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Abstract
In this paper, we experimentally demonstrated a 2-km high-speed optical interconnection with pulse-shaped pre-equalized four-level pulse amplitude modulation (PAM-4) signal generated by a 3-bit digital-to-analog converter (DAC) with the aid of in-band quantization noise suppression techniques under different oversampling ratios (OSRs) to reduce the influence of quantization noise. The simulation results show that the quantization noise suppression capability of high computational complexity digital resolution enhancer (DRE) is sensitive to taps number of the estimated channel and match filter (MF) response when OSR is sufficient, which will lead to further significant computational complexity increase. To better accommodate this issue, channel response-dependent noise shaping (CRD-NS) which also takes channel response into consideration when optimizing quantization noise distribution is proposed to suppress the in-band quantization noise instead of DRE. Experimental results show that about 2 dB receiver sensitivity improvement can be achieved at the hard-decision forward error correction (HD-FEC) threshold for 110 Gb/s pre-equalized PAM-4 signal generated by 3-bit DAC when the traditional NS technique is replaced by the CRD-NS technique. Compared to the high computational complexity DRE technique, in which channel response is also considered, negligible receiver sensitivity penalty is observed for 110 Gb/s PAM-4 signal, when the CRD-NS technique is utilized. Considering both the system cost and bit error ratio (BER) performance, the generation of high-speed PAM signal with 3-bit DAC enabled by the CRD-NS technique is regarded as a promising scheme for optical interconnection.
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1. Introduction
Dramatic IP traffic increase has been driven by the emergence of high bandwidth services, such as social media, cloud computing, and high-division television, and optical interconnection is being extensively studied to synchronize the system capacity with IP traffic growth [1–5]. For the short-reach optical interconnection, the intensity modulation and direct detection (IM/DD) architecture is considered as a promising solution because of its low cost, power consumption, and footprint [6–8]. To increase the capacity of the IM/DD system, advanced modulation formats instead of simple on-off-keying (OOK), such as pulse amplitude modulation (PAM), discrete multi-tone (DMT), and carrier-less amplitude and phase (CAP), which are compatible with IM/DD architecture as only amplitude of symbols is used to transmit signal. Transmission and reception of advanced modulation formats signal in IM/DD system have been explored and demonstrated [9–13]. While the PAM modulation format with much lower system linear dynamic range requirement and power consumption is preferable among those modulation formats and it has been appointed in IEEE 802.3cu-2021 as modulation format for 400GbE standard [14]. However, high bandwidth requirement of conventional PAM symbol makes it impractical to directly transmit in bandwidth limited channel to achieve high capacity. To better solve this issue, pulse shaping is adopted in the signal generation [15–17], since it can reduce the symbol bandwidth by introducing proper inter-symbol interference (ISI) except the decision point. System bandwidth limitation derived from components, such as the digital-to-analog converter (DAC) and the modulator, will induce serious performance impairments [15–18]. To this end, digital pre-equalization interacting with post-equalization is regarded as an effective solution and plays a fundamental role in high-speed PAM signal transmission [18–20].
Aforementioned incorporating digital signal processing techniques (DSPs) including pulse shaping and pre-equalization at the transmitter guarantee the overall system performance, while the implementation of those DSPs typically results in a large peak-to-average power ratio (PAPR), which indicates that the high-resolution DAC is necessary [21,22]. The utilization of high-speed DAC with high resolution significantly increases the power consumption and system cost, which is an obstacle to the cost-sensitive optical interconnection. In Ref. [23], it has been reported that the power consumption of DAC accounts for 80% of that in the transmitter. In addition, the power consumption and footprint of DAC increase linearly and exponentially with the resolution of DAC [23,24]. Above all, in contrast to the high-resolution DAC, the low-resolution one is more practical for cost-sensitive optical interconnection, while it will undoubtedly lead to a mass of in-band quantization noise.
