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Abstract
Baud rate clock recovery scheme that supports high order modulation formats is an essential part in digital signal processing for current short reach transmission. In this paper, we propose an improved multiplier-free Mueller-Müller timing error detector (MMTED) sampling at baud rate, which shows excellent performance with low complexity. Using the sign operation, the multiplier is eliminated. The further use of error signal to substitute the original data helps to reduce the jitter of the clock. 25 GBaud PAM-4/8 and 50 GBaud PAM-4 transmission are carried out to evaluate the TED performance. Compared to the sign MMTED, more than 12 dB timing jitter improvement is realized.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the explosive growth of global communication traffic, short reach optical interconnection represented by data center communication has become a hot topic over the past few years. The intensity-modulation direct-detection (IM/DD) technology plays one of the most important roles in the next generation optical communication system due to its low power consumption, compact integration, and low cost. To further expand the communication capacity, over 100 GBaud rate transmission with higher modulation formats such as PAM-4/8 are utilized to meet the demand of >200 Gbps/line short reach interconnection [1]. Recently, 100 GBaud PAM-4/6/8 transmission over 20 km SMF has been demonstrated [2]. Xi Chen et al. realized 200 GBaud PS-PAM-16 transmission over 10 km SMF achieving 700.4-Gbps line rate [3]. Clock recovery is one of the first and most essential procedure in digital signal processing (DSP) at the receiver side. For modern communication systems with limited bandwidth and high order modulation formats, traditional analog clock recovery circuits are faced with more challenges [4]. Digital TEDs are much more attractive in high speed optical communications in recent years [5]. Traditional clock recovery methods, e.g. Gardner TED [6] and Squared Gardner TED [7], usually operate at no less than 2 samples per symbol, which means a high demand on ADC sampling rates. When transmitting a signal exceeding 50 GBaud, hundred GSa/s ADC has to be applied, thus the cost and power consumption will be extremely high. Recently, a modified Godard timing recovery algorithm has been proposed, which enables clock recovery with less than 2 samples per symbol [8]. Compared with the above-mentioned TED, the baud rate TED is an attractive choice, which can significantly save resources in the DSP chip and integrated design. The most popular baud rate TED in IM/DD systems is the MMTED, which employs two adjacent symbols to extract timing phases [9]. Several modifications of MMTED are investigated [10–13]. And a sign-sign MMTED utilizing only logics and additions is proposed to realize clock recovery [14]. It is a good choice for PAM-4 signal, but would be faced with more challenges when it comes to PAM-8 or higher modulation formats. Compared to sign-sign MMTED, the sign MMTED appears to be a more preferred solution in non-coherent systems [10]. However, its jitter performance is still non-ideal.
In this paper, we propose an improved MMTED, namely modified MMTED (Modi. MMTED). 25 GBaud PAM-4/8 and 50 GBaud PAM-4 transmission over 2-km SMF is demonstrated to evaluate the performance. A digital phase locked loop system is implemented to simulate the baud rate sampling system. With the help of sign operation, Modi. MMTED can achieve similar system performance as the traditional TED, but without the involvement of any multiplier. Furthermore, this method could mitigate the transition density related TED self-noise, and the jitter performance is thus enhanced. Experimental results show that PAM-4/8 signal can be successfully synchronized, and 3.8e-3 FEC limit has been achieved in our offline experiment. With similar level of complexity, Modi. MMTED exhibits 12 dB timing jitter improvement compared to sign MMTED.
2. Principle
As depicted in Fig. 1(a), the traditional MMTED can be described by
where ${A_k}$ is the k-th data symbol, $e(k )$ is the TED output, and ${x_k}$ is the received signal defined by where ${h_m}$ represents the impulse response of the system, which also depends on the sampling phase, and m = 0,±1,±2,.. . Substituting Eq. (2) into Eq. (1), we obtain
Fig. 1. The structure and TEDC of: (a) traditional MMTED, (b) sign MMTED, and (c) proposed Modi. MMTED.
The first term in Eq. (3) is the desired value, which indicates that TED gain of MMTED is proportional to the square value of the incoming data. The second term is caused by inter-symbol-interference, it is usually minimized at the optimal sampling phase. For independent and equiprobable data, the expectation value of the second term would be 0, thus the approximation of Eq. (3) would be
For NRZ signals, this expectation expression infers a typical type-A MMTED [9]. Higher order modulation formats would have different TED characteristic (TEDC) for multiple transition edges.
The structure of sign MMTED is shown in Fig. 1(b), which exploits signs instead of decisions to reduce computational complexity [10], and it can be described as
Similarly, substituting Eq. (2) into Eq. (5), we obtain
The first term gives the sample phase error, and the TED gain is proportional to the absolute value of the incoming data. Transition density dependent TED self-noise appears in the second term, which would bring serious degradation in system performance. Considering that TED noise performance around the zero-crossing point is more important, we subtract the second term in Eq. (6) from sign MMTED by setting ${h_0}$ to 1, then obtain
whereThe structure of Modi. MMTED is shown in Fig. 1(c). Since output of sign(·) only consists of ±1, multiplication can be replaced by operating the signs.
