1. Introduction

The rapid growth of the data center business is reshaping the current optical communication market because of increasing traffic in intra- and inter- data center networks [1]. In parallel, silicon photonics (SiP) serves as an appealing platform for low cost and power efficient data center related communication solutions due to the maturity of compact components [2], and the complementary-metal-oxide-semiconductor (CMOS) compatibility of the platform [3].

High speed SiP intensity modulation direct detection (IMDD) systems for intra data center applications have been widely reported [4–8]. However, the accumulated chromatic dispersion (CD) and square law detection induced power fading effects in these double sideband (DSB) systems prohibits the applications of these systems in data center interconnects (DCIs) that typically cover 40-80 km of standard single mode fiber (SSMF) [9].

For such distances, single sideband (SSB) self-coherent systems provide an alternative to a full coherent solution that has CD compensation capabilities, since the complex field information of a single polarization SSB signal can be obtained from only one single-ended photodetector (PD) and one analog-to-digital converter (ADC) channel. The signal-signal beating interference (SSBI) in these SSB systems can be mitigated by using SSBI estimation and subtraction methods [10–12] or the Kramer-Kronig (KK) receiver algorithm [13,14]. Generally, there are two ways to generate a single polarization SSB signal. One can either implement a digital Hilbert transform using two digital-to-analog converter (DAC) channels with an IQ modulator or a dual-drive Mach-Zehnder modulator (DD-MZM) [15–17], or one can modulate a real waveform from one DAC channel (or a pattern generator) onto a single-drive intensity modulator and use an optical bandpass filter (OBPF) to suppress half of the spectrum [18–21]. The latter scheme is often referred to as vestigial sideband (VSB), since the limited sharpness of the filter edge usually leads to a non-ideal SSB spectrum. Both schemes can be implemented using SiP devices and systems. A 50Gb/s digitally generated single polarization single wavelength SSB 16-ary quardrature amplitude modulation (16QAM) transmission over 320 km SSMF using a packaged SiP IQ modulator at a bit error rate (BER) of 2.7 × 10⁻³ was recently reported in [15]. Also, an optically filtered single polarization VSB system was realized on SiP platform in [20], where a 4-wavelength 86 Gb/s/λ digital multitone (DMT) transmission over 40 km at a BER of 3.8 × 10⁻³ was achieved without SSBI mitigation. By using SSBI mitigation methods such as KK detection, a 25 GBaud single polarization single channel 16 QAM transmission over 80 km through a SiP MZM based VSB system was recently demonstrated with a BER of 3.8 × 10⁻³ [21].

DAC-less transmitter using multi-drive modulator has recently gained interest as a way of removing the need of electrical DACs for multi-level signal generation, which leads to lower complexity, lower cost, smaller footprint and lower power consumption at the transmitter [24,25]. Multi-drive modulators have been realized on different material platforms including Lithium Niobate (LN) [22,23], Indium Phosphide (InP) [24] and SiP [25–30]. Specifically, DAC-less PAM4 generation schemes using SiP modulators have been intensively studied in recent years. By using multi-drive structures such as multi-electrode Mach-Zehnder modulator (ME-MZM) [26], ring assisted Mach-Zehnder modulator [27], dual-drive Michelson interferometric modulator [28], dual-parallel Mach-Zehnder modulators [29], and cascaded micro-ring modulators [30], one can multiplex two non-return-to-zero (NRZ) signals generated by two binary pattern generator (BPG) channels in the optical domain to generate a PAM4 signal without using a high speed electrical DAC. In [26], a 100 Gb/s DAC-less PAM4 transmission over 1km SSMF based on SiP ME-MZM without any digital signal processing (DSP) was reported. To further extend the reach of such systems for DCI applications without resorting to a full coherent solution, we can combine the DAC-less transmitter with the SSB/VSB self-coherent receiver. Since no DAC channels are available at the transmitter, the VSB scheme should be used as it does not require transmitter-side DSP for SSB generation.

