limited AED, there are appropriate ranges of launch power and bit rate for a/d-OFDM. Further simulation results show the Q2 factor advantage of a/d-OFDM over q-OFDM is 0.5 dB, 0.4 dB, 0.3 dB, 0.2 dB, 0.15 dB and 0.06 dB respectively after 640 km, 720 km, 800 km, 880 km, 960 km and 1040 km single-channel transmission.
Table 5 Q2 factor penalty compared with a-OFDM (@linewidth = 100 kHz). Kinds of signal
Q2 factor penalty in the back-to-back case (no ASE)
Q2 factor penalty after 800 km transmission (launch power is 9 dB m)
t-OFDM f-OFDM
1.3 0.3
0.6 0.3
symbols in [25]. The training symbols could be used for synchronization, frequency offset estimation and polarization demultiplexing. In this way, the advantage of no need for apriori knowledge disappears, but the training symbol or the pilot subcarrier overhead still could be reduced due to the differential relation. Future work will focus on the solutions in the PDM system.
4.4. Performance comparison under laser linewidth 5. Conclusions The Q2 factor versus linewidth of lasers in the transmitter and the receiver of a/d-OFDM is shown in Fig. 11. The calculated Q2 factor penalties of t-OFDM and f-OFDM compared with a-OFDM, when the linewidth of laser in the transmitter and the receiver are both 100 kHz, are shown in Table 5. As could be seen from Fig. 11, t-OFDM and f-OFDM can relax the needs for pilot subcarriers, so the whole comparison in the paper is carried out between a-OFDM (7, 4%) (rather than a-OFDM (0, 0)) and d-OFDM.As can be seen from Eq. (5), t-OFDM is suitable if the channel changes little between two adjacent OFDM symbols. The first OFDM symbol performs like a training symbol, so the CD effect has little influence on t-OFDM. Although the laser linewidth will induce extra penalty, this penalty is only 0.6 dB after 800 km transmission. On the other hand f-OFDM is suitable if the channel changes little between two adjacent OFDM subcarriers. The first subcarrier is similar to a pilot subcarrier, so the laser phase noise has little influence on f-OFDM. Although the CD effect could decrease its performance, f-OFDM still performs well after transmission (as shown in Figs. 9 and 10). In practical system, synchronization and frequency offset compensation are needed, but this could be accomplished through blind estimation using cyclic prefix or zero virtual subcarriers [23,24], making the d-OFDM free from apriori knowledge like training symbols and pilot subcarriers. Besides, as RF pilot insertion method [14] is independent of the OFDM signal generation process, it is anticipated that the tolerance of DAPSK modulated OFDM signals towards fiber nonlinearity will be further increased with this method. t-OFDM and f-OFDM could be used in polarization division multiplexing (PDM) system using the training
11 a-OFDM(7,4%)
10
a-OFDM(165,4%)
Q 2 Factor (dB)
t-OFDM
9
f-OFDM
8 7 6 5 4 100
150
200
250
300
350
400
Linewidth (kHz) Fig. 11. Q2 factor versus laser linewidth of a/d-OFDM in back-to-back case and 800 km transmission.
Differential encoding has been introduced to APSK modulated CO-OFDM system to increase the tolerance towards fiber nonlinearity and release the need for channel estimation. Two kinds of DAPSK modulated OFDM signals can be generated according to different differential directions. Simulations are based on singlepolarization system. The results indicate that 16DAPSK modulated OFDM signal could achieve similar performance to 16APSK modulated OFDM signal towards fiber nonlinearity. The optimal launch power and the corresponding Q2 factor of 16(D)APSK modulated OFDM signal are respectively 2 dB and 0.5 dB higher than that of 16QAM modulated OFDM signal after 640 km transmission in both single-channel and WDM condition These advantages stem from the APSK modulation format, but DAPSK modulated OFDM signal relaxes the needs for training symbols and pilot subcarriers and consequently increases the spectral efficiency. This differential technique will also be helpful in direct detection system such as passive optical network. Acknowledgments This work was partly supported by NSFC Program 60932004, 61001121, 61006041, 973 Program 2011CB301702, 863 Program 2012AA011303, the Fundamental Research Funds for the Central Universities, China Scholarship Council. References [1] W. Shieh, H. Bao, Y. Tang, Coherent optical OFDM: theory and design, Opt. Express 16 (2008) 841–859. [2] J. Zhao, A. Ellis, Transmission of 4-ASK Optical fast OFDM with chromatic dispersion compensation, Photon. Technol. Lett. 24 (2012) 34–36. [3] J. Zhao, S.K. Ibrahim, D. Rafique, P. Gunning, A.D. Ellis, Symbol synchronization exploiting the symmetric property in optical fast OFDM, Photon. Technol. Lett. 23 (2011) 594–596. [4] P. Wei-Ren, T. Koki, M. Itsuro, T. Hidenori, T. Hideaki, Scattered pilot channel tracking method for PDM-CO-OFDM transmissions using polar-based intrasymbol frequency-domain average, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OWE6. [5] Q. Yang, H. Zhixue, L. Wu, Y. Zhu, Y. Shaohua, W. Shieh, I.B. Djordjevic, 1-Tb/s large girth LDPC-coded coherent optical OFDM transmission over 1040-km standard single-mode fiber, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference, 2011, p. JThA35. [6] C.T. Lin, C. Jyehong, W. Jiang Jr., H. Li-Ying Wang, S. Po-Tsung, H. Chun-Hung, C. Sien, Ultra-high data-rate 60 GHz radio-over-fiber systems employing optical frequency multiplication and adaptive OFDM formats, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OThJ6. [7] D. Qian, F. Shu-Hao, N. Cvijetic, J. Hu, T. Wang, 64/32/16QAM-OFDM using direct-detection for 40G-OFDMA-PON downstream, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011, p. OMG4. [8] X. Liu, Q. Yang, S. Chandrasekhar, W. Shieh, Transmission of 44-Gb/s coherent optical OFDM signal with trellis-coded 32-QAM subcarrier modulation, in: Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2010, p. OMR3.
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