## Abstract

A low-complexity joint symbol synchronization and SFO estimation scheme for asynchronous optical IMDD OFDM systems based on only one training symbol is proposed. Numerical simulations and experimental demonstrations are also under taken to evaluate the performance of the mentioned scheme. The experimental results show that robust and precise symbol synchronization and the SFO estimation can be achieved simultaneously at received optical power as low as −20dBm in asynchronous OOFDM systems. SFO estimation accuracy in MSE can be lower than 1 × 10^{−11} under SFO range from −60ppm to 60ppm after 25km SSMF transmission. Optimal System performance can be maintained until cumulate number of employed frames for calculation is less than 50 under above-mentioned conditions. Meanwhile, the proposed joint scheme has a low level of operation complexity comparing with existing methods, when the symbol synchronization and SFO estimation are considered together. Above-mentioned results can give an important reference in practical system designs.

© 2016 Optical Society of America

## 1. Introduction

To support the rapidly emerging bandwidth-hungry multimedia services such as HDTV, online game etc., the transmission capacity of the optical access networks are required to be increased. Optical orthogonal frequency division multiplexing (OOFDM) is considered as a promising candidate technology for next-generation passive optical networks (PONs), due to its inherent advantages including, for example, rich digital signal processing (DSP) realizations, high spectral efficiency and flexible dynamical bandwidth allocation [1–4]. Meanwhile, OOFDM systems with intensity-modulation and direct-detection (IMDD) approach have attracted a lot of attention in access scenario because of its low DSP complexity, stable performance and low-cost compared with coherent optical OFDM (CO-OFDM) systems.

However, IMDD OOFDM systems are in particular sensitive to synchronization error including sampling frequency synchronization and symbol synchronization. An offset from the correct start point of an OFDM symbol during the demodulation procedure causes inter-symbol interference and degrades the system bit-error-rate (BER) performance [5]. Moreover, a sampling frequency offset (SFO) between the clocks of the digital-to-analog converter (DAC) in the transmitter and analog-to-digital converter (ADC) in the receiver may also degrade the system performance as it causes phase rotation, amplitude reduction and inter-carrier interference between subcarriers [6,7]. Thus, precise symbol synchronization and SFO estimation are critical for IMDD OOFDM systems and have been extensively investigated in recent years [8–15].

A blind symbol synchronization scheme based on virtual subcarriers which carry no signal power is proposed in [8,9]. This scheme monitors the virtual subcarriers’ power to detect timing offset. But it is difficult for practically real-time realizing since feedback from the FFT operation which may lead additive latency is needed. A simple symbol synchronization technique based on cyclic prefix (CP) utilizing subtraction and Gaussian windowing is proposed and experimentally achieved in a direct-detection optical OFDM receiver [10,11]. However, the average operation employed in this technique still consumes multipliers. In [12,13] the sign of the received data is cross correlated with the sign of the training symbol to detect the start point of the training symbol, so the computational cost is reduced dramatically since multiplications are replaced by XNOR operators. In [14], the authors make use of a short cross correlator with an exponential average filter based on a repetitive preamble to achieve the symbol synchronization. On the other hand, to reduce or avoid SFO effects, a method based on the estimated position of symbol start is used to estimate the SFO in the receiver, and then feedback the value to a voltage controller oscillator (VCO) for eliminating the SFO effects [11], but this method needs additional circuits and a stable, high-precision clock source. The authors in [15] proposed a pilot-aided SFO estimation and compensation method for optical IMDD OFDM systems. However, the use of pilot will reduce the transmission spectral efficiency. A correlation SFO estimation method is achieved based on the training symbols of two consecutive OFDM frame in frequency domain in [16,17], but multiplication operations in this estimation method cost too many computing resources. In addition, to our best knowledge, the existing algorithms are mostly designed for only one kind of impairment, the interaction effects between the two above-mentioned impairments have not yet been considered.