In this paper, to the best of our knowledge, we experimentally demonstrate for the first time a DAC-less, one ADC solution for single wavelength single polarization 100 Gb/s transmission over 40-80 km of dispersion uncompensated link using a SiP ME-MZM and a VSB self-coherent receiver. The effects of CD, SSBI, device nonlinearity and fiber nonlinearity on this DAC-less VSB system and their mitigation methods are studied. We report a 112 Gb/s non-pulse-shaped PAM4 transmission over 40 km SSMF with a BER below the 7% overhead (OH) hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10⁻³, and a 120 Gb/s non-pulse-shaped PAM4 transmission over 80 km SSMF with a BER below the 20% OH soft-decision forward error correction (SD-FEC) threshold of 2 × 10⁻² with KK detection, frequency-domain CD compensation and time domain Volterra filter with a limited kernel memory length of 11.

2. DAC-less PAM4 modulation with SiP ME-MZM

The schematic of the SiP ME-MZM used for DAC-less PAM4 modulation is shown in Fig. 1. The device was fabricated on a silicon-on-insulator (SOI) wafer with a 220-nm thick silicon layer and a 2-$\mu m$ thick buried oxide (BOX) layer, through a multi-project wafer (MPW) run at IME A*STAR. It contains two series push-pull (SPP) phase shifting segments with identical lengths of 1.5 mm. Both segments have the same lateral p-n junction structures and electrode designs as the phase shifter of our previously proposed ME-MZMs, with a reported V_π L_π of 3.15 V-cm [31]. In this work, we use two short phase shifters to increase the electro-optic (E-O) bandwidth of the device, instead of using a 1.5-mm long segment and another 3-mm long segment as we did in [31], since shorter segments have lower microwave losses. The reported 3dB E-O bandwidth of a 1.5-mm long segment is greater than 45 GHz [31].

 

Fig. 1 Schematic of the SiP ME-MZM. V_i and V_bi (i = 1 or 2) are the alternating current (AC) driving signals and direct current (DC) bias voltages applied to the two phase shifting segments. V_w is a DC voltage applied to the thermal phase shifter to adjust the default phase difference between the two arms of the MZM. E_in and E_out represent the optical input and output.

Download Full Size | PDF

To obtain a PAM4 signal, two independent time-aligned binary signals with the same baud rate are used to drive the two phase shifting segments simultaneously. Both segments are driven in a push-pull scheme, therefore the chirp induced during modulation is negligible. The two segments have the same V_π’s. If there is no device nonlinearity, the peak-to-peak voltage (V_pp) of one of the driving signals should be twice that of the other.

In this experiment the two driving voltages are adjusted to be 6 V_pp and 2.3 V_pp to generate four PAM4 levels that are spaced as equally as possible. There are two main sources of device nonlinearities in our system. Firstly, the phase does not vary strictly linearly with the driving voltage when using a SiP phase shifter. Secondly, the amplitude change is not linearly proportional to the phase shift due to the choice of the bias point. As will be discussed in section 3, the self-coherent system detects the field. Ideally, the modulator should be biased at the null point which is in the middle of the linear region of the field transfer function [32]. However, in our system, we need to bias the modulator above the null point to obtain a relatively strong direct current (DC) component. We would like to point out that neither of these two sources of device nonlinearity is unique to the SiP ME-MZM based DAC-less transmitter, since the first problem is inevitable in any system that consists of a SiP phase shifting structure, and the second problem is shared by all SSB/VSB self-coherent systems that use bias point positions to control the carrier power.

Note that if the device nonlinearities are solely coming from the phase shifters, the four amplitude levels after detection will be unevenly spaced but still symmetrically distributed, which can be easily compensated for by adjusting the V_pp’s of the two driving voltages to pre-distort the PAM4 signal in the electric domain [26]. However, in our system, the combination of the phase-shifter nonlinearity and the choice of bias point will result in four unevenly spaced and asymmetrically distributed PAM4 levels, thus adjusting the V_pp’s does alleviate but cannot completely solve this problem. To further mitigate the device nonlinearities, receiver-side DSP should be used, as will be shown in section 4.

