1. Introduction

The exponential growth of Internet traffic in 5G Era has brought great challenges on the line rate of intra-data-center interconnect (intra-DCI). According to the Cisco Global Cloud Index [1], global data center IP traffic is growing at 25% compound annual growth rate (CAGR), in which >70% traffic are related in intra-DCI scenario. As 400-gigabit Ethernet (GbE) interface has been standardized in IEEE [2] using 4/8 lanes × 100/50 Gb/s 4-ary pulse amplitude modulation (PAM-4) with intensity-modulation and direct detection (IM-DD), there are also discussions on higher speed such as 800Gb/s. Generally, increasing the symbol rate is an effective solution for optical transmission, which reduces the overall system cost by decreasing the number of transceivers. Therefore, the sampling rate and bandwidth of digital-to-analog convertor (DAC) and analog-to-digital convertor (ADC) are critical for ultra-high baud rate signal generation [3].

The methods to generate ultra-high-speed signal can be categorized into electrical and optical schemes. For electrical schemes, a straightforward way is electrical time-division multiplexing (ETDM) [4–9]. In Ref. [4], based on InP technologies, up to 204Gbaud OOK signal is generated by cascaded 2:1 double heterojunction bipolar transistor selector multiplexer (MUX) and modulated through 100GHz monolithically integrated travelling-wave electro-absorption modulator (TWEAM). Later on, a higher record of 222Gbaud OOK generation is reported by using the same MUX and plasmonic-organic Mach-Zehnder modulator (MZM) with bandwidth larger than 100GHz [5]. To extend the electrical bandwidth, analog multiplexer (AMUX) [10–12] and digital-band-interleaved (DBI) [13–15] based DAC architectures are proposed respectively. The former elaborately realize frequency-domain interpretation through high-speed selector, while the latter up-converts baseband signal from each DAC onto different intermediate frequencies (IFs). Net data rate of 400Gb/s (162Gbaud) probabilistic shaped (PS) PAM-16 signal is reported with AMUX-DAC [12]. Recently, 700Gb/s entropy-loaded PS 256-ary quadrature amplitude modulation (256-QAM) and 200Gbaud PS-PAM-16 signal 10km transmission is achieved with DBI-DAC and thin-film LiNbO3 MZM [15]. On the other hand, for optical schemes, TDM is still feasible with high-speed optical pulses [16–19]. In Ref. [17], based on all-optical Nyquist pulses generated by an optical frequency comb (OFC), full-band transmission and coherent detection of 125Gbaud quadrature phase shift keying (QPSK) and 16-QAM signal is demonstrated. Alternately, the OFC source can be replaced by mode-locked laser, and 120Gbaud PAM-4/6 signal TDM generation is reported [18]. Enabled by the return-to-zero (RZ) pulse modulation characterization of MZM, 224Gb/s PAM-4 signal is realized with optical time- and polarization-interleaving (OTPI) technique [19]. In addition, time-interleaving IQ modulator (TI-IQM) is designed and fabricated as an optical version of AMUX-DAC, which successfully generates 150Gbaud 4/8/16-QAM signal with only 23GHz 3dB electrical-to-optical bandwidth [20].

Apart from the aforementioned works, precoding algorithms can be also employed to enhance the performance of single DAC, which realizes spectral shaping by introducing controlled inter-symbol interference (ISI) and offers a hardware-efficient solution. The most classic approach is duobinary shaping [21]. For cost-sensitive applications, 112Gb/s PAM-4 transmission with commercial 20GHz components is reported thanks to duobinary-based bandwidth narrowing [22]. Stronger spectral shaping is demonstrated with polybinary PAM, achieving a potential 7.95b/s/Hz at 14.32Gb/s [23]. Meanwhile, the precoder can be modified from the feed forward structure into feedback manner. Nonlinear partial response PAM (NLPRM) is proposed and validated through 93Gbaud PAM-4 O-band transmission with 14GHz 3dB bandwidth limitation [24]. Later, nonlinear differential coding PAM (NLDCP) is put forward with flexible tap coefficient for various bandwidth condition [25]. For detection techniques, maximum likelihood sequence detection (MLSD) provides better performance than symbol-by-symbol detection under a memory channel [26]. By combining transmitter-side digital anti-aliasing filter and receiver-side MLSD, up to 125Gbaud OOK signal transmission is achieved at sub-sampling rate of 0.736 [27]. Furthermore, 190Gbaud OOK generation and 180Gbaud OOK 2km transmission are demonstrated with 92GSa/s by proposing a coding and cutting technique [28]. The used cascaded duobinary or high-order partial response structure offers stronger filtering and maintains the most of the signal energy. Another famous approach is Tomlison-Harashima precoding (THP) [29,30], which relies feedback between the transmitter and receiver for coefficients estimation. After applying THP, 72.5Gbaud faster-than-Nyquist (FTN) PAM-4 signal is transmitted over 2km standard single-mode fiber (SSMF) with 70GSa/s DAC [31]. Later, the ability of THP to combat bandwidth limitation is fully demonstrated. In Ref. [32], 94Gbaud PAM-4 signal can be detected with 33GHz brick-wall electrical bandwidth limitation. Since the transmitted sequence after THP has more levels, the concept of generalized THP (GTHP) is recently introduced for transmitter-side nonlinearity compensation and geometrical shaping [33].