In this paper, a low-complexity joint symbol synchronization and SFO estimation scheme for optical IMDD OFDM systems with independent clock in the transmitter and receiver based on only one training symbol is proposed. Symbol synchronization is firstly achieved by using the cross-correlation properties of the training symbol utilizing bit summation operations. Then the sampling frequency offset can be estimated based on the characteristic that an additional sampling point will be introduced when the cross-correlation value periodically changes a cycle. Numerical simulations and experimental demonstrations are also under taken to evaluate the performance of the mentioned scheme. The experimental results show that robust and precise symbol synchronization and the SFO estimation can be achieved simultaneously at received optical power as low as −20dBm in asynchronous OOFDM systems. SFO estimation accuracy in MSE can be lower than 1 × 10^{−11} under SFO range from −60ppm to 60ppm after 25km SSMF transmission. Optimal System performance can be maintained until cumulate number of employed frames for calculation is less than 50 under above-mentioned conditions. Meanwhile, the proposed joint scheme has a low level of operation complexity comparing with existing methods, when the symbol synchronization and SFO estimation are considered together. Above-mentioned results can give an important reference in practical system designs.

## 2. Principle of proposed joint scheme

The proposed joint scheme for symbol synchronization and SFO estimation is based on a time-domain training symbol. The data sub-carriers of the training symbol are modulated with BPSK symbols, while the sub-carriers at highest frequencies and zero frequency direct current (DC) sub-carrier are filled with zeros. To generate the real-valued time-domain sequence, all the data (BPSK symbols and zeros) on the sub-carriers are then fed into an IFFT function by using Hermitain symmetry.

#### 2.1 Symbol synchronization

The symbol synchronization is implemented by using cross-correlation between the local training symbol and received signal because the cross-correlation algorithm can provide good performance at low SNR due to the averaging process of the correlator [18]. The timing metric can be expressed as

where where*R*(

*d*) is received energy,

*P*(

*d*) is correlation metric, and

*t*(

*n*) is the transmitted training symbol with length

*N*=

_{t}*N*+

*N*,

_{cp}*N*is the length of CP.

_{cp}*r*(

*n*) represents the discrete samples of the received OFDM signal.

*d*is the time index corresponding to first received sample in a window of

*N*samples.

_{t}Generally, parallel data processing technique can be applied for reducing the system operating frequency in the high-speed optical communication systems. However, the complexity of the aforementioned synchronization technique will be increased dramatically in a parallel channel receiver. To reduce the hardware complexity, signed bit is introduced in real-time direct detection optical OFDM systems during the symbol synchronization [12,13]. Computational complexity then can be reduced by using only sign-quantized signals because it does not require operations of multiplication or division, but only logical calculations and additions. Since *t*(*n*) is the known local training symbol, signed bit of *t*(*n*) is also known and the XNOR operation in [12,13] can also be reduced in our scheme. Here, a simplified symbol synchronization method based on Eq. (2) is proposed, and the timing metric is defined as

*n$\le $N*1.

_{t$-$}The symbol start point therefore can be estimated by searching for the maximum timing metric as follows

#### 2.2 Sampling frequency synchronization

Contributed by sampling frequency mismatch, the time shift from the nominal instants of n-th sample in the received signal can be given by

where*t*is the sampling instant of the first sample,

_{0}*Ts*is the sample period, Δ = (

*f*-

_{t}*f*)/

_{r}*f*is a relative SFO,

_{r}*f*and

_{t}*f*represent the sampling frequency in the transmitter and receiver, respectively. When the

_{r}*N*samples are received, the time shift of samples from their nominal positions is

_{R}*N*samples, where

_{D}*N*is an integer which can be expressed bywhere

_{D}*N*is the transmitted samples. For simplicity, the

_{T}*t*is consider as 0, then the relative SFO can be estimated by

_{0}Since Δ is much smaller than 1, we can assume that samples in the *k-th* (same as the frame index) training symbol have the same time shift *t _{k}*. The sampling phase offset (SPO) of the

