## Abstract

A simple optical OFDM (OOFDM) synchronization technique utilizing subtraction and Gaussian windowing at the symbol rate is proposed and implemented in FPGA-based OOFDM receivers. End-to-end real-time symbol synchronization of 128-QAM-encoded OOFDM signals at raw bit rates of 6.56Gb/s is experimentally demonstrated, for the first time, over directly modulated DFB laser-based 25km SMF intensity modulation and direct detection (IMDD) systems. Experimental investigations show that the proposed synchronisation technique offers a number of salient advantages including low complexity, fast tracking speed, high accuracy and suitability for high-capacity optical transmission systems.

© 2010 OSA

## 1. Introduction

In practical orthogonal frequency division multiplexing (OFDM) system designs, one of the most critical challenges is synchronization, as it significantly affects the system performance. In a wireless OFDM transmission system, a conventional autocorrelation synchronization technique has been widely adopted, which is based on sophisticated autocorrelation of incoming signals at signal sampling or over-sampling speeds [1–6], i.e., a sequence of samples is multiplied by a time-shifted copy of the same sequence. With altering the time shift, the multiplication and sum operations are performed and repeated to produce a time-dependent autocorrelation profile, which is then employed for synchronization. Clearly, such a technique is not suitable for end-to-end real-time high-capacity optical OFDM (OOFDM) transmission systems, as the complexity of the required digital signal processing (DSP) algorithms scales significantly with increasing signal bit rate.

In off-line OOFDM transmission systems using DSP approaches, synchronization is usually undertaken by transmitting training symbols once every certain number of symbols [7–10]. To achieve synchronization, the received training symbols are correlated. Clearly, the aforementioned off-line synchronization technique occupies the valuable transmission bandwidth and, more importantly, does not consider the limitations imposed by the precision and speed of practical DSP hardware required for realizing end-to-end real-time high-capacity optical transmission. The experimental demonstration of end-to-end real-time OOFDM synchronization is vital for not only rigorously validating the OOFDM technique but also establishing a strong platform for evaluating the true feasibility of the OOFDM technique for practical implementation in future high-capacity optical networks.

It is well known that, compared to wireless channels, optical fibre channels are relatively stable. Therefore, OOFDM symbol alignment does not have to take place frequently. Here it is also worth pointing out that, in comparison with coherent OOFDM transmission systems [11], intensity modulation and direct detection (IMDD) OOFDM systems [12] of interest of this paper are far less susceptible to phase noise, as the effect of laser intensity noise converted from phase noise is negligible for IMDD OOFDM systems involving typical DFB lasers [13]. In addition, the insertion of a cyclic prefix to each OFDM symbol brings about a repeated symbol pattern with a predetermined time period. Thus full use can be made of all the aforementioned features to significantly reduce the complexity of OOFDM signal synchronization. Furthermore, in IMDD OOFDM systems, baseband OFDM signals are utilised to produce intensity-modulated double sideband OOFDM signals, which are then transmitted along the fibre links, therefore, two major factors, namely symbol timing offset (STO) and sampling clock offset (SCO) [14], play dominant roles in determining the achievable system performance.

STO and SCO occur due to the time delay of a received OOFDM signal and the clock mismatch between the transmitter and receiver, respectively. STO-induced synchronization errors may cause a fraction of a fast Fourier transform (FFT) window for an OFDM symbol to occur in an extended region of an adjacent symbol, leading to system performance degradation due to the effects of inter-symbol-interference (ISI) and inter-channel-interference (ICI). STO may also cause that the FFT window for an OFDM symbol starts at the cyclic prefix region of the same symbol, thus leading to that the last several samples of the symbol are not covered by the FFT window. Though the subcarrier orthogonality still maintains, this, however, reduces the effective cyclic prefix length. If the resulting effective cyclic prefix length is shorter than the chromatic dispersion-induced time delay between the lowest and highest frequency subcarriers, the ISI effect occurs, which degrades considerably the system performance. It should be noted that, for the transmission systems considered in this paper, the time delay induced by both chromatic dispersion and frequency chirps associated with directly modulated DFB lasers (DMLs) employed are much smaller than the cyclic prefix length adopted. As a result, if the FFT window starts within the cyclic prefix region, almost perfect synchronisation profiles occur, as shown in Fig. 5
. Channel equalisation does not affect the synchronisation profiles obtained, as it is conducted after symbol synchronisation. On the other hand, SCO brings about the significant ICI effect, as the sampled values do not correspond to the peaks of the sinc (*sin(x)/x*) waveforms after the FFT in the receiver.