In Ref. [34], up to 205Gbaud OOK signal generation and 500m SSMF transmission is demonstrated with 120GSa/s DAC. Sub-sampling rate of 0.585 is achieved by using high-order partial response narrowing (HPRN). In this paper, we extend our previous work in the following aspects: (1) the influence of sub-sampling rate and partial response (PR) order are numerically investigated, which provides a reference for the trade-off between PR orders and modulation formats regarding OSNR penalty; (2) 210Gbaud OOK generation at 0.571 sub-sampling rate is further demonstrated through optimizing the setup configuration; (3) the application of HPRN for high-order modulation formats including PAM-3 and PAM-4 are experimentally studied; (4) sub-sampling generation of QPSK signal in coherent detection system is also realized with the help of carrier phase recovery consisting of pilot symbol group-based coarse estimation and shaped constellation-based blind phase search (BPS) algorithm.

The rest of this paper is organized as follows. In Section II, the principle of high-order partial response narrowing is presented. Section III investigates the influence of PR orders on sub-sampling generation performance with different formats in simulation. Section IV and V provide experimental results of PAM and QAM signals in IM-DD and coherent detection system, respectively. Finally, Section VI concludes the work.

2. Principle

In this section, we introduce the principle of sub-sampling signal generation based on the high-order PR method. Figure 1(a)–1(c) illustrate the principle of transmitter-side signal generation in the over-/sub-sampling cases, respectively. Here ${F_s}$ and ${F_{DA}}$ denote the target signal baud rate and DAC sampling rate, respectively. The red dashed lines represent the Nyquist frequency of DAC sampling rate, while the yellow dashed curve is the DAC bandwidth. For the conventional over-sampling case in Fig. 1(a), the original symbol sequence is firstly convoluted with digital root-raised cosine (RRC) filter with roll-off approaching zero. In this stage, the signal spectrum is narrowed from sinc-shape into rectangular-shape, whose spectral range is decreased from $[{ - {F_s},{F_s}} ]$ to $[{ - {{{F_s}} / 2},{{{F_s}} / 2}} ]$. According to the property of discrete Fourier transform (DFT), the spectrum of discrete digtal waveform has multiple replicas appearing at the period of ${F_{DA}}$ in the frequency domain. Since ${F_{DA}} > {F_s}$ is satisfied in the over-sampling case, the replicas do not overlap with baseband signal. After digital-to-analog conversion, electrical low-pass filter (LPF) is needed to remove the spectral replica. For high-speed signal generation, the DAC bandwidth limitation takes the role of LPF in practical implementation.

 

Fig. 1. Principle of transmitter-side signal generation in the case of (a) over-sampling, (b) sub-sampling, and (c) sub-sampling with HPRN and anti-aliasing filter based signal generation. HPRN: high-order partial response narrowing; RRC: root-raised cosine; F_S: signal baud rate; F_DA: DAC sampling rate.

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As the target signal baud rate gets larger, the over-sampling case will turn into the sub-sampling case as shown in Fig. 1(b) under the condition of ${F_{DA}} \le {F_s}$. In this case, the spacing between baseband signal and its spectral replica is smaller than Nyquist frequency, resulting in in frequency-domain overlap and severe ISI. Note that such ISI cannot be suppressed through DAC bandwidth filtering, since the overlap happens before digital-to-analog conversion. To avoid overlap, an effective method is applying a digital brick-wall anti-aliasing filter, which cuts off the out-of-band spectral components before down-sampling. However, another problem is that a significant part of signal energy would be lost. This issue becomes more serious when the sub-sampling rate gets lower.

To address both overlap and energy loss issues, high-order partial response narrowing can be employed as in Fig. 1(c). For k-order PR signaling, the symbol sequence convolutes with a finite impulse response (FIR) filter, whose taps can be obtained according to the coefficient of k-order polynomial ${({1 + D} )^k}$. Here D denotes one symbol period delay. Specifically, the coefficients of FIR filters with PR order up to 7 is displayed in Table 1. Correspondingly, the same coefficients are used in the receiver-side MLSD. With the help of HPRN, the signal energy can be concentrated in the low-frequency region, so that it will not be removed after passing the anti-aliasing filter. The PR order k can be optimized based on the sub-sampling rate.

Table 1. Coefficients used for high-order partial response signaling.

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Theoretically, the well known sampling theorem [35] states that, to reconstruct a one-dimensional signal from a set of samples, the sampling rate must equal to or greater than twice the highest frequency in the signal. According to the theorem, the sampling rate actually brings a fundamental limitation on the signal bandwidth rather than the symbol rate for distortionless transmission. Therefore, the key point of high-order PR narrowing scheme is to concentrate most of the signal energy in the low-frequency region within the Nyquist frequency of DAC. By this means, although the highest-frequency components outside the Nyquist frequency is still removed after anti-aliasing filter. The influence of such low-pass filtering can be reduced since the lost part of signal energy is greatly suppressed, making it possible to generate higher baud rate signal beyond the DAC sampling rate.

