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We propose and experimentally demonstrate a method for sampling frequency offset (SFO) estimation in optical communication systems based on periodically inserted identical binary prefix. Different from conventional cyclic prefix, binary prefix provides not only high tolerance to chromatic dispersion in dispersive fiber transmission, but also the ability to estimate SFO by simple receiver-side digital signal processing. Moreover, this binary prefix based scheme is generally applicable to any advanced modulation formats. A proof-of-concept experiment is conducted to quantify the accuracy and tolerance of the scheme in estimating SFO. It is found that over a wide SFO range up to 341 ppm, the estimation error is kept under 20 ppb and signals are recovered with the same quality as with zero-offset sampling. The experimental results also confirm that this method is tolerant to link signal-to-noise ratio loss and dispersion, showing no additional penalty after transmission over a 40-km standard single-mode fiber at 1550 nm.
© 2015 Optical Society of America
1. Introduction
As data traffic grows exponentially, throughput in optical communication systems is to be increased in various dimensions. More and more advanced modulation formats, such as pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), orthogonal and generalized frequency-division multiplexing (OFDM/GFDM), universal filtered multi-carrier (UFMC), and filter bank multi-carrier (FBMC) have been proposed to be used in different scenarios, such as passive optical networks, mobile fronthaul, and radio-over-fiber (RoF), for higher spectral efficiency and radio compatibility [1–3]. Different from a traditional on-off key (OOK) format, digital-to-analog and analog-to-digital converters (DAC/ADC) are needed for sampling these signal formats. In a communication system where DAC and ADC cannot be directly synchronized, sampling frequency offset (SFO) exists.
SFO can cause severe signal degradation [4]. When precise calibration between DAC and ADC is prohibited, estimation and compensation for SFO have to be done. Many estimation methods have been studied with either inaccurate results or complicated algorithm and computation that hinder their application in optical systems where signals are likely to have high bandwidths and baud rates [5,6]. Methods for optical transmissions based on pilots and decisions are also proposed but they are only applicable in OFDM systems [7,8]. Traditional clock recovery methods, such as Gardner’s [9], can only apply in BPSK, QPSK, or certain QAM formats that contain clock tones.
In optical or RoF transmissions, cyclic prefix (CP) is usually added at the front of every signal symbol or block to avoid inter-symbol interference (ISI) caused by filtering, dispersion, and multipath and to facilitate frequency-domain equalization (FDE). It is frequently and regularly distributed over time at the symbol or block rate of a signal.
In this paper, we propose an SFO estimation method that is independent of signal formats. We replace regularly distributed CP with identical binary prefix (BP) sequences. Using the BP, we can precisely estimate the SFO that causes sampling drifting at BP positions. The method gives accurate estimates and has simple implementation for high speed optical communications with advanced modulation formats. Furthermore, BP is as effective as CP in terms of ISI protection and FDE in dispersive transmissions.
2. Binary prefix for SFO estimation
2.1 Binary prefix
BP is an identical sequence added before each signal symbol or block. It replaces CP with the same length and power. It is defined as
where n ∈ Z is the index of sample points and Lp (Lp is even for simplicity) is the BP length. The BP and the signal symbol/block after it have a total length of L. After DAC, the waveform of BP is approximately a sinusoid with a frequency of half the signal sampling rate, as shown in Fig. 1(a).When there is an SFO at the receiver caused by the clock difference of ADC with respect to DAC, sampling will drift and cause variation on sampled BP sequences, as shown in Fig. 1(b). Focusing on the BP part, we can express the sampled BP sequence at the front of the k-th (k ∈ Z, k ≥ 0) symbol/bock under the influence of SFO as
where fS is the signal sampling rate at the transmitter, Δf is the SFO value, and denotes rounding to the nearest integer towards infinity. Since |Δf / fS| << 1 andthe length of BSFO,k in (2) can be approximated into 0≤n<Lp for the simplicity of our following analysis.2.2 SFO estimation
