## 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.

© 2012 OSA

## 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 [1–10]. 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 [8–10]. 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]. 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, 13]. 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}…d_{2}d_{1}d_{0}*), where

*d*denotes the input bits data. In our scheme, the data is differentially encoded between different subcarriers in the same OFDM symbol.

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

*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 asHere,

*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

_{k}and

*Δθ*are the differential parameters of amplitude and phase, M

_{k}_{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, A

^{2}, …, ${A}^{{2}^{{M}_{a}}-1}$). 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*obeys the Gray coding for phase differential coding. For example, when m

_{k}_{p,i}= (000),

*Δθ*= π/8; when m

_{k}_{p,i}= (011),

*Δθ*= 5π/8. For amplitude differential coding, m

_{k}_{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}= (

*d*) and m

_{0}_{a,i}= (

*d*) are illustrated in Fig. 2 .

_{1}d_{0}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

_{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

_{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]. 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.

## 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 (log_{2}(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/(nm^{2}∙km) respectively. The optical 64DAPSK-OFDM signal is set to −6 dBm before launching into the transmission link.

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.

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]. 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.

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.

## 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.

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