In addition, it is worth noting that the spectral replica also exist for the discrete-time signal in the digital domain after ADC sampling. Similarly, for sub-sampling reception at the receiver, anti-aliasing filter is still needed to avoid spectral overlap, which can be implemented in the digital or electrical domain at the transmitter, or using optical filter before ADC. In such scenario, high-order PR can help narrow the signal bandwidth before low-pass filtering as well, and thus mostly avoid signal energy loss during detection.

3. Numerical validation

In this section, we numerically investigate the sub-sampling generation performance of different modulation formats. For the sake of simplicity, IM-DD configuration at back-to-back (BTB) scenario is considered. Transmitter-side MZM and receiver-side photodiode (PD) are both ideal without bandwidth limitation. To suppress the modulation nonlinearity, the carrier-to-signal power ratio (CSPR) of modulated PAM signal is set as 25dB. Only optical noise is added to acquire the optical signal-to-noise ratio (OSNR) sensitivity. We change the target baud rate with fixed DAC sampling rate of 120GSa/s to keep consistent with the experimental parameters in Section IV.

3.1 DSP stacks

The transmitter- and receiver-side digital signal processing (DSP) stacks are shown in Fig. 2(a)-2(b). At the transmitter, OOK/PAM-3/4 symbols are mapped from binary bit stream. Notably, for PAM-3 formats, we first map every three bits onto a 8-QAM constellation. The constellation points (−2, 2), (0, 2), (2, 2), (2, 0), (2, −2), (0, −2), (−2, −2), and (−2, 0) correspond to bit group from 000 to 111 in ascending order. Then the in-phase (I) and quadrature (Q) components are transmitted at two neighboring time slots, achiving source entropy of 1.5(=3/2) bits/symbol. Each frame consists of a 128-symbol synchronization sequence, a 2048-symbol training sequence, and 30000 data symbols as payload. Then k-order PR signaling is applied at 1 sample per symbol (SPS). After 2-times up-sampling, the signal is digitally shaped by RRC filter with roll-off factor of 0.01. At this time, the overall spectral randge is $[{ - {F_s},{F_s}} ]$ at 2 SPSs. For sub-sampling case, digital anti-aliasing filter is employed to remove any components at frequencies $|f |> {{{F_{DA}}} / 2}$, which is implemented in the frequency domain in our simulation and experiment. For practical system, the brick-wall filter can be also implemented as a sinc-shaped time-domain finite-impulse-response (FIR) filter to reduce the processing latency. Larger tap length brings less out-of-band spectral leakage and can thus approach the performance of ideal rectangular-shaped anti-aliasing filter. According to our simulation evaluation, 1024 taps is sufficient to achieve negligible implementation penalty. Afterwards, re-sampling from 2 SPSs to 120/B SPSs is conducted to obtain the desired baud rate of B. For MZM simulation, direct current (DC) offset is added to emulate the quadrature biased state, and the CSPR is kept as 25dB to ensure linear modulation.

 

Fig. 2. (a) Transmitter-side and (b) Receiver-side DSP stacks. (c) Digital signal spectra with different PR orders at 2 samples per symbol. Tx: transmitter-side; Rx: receiver-side; SPS: sample per symbol; RRC: root-raised cosine; AWGN: additive white Gaussian noise; MLSD: maximum likelihood sequence detection; PR: partial response.

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After additive white Gaussian noise (AWGN) loading at target OSNR, the signal is detected by PD, which is simulated through modular square operation. In the receiver-side DSP, the received waveform is re-sampled back to 2 SPSs. After matched RRC filter and synchronization, T/2-spaced time-domain linear FIR equalizer is applied. For fast convegence, the filter taps are updated by the recursive least square (RLS) algorithm based on training sequence with k-order PR signaling. The number of taps is fixed as 101 in numerical simulation. After down-sampling to 1 SPS, MLSD based on Viterbi decoding algorithm [36] is used subsequently for symbol decision. For k-order PR and modulation format PAM-M (M = 2,3,4), the memory length and states of MLSD are k+1 and M^k, respectively. And the same coeffients as in Table.1 are used for distance metric calculation. Finally, BER is measured by error counting of 2¹⁸ bit samples.

Figure 2(c) displays the digital signal spectra with different PR orders at 2 SPSs. Note that 0-order PR means without partial response, and the spectrum (black curve) is rectangular due to Nyquist shaping. With higher-order PR, the signal energy is more tightly constrained. Additonally, blue block is used to represent the Nyquist region of DAC sampling rate, whose boundary is half of sub-sampling rate in the normalized frequency. Therefore, to achieve lower sub-sampling rate, higher-order PR is required to save more signal energy during anti-aliasing filtering.

3.2 OOK Performance

Figure 3(a) plots the simulated required OSNR for OOK signals with different baud rates and PR orders. Here the OSNR is defined as the ratio between signal power and integrated noise power within 0.1nm (12.5GHz). Note that the power of optical carrier is excluded in the OSNR definition. Strictly speaking, the OSNR can be understood as ‘effective OSNR’. To obtain the required OSNR, 20% hard-decision forward error correction (HD-FEC) threshold of 1.5×10⁻² [37] is chosen in Fig. 3(a)-3(c). For the colored curves with PR orders from 0 to 7, the DAC sampling rate is fixed at 120GSa/s regardless of signal baud rate. The blue and green region correspond to the case of over-sampling and sub-sampling, respectively. On the contrary, the gray curve is plotted as reference, which is obtained at 2 SPSs. Specifically, the sampling rate is adjusted to be twice of the target baud rate to avoid spectral overlap. Theoretically, the required OSNR increases proportional to the logarithm of baud rate.

