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Abstract
As for the photonic interconnection based on the multiple-lane intensity modulation direct detection (IM-DD) transmission, both intra-channel inter-symbol-interference (ISI) originating from bandwidth constraint, and inter-channel performance discrepancy emerging from inter-channel component differences are the major bottleneck for the throughput enhancement. Here, we propose a pairwise Tomlinson-Harshima precoding (P-THP) scheme, in order to simultaneously deal with both intra-channel ISI and inter-channel performance discrepancy. The effective function of the proposed P-THP scheme is experimentally evaluated by transmitting 4-channel 81-GBaud PAM4 signals over 2 km standard single-mode fiber (SSMF). Compared with the conventional scheme with only applying THP on individual wavelength channel, the required optical received power (ROP) under the back-to-back (B2B) transmission can be reduced by 0.75∼1 dB with the help of proposed P-THP in different experimental component configurations, at the 7% hard decision forward error correction (HD-FEC) threshold of BER = 3.8 × 10−3. After the 2 km SSMF transmission, only the use of proposed P-THP can guarantee to reach the designated HD-FEC threshold, leading to a net rate of >600 Gbit/s.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Various bandwidth-hungry applications, such as 4 K/8 K video streaming, the 5th generation (5 G) wireless communication, and cloud computing, have led to a rapid increase in datacenter traffic, which emphasizes the need to increase the capacity of short-reach optical link and datacenter interconnects (DCI) [1]. Compared with coherent detection scheme, intensity modulation direct detection (IM-DD) is preferred in short-reach photonic interconnection, because of its cost performance, simple configuration, as well as power efficiency [2]. 100 Gb/s and beyond single lane IM-DD transmission systems have been achieved, by the use of various modulation schemes, including pulse amplitude modulation (PAM), discrete multi-tone (DMT), and carrierless amplitude phase modulation (CAP) [3]. Among them, the use of PAM stands out as the optimal solution, in terms of transceiver complexity and power consumption. Thus, the IEEE 802.3bs has been standardized for 400 GbE up to 10 km standard single mode fiber (SSMF) transmission [4]. The enhancement of capacity demand indicates the urgency of increasing the data rate per lane from 100 Gbps to 200 Gbps and beyond per lane for next-generation 800 GbE and 1.6 TbE. In this context, the 800 G pluggable MSA (multi-source agreement) group has published its first 200 G per lane technical specification recently, based on 112.5-GBd 4-level pulse amplitude modulation (PAM-4) [5]. Meanwhile, IEEE Ethernet group has recommended the use of 106.25-GBd PAM-4 signals for the ease of a smooth upgrading from its 100 G per lane standard with the use of 53.125- GBd PAM-4 signals [4]. However, the generation of high baud-rate PAM4 signal may suffer from severe inter-symbol-interference (ISI), due to the bandwidth constraint of optoelectronic devices, such as digital-to-analog converter (DAC), analog to-digital converter (ADC), RF amplifiers, and modulators. In order to mitigate the ISI, sophisticated digital signal processing (DSP) is indispensable. In comparison with feedforward equalizer (FFE), the utilization of the decision-feedback equalization (DFE) at the receiver-side (Rx) increases the ISI tolerance without introducing noise enhancement. However, the intrinsic error propagation and the incapability of integrating itself with the channel coding make DFE impractical, especially for a long memory channel. This problem can be solved by shifting the feedback structure to the transmitter-side (Tx), where the sequence to be transmitted is known and thus wrong decisions will not occur [6,7]. This scheme is called Tomlinson-Harshima precoding (THP), and its application in high baud-rate IM-DD transmissions has already been experimentally verified. In [8], the error-free transmission of 30 GBaud PAM-4 signal over 20-km SSMF at the threshold of hard-decision FEC (HD-FEC) was realized with the help of THP. In [9,10], 94 GBaud transmission with a bit error ratio (BER) below the 7% overhead HD-FEC threshold after 2 km SSMF transmission have been achieved for a system with 33 GHz brick wall bandwidth, when a nonlinear equalizer is implemented at the Rx. In [11], the use of THP enables 4 × 81 GBaud PAM-4 transmission over 2 km SSMF, with a BER below the 7% overhead HD-FEC threshold, when the measured 10-dB bandwidth of end-to-end system is below 25 GHz.
