None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying

doi:10.1364/OE.20.022878

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None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying

Bo Liu, Lijia Zhang, Xiangjun Xin, and Jianjun Yu »View Author Affiliations

Optics Express, Vol. 20, Issue 20, pp. 22878-22885 (2012)
http://dx.doi.org/10.1364/OE.20.022878

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– Abstract
1. Introduction
2. Principle
3. Experimental setup and results
4. Conclusion
– References and links

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Abstract

This paper proposes a novel none pilot-assisted orthogonal frequency division multiplexing (OFDM) technology based on multi-differential amplitude phase shift keying (mDAPSK) for optical OFDM system. It doesn’t require any bandwidth-consuming pilot tones or training sequence for channel estimation due to the differential detection during demodulation. In the experiment, a 41.31 Gb/s 64DAPSK-OFDM signal without pilot tones is successfully transmitted over 160-km single mode fiber (SMF). The performance comparison between multi-quadrature amplitude modulation (mQAM) and mDAPSK is also given in the experiment, and the results indicate a prospect of this technology in optical OFDM system.

1. Introduction

High speed and large capacity are required to meet with the rapid growing Internet traffic in future optical network. Recent years, orthogonal frequency division multiplexing (OFDM) technology has received much attention in optical communications system due to its promise of high spectral efficiency (SE) and the resistance to chromatic dispersion [1

W. Shieh, “OFDM for flexible high-speed optical networks,” J. Lightwave Technol. 29(10), 1560–1577 (2011). [CrossRef]

–10

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “Pre-emphasis and RF-pilot tone phase noise compensation for coherent OFDM transmission systems,” in Proc. CLEO 2007, paper. MA1.2 (2007).

]. It is attributed to the high-order modulation scheme and flexible digital signal processing (DSP) with training sequence and pilot tones. In the previous optical OFDM system, multi-quadrature amplitude modulation (mQAM) format is usually adopted as a potential way to achieve a high SE. In mQAM modulated optical OFDM system, the signal is sensitive to the phase noise during transmission, so the channel estimation and equalization are required before the mQAM demodulation [8

X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-division-multiplexed CO-OFDM in long-haul fiber transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]

–10

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “Pre-emphasis and RF-pilot tone phase noise compensation for coherent OFDM transmission systems,” in Proc. CLEO 2007, paper. MA1.2 (2007).

]. Therefore, some signaling overhead must be spent by inserting preamble or pilot tones into the transmitted data stream, which would reduce the efficient bandwidth and increase the DSP complexity at the receiver end. In conventional high speed optical OFDM signal transmission, the use of training sequence (TS) and pilots incurs excess overhead and this reduces the SE(typical 10%-20%) [11

A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-Guard-Interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. 27(16), 3705–3713 (2009). [CrossRef]

]. To avoid the influence from phase noise, differential modulation can be applied in optical OFDM system, which doesn’t need any pilot tones and can simplify the DSP at the receiver end. As a special form of differential modulation, the multi-differential amplitude phase shift keying (mDAPSK) modulation can mitigate the phase noise and reduce the system complexity due to its differential modulation on both amplitude and phase [12

N. Toender and H. Rohling, “DAPSK schemes for low-complexity OFDM systems,” IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, 735–739 (2006).

, 13

C.-C.Fang, Y.-J. Lin, S.-W. Wei, and J.-F. Chang, “Performance analyses of DAPSK in a very high mobility environment,” in Proc.WIRLES 2005, 570–575 (2005).

]. Compared with mQAM modulation, the TS and pilot tones can be eliminated, which thus improves the SE. Due to the differential coding, the correlation between adjacent subcarriers and symbols can be increased, which could mitigate the dispersion-induced interference and reduce the CP length to some extent. Less cyclic prefix (CP) and guard-band interval (GI) would further improve the SE in mDAPSK-OFDM transmission.