3. CD post-compensation with VSB self-coherent detection

The CD compensation capability of SSB/VSB PAM4 self-coherent systems has been intensively studied [16–21]. Here we summarize the principle in Fig. 2. Any DSB real signal with a Hermitian symmetric Fourier transform can be uniquely determined by its right sideband (RSB) or left sideband (LSB), which are denoted by the light blue and dark blue squares respectively in Fig. 2(a). Therefore, by removing half of the spectrum before PD detection, we do not lose information, and we can avoid the power fading problem since it becomes a SSB system [16]. The red arrow in Fig. 2(a) represents the DC carrier introduced during modulation by adjusting the bias point of the modulator, which serves as the “local oscillator” tone required by the self-coherent system. The spectra of the SSB and pseudo-SSB signals generated through perfect and imperfect optical filtering are shown in Fig. 2(b) and Fig. 2(h). The square law detections of these signals and the following processing steps in these two scenarios are shown in Fig. 2(c)-2(g) and Fig. 2(i)-2(m), respectively.

 

Fig. 2 Principle of CD post-compensation in SSB/VSB PAM4 systems. FD-CDC and TDE represents frequency-domain CD compensation and time domain equalization, respectively.

Download Full Size | PDF

The square law detection of a perfectly filtered RSB S(t) and the DC carrier C can be written as:

where the first term on the right-hand side of Eq. (1). is the constant carrier to carrier beating term, the second term is a linear combination of the RSB signal and its complex conjugate, which is the useful term, and the third term is the SSBI. When the carrier-to-signal power ratio (CSPR) is large enough, SSBI becomes relatively weak compared to the second term, therefore by digitally filtering out the RSB, we can obtain its complex field information, and CD compensation can be implemented either in the time domain or the frequency domain. Practically, CSPR cannot be arbitrarily large, and SSBI should not be neglected [10]. Most published SSBI cancellation methods can be categorized into two groups: SSBI estimation and subtraction (SSBI-E-S) [10–12], and KK detection [13,14]. KK detection has been reported to outperform most existing SSBI-E-S methods especially at relatively short distances such as 80 km [10].

For the baseband SSB/VSB PAM4 scheme that does not require frequency up-conversion or down-conversion, the strongly coupled SSBI and CD can also be compensated simultaneously using nonlinear equalizers [16,18]. A complete second-order Volterra filter is required to efficiently describe the inter-symbol interference (ISI) induced by CD and the system bandwidth limit, as well as the SSBI coupled with ISI. The equalization equation can be written as:

Recently a simplified Volterra equalizer (SVOL) sufficient for SSBI mitigation has also been reported, which limits the second-order term to only the squared term of the samples [18]. The equalization equation can then be written as:

Nonlinear equalization techniques can be regarded as variations of SSBI-E-S methods, in which ISI and SSBI are estimated and cancelled at the same time. Since all the taps can be adaptively obtained, manual optimization of coefficients is not required as in [10–12]. A Volterra equalizer can also compensate partially for other nonlinear impairments like device nonlinearity and fiber nonlinearity that are coupled with ISI, as will be shown in section 4. However, the more severe the ISI is, the longer the nonlinear kernel memory will be required, creating a trade-off between the performance and the complexity, especially in our DAC-less system. This is because in the absence of pulse shaping, the signal generated in a DAC-less scheme requires twice the bandwidth of a Nyquist shaped signal with the same symbol rate and experiences more ISI [33].

In the above analysis, we assume that the signals detected by the PD are perfect RSB signals with no LSB residues. However, in a DAC-less VSB system, we cannot insert a guard band between the SSB signal and the carrier as was done in [21], and therefore the LSB residue is inevitable due to the limited roll-off factor of the OBPF response, as shown in Fig. 2(h). Detection of such a pseudo-SSB signal S’(t) violates the minimum phase condition, which results in penalties to KK based algorithm, as shown in Figs. 2(j)-2(k). On the other hand, Eq. (2) still holds for S’(t), but the complex conjugate of the LSB residue will be superimposed onto the RSB. In other words, even if we do not use KK based methods but use a digital RSB filter, the second term in Eq. (2) now has frequency aliasing as shown in Figs. 2(l)-2(m), which negatively affects the accuracy of the SSBI estimation, and degrades the performance of SSBI-E-S algorithms as well as nonlinear equalization based methods.