On the other hand, in a typical 800 G/1.6 T IM-DD system employing 4/8 wavelength lanes, different wavelength channels may show different transmission performances, due to the inconsistent frequency response of involved optoelectrical devices, and interactions between chirp and chromatic dispersion (CD) [12]. Large performance difference among multiple lanes can significantly degrade the average pre-FEC BER performance, which determines the best post-FEC BER performance that can be achieved with the bit-level interleaving over all lanes [13]. For example, in an extreme case where the pre-FEC BER of one channel is worse than that of the other three channels by several orders, the average pre-FEC BER will be “clamped” to the pre-FEC BER of that “bad” channel divided by four, regardless of how “good” the rest channels are. In [14], we have proposed to employ a symbol-level wavelength-interleaver in conjunction with four-dimensional-PAM4-trellis coded modulation (4D-PAM4-TCM) to improve the system robustness against the inter-channel performance discrepancy, and we experimentally observe that wavelength-interleaved 4D-PAM4-TCM outperforms conventional time-interleaved 4D-PAM4-TCM, in terms of receiver sensitivity, when there exists a sizable inter-channel performance discrepancy. However, the coding gain of using 4D-PAM4-TCM will not be reserved or even be reversed for the bandwidth limited IM-DD transmissions, as the symbol rate of 4D-PAM4-TCM system is naturally higher than that of the PAM-4 system, in term of the same transmission capacity.
In this paper, we propose a pairwise Tomlinson-Harashima Precoding scheme (P-THP) in order to enhance the performance of multiple-lane IM-DD systems, by simultaneously mitigating both ISI at each wavelength channel and the performance discrepancy among multiple lanes. We experimentally investigate the performance of our proposed P-THP scheme in a 4-lane IM-DD configuration. In comparison with the conventional schemes without/with the THP on individual wavelength channel, the proposed P-THP scheme is verified to enable better receiver sensitivity at the HD-FEC threshold of BER = 3.8 × 10−3, under conditions of the back-to-back (B2B) and 2 km SSMF transmissions.
2. Operation principle
Here, we propose a P-THP scheme by integrating Tx pairwise precoding with THP, to simultaneously deal with both the bandwidth limitation induced ISI and the inter-channel performance discrepancy, as shown in Fig. 1. The pairwise precoding using constellation rotation has been investigated to tackle with the frequency selective fading issue in wireless communication [15,16], and inter-channel interference (ICI) as well as polarization dependent loss (PDL) issues in fiber optical coherent communication [17,18]. We also apply the pairwise precoding to deal with the inter-channel performance discrepancy, originating from different device frequency responses, noise levels, and receiver responsivities among wavelength channels. In addition to exploiting the rotated constellation, we propose the use of staggered constellation for the pairwise coding, and its superiority over rotated constellation is verified in following discussions. The implementation of the pairwise precoding and decoding is shown in Fig. 1. At Tx, bit to symbol mapping is first performed according to the rotated constellation (rotation angle is fixed at 45 degrees for the ease of discussion) and staggered constellation. Gray coding for both rotated and staggered constellations is approximately realized by specific bit allocation, when the signal-quality degradation of bad channel is dominant in the IM-DD transmission system. Then, the real and imaginary parts of the two-dimension (2D) symbols are obtained and fed to the “good” and “bad” wavelength channels for the consequent THP. Obviously, as for the staggered or rotated constellation, the Euclidean distance in the vertical direction is enhanced significantly, making the staggered or rotated constellation more tolerant to the signal-quality degradation on “bad” wavelength channels. At Rx, the signal-to-noise ratio (SNR) estimation is first applied for the “good” and “bad” channels utilizing the statistical moments method, for the purpose of pairwise decoding [19]. Then, the received symbols after applying the modulo operation in each wavelength channel are rescaled, according to the estimated SNR. Thereafter, the maximum likelihood detection (MLD) is applied for the symbol decision, as shown in Eq. (1),
Fig. 1. (a) Block diagram of proposed P-THP. (b) Block diagram of pairwise precoding and decoding. (c) Block diagram of THP.