Recently, we have proposed a novel OOFDM synchronization technique utilizing simple operations including subtraction and Gaussian windowing [15]. Gaussian windowing is achieved by multiplying an obtained synchronization profile and a Gaussian function with an optimum profile. The performance of the proposed synchronization technique has been theoretically investigated extensively [16]. In this paper, based on the previously proposed synchronization technique [15,16] and a series of world-first experimental demonstrations of end-to-end real-time OOFDM transceivers employing manually adjusted symbol synchronization [17–19], experimental demonstrations of end-to-end real-time OOFDM symbol synchronization are reported, for the first time, in DML-based 25km single-mode fiber (SMF) IMDD systems for raw signal bit rates of up to 6.56Gb/s. It is shown that the proposed OOFDM synchronization technique has a number of salient advantages including low complexity, fast tracking speed, high accuracy and suitability for real-time high-capacity optical transmission systems. Here it is also worth mentioning that, apart from the real-time OOFDM transmitter and the real-time OOFDM receiver experimentally demonstrated in [9] and [10], respectively, a 12.1Gb/s real-time OOFDM transmitter [20] and a 41.25Gb/s real-time OOFDM receiver [21] have also been experimentally achieved.

## 2. Proposed symbol synchronization technique

Figure 1
shows the diagram of the proposed and experimentally implemented symbol synchronization technique using subtraction and Gaussian windowing. A received real-valued digital OOFDM sample sequence is first truncated and subsequently converted from serial to parallel, each of the parallel sample group contains L consecutive samples. Here L is the symbol length. After that, a sample group having *(L + N)* samples is produced by copying a part (*N* samples) of the previously stored *L* samples into another register. Here *N* is the IFFT/FFT window length. The captured *n-th* sample group is denoted as ${r}_{n}\left({i}^{*}\right),{i}^{*}=0,1,2,\cdots ,L+N-1$ . At the symbol rate, an un-averaged symbol synchronisation profile, ${x}_{n}\left(i\right)$ , is generated by performing *L* parallel subtraction operations described below

Each point in Eq. (1) corresponds to a sample in the OFDM symbol region. As the sample amplitudes and phases are random in the FFT/IFFT window region, and repeated sample patterns occur only in the cyclic prefix region, the exact value of ${x}_{n}\left(i\right)$ in Eq. (1) strongly depends upon whether the sample *i* locates in the cyclic prefix region or not:

- • If the sample at
*i*locates in the cyclic prefix region, its value is very similar to that corresponding to the sample at*i + N*. Thus ${x}_{n}\left(i\right)$ approaches zero. Of course, slight deviations from zero may occur from symbol to symbol due to system random noise and the ISI and ICI effects; - • If the sample at
*i*does not belong to the cyclic prefix region, ${x}_{n}\left(i\right)$ has a random value, which varies from sample to sample and from symbol to symbol.

To effectively reduce the abovementioned random variations of the un-averaged symbol synchronisation profile, an average operation continuously accumulated over all the previously obtained un-averaged synchronisation profiles is performed by

where*y*is the symbol synchronization profile vector in the register and

_{n}(i)*y*.

_{0}(i) = 0*α*is the coefficient, which controls the growth of

*y*. After averaging,

_{n}(i)*y*has minimum values in the cyclic prefix region.

_{n}(i)To improve the accuracy of the symbol synchronization profile, the residual random variations of *y _{n}(i)* outside the cyclic prefix region should be reduced further. To achieve such a goal, Gaussian windowing is introduced in the cyclic prefix region by multiplying the synchronization profile and a Gaussian window function. The Gaussian windowing operation is expressed below:

*where*$y{\text{'}}_{n}$ is the maximum value within y

_{n}(i).

*The*operation of $y{\text{'}}_{n}-{y}_{n}\left(i\right)$ is to ease the implementation of Gaussian windowing. g(i) is the super-Gaussian windowing function with a pulse width of i

_{w}. The power parameter of 6 is obtained through theoretical simulations [16]. i

_{c}is the centre position of the Gaussian windowing function, which is determined by the position of the synchronization profile, as discussed in the last paragraph of this section. After the Gaussian windowing operation, the obtained synchronization profile in the cyclic prefix region can be preserved very well, whilst the random y

_{n}(i) variations outside the cyclic prefix region is reduced significantly. Therefore, such an operation can improve the accuracy of the synchronization profile, as discussed in Section 4.