4. Transmission experiment and result

4.1 Experiment setup

The schematic of the experimental setup and the receiver DSP blocks are shown in Fig. 3. Two independent user-defined NRZ signals are first generated from two channels of a BPG, then applied to the SiP ME-MZM. Note that matched cables and tunable delay lines are used to ensure that the two binary signals are properly time aligned. A 15.5 dBm tunable laser operating at 1550.1 nm is used as the light source. The SiP chip has 18 dB fiber-to-fiber insertion loss, including 11 dB loss from the vertical grating coupler pairs, 4 dB loss from the modulator when biased at the maximum point and 3 dB loss from the routing waveguide. The OBPF serves as both the VSB filter and the out of band amplified spontaneous emission (ASE) noise filter, which has 6 dB insertion loss and ~3 dB extra loss from VSB filtering. Two erbium-doped fiber amplifiers (EDFAs) and variable optical attenuators (VOAs) are used to compensate for the loss and to control the launched power and received power separately. After band pass filtering, the optical signal is detected by a PD without a transimpedance amplifier (TIA), then digitized by a 160 GSa/s real time oscilloscope (RTO) and processed offline. The OBPF response and the wavelength offset are shown in the inset of Fig. 3(a). In the experiment, we first fixed the wavelength offset, then jointly optimized the modulator bias point and the peak-to-peak values of the two driving voltages to achieve the best performance at back-to-back (B2B). The CSPR for a 56 GBaud signal at the optimized point is 11.4 dB.

 

Fig. 3 (a) Experimental Setup, inset shows the spectrum of a 56 GBaud signal before filtering, the OBPF response and the spectrum of a 56 GBaud signal after filtering, and (b) receiver-side DSP blocks.

Download Full Size | PDF

All DSP blocks before demodulation are operated at 2 samples per symbol (Sps). The complex RSB component of the received signal is first obtained through either KK detection or a digital RSB filter. A frequency domain CD compensation (FD-CDC) block can be inserted before PAM4 reconstruction by taking the real part of the RSB. A linear/nonlinear time domain equalizer (TDE) is then applied to compensate for the residue ISI and nonlinear impairments. Next we down-sample the stream to 1 Sps for the following demodulation and BER counting. It has been reported that typically 4 Sps is required for KK detection in a passband 16 QAM SSB system since KK contains the square root and logarithm operations [10,13]. In this work, we are instead processing a baseband PAM4 signal with twice the baud rate of a passband 16 QAM signal that covers the same bandwidth as the RSB. Therefore 2 Sps in our baseband system is equivalent to 4 Sps in a passband 16 QAM system with the same bandwidth requirement. Figure. 4(a) shows that further increasing the oversampling ratio will not improve the performance.

 

Fig. 4 (a) BER of 56 GBaud DAC-less PAM4 at B2B versus oversampling ratio when processed with KK and FFE, and (b) typical linear FFE taps converged for 56 GBaud PAM4 at B2B, 80km without FD-CDC and 80 km with FD-CDC using KK detection.

Download Full Size | PDF

4.2 Linear and nonlinear impairments and mitigation methods

Figure. 4(b) shows the number of linear TDE taps required to compensate for the ISI of a 56 GBaud non-pulse-shaped PAM4 signal after 0/80 km transmission, where we use KK detection to suppress the SSBI and limit the TDE to a linear feed forward equalizer (FFE), which contains only the first order terms in Eqs. (2) and (3). The least-mean-square (LMS) algorithm is used for tap adaptation. We find that L₁ = 25 is required in B2B transmission, which corresponds to L₁ × 2 + 1 = 51 T/2-spaced taps to compensate for the ISI caused by the bandwidth limit of the system. After 80 km transmission, around 50 neighboring samples on each side (L₁ = 50) should be included in TDE due to the CD induced pulse broadening. In addition, by applying FD-CDC before TDE in the 80km transmission scenario, L₁ can be reduced back to 25. We keep using these L₁ values for 56 GBaud signals with or without FD-CDC in the following discussions.