In this paper, we propose a novel OFDM system employing mDAPSK technology, where none pilot tones or training sequence are needed for signal demodulation. The proposed scheme can reduce the redundancy and complexity while maintaining a high SE for optical OFDM system. In our experiment, a 41.31 Gb/s 64DAPSK-OFDM signal is generated and transmitted over 160-km single mode fiber (SMF) successfully. We also compare the performance of mDAPSK-OFDM signal with mQAM-OFDM signal in the experiment.

2. Principle

Figure 1 illustrates the principle of the mDAPSK-OFDM system. The input PRBS data is fed into the mDAPSK modulation module after serial to parallel conversion. The modulation diagram of mDAPSK is illustrated in the bottom of Fig. 1. The input bits are divided into amplitude mapped bits and phase mapped bits, which are represented by m_a,i and m_p,i respectively, and then go through differential modulation. The format of m_a,i or m_p,i can be written as (d_j…d₂d₁d₀), where d_j denotes the input bits data. In our scheme, the data is differentially encoded between different subcarriers in the same OFDM symbol.

Fig. 1 The principle of optical mDAPSK-OFDM system (IFFT: inverse fast Fourier transform; CP: cyclic prefix; Coh. Rx: coherent receiver).

The m^th sample of baseband mDAPSK-OFDM signal in the n^th symbol interval can be expressed as

s (t) = \sum_{k = 1}^{N} X_{i, k} \cdot e^{j 2 π k t / T_{s}}, t = m T_{s} / N

(1)

where k is the index of the OFDM subcarrier, N is the total number of the subcarriers, T_s is the time duration of each sample and X_{i, k} means the mDAPSK modulated data symbol on the k^th subcarrier. X_{i, k} is represented as

X_{i, k} = α_{i k} e^{j θ_{i k}}

(2)

Here, i is i^th data symbol, α_ik and θ_ik are the amplitude and absolute phase of data symbol respectively, which can be expressed as

{\begin{cases} α_{i k} = γ_{k} α_{i (k - 1)} {\begin{matrix} , & γ_{k} \in (A^{\pm (2^{M_{a}} - 1)}, A^{\pm (2^{M_{a}} - 2)}, ..., ​ ​ A \end{matrix}}^{0}) \\ θ_{i k} = θ_{i (k - 1)} + Δ θ_{k} \begin{matrix} , & Δ θ_{k} = (2 l + 1) π / 2^{M_{p}}, l = 0, 1, ..., 2^{M_{p} - 1} \end{matrix} \end{cases}

(3)

In Eq. (3), γ_k and Δθ_k are the differential parameters of amplitude and phase, M_a and M_p are the bit numbers of m_a,i and m_p,i, A is a constant value and α_ik∈(1, A, A², …,

A^{2^{M_{a}} - 1}

). For example, M_a = 1 and M_p = 3 are for 16DAPSK modulation, and M_a = 2 and M_p = 4 are for 64DAPSK modulation. The mapping rule from m_p,i to Δθ_k obeys the Gray coding for phase differential coding. For example, when m_p,i = (000), Δθ_k = π/8; when m_p,i = (011), Δθ_k = 5π/8. For amplitude differential coding, m_a,i can choose different γ_k according to the values of α_i(k-1) and m_a,i. We also adopt Gray coding for the input bits of m_a,i. The status transition diagrams for m_a,i = (d₀) and m_a,i = (d₁d₀) are illustrated in Fig. 2 .

Fig. 2 The status transition diagrams of amplitude differential mapping: (a) two amplitude levels; (b) four amplitude levels.

After the insertion of the CP and the parallel to serial conversion, the mDAPSK-OFDM signal is produced through digital to analog (D/A) conversion. Then it can be modulated onto the optical carrier with the help of optical I/Q modulator. At the receiver, it executes the corresponding inverse processing to recover the bits stream. The received mDAPSK symbol of the k^th subcarrier can be expressed as

R_{i, k} = H_{i, k} \cdot S_{i, k} + N_{i, k}

(4)

where H_i,k is the channel transfer function of the subcarrier, S_i,k is the frequency domain information of transmitted signal and N_i,k is the noise. There we assume the channel in the optical fiber is a kind of slow time-varying channel, and the differential factor can be expressed as

D_{i, k} = \frac{R_{i, k}}{R_{i - 1, k}} = α'_{i, k} \cdot e^{j θ'_{i, k}}

(5)

Here, α’_i,k is the received amplitude parameter and θ’_i,k is the received phase parameter. We can get the original bits stream with the two parameters. Due to the differential coding, there is no need to know the channel function H_i,k, which can reduce the complexity and redundancy of the receiver.