 

Fig. 3. Simulated required OSNR at BER of 1.5×10⁻² for (a) OOK, (b) PAM-3, and (c) PAM-4 signals with different baud rates and PR orders. (i)-(viii) Typical eye-diagrams of 120Gbaud OOK signal with different PR orders. (ix)-(xiii) Typical eye-diagrams of 120Gbaud PAM-3 signal with different PR orders. (xiv)-(xvii) Typical eye-diagrams of 120Gbaud PAM-4 signal with different PR orders.

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For 0-order PR case (Nyquist shaping only), the black curve coincides with the reference gray curve of 2 SPSs when the baud rate is less than 120Gbaud, indicating that up-sampling rate between 1 and 2 do not induce additional penalty. However, once baud rate goes beyond 120Gbaud, the penalty grows rapidly even through anti-aliasing filter is applied. It can be explained as the significant signal energy loss in Section II. Fortunately, if 1-order PR is used, we can further increase the baud rate to approximately 160Gbaud at a fixed additional penalty with respect to 0-order PR. Such ∼2dB penalty results from the increased eye levels after duobinary operation, making the signal less tolerant to noise. Moreover, if we compare different high-order PR curves at baud rates from 60Gbaud to 120Gbaud, a fixed OSNR penalty can be observed. Since there is neither bandwidth limitation nor subsampling-induced spectral truncation/overlap in such region, the only ISI can be attributed to the precoding process of high-order PR. In other words, although MLSD can effectively eliminate the ISI from PR, additional OSNR penalty will be brought by the increased signal levels after high-order PR, and such penalty grows with both modulation format and PR order. Nevertheless, all the transition points for PR order shifting are provided in Fig. 3. These points appear as a trade-off between PR-induced penalty and bandwidth cutting in sub-sampling case. Another phenomenon observed in Fig. 3(a) is that n^th-order PR has similar performance as (n+1)^th-order PR in the transition region for PR order higher than 2. When approaching the cross points from lower baud rate with lower-order PR, the curve gradually becomes steeper since the signal energy is getting lost as the ratio between the Nyquist frequency of DAC sampling rate and signal bandwidth decreases. Meanwhile, the higher-order PR has better tolerance since more signal energy is concentrated in the low-frequency region, leading to a relatively slower growth trend. Such tendency is more obvious among lower-order PR because the in-band signal energy ratio gradually gets saturated with increased PR order. According to the simulation results, by applying 7-order PR, up to 280Gbaud OOK signal can be generated based on 120GSa/s DAC. The required OSNR is 9.5dB higher than standard OOK generation at 2 SPSs condition using 240GSa/s DAC. It should be noted that such extremely low sub-sampling rate of 0.429 is achieved without considering transceiver bandwidth limitation or quantization noise, which would bring distortions on the generated waveform in practical situation.

To get a intuitive understanding, Fig. 3(i)-(viii) display the typical eyediagrams of 120Gbaud OOK signal with different PR orders. At the optimal sampling point, there are 2, 3, 5, 9 eye levels with 0/1/2/3-order PR, respectively. Although higher PR orders result in complicated eyes with many levels, MLSD is still capable of decoding with known tap coefficients according to the PR order. Consequently, high-order PR narrowing based sub-sampling scheme actually gains bandwidth utilization at the expense of SNR sensitivity.

3.3 PAM-3 Performance

For higher-order modulation formats, the higher-order PR narrowing scheme is also applicable. Figure 3(b) shows the required OSNR versus baud rate with different PR orders for PAM-3 signal. Similar to OOK format, the required OSNR without PR (black curve) increases along with the reference gray curve of 2 SPSs in the interval of [60Gbaud, 120Gbaud]. Afterwards, 1-order PR should be employed instead of Nyquist shaping only to overcome the dramatic increase in OSNR penalty. With the help of 1/2/3/4-order PR, 140/165/180/195Gbaud PAM-3 signals can be generated, corresponding to bitrates of 210/247.5/240/292.5Gb/s. Compared with OOK signal, the achievable sub-sampling rate of PAM-3 format is larger with the same PR order. Figure 3(ix)-(xiii) show typical eye-diagrams of 120Gbaud PAM-3 signals with various PR orders. Correspondingly, 3, 5, 9 and 17 levels can be observed with 0/1/2/3-order PR, which is much larger than with OOK format. The eye-diagrams can be used to confirm that higher-order modulation format is more sensitive to noise. Nevertheless, the maximum bitrate is increase to 292.5Gb/s.

3.4 PAM-4 Performance

Moreover, the sub-sampling generation performance of PAM-4 format is simulated in Fig. 3(c). A dramatic rise occurs when the baud rate increases from 120Gbaud to 125Gbaud with 0-order PR (black curve). After applying 1/2/3-order PR, the achievable baud rate are extended to 130Gbaud, 155Gbaud and 170Gbaud, respectively, leading to sub-sampling rate of 0.706. Since 2bits are delivered by each PAM-4 symbol, the bitrates can be calculated as 260Gb/s, 310Gb/s and 340Gb/s. Therefore, although the capability of sub-sampling generation of our scheme becomes weaker for higher-order formats, the achivable bitrate still continuously increases. The eye-diagrams of 120Gbaud PAM-4 signals with different PR orders are shown in Fig. 3(xiv)-(xvii).