After the pairwise precoding, we apply the THP for the purpose of ISI mitigation. The structure of THP is shown in Fig. 1(c), which is the same as the DFE configuration that is shifted to the Tx, except that the decision device is replaced by a modulo operation. Please note that, the THP inputs are the PAM-4 and PAM-8 signal for the “bad” and “good” channels, respectively, as a result of the pairwise precoding with staggered constellation. Similarly, the THP inputs are both PAM-7 signals for the “bad” and “good” channels, when the pairwise precoding with rotated constellation is applied. The linearized description of the pre-coded sequence after THP is [20]:
We numerically verify the performance of P-THP under the condition of a 2-channel transmission, and the results are shown in Fig. 2. The impulse responses of two channels are set identical as $H(z) = 1 + 0.2 \cdot {z^{ - 1}} + 0.1 \cdot {z^{ - 2}} + 0.05 \cdot {z^{ - 3}}$, in order to emulate the bandwidth constraint effect. AWGN is added for each channel to adjust the SNR. Inter-channel performance discrepancy is managed by introducing the SNR penalty for the “bad” channel and the SNR gain for the “good” channel. The averaged SNR of two channels, in case all channels are assumed to have the same power, is fixed to be 14 dB, so that the BER variation is only due to the inter-channel performance discrepancy. Besides the pairwise precoding, another commonly-used method to deal with inter-channel performance discrepancy for the optical communication is the space-time precoding [21,22]. For the purpose of performance comparison, the scheme integrating the transmitter-side space-time precoding based on Walsh-Hadamard transform, together with the THP, which is denoted as STP-THP, is also under investigation. As shown in Fig. 2(a), when two channels have the same SNR, the use of THP guarantees the best BER performance. We owe this phenomenon to the fact that the THP loss is enlarged as a result of increased PAM alphabet after the pairwise precoding and space-time precoding. However, when the inter-channel performance discrepancy gradually enhances and becomes the dominating factor limiting the transmission performance, the BER performance degrades significantly for the case of using THP. In this context, a large performance gain is obtained by using the pairwise precoding, STP-THP, and P-THP schemes, in comparison with the THP scheme. Additionally, we observe both the pairwise precoding and P-THP schemes outperform the STP-THP scheme, because the pairwise precoding is more efficient of dealing with inter-channel performance discrepancy, when compared with the space-time precoding. By simultaneously mitigating both ISI at each channel and performance discrepancy between two channels, the P-THP scheme is found superior to other schemes. Furthermore, we find that the P-THP scheme relying on the staggered constellation presents a better BER performance than that with the use of rotated constellation, when the inter-channel performance discrepancy is sufficiently large. We owe this phenomenon to the fact that the Euclidean distance in the vertical direction of the staggered constellation is larger than that of the rotated constellation, considering the same average power. The constellations for different schemes using the PAM sequencies on the two channels as In-phase and quadrature components are also presented in Fig. 2(b), when the SNR values of two channels are 10 dB and 18 dB, respectively. Obviously, the constellation point clusters are more separated, when the THP and STP-THP is replaced with P-THP, leading to the performance gain in the decision process.