The QAM-OFDM and DAPSK-OFDM frame structures are shown in Fig. 3 . In both of the structures, the synchronization sequence is indispensable. But for QAM-OFDM signal, it still needs additional training sequence and pilots to execute the channel estimation and equalization. Compared with QAM-OFDM signal, the DAPSK-OFDM signal could keep a lower complexity while mantaining a higher SE. For a real-time optical QAM-OFDM signal, we take Ref [5

N. Kaneda, Q. Yang, X. Liu, W. Shieh, and Y.-K. Chen, “Realizing real-time implementation of coherent optical OFDM receiver with FPGAs,” in Proc. ECOC’2009, paper.5.4.4 (2009).

]. as an example. It inserts 16 training symbols every 496 data symbols. Out of 128 subcarriers, 10 pilot subcarriers are added into 107 data subcarriers. The SE will reduce by 11% compared with DAPSK-OFDM signal, which is enough for forward error correction (FEC) coding. Without channel estimation and equalization, it can also reduce the complexity and cost at both the transmitter and receiver.

Fig. 3 The structures of QAM-OFDM and DAPSK-OFDM frames.

3. Experimental setup and results

The experimental setup for the proposed scheme is shown in Fig. 4 , where 64DAPSK-OFDM signal is adopted for the demonstration. To reduce the probability bit error, we further adopt Gray code for the input bit stream. In the experiment, the 64DAPSK-OFDM signal is generated through Matlab processing offline and uploaded to an arbitrary waveform generator (AWG) with 10 Gs/s sample rate for D/A conversion. For 64DAPSK mapping, the six input bits which determine the modulation status are divided into two parts for differential amplitude and phase mapping respectively. Two bits are used for amplitude mapping and four bits are used for phase mapping. As the next step, the inverse fast Fourier transform (IFFT) is processed in order to calculate the time discrete OFDM signal. The electrical spectra of I and Q parts of the signal are shown as insets in Fig. 1, where we can see the bandwidths of the two parts are both about 3.47 GHz. The IFFT size is 256 and no pilot subcarrier or training sequence are added to OFDM data. The middle two subcarriers are filled with blank. Considering the total bandwidth of 6.94 GHz for I and Q parts, the resultant data rate in the uniform loading of 64DAPSK is 41.31 Gb/s (log₂(64)х6.94х(254/256)). The output I/Q parts from AWG are used to drive the optical I/Q modulator to produce the modulated optical signal. We employ a couple of DFB lasers at 1550.92nm with a linewidth of 5kHz as the optical source and local oscillator (LO). Transmission is performed through a 160 km single mode fiber (SMF), and the fiber loss, dispersion and dispersion slope is 0.22 dB/km, 16 ps/(nm∙km) and 0.06ps/(nm²∙km) respectively. The optical 64DAPSK-OFDM signal is set to −6 dBm before launching into the transmission link.

Fig. 4 The experimental setup (AWG: arbitrary waveform generator; TDS: real-time digital scope).

At the receiver, an optical hybrid is adopted for the coherent detection of OFDM signal. A real-time sampling oscilloscope (TDS) with two embedded 20-GS/s ADCs is used for the sampling of received 64DAPSK-OFDM signal. The signal processing and demodulation are executed offline on the computer, and Monte-Carlo analysis based on Matlab has been carried out in our experiment. Figure 5 shows the bit rate error (BER) as a function of the optical signal-to-noise ratio (OSNR). The single channel without pilot tones is measured before and after 160 km transmission. The required OSNR to achieve a BER of 10⁻³ are 19.87 dB and 22.5 dB respectively. An additional penalty of 2.63 dB is incurred in Fig. 5, which is mainly due to the fiber dispersion as well as nonlinearity during transmission. Although the CP of 1/32 can resolve the channel dispersion-induced inter-carrier interference (ICI) and inter-symbol interference (ISI), the phase noise on each subcarrier cannot be eliminated; furthermore, the signal suffers both nonlinearity and fiber dispersion, and no equalization is adopted for signal demodulation.