We use the magnitude of the inner product of B and BSFO,k to measure the variation of the BP sequence at the front of the k-th block caused by SFO. The magnitude of the inner product can be expressed as
P(k) has an amplitude of Lp and a period ofwhich is used to estimate SFO proportion |Δf / fS|.The acquisition of P(k) can be achieved by the flow diagram shown in Fig. 2. In the flow S(n) is the received signal sampled with SFO, denotes rounding to the nearest integer towards minus infinity, and x(n) is an intermediate sequence that is defined as the cross correlation between B and S with a shift of Lp-1, or
Because BSFO,k is contained in S as sequences, each inner product P(k) is contained in |x(n)|. To get each P(k), we use the maximum of |x(n)| over a range of kL ≤ n < (k + 1)L, as shown in the last two blocks in Fig. 2 where each P(k) is initiated to zero at the beginning for the discrimination block. Under normalized signal power, the magnitude of x(n) varies between 0 and Lp when the correlation falls on a BP part while the mean magnitude of x(n) is when the correlation falls on a signal part. This ensures that P(k) derived by finding maxima can compose a pattern with a fundamental frequency that is 1/T.Another motivation of using BP to estimate SFO is its DSP-efficient implementation for correlation. Different from conventional methods where each correlation output x(n) usually involves Lp times of multiplication and Lp-1 times of addition, using BP can simplify the computation into only four times of addition for each x(n), as shown in the dashed block in Fig. 2. This can be seen as follows. From (6) we have
which has the same expression as the block diagram. Noting that S(n) = x(n) = 0 when n<0, we have the block equivalent to a correlation computation.2.3 BP for dispersion compensation
Traditional CP is added before a signal symbol or block in order to combat dispersion and facilitate FDE. By replacing traditional CP by BP, we have to ensure that dispersion compensation is still feasible and no redundant overhead is added. Actually this can be seen from the comparison in Fig. 3. In traditional CP mode, a segment of the original symbol is added in front, while in BP mode a fixed binary sequence is added. Both have the same prefix length that is subject to dispersion. In BP mode, instead of doing truncation, we segment the dispersed signal before doing FDE. The segmentation limits all the energy of the symbol inside and keeps the head and tail cyclic because of the repeatable and identical BP, so that the same FDE procedure can be followed as in CP mode. The only difference is that the output from FDE includes two half pieces of the BP pattern at the head and rear of the symbol and consequently the FFT/IFFT size is increased by Lp during the FDE process.
3. Experimental setup and results
The setup we use to verify our method is shown in Fig. 4. In general, it is a standard intensity modulation and direct detection (IM/DD) transmission system. Tunable laser and Mach-Zehnder modulator (MZM) are used as the optical transmitter. Wavelength is fixed at 1,550 nm. Optical output is fixed at 0 dBm before injected to fiber. Standard single mode fiber (SSMF) with different lengths is used for optical transmission. At the receiver, an avalanche photodiode (APD) is used to increase sensitivity so that received-optical-power tests can span a large range. A tunable optical attenuator (TOA) is used to change and maintain the optical power at the APD. For signal generation and capture, an arbitrary waveform generator (AWG) and an oscilloscope are used at the transmitter and receiver, respectively. To have control of sampling frequencies, a microwave source is synchronized with the scope at the AD sampling rate of fAD. With respect to this frequency, the microwave source generates another frequency at fDA as the DA sampling rate to drive the AWG. Signals are generated at a baud rate of 4 Gbaud, i.e. the signal sampling rate fs is 4 GS/s. As actual sampling rates at the AWG and the scope are around 12 GS/s and 20 GS/s, respectively, 3-time up-sampling and 5-time down-sampling are done as the very last and first step at the AWG and the scope, respectively. As a result, fs = fDA / 3 = fAD / 5 = 4 GS/s when there is no SFO. SFO is added as ∆f = fAD / 5 - fDA / 3 by tuning the microwave source. The up-sampling at the AWG is done by adding zeros at high frequency side in FFT domain. An anti-aliasing filter of 5 GHz is used at the AWG output for pulse shaping.