*k-th*training symbol is the decimal part of its time shift, which can be given by

*L*is the distance of the training symbol of two continuous OFDM frame and it can be consider as a constant for simplicity. The SPO range is [−0.5

*T*, 0.5

_{S}*T*]. In Fig. 1, the

_{S}*t*,

_{k}*round*(

*t*) and

_{k}*P*as function of the frame index

_{k}*k*are depict. As shown in Fig. 1(a), when Δ>0,

*t*increases with the frame index

_{k}*k*,

*P*increases form −0.5

_{k}*T*to 0.5

_{S}*T*periodically with the increasing

_{S}*k*, and the time shift of samples

*round*(

*t*) increases one sample when the

_{k}*P*drop from 0.5

_{k}*T*to −0.5

_{S}*T*. When Δ<0 as shown in Fig. 1(b),

_{S}*t*will decreases with the increasing frame index

_{k}*k*,

*P*decreases form 0.5

_{k}*T*to −0.5

_{S}*T*periodically with the increasing

_{S}*k*, and the time shift of samples

*round*(

*t*) decreases one sample when the

_{k}*P*jump from −0.5

_{k}*T*to 0.5

_{S}*T*.

_{S}For an ideal transmission system with a δ-function impulse response, the proposed symbol synchronization approach has an impulse-like timing metric. Meanwhile for a practical transmission system without considering the impact of noise, the resulting symbol cross-correlation profile is a convolution of the ideal timing metric with system impulse response as illustrated in Fig. 2.

Since the practical timing metric can be considered as samples of the generated cross-correlation profile, the SFO-caused SPO for every training symbol will affect the performance of symbol synchronization, as depict in Fig. 3. To indicate the SPO, the phase offset metric (POM) is introduced. The POM in the *k-th* training symbol is defined as the timing metric difference between the points beside the *k-th* estimated training symbol start point ${\widehat{d}}_{k}$.

Signed bit extractor in Eq. (10) is used to counteract the impact of signed bit ambiguity of the timing metric, since the use of phase reverser such as inverting amplifier will produce a 180° phase difference between the received and transmitted signals. The SPO is considered in the numerical simulation without noise for simplicity. In the simulation, the size of IFFT/FFT is set to 64, and the length of CP is *N*/8. In order to plot Fig. 4, a highly over-sampled OFDM signal is generated and over-sampling rate is 32 to ensure sufficient time domain resolution. Then the OFDM signal with different SPOs can be obtained from it. The maximum values of *M _{Pro}*(

*d*) and the POM versus SPOs are shown in Fig. 4 which indicate that

*M*(

_{Pro}*d*) decreases with the increasing |SPO| and the POM increases with SPO.

Since the POM and SPO have an approximate linear relationship as shown in Fig. 4, the relationship between POM *D*(*k*) and the frame index *k* is similar with the relationship between SPO *P _{k}* and the frame index

*k*, as shown in Figs. 5(a) and 5(b). The received samples is one sample less than the transmitted samples when

*D*(

*k*) drop from the peak to bottom or one sample more when

*D*(

*k*) jump from the bottom to peak. In order to search the catastrophe point of

*D*(

*k*) and calculate the difference between the received and transmitted samples, we use the difference equation of

*D*(

*k*),

*D*'(

*k*) reaches peak value at the catastrophe point of

*D*(

*k*) as shown in Figs. 5(c) and 5(d). We can set a counter

*N*to count the time shift of samples between the received and transmitted samples and a counter

_{D}*N*to count the received samples.

_{R}*N*minus one when

_{D}*D*'(

*k*) is higher than the threshold value

*Th*, and plus one when

*D*'(

*k*) is less than −

*Th*. Then the SFO can be estimated by Eq. (8).