Fig. 2. (a) Relationship between BER and SNRs of the two channels. (b) Constellations for different schemes when the SNRs of the two channels are 10 dB and 18 dB, respectively. (Pairwise precoding: PP)
3. Experimental setup, results, and discussions
We experimentally study the performance of our proposed P-THP scheme for a 4-channel IM-DD system, as shown in Fig. 3(a). The symbol rate is 81 GBaud. As for the Tx DSP, we use 50-tap THP to mitigate ISI after applying the pairwise precoding, and the weighting coefficients are obtained from a training symbol aided DFE at Rx, as what we did in [23]. We fix the number of THP taps during our investigation, but practically the number of THP taps should be optimized, considering the trade-off between the feedback delay and THP performance. The signals after P-THP are then up-sampled to 2 samples per symbol (sps) with the zero insertion, followed by a root-raised-cosine (RRC) pulse shaping with a roll-off factor of 0.1. Thereafter, the electrical signals are resampled to match the arbitrary waveform generator (AWG) sampling rate of 120 GSa/s. Meanwhile, clipping is applied to reduce the peak to average power ratio (PAPR) of electrical signals. Afterwards, the four-lane signals are loaded into AWG. The converted four-lane analog signals are electrically amplified by four electrical amplifiers (EAs) with a 3 dB bandwidth of about 60-GHz. And then the four-lane amplified analog signals are, respectively, modulated by four 40-GHz Mach-Zehnder modulators (MZMs), which are biased at the quadrature point with a Vpi of about 6.2 V. Meanwhile, four C-band tunable external cavity lasers (ECLs) with wavelengths of 1547.12 nm, 1548.12 nm, 1549.12 nm and 1550.12 nm are employed as optical carriers. The output power of each ECL is fixed to 16 dBm. After transmissions over 2 km of SSMF, four wavelength channels are separated by a wavelength division demultiplexer (DeMUX), then detected by four photodetectors (PDs) without transimpedance amplifiers (TIA), followed by four 160 Gsa/s real-time oscilloscope (RTO) channels. Each RTO channel has a brick-wall bandwidth limit of 59 GHz. We use four variable optical attenuators (VOAs) after the DeMUX on all four channels to vary the received optical power (ROP). As for Rx DSP, the digital waveform of each lane is first resampled to 2 sps, and then passed through a matched RRC filter. Afterwards, the signal is equalized by a FFE based on the recursive least square (RLS) algorithm, whether THP is applied or not. After implementing the modulo operation for THP and pairwise decoding, the BER is counted and averaged among all four channels.
Because of component differences, four wavelength channels achieve different transmission performances in our experiment. Here, component differences mean the differences of thermal noise, flicker noise and nonlinear distortions introduced by the RF components, frequency responses of optoelectrical devices, relative intensity noises of the lasers, modulation efficiencies of MZMs and etc. Figure 3(b) shows two component matching configurations considered in this work. Four channels are divided into two groups. As for the “bad” matching case, the best AWG channel, MZM, and RTO channel are chosen in one wavelength channel, and the worst AWG channel, MZM, and RTO channel are chosen in the other wavelength channel. As for the “good” matching case, we minimize the component-induced channel difference through proper re-arrangement of components (e.g. matching a “bad” AWG channel and a “good” MZM with a “bad” RTO channel). Please note that, searching for the best component matching configuration for a practical link is challenging, as it requires prior knowledge of both transmitter and receiver components.
We first evaluate the inter-channel performance differences under the condition of B2B, by calculating the SNR of each wavelength channel after FFE and modulus operation for the THP case under different ROP values. We manually adjust the VOA to ensure the ROP for each channel is the same during our investigation. The number of FFE taps is optimized to be 101 for each channel, in order to sufficiently compensate for the pre-cursor ISI, so that the equalized signals after the modulus operation can be regarded as the noise-limited. As we can see from Fig. 4, different channels achieve different SNRs under the B2B transmission, due to the hardware differences. In terms of the “good” matching case, the SNR difference between the channel-1 and channel-2 is averaged to be 2.7 dB, and the SNR difference between the channel-3 and channel-4 is averaged to be 2.8 dB when the ROP varies from -2 dBm to 4 dBm. However, the averaged SNR difference between the channel-1 and channel-2 can be increased to around 4.9 dB, and the averaged SNR difference between the channel-3 and channel-4 can be increased to around 3.6 dB when a bad component matching configuration is implemented. We should note that the average BER performance is mostly influenced by the worst channel in this context [14].