Fig. 5 Measured BER curves and constellation of 64DAPSK-OFDM signal before and after transmission (resolution: 0.1nm).

We also compare the transmission performances with conventional mQAM-OFDM signal, where the modulation orders are 16, 32 and 64. Figure 6 (a) -6(c) illustrate the measured BER curves for different mQAM-OFDM and mDAPSK-OFDM signals respectively, and the transmission link is 160 km SMF. For mQAM-OFDM signals, the total number of subcarriers is 256, where 16 subcarriers are for pilot tones and 2 subcarriers are blank. The training sequence is attached to every 120 OFDM symbols. The same AWG is adopted for the generation of the signal, which produces data rates of 25.8 Gb/s, 32.26 Gb/s and 38.71 Gb/s for 16/32/64QAM modulated OFDM signals respectively. It is obvious that the BER of mQAM-OFDM signals without equalization is beyond 3 × 10⁻³ (FEC limit), while the mDAPSK-OFDM signals can get a good performance without equalization, which indicates the robustness to the phase noise due to differential modulation. After equalization, the performances of mQAM-OFDM signals become better than mDAPSK-OFDM signals. Although the BER of mQAM-OFDM signals are obviously improved after channel estimation and signal equalization, it would increase the complexity and cost at the receiver. From Fig. 6, we can see that the OSNR penelties at BER of 10⁻³ between mQAM-OFDM and mDAPSK-OFDM signals is about 4.3 dB for the three cases. It is because the mQAM-OFDM signal has a maximized average Euclidean distance between each constellation point compared with mDAPSK-OFDM. On the other hand, due to the absence of channel estimation and equalization, the demodulation of mDAPSK-OFDM signal can be simplified, but leading to loss of OSNR. The OSNR penalties become smaller as the BER increases. If EFEC is adopted, the OSNR penalties in Fig. 6(a)-6(c) would reduce to 3.55 dB, 2.82 dB and 1.49 dB respectively. In the experiment, we adopt offline processing for signal demodulation and the performance has been shown in Fig. 6. In real OFDM receiver, there might be about an additional penalty of 1.5 dB existing during channel estimation and equalization [14

T. May, H. Rohling, and V. Engels, “Performance analysis of Viterbi decoding for 64-DAPSK and 64-QAM modulated OFDM signals,” IEEE Trans. Commun. 46(2), 182–190 (1998). [CrossRef]

]. This means the performance of 64DAPSK-OFDM signal at EFEC limit is almost the same as 64QAM-OFDM with pilot tones and training sequence, while keeping a lower complexity and higher SE. Figure 7 shows the constellations of 64DAPSK and 64QAM mapped OFDM signals after transmission.

Fig. 6 The measured BER curves for different mDAPSK-OFDM and mQAM-OFDM signals after 160km transmission: (a) 16QAM-OFDM v.s. 16DAPSK-OFDM; (b) 32QAM-OFDM v.s. 32DAPSK-OFDM; (c) 64QAM-OFDM v.s. 64DAPSK-OFDM (w/: with; w/o: without, resolution: 0.1nm).

Fig. 7 The constellation of 64DAPSK-OFDM and 64QAM-OFDM signal after transmission.

Then we compare the nonlinearity during the transmission of 64QAM-OFDM and 64DAPSK-OFDM in single channel case. Figure 8 illustrates the BER versus launched optical power with 160 km transmission. We can see that the optimum optical powers for both the signals are almost the same. However, as the input power increasing, the BER of 64QAM-OFDM signal degrades faster than 64DAPSK-OFDM signal. The DAPSK-OFDM signal shows higher tolerance towards fiber nonlinearity.