From the perspective of optimal OSNR sensitivity for the target bitrate, we need to compare the OSNR penalty and determine whether to apply high-order PR on low-order modulation format, or switch low-order modulation format to higher ones. For example, when targeting at 150Gb/s bitrate, the required OSNR values are 16.9dB, 17.1dB and 18.2dB with OOK (1-order PR), PAM-3 and PAM-4 formats, respectively. As a consequence, OOK format with 1-order is a better choice in this case. However, for 210Gb/s bitrate, the required OSNR of 19.7dB with PAM-4 is lower than 21.6dB with OOK (3-order) and 22.0dB with PAM-3 (1-order). The reason is that as PR order increases, the penalty caused by high-order PR gradually becomes larger than using higher-order formats. Nevertheless, Fig. 3(a)-3(c) can be regarded as a reference for joint optimization of PR order and modulation format for a target bitrate based on 120GSa/s DAC sampling rate.

3.5 Influence on Signal PAPR

Furthermore, as shown in Fig. 4(a)-(c), we simulate the influence of baud rate and PR order on the peak-to-average power ratio (PAPR) of the transmitted waveform with fixed 120GSa/s sampling rate. The dashed horizontal dashed lines show the PAPR of the symbol sequence after applying PR signaling without upsampling and pulse shaping as references, which increases with both PR orders and modulation formats. For RRC shaping with small roll-off factor of 0.01, the PAPR of the transmitted waveform is mainly determined by the amplitude of the non-optimal sampling points, and can be much larger than the PAPR of symbol sequence. It should be noted that high-order PR enhances the correlation between neighboring points, the waveform can thus be ‘smoothed’ and the non-optimal sampling points are less deviated from the optimal sampling points. As a consequence, the PAPR of the transmitted waveform is more stable and gets closer to the PAPR of symbol sequence. Interestingly, there is a drop in PAPR at 120Gbaud, because the waveform at 1SPS is similar to the symbol sequence. Afterwards, as the baud rate increases in the sub-sampling region, the PAPR of the transmitted waveform first keeps unchanged and then rises around the cross points in Fig. 3(a)-3(c). It can be attributed to the severe ISI from brick-wall filter at low sub-sampling rate.

 

Fig. 4. Simulated PAPR for (a) OOK, (b) PAM-3, and (c) PAM-4 signals with different baud rates and PR orders.

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4. IM-DD experiment with PAM signal

4.1 Experimental setup

Figure 5(a) illustrates the experimental setup of PAM-2/3/4 signal generation and transmission in a IM-DD system. At the transmitter, an external cavity laser (ECL) centered at 1549.99nm wavelength is employed as optical source. PAM-2/3/4 signals are generated by arbitrary waveform generator (AWG, Keysight M8194) with 120GSa/s sampling rate and 45GHz 3dB bandwidth. The electrical waveform then modulates the optical carrier through 35GHz Mach-Zehnder modulator (MZM, Fujistu FTM7937) biasing at quadrature point. The launch optical power is measured as 6dBm. In our experiment, differential driven mode is utilized to enhance the modulation index instead of electrical amplifiers (EAs), which would bring additional bandwidth limitation. In such case, the CSPR is estimated to be larger than 20dB. Therefore, the bias-induced strong optical carrier occupies most of the optical power and the modulation formats and PR orders have little influence on it. To emulate intra-DCI scenario, 500/1000m SSMF transmission are tested as well as BTB case. The accumulated chromatic dispersion is estimated as 8.5ps/nm and 17ps/nm for 500m and 1000m fiber, respectively. No optical amplifier is used due to the negligible fiber loss.

At the receiver, a variable optical attenuator (VOA) is placed to adjust the received optical power (ROP). A 50GHz PD is used to detect the optical signal. After amplified by EA (SHF S807) with 50GHz bandwidth and 23dB gain, the electrical waveform is sampled and stored by a real-time oscilloscope (RTO, Keysight DSA-X 96204Q) with 160GSa/s sampling rate and 63GHz bandwidth. It should be noted that different from Ref. [34], no cables are used for connecting PD, EA, and RTO. By this means, slightly larger receiver bandwidth is acquired, and higher baud rate of 210Gbaud is thus realized. Besides, it is worth mentioning that high-order PR is employed not only for 210Gbaud OOK sub-sampling generation with 120GSa/s DAC, but also for sub-sampling reception with 160GSa/s ADC. To compensate for the modulator nonlinearity with moderate complexity, 3^rd-order Volterra nonlinear equalizer with only diagonal terms are used. The filter taps are 201, 25, and 1 for 1^st-, 2^nd-, and 3^rd-order terms, respectively. The rest of the transmitter- and receiver-side DSP are the same as simulation in Fig. 2(a).