For NRZ signals where Ak equals sign(Ak), all of the three TEDs have identical TEDC. When it comes to high order modulation formats like PAM-4/8, the second term in Eq. (6) would introduce a transition density related TEDC offset, which means the TED outputs a non-zero value at the optimal sampling point. The TEDC of these three TEDs for different transitions in PAM-4 signal filtered by Raised-cosine-Filter at a roll-off-factor (ROF) of 0 are depicted in Fig. 1.
As can be seen in Fig. 1(b), the sign MMTED produces offset TEDC in the transition edges between adjacent symbols with unequal absolute values, which would introduce transition dependent noise. Therefore, the performance of the whole clock recovery loop is severely damaged. This transition dependent TEDC offset induced impairments would become more severe in PAM-8 signals since there are larger absolute value differences between adjacent symbols. Usually, this impairment can be mitigated by the combination of a transition detector and a data selector, but additional complexity would be introduced. Furthermore, the convergence time of the clock will be highly dependent on the incoming data sequence. In our proposed Modi. MMTED, the optimal sampling point is also the zero-crossing point of TEDC for different transition edges, where the TED noise is greatly reduced accordingly.
3. Numerical simulation
A main consideration of TED implementation should be the locking time. Several methods have been proposed to accelerate the convergence speed [15–16]. To compare the convergence and jitter performance of traditional MMTED, sign MMTED and the proposed Modi. MMTED, a numerical simulation of ideal PAM-4/8 transmission system is carried out at first. Since MMTEDs utilize the decision results to acquire timing phase error, TED outputs would be quite noisy at sample phase far from the optimal sample point because of heavy ISI, which in turn will affect the convergence speed. In the simulation, the timing phase is set to 0.5UI from the optimal sample point firstly, and then the convergence required sample points (CRSP), which represents the number of symbols required for the full timing convergence, is observed and recorded for each case. In this paper, we declare convergence when the phase error is less than 0.02 UI for 200 consecutive symbols. The convergence process of PAM-8 signal with a ROF of 0.1 is shown in Figs. 2(a-b), in which the normalized loop bandwidth (NLBW) in clock recovery loop is 2E-4 and 1E-3 respectively. Among them, sign MMTED shows the fastest convergence speed. However, the jitter is still large after phase locking while the other two achieve almost zero jitter.
Fig. 2. Simulation results: Convergence process of three TEDs with (a) 2E-4 loop bandwidth and (b) 1E-3 loop bandwidth, CRSP of three TEDs for (c) PAM-4 and (d) PAM-8 cases, (e) jitter performance of sign MMTED.
We further compare the convergence speed for PAM-4/8 signals with different ROFs, which is depicted in Figs. 2 (c-d). It can be seen that more points are required for phase locking when ROF goes down to 0.1 from 0.3, which means that timing phase could be locked faster with higher system bandwidth. For PAM-4 cases in Fig. 2(c), the effect of NLBW is studied. With a NLBW of 2E-4, the required convergence time of MMTED is almost twice that of sign MMTED. The CRSP decreases with increased loop bandwidth. When it becomes larger than 6E-4, all the three TEDs show fast and similar convergence speed. Figure 2(d) depicts the required sample points for the PAM-8 cases. More convergence time is required compared to the PAM-4 cases because the visible region is narrower in higher order modulation formats. Unlike the other two MMTEDs that output zero at optimal phase, sign MMTED exhibits large phase jitter due to transition dependent TED self-noise. The timing jitter performance is also analyzed and the results are shown in Fig. 2(e). The jitter is defined as the variance of sampling phase in NCO, i.e., $\textrm{jitter} = 20lo{g_{10}}({\delta t} )$, where $\delta t$ is the standard deviation of sampling phase. Lower timing jitter means a more stable clock. Due to the involvement of more transition types, the timing jitter in the PAM-8 cases are larger than that in the PAM-4 cases.
4. Experimental setup
The experimental setup is depicted in Fig. 3. At the transmitter side, a pseudo random bit sequence (PRBS15) is first offline mapped onto PAM-4/8 modulation with a raised cosine (RC) pulse shape (ROF is 0.1). The baud rate is set at 25/50 GBaud. The electrical signal is generated by an arbitrary waveform generator (AWG, Keysight M8196A) with maximum sampling rate of 92 GS/s. The wavelength of the CW laser is 1550 nm. A Mach-Zehnder modulator (MZM) is applied to up-convert the electrical signal to optical domain. After fiber transmission, a variable optical attenuator is utilized to optimize the received optical power (ROP). At the receiver side, a 31-GHz photodiode is used to detect the signal, which is then captured by a digital sampling oscilloscope (DSO, LeCroy SDA 830Zi-A) operating at 80 GS/s. After clock recovery in the DSP, a 31-tap FFE equalizer is used to compensate and recover the signal. In order to evaluate the performance of this Modi. MMTED, we implemented a digital clock recovery system comprising the interpolator, TED, loop filter and numerically-controlled oscillator (NCO) [17]. For 50 GBaud PAM-4 transmission, a 7-tap FFE is placed before TED. According to the timing information supplied by NCO, the interpolator generates recovered baud rate sampling signal. The Lagrange cubic interpolator is employed to emulate the analogue-to-digital converter sampling process. The output signal is fed into TED for timing phase detection. A proportional-integral (PI) structure mentioned in [18] is used here as a loop filter to filter the out-band phase noise and extract the stable component to control the NCO. The parameters are calculated by ${\kappa _p} = 2\xi {\omega _n}/{\kappa _d}$, ${\kappa _i} = \omega _n^2/{\kappa _d}$ and ${\omega _n} = 8{B_L}\xi /({1 + 4{\xi^2}} )$, where ${B_L}$ is the NLBW, $\xi $ is the damping factor and set at 0.707, and ${\kappa _d}$ is the TED gain to normalize the outputs of different TEDs. The stability of recovered clock can be evaluated by calculating the phase jitter of NCO.