Fig. 8 The measured BER after transmission vs. launced optical power for 64QAM-OFDM and 64DAPSK signals (at OSNR of 25dB, resolution: 0.1nm).

4. Conclusion

We have proposed and experimentally demonstrated a novel no pilot tones and training sequence assisted OFDM technology based on mDAPSK modulation. The differential modulation can mitigate the phase noise caused by the fiber dispersion during transmission. There is no need to execute the channel estimation and can reduce the complexity of the optical OFDM system. A 41.31 Gb/s 64DAPSK-OFDM signal has been successfully transmitted over 160 km fiber in the experiment. The performance comparision between mQAM-OFDM and mDAPSK-OFDM is also executed in the experiment. Considering the penelty during channel equalization, the performance of 64DAPSK-OFDM is almost the same as pilots and training sequence inserted 64QAM-OFDM signal. The results show the prospect of DAPSK-OFDM in optical OFDM system.

Acknowledgment

The financial supports from National Basic Research Program of China with No. 2010CB328300, National High Technology 863 Program of China with No.2012AA011300, National International Technology Cooperation with No.2012DFG12110, National NSFC with No. 60932004, 61077050, 61077014, 61205066 and BUPT Excellent Ph. D. Students Foundation are gratefully acknowledged. The project is also supported by the Fundamental Research Funds for the Central Universities with No. 2012RC0311.

References and links

1.	W. Shieh, “OFDM for flexible high-speed optical networks,” J. Lightwave Technol. 29(10), 1560–1577 (2011). [CrossRef]
2.	N. Cvijetic, M. Cvijetic, M.-F. Huang, E. Ip, Y.-K. Huang, and T. Wang, “Terabit optical access networks based on WDM-OFDMA-PON,” J. Lightwave Technol. 30(4), 493–503 (2012). [CrossRef]
3.	J. L. Wei, C. Sánchez, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Significant improvements in optical power budgets of real-time optical OFDM PON systems,” Opt. Express 18(20), 20732–20745 (2010). [CrossRef] [PubMed]
4.	D. Qian, M.-F. Huang, E. Ip, Y.-K. Huang, Y. Shao, J. Hu, and T. Wang, “High capacity/spectral efficiency 101.7-Tb/s WDM transmission using PDM-128QAM-OFDM over 165-km SSMF within C- and L-bands,” J. Lightwave Technol. 30(10), 1540–1548 (2012). [CrossRef]
5.	N. Kaneda, Q. Yang, X. Liu, W. Shieh, and Y.-K. Chen, “Realizing real-time implementation of coherent optical OFDM receiver with FPGAs,” in Proc. ECOC’2009, paper.5.4.4 (2009).
6.	A. J. Lowery and L. B. Du, “Optical orthogonal division multiplexing for long haul optical communications: A review of the first five years,” Opt. Fiber Technol. 17(5), 421–438 (2011). [CrossRef]
7.	J. Zhao and A. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photon. Technol. Lett. 24(1), 34–36 (2012). [CrossRef]
8.	X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-division-multiplexed CO-OFDM in long-haul fiber transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009). [CrossRef]
9.	Q. Zhuge, M. Morsy-Osman, and D. V. Plant, “Analysis of dispersion-enhanced phase noise in CO-OFDM systems with RF-pilot phase compensation,” Opt. Express 19(24), 24030–24036 (2011). [CrossRef] [PubMed]
10.	S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “Pre-emphasis and RF-pilot tone phase noise compensation for coherent OFDM transmission systems,” in Proc. CLEO 2007, paper. MA1.2 (2007).
11.	A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-Guard-Interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol. 27(16), 3705–3713 (2009). [CrossRef]
12.	N. Toender and H. Rohling, “DAPSK schemes for low-complexity OFDM systems,” IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, 735–739 (2006).
13.	C.-C.Fang, Y.-J. Lin, S.-W. Wei, and J.-F. Chang, “Performance analyses of DAPSK in a very high mobility environment,” in Proc.WIRLES 2005, 570–575 (2005).
14.	T. May, H. Rohling, and V. Engels, “Performance analysis of Viterbi decoding for 64-DAPSK and 64-QAM modulated OFDM signals,” IEEE Trans. Commun. 46(2), 182–190 (1998). [CrossRef]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation
(060.4250) Fiber optics and optical communications : Networks