We then study the receiver sensitivity requirement under the B2B transmission, as shown in Fig. 5. As we can see, the scheme without the use THP shows the worst BER performance under various ROP conditions, and the obtained BER can’t reach the HD-FEC threshold by increasing the ROP. Due to the use of THP for each wavelength channel, the obtained BER is decreased, due to the mitigation of post-cursor ISI. The required ROP to reach the HD-FEC threshold for the THP scheme is 3.15 dBm and 3.9 dBm for the “good” and “bad” matching configurations, respectively. The performance can be further improved by utilizing our proposed P-THP with either the rotated or staggered constellations, when the ROP is more than 0 dBm, because of the simultaneous mitigation of intra-channel post-cursor ISI and inter-channel performance discrepancy. We should mention that both the THP and P-THP schemes show similar performance, when the ROP is less than 0 dBm, because the system performance is ultimately limited by the receiver noise at this time. Additionally, we find that the P-THP scheme using staggered constellation outperforms that using rotated constellations, which is in line with our simulated observation, when the SNR difference between channels is large enough. The required ROP to reach the HD-FEC threshold for the P-THP scheme with staggered constellation is 2.4 dBm and 2.9 dBm for the “good” and “bad” matching configurations, respectively. As a result, the receiver sensitive can be enhanced by 0.75 dB and 1 dB by replacing the THP scheme with the P-THP scheme under the “good” and “bad” matching configurations, respectively.
Fig. 5. The relationship between averaged BER among 4 channels and ROP at B2B in (a) “good” and (b) “bad” matching configurations.
Thereafter, we can obtain the relationship between averaged BER among 4 channels and ROP after 2 km SSMF transmission, as shown in Fig. 6. On the one hand, the signal quality is deteriorated after 2 km SSMF transmission, because of the CD induced power fading. Consequently, we observe a performance penalty for all schemes under the variable ROPs, in comparison with the B2B case. On the other hand, the obtained BER for the THP scheme cannot reach the HD-FEC threshold in both “good” and “bad” matching configurations after 2 km SSMF transmission, due to the occurrence of inter-channel performance discrepancy. By simultaneous mitigating intra-channel ISI and inter-channel performance discrepancy, the use of proposed P-THP scheme can further improve the BER performance to reach the HD-FEC threshold. Once again, we observe a performance gain for the P-THP scheme using staggered constellation in comparison with that using rotated constellation. The required ROP to achieve the HD-FEC threshold for the P-THP scheme with staggered constellation is identified to be 3.05 dBm and 3.3 dBm under the “good” and “bad” matching configurations, respectively. Considering the 7% overhead, the net transmission rate can be 81*2*4/1.07 = 605.6 Gbit/s. Figure 7 presents the constellations in term of implementing P-THP between channel-1 and channel-2, when the ROP is 4 dBm for the “bad” matching configuration. As we can see, there exists a prominent inter-channel performance discrepancy phenomenon. Without the use of P-THP, the constellation clusters overlap due to the inter-channel performance discrepancy. With the help of P-THP, we observe clear and separated constellation clusters, indicating of BER performance improvement.
Fig. 6. The relationship between averaged BER among 4 channels and ROP after 2 km SSMF transmission in (a) “good” and (b) “bad” matching configurations.
Fig. 7. Constellations for different schemes when the ROP is 4 dBm in the “bad” matching configuration after 2 km SSMF transmission.
4. Conclusion
We have proposed a P-THP scheme for multiple-lane IM-DD transmissions, with the capability of simultaneously mitigating both intra-channel ISI and inter-channel performance discrepancy. The proposed P-THP method is numerically and experimentally verified to guarantee better transmission performance, when it is compared with the conventional schemes without/with the use of THP on individual wavelength channel. Moreover, the use of staggered constellation is justified to be a better option than the rotated constellation for the implementation of P-THP. With the help of proposed P-THP scheme, we have experimentally demonstrated the C-band 4-channel 81-GBaud IM-DD transmission over the 2-km SSMF, with a net rate of 605.6 Gbit/s, when the 7% HD-FEC threshold is considered.
Funding
National Key Research and Development Program of China (2021YFB2900702); National Natural Science Foundation of China (62075046, U21A20506); Guangdong Introducing Innovative and Entrepreneurial Teams of “The Pearl River Talent Recruitment Program” (2021ZT09X044).
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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