Recently, many studies concentrate on promoting the utilization of low-resolution DAC with quantization noise suppression techniques, such as noise shaping (NS), and digital resolution enhancer (DRE) [21,25–32]. Both of them reduce the quantization noise influence by redistributing the quantization noise between the signal band and the unused band. Therefore, an additional oversampling ratio (OSR) of 1.5∼2 is necessary for the implementation of quantization noise suppression techniques [21,25–28]. In both IM/DD and coherent systems, comprehensive comparison between NS and DRE has been executed in Ref. [28], which indicates that when the DAC resolution is higher than 3, the noise-suppression capability of the NS technique is similar to the DRE technique, and the required computational complexity and processing delay decreased significantly. Thus, for low-cost optical interconnection, it is preferable to adopt the NS technique. However, there still exists some penalty for the signal with NS compared to the signal with the DRE technique when the DAC resolution is as low as 3. To further improve the noise-shaping capability of the NS technique, channel response-dependent noise shaping (CRD-NS) is investigated for pre-equalized DMT signal to mainly overcome the residual quantization noise unevenly distributed issue [27]. The experiment results indicate that for the DMT signal generated by a 3-bit DAC, the CRD-NS technique shows a better noise-shaping capability with traditional NS, and a similar noise-shaping capability with DRE technique. Different from the DMT signal, PAM signal is insensitive to the unevenly distributed quantization noise. Therefore, the effectiveness of CRD-NS for the high-speed PAM signal with the low-resolution DAC needs to be further studied and explored to reduce the cost of optical interconnection.
In this paper, the transmission of high-speed pulse-shaped pre-equalized PAM-4 signals with different OSRs using 3-bit DAC are studied with the quantization noise suppression technique. For high-speed PAM signal, the CRD-NS shows a better noise-shaping capability compared to the traditional NS technique, as it considers the residual quantization elimination during channel transmission. Compared to DRE in which the problem of inaccuracy channel and match filter (MF) response estimation appears when OSR is sufficient, the CRD-NS technique exhibits similar noise shaping capability with much lower computational complexity. The experiment results show that about 2 dB receiver sensitivity improvement can be observed at the hard-decision forward error correction (HD-FEC) threshold for 110 Gb/s PAM-4 signal generated by 3-bit DAC when the CRD-NS technique is applied to replace the traditional NS technique, without additional computational complexity. Compared to the high computational complexity DRE technique, in which channel response is also considered for quantization noise suppression, negligible receiver sensitivity penalty is observed for 110 Gb/s PAM-4 signal, when CRD-NS technique is utilized. Thus, among traditional NS, CRD-NS and DRE techniques, considering both system cost and noise suppression capability, CRD-NS is regarded as a promising technique to assist the high-speed PAM-4 signal generation with a 3-bit DAC in optical interconnection.
The rest of this paper is organized as bellows. A simulation demonstration of CRD-NS and DRE techniques is shown in Section 2. Experiment setups and results are respectively introduced in Section 3 and Section 4. Finally, the summarization of this paper is given in Section 5.
2. CRD-NS Versus DRE with Various Data Rates
Figure 1 shows the architecture of CRD-NS and DRE techniques, where $ x(n )$, $y(n )$, and $v(n )$ represent the transmitted signal, the received signal, and the output signal after CRD-NS or DRE, respectively. $h(n )$, $p(n )$, and $g(n )$ respectively represent the channel response of the transmission link, its inverses utilized for digital pre-equalization, and the channel response of the feedback linear filter for the CRD-NS technique. The feedback linear filter of the CRD-NS technique is realized by a finite impulse response (FIR) filter, whose coefficient is obtained with the principle of minimizing the difference between the transmitted and received signal. Different from the CRD-NS technique, the DRE is realized by the Viterbi algorithm, and it aims to shape the quantization noise spectrum inversely to the combined channel and MF response. Both CRD-NS and DRE techniques consider channel response to better suppress the in-band quantization noise [27,33]. For the CRD-NS technique, the noise suppression capability is related to the number of taps of FIR, the value of the weighting function Ws and the bandwidth using Ws to weight. All parameters need to be optimized based on the corresponding transmitted signal. The noise shaping capability and computational complexity of DRE are closely related to the number of soft quantization possibilities M, the number of taps of the channel and MF response L. In previous studies, both the soft quantization possibilities M and the number of taps L are both set as 3 by considering the noise shaping capability and computational complexity [25,27,28,34]. It is noted that the signal after soft quantization may be beyond DAC minimal or maximal values. Therefore, the output sequence after DRE beyond DAC minimal or maximal values must be constrained to corresponding minimal or maximal values. The shorted channel and MF response can be obtained by designing a new FIR filter with the principle of least-square sense to best match the original frequency response [21,27].