The generated symbol synchronization profile mimics the position of the cyclic prefix region, as illustrated in Fig. 2
and Fig. 3
. For an ideal transmission system with a δ-function impulse response, the symbol synchronization profile has a rectangular shape over the cyclic prefix region. Whilst for a practical transmission link, the resulting symbol synchronization profile is a convolution of the ideal rectangular synchronization profile with an impulse response of the transmission system, as illustrated in Fig. 2. This can be understood by assuming that the transmission link is linear and has an impulse response of *h(t)*, the received OOFDM signal, s**(t),* is written as

*s(t)*is the OOFDM signals in the transmitter,

*w(t)*is additive white Gaussian noise (AWGN) in the receiver. By substituting Eq. (5) in Eq. (1),

*x*can be expressed as

_{n}(i)*n-th*sample group generated in the transmitter.

*T*is the time period of the FFT window,

_{F}*T*is the sampling period in the receiver,

_{S}*w'(t)*is the AWGN with a double power of

*w(t)*.

To achieve symbol synchronisation, the centre of gravity (COG) of the symbol synchronization profile is also required, which is defined as the position that divides the synchronisation profile into two equal areas, as illustrated in Fig. 3. The integer part of the COG is used to determine STO and mark the starting point of a FFT window. In addition, the COG can also be utilised to minimise the SCO effect. For baseband IMDD transmission systems, the COG variation is proportional to SCO [16]. By measuring two COGs, *P _{1}* and

*P*, at two different times, the SCO,

_{2}*ξ*, can be estimated by

*M*is the total number of samples during the time interval for measuring

*P*and

_{1}*P*.

_{2}*ξ*can be used to generate a synchronisation signal to control and lock, via a voltage control oscillator (VCO), the frequency of the receiver clock.

It should be pointed out that, in implementing Gaussian windowing, the centre of the Gaussian window is chosen to be the COG when the distance between the COG and the resulting symbol synchronization profile peak is less than the cyclic prefix period. Beyond such a regime, the Gaussian window centre is taken to be the symbol synchronization profile peak. Furthermore, the Gaussian window centre is continuously updated according to the measured COGs. Here an optimum Gaussian window width of 1.3 times higher than the cyclic prefix period is employed [16]. It is also worth mentioning that, in comparison with the conventional correction synchronisation technique, the proposed technique is capable of reducing the number of operations by a factor of approximately 3. The factor can be further increased when both STO and SCO are considered. This confirms that the proposed synchronisation technique has an advantage of low complexity.

## 3. Real-time experimental system setup with symbol synchronization

Figure 4
shows the setup of the real-time OOFDM experimental system with symbol synchronization, in which use is made of the end-to-end real-time OOFDM transceiver architectures similar to those reported [17–19]. In particular, on-line performance monitoring and live parameter optimization [18] are also implemented. The digital-to-analogue/analogue-to-digital converter (DAC/ADC) sampling rates are set to 2GS/s and subcarrier amplitudes prior to the IFFT in the transmitter are set to be identical. The symbol length is *L =* 40 samples (20ns), and the cyclic prefix length is 8 samples (4ns). As the detailed descriptions have already been made of the real-time OOFDM transceiver designs incorporating the IFFT/FFT logic functions, channel estimation and system frequency response measurement [19], here an outline of the experimental system is, therefore, presented.

In the FPGA-based real-time transmitter, the 32 point IFFT logic function supports 32 equal frequency spaced subcarriers, of which 15 are located in the positive frequency bins occupying the whole Nyquist band. Prior to performing the IFFT, 15 parallel pseudo random data and pilot sequences of length of 88500 words are employed to feed 15 parallel encoders [19], which encode input and pilot data using one of the following signal modulation formats: differential quadrature phase shift keying (DQPSK), 32-quadrature amplitude modulation (QAM), and 128-QAM. At the input of the IFFT, the encoded 15 subcarriers and one extra subcarrier having zero power at zero frequency are arranged to satisfy the Hermitian symmetry with respect to their complex conjugate counterparts. The self-developed IFFT logic function [17–19] is then employed to perform the IFFT on all the 32 complex subcarriers. At the output of the IFFT, real-valued OFDM symbols having 32 samples are produced. The amplitude of the output symbol is scaled to a fixed level and then quantized to 8-bits to match the resolution of the employed DAC.