After the SFO is estimated, the SFO-caused phase rotation of the mapped symbol can be compensated by multiplying a factor with the form of exp(*j2πlm*Δ*N*/*N _{t}*) at the

*l*-th output symbol of FFT [7], where

*m*is the index of subcarrier.

## 3. Experimental verifications of proposed scheme

An optical IMDD OFDM system which illustrated in Fig. 6 is employed to experimental investigate the performance of the proposed joint scheme. In this system, DSP procedure for both transmitter and receiver are realized by offline approach. At the transmitter, 64 sub-carriers are involved and half of them can be used to allocate user data in order to satisfy the Hermitian symmetry for real-valued IMDD OFDM system. The input pseudo random data is firstly mapped into parallel complex data by using the 16-QAM encoder. 64 points real value OFDM signals are then generated through 64-point IFFT module. After 8 samples CP are appended to the beginning of every 64 IFFT output samples, length of an OFDM symbol become 72 samples. After CP insertion, the training symbol used for symbol synchronization and SFO estimation is inserted at the beginning of the OFDM frames, and one training symbol is employed every 80 data symbols for channel estimation. The generated OFDM signal is loaded into an Arbitrary Waveform Generator with 2GS/s sampling rate and 8-bit DAC (AWG, Tektronix, 7122C). The electrical analog OFDM after passing through an electrical low-pass filter (LPF) with 3-dB bandwidth of 1GHz is amplified to 2V peak-to-peak voltage by an electrical amplifier (EA). Then the electrical OFDM signal is directly drive a 1550nm DFB laser with 3GHz modulation bandwidth. The 8dBm optical OFDM signal is launched into 25km standard single mode fiber (SSMF).

In the receiver, after passing through a variable optical attenuator (VOA), the received OOFDM signal is converted into the electrical domain by using a 10GHz PIN detector. After passing through the electrical EA and LPF, the signal is sampled by a digital storage oscilloscope (DSO, Keysight, DSO-S 804A) with 2GS/s@10-bit ADC for off-line processing. A reference clock output with the frequency of 10MHz from AWG is connected to DSO as the reference clock input in order to introduce proper SFO for measurements. The threshold *Th* is 33 for the proposed SFO estimation method.

After 25km SSMF transmission at a received optical power of −15dBm and with a SFO of 5ppm, the measured timing metrics with the SFO near 0Ts and 0.5Ts are shown in Figs. 7(a) and 7(b), respectively. The phase offset metric in Fig. 7(a) is 0, so the SPO in the training symbol of this frame nears 0Ts considering the influence of noise. In Fig. 7(b), the phase offset metric is 42 and the values of *M _{Pro}*(0) and

*M*(−1) are close, so the SPO in the training symbol of this frame is close to 0.5Ts. Although the peak of the timing metric at a SPO of 0.5Ts is smaller than that at 0Ts, but it is still very obvious, showing that the start point in each OFDM frame can be precisely detected by proposed scheme.

_{Pro}Mean square error (MSE) is also induced to evaluate the SFO estimation performance. The MSE of the estimated SFO is defined as

*N*is the times of the estimation. The accuracy of the proposed SFO estimation method is affected by the cumulate time, which is equivalent to the received samples

_{times}*N*. Since the length of OFDM frames in our system is identical, frame number is used to represent the cumulate time. 500 times estimation for each frame number is taken during the measurements. Figure 8 shows the BER performance at −15dBm received optical power and the MSE of the estimated SFO versus cumulate frame number when the SFO is 20ppm. It can be seen from Fig. 8 that the MSE of the proposed SFO estimation method increases with the decrease of the frame number at different received optical power, and it increases rapidly when the frame number is less than 50. The MSE degrade slightly when the received optical power is lower than −20dBm which indicates the robustness of proposed SFO estimation method even at low received optical power. It also can be found from Fig. 8 that the BER curve can keep almost flat until cumulate number is less than 50 frames. Above-mentioned results can give an important reference in practical system designs. The MSE of the estimated SFOs is less than 10

_{R}^{−11}after 25km SSMF transmissions when the cumulate number is more than 50 frames.