4.2 OOK results

Figure 5(b) compares the measured optical spectra of 210Gbaud OOK signal with different PR orders. The resolution is set as 0.01nm to see the details. Here 0-order represents for Nyquist shaping. It can be observed that with higher-order PR signaling, the low-frequency components around optical carrier gets larger, while the high-frequency region fades more rapidly. Therefore, the signal bandwidth is effectively narrowed, which fits well with digital signal spectra in Fig. 2(c). Figure 5(c) depicts the measured optical spectra with baud rates ranging from 160Gbaud to 210Gbaud at 0.01nm resolution. The PR order is fixed at 7 for fair comparison. Since the practical bandwidth of AWG and MZM becomes the dominant limitation, the spectral width of 210Gaud signal is only slightly larger than 160Gbaud signal.

 

Fig. 5. (a) Experimental setup of IM-DD system. ECL: external cavity laser; AWG: arbitrary waveform generator; MZM: Mach-Zehnder modulator; SSMF: standard single-mode fiber; VOA: variable optical attenuator; PD: photodiode; EA: electrical amplifier; RTO: real-time oscilloscope. (b) Measured optical spectra of 210Gbaud OOK signal with different PR orders at 0.01 nm resolution. (c) Measured optical spectra of different baud rate OOK signals with 7-order PR. (d) Measured BER versus PR orders with different baud rate OOK signals. (e) Measured BER versus bitrate at BTB, after 500 m and 1 km SSMF transmission, respectively. (f) Measured BER versus ROP for 210Gbaud OOK signal at different transmission distances. (i)-(viii) Typical eye-diagrams of 160/170/180/190/200/205/210Gbaud OOK signal with 3-order PR.

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Then the BER performance is quantitatively evaluated. Figure 5(d) shows the measured BERs versus PR orders with different baud rates at BTB case, respectively. The ROP is fixed at 3dBm through the VOA. For lower-order PR signaling, more signal energy would be lost after anti-aliasing filter. On the other hand, higher-order PR increases the number of signal levels. Consequently, PR order should be optimized as a trade-off between ISI and SNR. According to Fig. 5(d), as the bitrate goes up from 160Gb/s to 200Gb/s, the optimal PR order gradually increases from 2 to 5, and then converges to 7 for 205Gbaud and 210Gbaud. Note that the optimal PR order is higher in the experiment compared with simulation results in Fig. 3(a), which is mainly caused by the bandwidth limitation of transceiver.

Figure 5(e) plots the measured BERs as a function of bitrate at BTB, and after 500m/1000m SSMF transmission, respectively. The PR order has been optimized according to the baud rate. To be specific, the PR orders are 2/3/4/4/5/7/7 for 160/170/180/190/200/205/210Gb/s, respectively. For the BTB and 500m SSMF transmission, 210Gb/s and 180Gb/s OOK signals can achieve the 20% and 7% HD-FEC thresholds, respectively. For 1km SSMF transmission, the maximum bitrate is decreased to 205Gb/s. It can be explained by the fiber dispersion and square-law detection induced frequency-selective power fading effect [38], which acts as an additional low-pass filter and makes the system bandwidth limitation more seriously. Figure 5(f) shows the measured ROP sensitivity for 210Gb/s OOK signal at different transmission distances. The optimal PR order of 7 is used. At the 20% HD-FEC threshold, the ROP sensitivities are 0.5dBm and 2.7dBm at BTB and after 500m transmission, respectively. Figure 5(i)-(vi) display the typical eye-diagrams of different baud rates after equalization at BTB scenario. 3-order PR is chosen to show relatively clear eyes with reduced levels. The eyes gradually become unclear due to the influence of ISI.

4.3 PAM-3 Results

For PAM-3 format, the optical spectra with different baud rates are shown in Fig. 6(a). The PR order is fixed as 2. When the baud rate is higher than 120Gbaud, the theoretical Nyquist electrical bandwidth is beyond 60GHz, which is much larger than the MZM bandwidth of 35GHz. In such band-limited case, the optical spectrum can no longer expand linearly with the baud rate. Figure 6(b) shows the measured BER versus PR order for PAM-3 signals from 120Gbaud to 145Gbaud. The optimal PR order is 3 for 145Gbaud, and the value decreases to 2 for the rest baud rates. Different from simulation result in Fig. 3(b), 2-order PR instead of 1 is needed for 120Gbaud, indicating that PR can also improve the bandwidth tolerance in our experiment. Compared with OOK results, the optimal PR order grows slower as a function of signal baud rate. The reason is that the eye level goes up more rapidly as PR order increases for PAM-3 than OOK, which would lead to higher error floor limited by the DAC pattern effect and modulation nonlinearity. Figure 6(c) provides the measured BER versus bitrate at different transmission distances, respectively. For the BTB case, 217.5Gb/s PAM-3 can be successfully generated at the 20% HD-FEC threshold. For 500m and 1km SSMF transmission, 210Gb/s and 202.5Gb/s can be supported. Typical eye diagrams of PAM-3 signals at different baud rates are displayed in Fig. 6(i)-(vi), in which the 2-order PR is adopted.

 

Fig. 6. (a) Measured optical spectra of different baud rate PAM-3 signals with 2-order PR. (b) Measured BER versus PR orders with different baud rate PAM-3 signals. (c) Measured BER versus bitrate at BTB, after 500 m and 1 km SSMF transmission, respectively. (i)-(vi) Typical eye-diagrams of 120/125/130/135/140/145Gbaud PAM-3 signal with 2-order PR.