A cyclic prefix of 8 samples is added to each symbol, giving rise to 40 samples per symbol. The internal system clock is set to 50MHz, which is equal to the symbol rate. The 50MHz symbol rate and 40 samples per symbol give a sample rate of 2GS/s. The signed samples are converted to unsigned ones by adding an appropriate DC offset. After performing sample ordering and bit arrangement, the unsigned 40 samples are streamed to the DAC interface at 2GS/s. The entire symbol is fed in parallel to 32 high-speed 10:1 dedicated hardware serialisers, the interface consists of 4 samples transferred in parallel at a rate of 0.5GHz, giving the required aggregated sample rate of 2GS/s. The DAC generates an analogue electrical OFDM signal having a maximum peak-to-peak voltage of 636mV. The signal is attenuated as necessary and subsequently, together with an appropriate DC bias current, injected into a 1550nm DML with a 3-dB modulation bandwidth of approximately 10GHz, a maximum optical output power of about 0dBm and a threshold current of 29mA.

The OOFDM signal emerging from the DML is coupled into an erbium-doped fibre amplifier (EDFA) with a 15dB optical gain and a 5dB noise figure. After passing through a 0.8nm optical filter, the amplified optical signal is coupled into MetroCor^{TM} SMFs. It should be noted that the use of the EDFA is to vary the optical launch power only. The use of the EDFA is not necessary when a DFB laser with an optical output power of >7dBm is used.

In the receiver, after passing through an optical attenuator, the received OOFDM signal is converted into the electrical domain using a multi-mode fibre (MMF) pigtailed 12GHz PIN with TIA. The PIN has a receiver sensitivity of −17dBm (corresponding to 10 Gb/s non-return-to-zero data at a bit error ratio (BER) of $1.0\times {10}^{-9}$ ). The electrical signal is first amplified with a 2.5GHz, 20dB RF amplifier, then attenuated as needed to optimise the signal amplitude to suit the input range of the ADC. After passing through an electrical low-pass filter, the signal is converted via a balun to a differential signal and then digitized by a 2GS/s, 8-bit ADC in the receiver. Finally, the digital samples are fed, via a digital interface identical to the interface of the DAC, to a receiver FPGA, in which symbol synchronization is implemented. After symbol synchronization, sample groups, each of which contains *N = 32* samples, are obtained and used to recover the data following an inverse process compared to that in the transmitter. In addition, after the FFT, pilot subcarrier detection, channel estimation, channel equalization and measurement of system frequency responses are also performed following the procedures detailed in [17–19].

The bit error count over 88500 symbols is continuously updated and displayed with the embedded logic analyser for the entire channel and also for each individual subcarrier over a specific measurement period. This enables the fine adjustment of system parameters to maximize the transmission performance. In addition, the logic analyser also displays and continuously updates the total number of bit errors and the corresponding symbols accumulated since the start of a transmission session. This enables the measurement of BERs of the entire transmission channel at unlimited low values, provided that a sufficiently long operation time is allowed.

## 4. Experimental results

Based on the end-to-end real-time OOFDM transceiver architectures described above, the performance of the proposed symbol synchronization technique is experimentally demonstrated in DML-based 25km MetroCor^{TM} SMF IMDD links operating at different signal bit rates of up to 6.56Gb/s (128-QAM). For all the experimental measurements presented in this Section, the DML driving voltage is approximately 0.4 Vpp and the bias current is 36mA, corresponding to which the optical output power is −3.5dBm. After appropriately adjusting the optical gain of the EDFA followed by a 0.8nm optical filter, the optical power injected into the MetroCor^{TM} SMF is fixed at 7dBm. To highlight the operating principle of the proposed symbol synchronisation technique and the STO effect, clock synthesizers based on a common reference clock are adopted to produce the system clocks for both the transmitter and receiver.

To demonstrate the impacts of Gaussian windowing and α coefficient on the symbol synchronisation profile, Fig. 5(a) [Fig. 5(b)] is plotted, which shows the synchronization profiles measured before (after) applying Gaussian windowing for different α coefficients in 25km MetroCor^{TM} SMFs. It can be seen in Fig. 5 that the Gaussian windowing-enabled synchronization profiles are very clean over the cyclic prefix region, and that for a smaller α, the random profile variations outside the cyclic prefix regions becomes much lower and the profile edges become sharper.

The dynamic process of how a clean synchronization profile and a stable COG are established is shown in Fig. 6
, in obtaining which an extra 8 sample delay is inserted into a normally running synchronised transmission system at a received optical power of −16dBm. It can be seen in Fig. 6 that, for a small α, a long time period is required to stabilise the COG, which, however, has a much clean evolution curve, as expected from Fig. 5(a) and Fig. 5(b). On the other hand, a large α value is capable of increasing tracking speed. For example, when *α* increases from 2.4 × 10^{−4} to 1.3 × 10^{−1}, the corresponding time period required for stabilizing the COG decreases from 2 × 10^{−4} s to 8 × 10^{−6} s, which correspond to 10000 and 400 OOFDM symbols, respectively. Considering the above-mentioned trade-off between the COG accuracy and tracking speed, in this paper, *α* = 2.0 × 10^{−3} is adopted in measuring the transmission performance of the real-time OOFDM transmission systems with synchronisation.