Numerical studies are executed to make a comparison between CRD-NS and DRE techniques in 80/100/110 Gb/s PAM-4 signal generation with a 3-bit DAC. The channel response during the simulation is obtained from the experiment setup which can be found in Section 3. For 80/100/110 Gb/s PAM-4 signals, the value of Ws is set as 16 and the WI is set as 1. The taps length of feedback filter g for the CRD-NS technique is set as 5. Both of them are optimized based on the corresponding pulse-shaped pre-equalized PAM-4 signal generated by a 3-bit DAC with 80 GSa/s. For the DRE technique, the soft quantization possibilities M is set as 3, while the number of taps of the estimated FIR filter for DRE is adjusted during the study. Figure 2 shows the calculated power spectrum density (PSD) of signal during the DRE and CRD-NS process. As can be seen, the quantization noise within signal bandwidth can be effectively suppressed after DRE and CRD-NS are utilized. For the 110 Gb/s signal, the 3-taps FIR-supported DRE exhibits comparable noise shaping capability to both the 5-taps FIR-supported DRE and CRD-NS technique. However, for the 100 Gb/s signal, there is a slight inferiority in the performance of the 3-taps FIR-supported DRE. This inferiority becomes more pronounced for the 80 Gb/s signal. The occurrence of this phenomenon can be attributed to the imprecise estimation of channel and MF response, as shown in Fig. 2. The use of a 3-taps FIR becomes less effective for channel and MF response estimation as the OSR is increased. Table 1 shows the signal-to-quantization noise ratio (SQNR) of signals with various schemes, revealing that the penalty between 3-taps FIR-supported DRE and 5-taps FIR-supported DRE, CRD-NS technique is increased with the OSR. The SQNR performance of the CRD-NS in different OSRs is comparable to that of 5-taps FIR-supported DRE. Since the required computational complexity of DRE is much higher than CRD-NS technique, thus, the CRD-NS is regarded as a promising technique to assist the high-speed PAM-4 signal generation with a 3-bit DAC in optical interconnection by considering the computational complexity and noise-shaping capability. In this part, only quantization noise is considered. In the following part, the proof-of-concept experiment of 100 and 110 Gb/s PAM-4 signal generated by 3-bit DAC will be executed to further illustrate the effectiveness of the CRD-NS technique.
Table 1. The SQNR of signals with various solutions.
3. Experiment Setups
The offline DSPs and experimental setups of 100 and 110 Gb/s PAM-4 signal are shown in Fig. 3. The PAM-4 signal is first generated by pseudo-random binary sequence (PRBS). Since serious bandwidth limitation can be observed in the measured channel response in Fig. 3(a), pre-equalization realized is executed with a 19-taps FIR filter. After pre-equalization, a root-raised cosine (RRC) filter with a roll-off factor of 1/16 is used for pulse shaping to improve the spectrum efficiency. After that, a 3-bit DAC combined with NS/CRD-NS/DRE techniques are used to quantize the signal and redistribute quantization noise. For both 100 and 110 Gb/s PAM-4 signal, the value of Ws is set as 16 and the WI is set as 1. For 100 Gb/s PAM-4 signal, the bandwidth using Ws to weight for the traditional NS and CRD-NS technique are 0.55${\ast }\left( {\frac{{{f_s}}}{2}} \right)$ and 0.6${\ast }\left( {\frac{{{f_s}}}{2}} \right)$, respectively. For 110 Gb/s PAM-4 signal, the bandwidth using Ws to weight for the traditional NS and CRD-NS technique are 0.6${\ast }\left( {\frac{{{f_s}}}{2}} \right)$ and 0.65${\ast }\left( {\frac{{{f_s}}}{2}} \right)$, respectively. It is noted that the ${f_s}{\; }$ represent the sampling rate of DAC. The taps length of feedback filter g for both CRD-NS and traditional NS techniques are set as 5, which indicates that no additional computational complexity is required for the CRD-NS technique. Both of them are optimized for NS and CRD-NS based on the corresponding pulse-shaped pre-equalized PAM-4 signal generated by a 3-bit DAC with 80 Gsa/s. For the DRE technique, the soft quantization possibilities M is set as 3. The number of taps L of FIR is set as 3 in this experiment to effectively reduce the computational complexity. The utilized DRE parameters are kept consistent with Refs. [25,27,28,34]. Then the analog signal is generated by an 8-bit DAC with an 80 GSa/s sampling rate to realize digital-to-analog conversion. The generated analog signal is amplified by an electrical amplifier (EA) with fixed 23 dB gains. Then, a 30 GHz commercial Mach-Zehnder modulator (MZM) based on a quadrature point is utilized to realize electric-to-optical conversion. The optical spectra of signal with and without the pre-equalization technique are shown in Fig. 3(b). The power of the signal after pre-equalization is more concentrated at the high-frequency area to avoid the signal being unevenly distributed at the receiver. The generated optical signal is launched into a 2-km single-mode fiber (SMF). At the receiver, to observe the improvement of the investigated scheme, a variable optical attenuator (VOA) is utilized to adjust the receiver optical power (ROP). A photodiode (PD) is utilized to realize optical-to-electric conversion and the output electric signal of PD is detected by a real-time 80 Gsa/s oscilloscope (OSC) with 8-bit resolution. For the receiver DSP, a MF implemented by a RRC filter with the same roll-off at the transmitter is applied to improve the signal-to-noise ratio (SNR) of the signal, then synchronization and post-equalization implemented by a 19-taps feed-forward equalizer (FFE) are used for data recovery.