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4.4 PAM-4 results

When the modulation format is shifted to PAM-4, the ability of sub-sampling generation is further limited. Figure 7(a) plots the optical spectra of 120/125/128Gbaud PAM-4 signals at 0.01nm resolution with PR order of 2. Figure 7(b) shows the measured BER versus PR order for 120/125/128Gbaud PAM-4 signals. The optimal PR order is 2 for all the baud rates. Figure 7(c) shows the measured BER versus bitrate at different transmission distances, respectively. For 500m SSMF transmission, negligible penalty is observed, and 256Gb/s PAM-4 can be still achieved the same as BTB case at the BER threshold of 1.5×10⁻². When the transmission distance increases to 1km, the maximum bitrate is slightly reduced to 250Gb/s. By comparing Fig. 7(c) with Fig. 5(f) and Fig. 6(c), a larger BER gap is observed between 500m and 1000m with higher modulation format. The reason is that the fading effect caused by fiber dispersion and square-law detection acts as a low-pass filter. In such case, higher order modulation format is more sensitive to the impairment since the induced-ISI is more complicated with larger number of symbol levels. Figure 7(i)-(iii) provide the typical eye diagrams of PAM-4 signals at different baud rates with PR order of 2, in which 13 eye levels can be observed.

 

Fig. 7. (a) Measured optical spectra of different baud rate PAM-4 signals with 2-order PR. (b) Measured BER versus PR orders with different baud rate PAM-4 signals. (c) Measured BER versus bitrate at BTB, after 500 m and 1 km SSMF transmission, respectively. (i)-(iii) Typical eye-diagrams of 120/125/128Gbaud PAM-4 signal with 2-order PR.

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According to both simulation and experimental results of OOK, PAM-3 and PAM-4, it is shown that the maximum baud rate with fixed DAC sampling rate decreases as the modulation format increases. Nevertheless, based on 120GSa/s DAC, the maximum bitrate at BTB case still increases from 210Gb/s to 256Gb/s by upgrading from OOK to PAM-4. Therefore, joint optimization of modulation formats and PR order is more effective than only increasing the baud rate with very high-order PR signaling.

5. Coherent detection experiment with QAM signal

Based on the principle in Section II, real-valued waveform can be maintained after high-order PR and anti-aliasing filter with PAM signals. Therefore, such scheme can be separately applied on the in-phase and quadrature components of QAM signal, if laser phase noise is compensated. In this section, we further demonstrate the feasibility of high-order PR narrowing for QAM signals in coherent detection systems.

5.1 Experimental setup and DSP stacks

The experimental setup is shown in Fig. 8(a). At the transmitter, a continuous-wave 1550nm optical carrier is emitted from an ECL with 100kHz linewidth. Electrical QPSK signal is generated by AWG operating at 120GSa/s. After amplified by a pair of EAs (SHF S807) with 50GHz bandwidth and 23dB gain, the in-phase and quadrature waveforms modulate the single-polarization IQ modulator (IQM, EOspace) biasing at the null point. The bandwidth of EA and IQM are respectively 50GHz and 30GHz, which is smaller compared with the IM transmitter in Section IV. At the receiver, polarization controller (PC) is used to align the signal to X-polarization. The reason is that the RTO in our experiment has only 2 channels operating at 160GSa/s and 63GHz bandwidth, which is not capable for polarization-diversity detection. After mixed with local oscillator (LO) in the 90° optical hybrid, 2 balanced PDs (BPDs) are used to realize optical-to-electrical conversion. Only the 2 channels corresponding to X-polarization is amplified and captured by RTO.

 

Fig. 8. (a) Experimental setup. PC: polarization controller; IQ Mod.: IQ modulator; EDFA: erbium-doped fiber amplifier; BPD: balanced PD; LO: local oscillator. (b) Frame structure. (c) Transmitter- and (d) Receiver-side DSP.

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Figure 8(b)-8(d) also provide the frame structure, transmitter-side and receiver-side DSP stacks. After QPSK mapping, a group of k+1 consecutive pilot symbols are inserted together in each 256-symbol block for phase recovery. Here k is the employed PR order, which varies from 0 to 4 in the following test. After applying high-order PR on the real and imaginary parts separately at 1 SPS, the transmitted sequence is up-sampled to 2 SPSs, and shaped by digital RRC filter with 0.01 roll-off. Then the waveform passes anti-aliasing filter to avoid overlap. To acquire the target baud rate of B with 120GSa/s AWG, the waveform is re-sampled to 120/B. Before sending to AWG, pre-emphasis is applied to deal with the transmitter-side bandwidth. Here we use quadrature curve (QC) fitting to raise the high-frequency components [39]. The response of QC fitting H(f) in the frequency domain is written in Eq. (1).