Next we study the effects of nonlinear impairments on the system performance, including the SSBI, the device nonlinearity and the fiber nonlinearity, and their mitigation methods. Figures. 5(a) and 5(b) show the dependencies of the BER performance for different DSP combinations of the memory lengths of the TDE nonlinear kernels (2 × L₂ + 1) for 56 GBaud signals in B2B and over 80 km, where the zero-memory points correspond to the linear FFE cases.

 

Fig. 5 (a) BERs as functions of nonlinear kernel memory lengths with different DSP combinations for a 56 GBaud PAM4 at B2B with a launch power of −3 dBm, (b) BERs as functions of nonlinear kernel memory lengths with different DSP combinations for a 56 GBaud PAM4 at 80km with a launch power of 8 dBm and (c) transmission performances of different DSP combinations with 56 GBaud PAM4 at 80 km.

Download Full Size | PDF

As we can see in the B2B measurements (no fiber nonlinearity), when KK detection is not applied, better BER performance can be achieved by using both the Volterra equalizer (VOL) described as Eq. (2) and SVOL described as Eq. (3) compared with the linear FFE case, because both algorithms can combat SSBI [16,18]. However, if KK detection is applied, SVOL no longer improves the BER performance since SSBI is already suppressed by KK [13]. Furthermore, we observe that using the VOL always shows better performance than using the SVOL even when KK detection is applied. We attribute this phenomenon to the fact that our system suffers from device nonlinearities. As discussed in section 2, these device nonlinearities can be partially compensated for by adjusting the V_pp’s of the two driving signals. Figure 5(a) shows that the remaining device nonlinearity after carefully tuning the V_pp’s can be efficiently mitigated by the VOL but not the SVOL. Afterwards, we find that the RSB filtering scheme outperforms the KK detection schemes in the B2B measurement, even using FFE, since the LSB residue resulting from the imperfect filtering leads to a large KK detection penalty.

On the other hand, after 80 km transmission, the system suffers from fiber nonlinearities due to the relatively high launch power into the SSMF. VOL can also be used to mitigate the fiber nonlinearity, as we can see from the BER versus launch power curves shown in Fig. 5(c). By increasing the nonlinear kernel memory length of the VOL the optimum launch power allowed by the system is increased as well. On the contrary, increasing the memory length of the SVOL nonlinear kernel does not change the optimum launch power, which indicates that the SVOL is not sufficient to compensate for fiber nonlinearities in a dispersion uncompensated link. In addition, after 80 km transmission, when the kernel memory is short, KK detection starts to show advantages over the RSB filtering scheme, as we can see from the blue curves and the red curves in Fig. 5(b). This is because when SSBI interacts with CD, a longer nonlinear kernel memory is required for SSBI mitigation compared to the B2B case, and the remaining SSBI after memory-limited TDE in the RSB filtering scheme outweighs the penalty of KK detection induced by imperfect filtering. However, we find that the KK detection is more sensitive to the fiber nonlinearity than the RSB filtering scheme. From Fig. 5(c) we observe that, if not using VOL, applying KK will shift the optimum launch powers towards lower values. This explains why the RSB filtering scheme outperforms KK detection again at 80 km, when the SVOL with enough kernel memory is used, but when the VOL is used, KK always provides better result.