The proposed synchronisation technique can cope with arbitrary initial STO values seen by the receiver at the starting stage of synchronising a transmission system, and subsequently produce an optimum and stable COG to mark the starting position of the FFT window. The optimum COG corresponds to the zero STO point shown in Fig. 7 . The synchronisation process results in the independence of the measured BER on initial STO, as shown in Fig. 7. Such flat BER curves locate at the bottom of the BER curves obtained for transmission systems with manual synchronisation corresponding to STO = 0, confirming that the proposed synchronization technique can efficiently compensate for the STO effect, regardless of the adopted signal modulation formats.

For the DML-based MetroCor^{TM} IMDD system, the positive transient frequency chirp effect associated with the DML is very low. Therefore, for the entire system considered, the dispersion-induced ISI effect is negligible for relatively low signal modulation formats. According to the discussions in Section 1 and Section 2, for transmission systems with manual synchronisation, Fig. 7 shows almost symmetrical BER curves with respect to zero STO. The stable operation ranges of these curves are mainly determined by the employed cyclic prefix length. In addition, a high modulation format also narrows considerably the stable operation range, as shown in Fig. 7. This is because, for achieving a specific BER, a high modulation format-encoded OOFDM signal gives rise to a large signal bit rate, and requires a large SNR, thus the signal is more susceptible to the imperfect synchronization-induced ISI effect. Figure 7 also shows that, at a BER of 10^{−3}, the received optical powers for the DQPSK-, 32-QAM- and 128-QAM-encoded OOFDM signals are −21.0, −14.2 and −8.3dBm, respectively.

To explore the accuracy of the proposed symbol synchronisation technique, the real-time OOFDM transmission performance over 25km MetroCor^{TM} SMF IMDD systems using the synchronisation technique is plotted in Fig. 8
, which shows the received optical power dependent BERs for DQPSK-, 32-QAM- and 128-QAM-encoded OOFDM signals corresponding to raw signal bit rates of 1.88Gb/s, 4.69Gb/s and 6.56Gb/s, respectively. It is seen in Fig. 8 that, for the 128-QAM-encoded OOFDM signal, the minimum achievable BER is 2.3 × 10^{−3}, whilst the minimum achievable BER when manual synchronisation is utilised is approximately 1.0 × 10^{−3} [17] for the same system. The minimum received optical powers required for achieving a forward error correction (FEC) BER limit of 4 × 10^{−3} [7] are −21.5dBm for DQPSK, −15.0dBm for 32-QAM and −10.8dBm for 128-QAM. These system performances confirm that the proposed synchronization technique is highly accurate for use in different OOFDM systems.

A SCO of 0 with an accuracy of ± 1ppm is also measured, which is identical to the real SCO value adopted in the experiments. This confirms that the proposed synchronisation technique has good stability. For transmission systems using two different clocks in the transmitter and receiver, preliminary theoretical investigations have shown [16] that the proposed synchronisation technique is also capable of accurately controlling and locking the frequency of the receiver clock, by making use of Eq. (7). For example, for an OOFDM transmission system with a received OSNR as low as 12.5dB and an initial SCO as large as −218.7ppm, a stable COG almost identical to its ideal value is still obtainable. Extensive experimental investigations of the SCO effects are currently being undertaken, and results will be reported elsewhere in due course.

## 5. Conclusions

A simple OOFDM synchronization technique using subtraction and Gaussian windowing at the symbol rate has been proposed and implemented in FPGA-based OOFDM receivers. End-to-end real-time symbol synchronization of OOFDM signals encoded using different signal modulation formats varying from DQPSK to 128-QAM (corresponding to raw signal bit rates of 1.88Gb/s and 6.56Gb/s, respectively) has been experimentally demonstrated, for the first time, over DML-based 25km MetroCor^{TM} IMDD systems. Experimental results have also shown that the proposed synchronisation technique offers a number of salient advantages including low complexity, fast tracking speed, high accuracy and suitability for high-capacity optical transmission systems.

## Acknowledgments

This work was partly supported by the European Community's Seventh Framework Programme (FP7/2007-2013) within the project ICT ALPHA under grant agreement n° 212 352, and in part by the Bangor University ESDF fund.

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