Here A is the QC fitting coefficient, and f is the frequency in Hz. Larger value of A enhances the high-frequency much more than low-frequency components. In our experiment, the QC fitting coefficient A is optimized as 2×10⁻⁹. At the receiver, the captured waveform is firstly resampled from 160/B SPSs to 2 SPSs. Then the frequency offset between ECL and LO is estimated, which is calculated according to the maximum position of the 4^th-power of received waveform in the frequency domain [40]. After time-domain training sequence-based RLS equalization, coarse and fine phase recovery is conducted. In the 1^st stage, phase noise in each block is estimated based on the phase difference between the received pilot symbols and the transmitted pilot symbols after PR signaling. To avoid the influence from unknown data symbols, only the (k+1)^th pilot symbol in each group is utilized to perform phase correction. In the 2^nd stage, shaped constellations are used instead of standard QAM format for cost function calculation in BPS algorithm [41] to accommodate with high-order PR signaling. To be specific, the target constellation for symbol decision and cost function calculation is switched to 4/9/25/81-QAM for 0/1/2/3-order PR. Then decision-directed RLS equalizer is utilized to eliminate time-varying ISI and improve the signal quality. The target constellation is the same as that in the BPS algorithm. Finally, 2^k-state MLSD is applied on the in-phase and quadrature parts separately for k-order PR to reduce the computational complexity.

5.2 QPSK Results

In Fig. 9(a), the influence of PR order on BER is measured for QPSK signals at BTB case. The optimal order starts at 1 for 120Gbaud and 130Gbaud, and increases to 2 for 140Gbaud and beyond. The BER versus bitrate is shown in Fig. 9(b). Here the optimal PR order is used for each bitrate according to Fig. 9(a). The BER of 320Gb/s QPSK is measured as 8.5×10⁻³, which is lower than the 20% HD-FEC threshold. Theoretically, QPSK can potentially achieve the same sub-sampling rate as OOK since both in-phase and quadrature components are 2 levels. In our experiment, the worse result of QPSK than OOK mainly comes from the IQ crosstalk induced by laser phase noise and transmitter/receiver IQ imbalances. Such penalty increases with the number of constellation points, and the performance of high-order PR is thus severely degraded. The transmitter bandwidth limitation is also an influence factor. Specifically, the bandwidth of IQ modulator is smaller than MZM, and use of EAs impose additional limitation. Although the pre-emphasis is applied for QPSK experiment, the electrical SNR is reduced due to the increase in PAPR. Moreover, the OSNR sensitivity of 160Gbaud QPSK signal with 2-order PR is measured at BTB scenario in Fig. 9(c). Compared with theoretical curve, there are 18.7dB OSNR penalty at 20% HD-FEC threshold for 160GBaud sub-sampling generation. Since high-order PR is separately applied on the I/Q components of QPSK signal, the 2-order PR induced OSNR penalty can be estimated from the influence on OOK format. By comparing at 160GBaud in Fig. 3(a), there is ∼3.5dB additional penalty observed for 2-order PR than only Nyquist shaping at 2 SPSs. The rest huge penalty can be mainly attributed to the transceiver bandwidth limitation, and partly by the quantization noise of AWG and RTO. Figure 9(d) shows the measured optical spectra of 160Gbaud QPSK signal with different PR orders at 0.01nm resolution. Flat spectrum can be found with 0-order PR thanks to pre-emphasis, and high-frequency components are relatively suppressed as the PR order increases. Figure 9(e) compares the optical spectra of 120/130/140/150/160Gbaud QPSK signals. The PR order is set as 2. Figure 9(i)-(v) present typical constellations of 120/130/140/150/160Gbaud QPSK with PR order of 1 to see the constellation points. The constellation points of 9-QAM spreads out as baud rate increases. In addition, for 2-order PR signaling, the QPSK constellation can be further shaped into 25-QAM with non-uniform probabilities, which is also displayed in Fig. 9(vi)-(x) with baud rate varying from 120Gbaud to 160Gbaud.

 

Fig. 9. (a) Measured BER versus PR orders with different baud rate QPSK signals. (b) Measured BER versus bitrate at BTB case. (c) Measured OSNR sensitivity for 160Gbaud QPSK signal at BTB. (d) Measured optical spectra of 160Gbaud QPSK signal with different PR orders at 0.01 nm resolution. (e) Measured optical spectra of different baud rate QPSK signals with 2-order PR. (i)-(v) Typical constellations of 120/130/140/150/160Gbaud QPSK signal with 1-order PR. (vi)-(x) Typical constellations of 120/130/140/150/160Gbaud QPSK signal with 2-order PR.

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6. Conclusions

In conclusion, we provide a comprehensive evaluation of high-order PR narrowing scheme for ultra-high baud rate PAM signal sub-sampling generation with a single DAC. High-order PR can achieve signal bandwidth reduction to avoid energy loss during digital anti-aliasing filter. Through numerical simulation, the required OSNR with different PR orders are evaluated for OOK, PAM-3 and PAM-4 formats respectively, which offers a reference for joint optimization of PR order and modulation format for target bitrate with fixed sampling rate. In the experiment, based on 120GSa/s AWG and 160GSa/s RTO, up to 210Gb/s (210Gbaud) OOK, 217.5Gb/s (145Gbaud) PAM-3 and 256Gb/s (128Gbaud) PAM-4 signal can be successfully generated and detected in an IM-DD system. The sub-sampling rates are 0.571, 0.828, and 0.938, respectively. For QAM signal with coherent detection, after applying pilot symbol group-based coarse estimation and shaped constellation-based BPS for phase noise compensation, 320Gb/s (160Gbaud) QPSK signal sub-sampling generation is also demonstrated at BTB scenario based on 2-channel 120GSa/s DACs. Both simulation and experimental results confirm that the combination of high-order PR signaling and digital anti-aliasing filter can extend the usage of DAC at the expense of higher required OSNR.