5. Results and discussion
The performance of different TEDs is evaluated and compared in a 2-km transmission scenario, as shown in Figs. 4–7. We have measured the TEDC performance. The signal was first resampled to a higher sampling rate, then the TED outputs with different time offset were calculated to obtain a single TEDC trace. To observe the jitter performance of different MMTEDs, we utilized several traces to fit the probability distribution graph. Every TEDC trace is measured using 1024 symbols, and 256 traces are employed to obtain the probability distribution graph in Figs. 4 and 5. The TEDC performance for PAM-4 signal with ROP at -8 dBm are depicted in Figs. 4(a-c). As shown, the probability distribution graph of MMTED as well as Modi. MMTED are more concentrated compared to sign MMTED in Fig. 4(b), which indicates a better consistency of the 256 traces. We further investigate the timing jitter performance by analyzing the jitter of clock recovered by NCO, and the results are show in Fig. 4(d). The timing jitter performance deteriorates as the NLBW increases, while both MMTED and Modi. MMTED achieve consistently much better performance compared to sign MMTED. As can be seen in Fig. 4(d), Modi. MMTED shows similar convergence speed as sign MMTED with much better jitter performance.
Fig. 4. Measured TEDC performance of (a) traditional MMTED, (b) sign MMTED, and (c) proposed Modi. MMTED for PAM-4, (d) Jitter and CRSP versus NLBW for 25 GBaud PAM-4 with ROP at -10 dBm.
Fig. 5. Measured TEDC performance of (a) traditional MMTED, (b) sign MMTED, and (c) proposed Modi. MMTED for PAM-8, (d) Jitter and CRSP versus NLBW for 25 GBaud PAM-8 with ROP at 0 dBm.
The TEDC and timing jitter performance for PAM-8 signal are depicted in Fig. 5 with ROP at 0 dBm. The worst TEDC performance can be observed in sign MMTED, while the other two TEDs show great performance agreement. The timing jitter and convergence performance are shown in Fig. 5(d). Modi. MMTED obtains the lowest timing jitter. Compared to sign MMTED, more than 12 dB jitter improvement could be observed.
BER measurements are also carried out and shown in Fig. 6. Modi. MMTED and MMTED perform better than sign MMTED both in the PAM-4 and PAM-8 cases with NLBW at 1E-3. The BER improvement is particularly evident for PAM-8 signals mainly because the high order modulation formats require a more stable reference clock than lower order modulation formats. When NLBW is 1E-3, the BER of sign MMTED cannot reach the FEC limit in the PAM-8 case, while the receiver sensitivity of Modi. MMTED and MMTED at HD-FEC limit achieves -2.6 dBm. Tuning NLBW to 2E-4 (5 MHz in 25 GBaud system) could help to lower the BER, but it is still non-ideal. The equalized PAM-4 signal with ROP at -10 dBm and PAM-8 signal with ROP at 0 dBm are shown in the inserted figures in Figs. 6(a-b), respectively.
Next, we investigate the performance of the three TEDs in high baud rate communication systems. A 50 GBaud PAM-4 transmission over 2-km SMF was established to make the comparison. As can be seen in Fig. 7(a), adaptive equalizer enables a smooth jitter curve of sign MMTED when ROP decreases. But the timing jitter of sign MMTED is still large. BER performance degradation is observed in Fig. 7(b) when the NLBW equals 1E-3.
6. Conclusion
In this paper, we propose an improved multiplier-free MMTED, which can mitigate the transition density related TED self-noise. Multiplier-free is realized by symbolic computation, and error signal are employed to reduce the TED noise. It enables clock recovery to operate at baud rate and shows excellent timing jitter performance especially for high order modulation formats. In the experimental demonstration, 25 GBaud PAM-4/8 and 50 GBaud PAM-4 signal can be successfully synchronized by offline data processing. Under much reduced complexity, this Modi. MMTED shows similar jitter performance as MMTED but higher convergence speed. And over 12 dB jitter improvement compared to sign MMTED is observed. With low complexity and superior performance, the proposed Modi. MMTED appears to be a good candidate for short reach communications.
Funding
Science and Technology Planning Project of Shenzhen Municipality (JCYJ20200109142010888).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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