Fig. 3. The offline DSPs and experimental setups of 100 and 110 Gb/s PAM-4 signal. (a) The amplitude response of system and (b) the optical spectrum of the transmitted 110 Gb/s PAM-4 signal.
4. Experimental results
In this part, we will further show the effectiveness of CRD-NS for the high-speed pulse-shaped pre-equalized PAM-4 signal generated by a 3-bit DAC. The experimental results of 100 and 110 Gb/s PAM-4 signals with various schemes are shown in Fig. 4, where the results of optical back-to-back (OBTB) transmission are given in Fig. 4(a), and Fig. 4(b) shows the results over 2-km SMF transmission. Figure 4(c) gives the complementary cumulative distribution function (CCDF) curve of signals with various schemes. The PAPR of signal with DRE technique is much higher than the signal with CRD-NS and traditional NS technique, which indicated that the signal with the CRD-NS and traditional NS techniques suffer from less nonlinear distortions [35]. Due to the implementation of pulse shaping and pre-equalization, serious quantization noise appears when 3-bit DAC is utilized for signal generation, as shown in Fig. 4(a). Obvious bit error ratio (BER) performance improvement can be observed as NS, CRD-NS, and DRE techniques are applied. Compared with the signal with the traditional NS technique, about 0.5 dB receiver sensitivity improvement is achieved at the HD-FEC threshold when the CRD-NS technique is utilized for 100 Gb/s PAM-4 signal, and the corresponding improvement is 2 dB for 110 Gb/s PAM-4 signal. This improvement among different data rate is mainly induced by the increased influence of quantization noise. At the HD-FEC threshold, the CRD-NS technique can bring about 1 dB receiver sensitivity improvement compared to the DRE technique for 100 Gb/s signal, while similar receiver sensitivity for 110 Gb/s PAM-4 signal. This performance differences are induced by the accuracy of channel and MF response estimation using 3-taps FIR. The aforementioned improvement can still be observed when the signal is over 2-km SMF transmission as shown in Fig. 4(b). Since the required computational complexity of DRE required 81 real multiplications per sample is much higher than the CRD-NS technique required 5 real multiplications per sample [27,28], thus, for the generation of the high-speed pulse-shaped pre-equalized PAM-4 signal, considering system cost and BER performance, the 3-bit DAC with CRD-NS technique is regarded as a promising scheme for optical interconnection.
Fig. 4. BER versus ROP of 100 and 110 Gb/s PAM-4 signal generated by 3-bit DAC with the various schemes over (a) OBTB and (b) 2-km SMF transmission. (c) The CCDF curve of 100 Gb/s PAM-4 signal with various schemes.
5. Conclusion
In this paper, the transmission of high-speed pulse-shaped pre-equalized PAM-4 signals over 2-km SMF using 3-bit DAC are studied with different quantization noise suppression techniques. For the pulse-shaped pre-equalized PAM-4 signal, the CRD-NS technique shows a better noise-shaping capability than traditional NS technique. The BER performance of the signal with DRE technique similar to the signal with the CRD-NS technique, while the required computational complexity increases significantly, the number of real multiplications per sample is increased from 5 to 81. Thus, for the generation of high-speed pulse-shaped pre-equalized PAM-4 signal, taking both the system cost and BER performance into consideration, 3-bit DAC with CRD-NS technique is regarded as a promising scheme for the cost-sensitive optical interconnection.
Funding
National Natural Science Foundation of China (U2001601, 62261051, 62271517, 62035018); Local Innovation and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121).
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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