As mentioned in Section 2, the SFO estimate is derived from the period in array P(k). Whether SFO can be successfully estimated mainly depends on whether the fundamental frequency can be extracted. As a result, we first test the ratio R, which is defined as the power difference (in dB) between the fundamental frequency component and the highest noise or harmonic component. The test is done under a 20-km fiber transmission of Gaussian signals to emulate a general form of arbitrary advanced modulation formats. 924 Gaussian samples framed as one block and 100-point BP added before the block assemble a symbol length of L = 1024. R under two SFO values is tested. The results are shown in Fig. 5(a). Sequences of P(k) and their spectra at received optical power of −35 and −25 dB are also given in Fig. 5(b)-(g). When received optical power is high, R does not change obviously and is basically determined by the harmonics of the |cos(·)| waveform. At low received power, noise impairs the BP sequence and the |cos(·)| waveform and therefore R decreases gradually. It is worth noting that SFO can be successfully estimated as long as R is higher than 0 dB. This threshold is much lower than the threshold for signal recovery. Therefore, the method is robust to SNR loss.
Fig. 5 Ratio R under different (a) received optical power and (h) BP length. (b)-(g): P(k) sequences and corresponding spectra.
Similarly, we test R versus various BP length Lp. The symbol length L is fixed at 1,024, and thus the length for payload data is 1,024 - Lp. To purely see the effect of changing Lp, a optical back-to-back (BTB) test without fiber transmission is done at received optical power fixed of −8 dBm. As shown in Fig. 5(h), when BP length is greater than 10, R is kept beyond 20 dB. As BP length decreases R drops until it meets the 0-dB threshold. This reveals that the minimal length of BP is 4 points for successful SFO estimation under −8 dBm optical power and without the impairment of chromatic dispersion.
Secondly, we examine the accuracy of the estimates derived from our method. An SFO range from 167 ppb to 341 ppm is tested. The symbol length is L = 1024 including 100 BP points and 924 Gaussian signal points. The received optical power is fixed at −8 dBm after 20-km fiber transmission. The memory length to store P(k) and its analysis is 8,000 points. As shown in Fig. 6(a), over the whole tested range, SFO can be accurately estimated. To show more details, Fig. 6(b) gives the estimation error over the range. At all SFO points, errors are kept below 20 ppb, which is negligible for signal recovery as experimentally verified in the following transmission tests with both SFO estimation and compensation.
In this test, we first execute a 20-km transmission of 4-ASK signals. The SFO is estimated at the receiver using our method and samples are correspondingly re-sampled to corrected rate by adding or cutting zeroes in frequency domain. An SFO range up to 25 ppm is tested. The symbol structure and other configurations are the same as the previous test. From Fig. 7(a) we can see that by using our method signal quality is maintained at the same level. Over the whole range, no visible penalty is induced by SFO compared with zero-SFO transmission. A test without estimation and compensation is also done as a reference. Under the influence of SFO, signal quality drops as SFO increases. Similarly, Fig. 7(b) gives the results of using the same setup to transmit OFDM signals. Similar results are observed from the error vector magnitude (EVM) curves.
Lastly, as described in Section 2.3, we need to verify that BP does not cause penalty with respect to traditional CP in terms of signal quality after transmission. Therefore, a Q-versus-distance test is done without adding SFO. Figure 8(a) shows the curves of Q factor when CP and BP are added separately. Both directly modulated laser (DML) with chirp and external modulation with zero-chirp MZM are used. The symbol structure and other configurations are the same as the previous test. When MZM is used, although the baud rate in our trial determines that dispersion cannot exceed the CP or BP protection and that dramatic change on Q cannot be observed over the tested distance range, the overlap of CP and BP curves can still reveal their similarity in terms of signal recovery after the two procedures illustrated in Fig. 3. When DML is used, laser chirp causes intermixing interference and performance degradation as distance increases [10], but BP and CP still have the same performance, showing no additional performance penalty caused by the use of BP. In addition, we also examine the equivalency between BP and CP by changing their prefix length under a 40-km fiber transmission. As shown in Fig. 8(b), when prefix is longer than 4 points, further increasing the length of BP or CP does not further improve the signal quality. When prefix is shorter than 4 points, both CP and BP have impairments on Q caused by ISI. Over all lengths, BP performs no worse than traditional CP.