Another phenomenon observed from Fig. 5(b) is that 56 GBaud PAM4 transmission over 80 km with a BER below the 7% OH HD-FEC threshold of 3.8 × 10⁻³ is achievable with KK detection and the VOL if a kernel memory length of 41 (L₂ = 20) is used. However, the number of adaptive taps N = (L₂ + 1) × (2 × L₂ + 1) increases dramatically with the memory length for the second order Volterra series, which makes such a long-memory equalizer impractical. Directly limiting the memory length of VOL kernel will degrade the performance significantly, as all nonlinear impairments are coupled with severe ISI after fiber transmission. Since the ISI is dominated by CD, we can insert an FD-CDC block before TD equalization to reduce the ISI first. Note that the device nonlinearity can be easily mitigated by a VOL with a short memory length after applying FD-CDC, because it is introduced before the dispersive fiber (at the transmitter). On the contrary, SSBI is instead introduced after the fiber (at the PD), thus should be suppressed before applying FD-CDC. As can be seen from the red curves and the magenta curves in Fig. 5(b), applying FD-CDC directly to a SSBI contaminated signal in fact degrades the performance when KK detection is not used. The fiber nonlinearity is introduced in the fiber together with CD, thus performing FD-CDC before nonlinear equalization does help to reduce the required memory length, though this 2-step approximation also leads to performance penalty. By comparing the blue curves and the green curves in Fig. 5(b), we find that when SSBI is removed by KK, FD-CDC improves the BER performance if the kernel memory is less than 20, but also limits the best performance achievable with longer memory. We should note that when combined with KK detection and FD-CDC, the SVOL can also mitigate fiber nonlinearity to some extent. As we can see for the KK scheme where SSBI is suppressed, increasing the kernel memory of the SVOL results in better BER performance after 80 km transmission when FD-CDC is applied, while the BER keeps almost the same in the B2B case.

To balance the performance and the complexity, through the remainder of this experiment, we use KK detection to eliminate SSBI, FD-CDC to reduce the required nonlinear kernel memory length, and a memory-limited VOL (L₂ = 5, 66 nonlinear taps) to compensate for the remaining ISI, device nonlinearity and fiber nonlinearity.

4.3 100 Gb/s transmission demonstration

To explore the capacity limit of this DAC-less VSB self-coherent system when processed with the DSP combination discussed above, we sweep the symbol rate at B2B, 40 km and 80 km with a received power of 7 dBm. The memory length of linear kernel and launch power are re-optimized for different baud rates and distances, while the nonlinear kernel memory length is kept as 11 (L₂ = 5). The results are shown in Fig. 6(a). We find that a 112 Gb/s transmission with a BER below the HD-FEC threshold at 40 km and a 120 Gb/s transmission with a BER below the SD-FEC threshold at 80 km can be achieved. Therefore, for links up to 40 km, HD-FEC is sufficient to achieve 100 Gb/s/λ transmission. As for longer distances such as 80 km, more advanced FEC should be used to achieve the same capacity.

 

Fig. 6 (a) BERs as functions of symbol rate at B2B, 40 km and 80 km with 7 dBm received power and (b) Receiver sensitivity requirements for a 56 GBaud PAM4 signal at B2B, 40 km, and 80 km, when processed with 1) KK detection and short memory VOL, 2) KK detection, FD-CDC and short memory VOL.

Download Full Size | PDF

Then we use the 56 GBaud signal as an example to study the receiver sensitivity requirements with or without FD-CDC at different distances. Figure 6(b) plots the BER performance as a function of the received power. We observe that by applying FD-CDC, only 0.4 dB sensitivity gain is obtained at the HD-FEC threshold after 40 km SSMF, and the gain at the SD-FEC threshold is negligible. However, after 80km transmission, a 1.3 dB gain is obtained when using FD-CDC. As mentioned before, FD-CDC becomes helpful when there are strong interactions between the ISI and the nonlinear impairments that make the nonlinear impairments exceed the compensation capability of a memory-limited VOL. Compared with the 40-km scenario, both ISI and fiber nonlinearity are much more severe after 80 km transmission, which explains why FD-CDC provides better sensitivity gain at 80 km. As can be seen in Fig. 5(b), the BER curves converge at low received power, regardless of the transmission distances, which indicates that the system is predominantly limited by noise instead of ISI and ISI-nonlinearity coupling when the received power is low.

5. Conclusion

112 Gb/s transmission over 40 km below the HD-FEC threshold and 120 Gb/s transmission over 80 km below the SD-FEC threshold are achieved using a SiP ME-MZM based DAC-less PAM4 transmitter and a VSB self-coherent receiver. In the absence of transmitter DSPs such as pulse-shaping and pre-emphasis, KK detection, FD-CDC and memory limited TD VOL equalization are used at the receiver to suppress the SSBI, relax the kernel memory requirement for nonlinear equalization, and compensate for the residue ISI, device and fiber nonlinearity. The proposed DAC-less single ADC single lane 100G solution may find its application in cost effective power efficient data center interconnects.