The relationship between BER and SFO with or without SFO compensation is shown in Fig. 9. In this case, the received optical power is −15dBm and the cumulate frame number used to estimate the SFO is 50. System BER without the SFO compensation will be rapidly deteriorated with the increasing of SFO effect. Nevertheless, at the SFO from −50ppm to 50ppm, the BER performance after compensated with the proposed sampling frequency synchronization scheme can be almost same with the BER at 0ppm. At adopted FEC limit of 3.8 × 10^{−3}, more than 60ppm SFO effects can be compensated by using proposed sampling frequency synchronization scheme. The MSE versus SFO is also plotted in Fig. 9. As we can see, the MSE increases rapidly when the SFO is more than 60ppm which is also verified in Fig. 8.

The 16-QAM constellations of the 26th subcarrier without and with SFO compensation at a SFO of 40ppm are shown in Figs. 10(a) and 10(b), respectively. It is obvious that SFO-caused phase rotation can be effectively compensated by the proposed scheme.

Figure 11 shows the BER performance versus received optical power at a SFO of 20ppm and 40ppm with and without the proposed compensation scheme in place. It shows that for the presence of 20ppm and 40ppm without compensation, the error floors keeps at a very high error rate for both cases. Meanwhile, the BER performance after compensation is very close to the BER performance in the case without SFO.

## 4. Algorithm complexity comparisons

The complexity comparison between the proposed symbol synchronization method and the conventional synchronization methods is shown in Table 1. *N _{ss}* is the length of short symbols used in [14].

*L*samples in parallel process for high-speed OOFDM systems are involved in synchronization methods. For the proposed symbol synchronization method, there are

*L*(

*N*− 2) addition and

_{t}*L*subtraction operations for the target timing metric generation according to Eq. (4). In addition, an operation in order to find the maximum value for determining the correct timing position of the symbol start point is also needed according to Eq. (5). It is noteworthy that the input width of the adders and subtracters in [10, 11] is same as that of the received data, where the input width of the adders and subtracters in [13, 14] and proposed method is only 1bit. The reduction of the input width for adders and subtracters dramatically reduces the hardware complexity.

Table 2 shows the complexity comparisons between proposed SFO estimation method and the conventional SFO estimation methods. In Table 2, arg{·} stands for the angle operator and *M* is the number of the pilot symbols. For the proposed SFO estimation method, according to Eq. (10), there are 1 multiplication and 1 subtraction operations in order to generate *D*(*k*). *D'*(*k*) is generated by 1 subtracter according to Eq. (11). Besides that, 2 addition operations are needed for counting the number of *N _{D}* and

*N*, and subsequently 1 divider is needed for calculating the SFO according to Eq. (8).

_{R}It can be figured out from Tables 1 and 2 that the proposed joint scheme has the lowest operation complexity when the symbol synchronization and SFO estimation are considered together.

## 5. Conclusions

A low-complexity joint symbol synchronization and SFO estimation scheme for asynchronous optical IMDD OFDM systems based on only one training symbol is proposed. The experimental results show that robust and precise symbol synchronization and the SFO estimation can be achieved simultaneously at received optical power as low as −20dBm in asynchronous OOFDM systems. At adopted FEC limit of 3.8 × 10^{−3}, more than 60ppm SFO effects can be compensated by using proposed sampling frequency synchronization scheme and estimation accuracy in MSE can be lower than 1 × 10^{−11}. Meanwhile, the proposed joint scheme has a low level of operation complexity comparing with existing methods, when the symbol synchronization and SFO estimation are considered together.

## Acknowledgments

This work was supported in part by the Natural Science Foundation of China (Project No. 61132004, 61275073, 61420106011) and the Shanghai Science and Technology Development Funds (Project No.13JC1402600, 14511100100, 15511105400, 15530500600, 16YF1403900).

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