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 25, 2012
Revised Manuscript: September 14, 2012
Manuscript Accepted: September 18, 2012
Published: September 20, 2012

Citation
Bo Liu, Lijia Zhang, Xiangjun Xin, and Jianjun Yu, "None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying," Opt. Express 20, 22878-22885 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22878

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References

W. Shieh, “OFDM for flexible high-speed optical networks,” J. Lightwave Technol.29(10), 1560–1577 (2011). [CrossRef]
N. Cvijetic, M. Cvijetic, M.-F. Huang, E. Ip, Y.-K. Huang, and T. Wang, “Terabit optical access networks based on WDM-OFDMA-PON,” J. Lightwave Technol.30(4), 493–503 (2012). [CrossRef]
J. L. Wei, C. Sánchez, R. P. Giddings, E. Hugues-Salas, and J. M. Tang, “Significant improvements in optical power budgets of real-time optical OFDM PON systems,” Opt. Express18(20), 20732–20745 (2010). [CrossRef] [PubMed]
D. Qian, M.-F. Huang, E. Ip, Y.-K. Huang, Y. Shao, J. Hu, and T. Wang, “High capacity/spectral efficiency 101.7-Tb/s WDM transmission using PDM-128QAM-OFDM over 165-km SSMF within C- and L-bands,” J. Lightwave Technol.30(10), 1540–1548 (2012). [CrossRef]
N. Kaneda, Q. Yang, X. Liu, W. Shieh, and Y.-K. Chen, “Realizing real-time implementation of coherent optical OFDM receiver with FPGAs,” in Proc. ECOC’2009, paper.5.4.4 (2009).
A. J. Lowery and L. B. Du, “Optical orthogonal division multiplexing for long haul optical communications: A review of the first five years,” Opt. Fiber Technol.17(5), 421–438 (2011). [CrossRef]
J. Zhao and A. Ellis, “Transmission of 4-ASK optical fast OFDM with chromatic dispersion compensation,” IEEE Photon. Technol. Lett.24(1), 34–36 (2012). [CrossRef]
X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-division-multiplexed CO-OFDM in long-haul fiber transmission,” J. Lightwave Technol.27(16), 3632–3640 (2009). [CrossRef]
Q. Zhuge, M. Morsy-Osman, and D. V. Plant, “Analysis of dispersion-enhanced phase noise in CO-OFDM systems with RF-pilot phase compensation,” Opt. Express19(24), 24030–24036 (2011). [CrossRef] [PubMed]
S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “Pre-emphasis and RF-pilot tone phase noise compensation for coherent OFDM transmission systems,” in Proc. CLEO 2007, paper. MA1.2 (2007).
A. Sano, E. Yamada, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, Y. Miyamoto, R. Kudo, K. Ishihara, and Y. Takatori, “No-Guard-Interval coherent optical OFDM for 100-Gb/s long-haul WDM transmission,” J. Lightwave Technol.27(16), 3705–3713 (2009). [CrossRef]
N. Toender and H. Rohling, “DAPSK schemes for low-complexity OFDM systems,” IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications, 735–739 (2006).
C.-C.Fang, Y.-J. Lin, S.-W. Wei, and J.-F. Chang, “Performance analyses of DAPSK in a very high mobility environment,” in Proc.WIRLES 2005, 570–575 (2005).
T. May, H. Rohling, and V. Engels, “Performance analysis of Viterbi decoding for 64-DAPSK and 64-QAM modulated OFDM signals,” IEEE Trans. Commun.46(2), 182–190 (1998). [CrossRef]

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