4. Discussion
4.1 Fundamental frequency extraction
In the experimental analysis above we state that SFO can be successfully estimated if R > 0 dB. R is defined as the ratio between the fundamental frequency component and the largest noise or harmonic component. The condition R > 0 dB implies that the fundamental component is the highest component in P(k). In this case the system can extract it without getting confused by other components. Once the system gets the correct component it gets the correct T for SFO as in (5). Therefore, whether R > 0 dB is a threshold to judge if the method works.
There are different methods to extract the fundamental frequency or T from P(k), from both the time and the frequency domain. Different methods have different accuracy and resolution.
4.2 Resolution and window length
The most straight-forward approach is to do FFT on P(k) and select the largest FFT output (other than DC), as adopted in the experiment. In this case the resolution of estimation is
where K is the FFT size, i.e. the window length of P(k). Thus the maximal estimation error is 1/2LK. To further improve the resolution and reduce error, interpolation can also be applied, as adopted in the derivation of the results shown in Fig. 6. It is worth noting that the estimation error is determined by the extraction method. Different methods may apply to different scenarios relating to SFO, symbol/block length, memory depth, and transmission mode.When SFO does not have strong fluctuation, the longer the window length of P(k) is, the more precise estimate the system can get. In an FFT extraction method without succeeding processing, the resolution is inversely proportional to the window length as in (8). However, a large window length causes either deep memory depth or the degradation of the signal received during the window. The degradation is due to the SFO that is not compensated by an available estimate. How to optimize the window length associating SFO distribution and compensation methods that may also need a certain window length is one of the future work directions.
4.3 Frequency position
At DAC, BP shapes a pure tone waveform, it is less sensitive to dispersions compared with full-bandwidth sequences, such as Zadoff-Chu sequence [11]. In addition, it can accumulate SFO information with a good number of BP points. As analyzed in Section 2.2, the correlation generates a |cos(·)| sequence whose amplitude is 10log(Lp) higher than the average of |x(n)| in dB. This makes BP have high tolerance to power loss. Another mechanism that can keep BP from severe frequency-selective degradation is that its analogue frequency fp can be changed by modifying the sequence or the oversampling rate at DAC. In the case in Section 2 and 3, fp = fS/2. It is possible to move fp away from fS/2 towards either DC or fDA/2 (fDA is the sampling rate of DAC which is different and higher than the signal sampling rate fS due to oversampling). Correspondingly, the flow diagram in Fig. 2 will be modified into a more general form as shown in Fig. 9.
Consequently, the fundamental period derived from P(k) will also be changed. The relationship between the period T and the analogue prefix frequency fp can be derived from (5) as
On the one hand, we want to increase fp so that T and window length for P(k) can be smaller. On the other hand, we want to decrease fp so that it suffers less filtering, considering we usually install an anti-aliasing filter at the DAC output, and that the upper limit of detectable |Δf | expressed as fS2/4Lfp can be higher. Therefore, half of the signal sampling rate fS/2 could be a primary option for us.4.4 Polarity ambiguity
In the method, correlation is used to examine the variation of BSFO,k. This gives us amplified information about the variation but without the detail of the elements in BSFO,k. This leads to an uncertainty on the direction of the sampling drifting and thus an ambiguity about the polarity of Δf. Whether ∆f is positive or negative needs to be afterward determined. One of the possible approaches is to compare compensation outputs with the two possibilities.
5. Conclusion
We have proposed a novel method based on the use of BP for SFO estimation in optical transmission with DACs and ADCs. In the method, SFO is precisely estimated by replacing traditional CP with BP at the transmitter and by simple digital signal processing at the receiver. Symbols are protected from ISI by BP and dispersion is compensated by using FDE. A 4-Gbaud proof-of-concept experiment has been performed with intentionally induced SFO. Results show that the method can work under extremely low SNR scenarios. The estimation error is kept under 20 ppb and signals are recovered with the same quality as with zero-SFO sampling. Compared with CP, no penalty is induced by using BP with the same length and power after fiber transmission. This SFO estimation method is applicable to signals with arbitrary modulation formats and to systems where large SFO (e.g., >100 ppm) may exist.
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