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Abstract
In this paper, 100 Gb/s/λ 32 quadrature amplitude modulation discrete multi-tone (QAM-DMT) transmission using 10 G-class electro-absorption modulated laser (EML) and 4/5-bit digital-to-analog converters (DACs) are experimentally demonstrated to meet the requirement of intra-datacenter interconnection (intra-DCI). Unequal length multi-band (ULM) discrete Fourier transform spread (DFT-S) precoding is investigated to alleviate the distortion induced by the high peak-to-average power ratio (PAPR) of DMT. The results show that the required computational complexity of ULM DFT-S precoding with 2-bands (k1=256, k2=64) decreases sharply compared to the traditional DFT-S technique with only about 0.5 dB receiver sensitivity penalty. In addition, compared to the equal length multi-band (ELM) DFT-S precoding, the ULM DFT-S precoding can bring about 2.5 dB receiver sensitivity improvement with slight added computational complexity. With the assistance of ULM DFT-S precoding and noise shaping (NS) technique, the bit-error ratio (BER) of 100 Gb/s 32 QAM-DMT signal generated by 5-bit DAC over 2-km single-mode fiber (SMF) transmission can reach the hard-decision forward error correction (HD-FEC) threshold with received optical power (ROP) of -6.5 dBm, with only additional 39.9% multiplier and 33.7% adder.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The emergence of explosive high-bandwidth services, such as high-definition television, and smart cities, result in the rapid development of data centers [1–4]. Datacenter interconnection (DCI) served as the information interaction for data centers is a hot topic that needs to be researched and studied. According to the application of different data centers, DCI can be divided into intra-DCI and inter-DCI, where the intra-DCI is within 2-km, and inter-DCI is about 2-km to 80-km. Generally, the IP traffic in intra-DCI is much higher than the traffic in inter-DCI, thus the research in intra-DCI is essential. For intra-DCI, 100 Gb/s/$\lambda $ intensity modulation and direct detection (IM/DD) enabled by wavelength-division multiplexing (WDM) technique with low cost, footprint, and power consumption is regarded as the primary solution for the next generation deployment [2–11].
Nowadays, vendors are trying to explore new solutions for high data rates to reuse the on-off-shelf deployed components, such as 10 G-class electro-absorption modulated laser (EML) and directly modulated laser (DML) [9–11], reducing the deployment cost of next-generation DCI. In this scenario, discrete multi-tone (DMT) is a potential modulation formant due to its high inter-symbol interference (ISI) tolerance, and spectra efficiency [2, 7, 8]. However, the high peak-to-average power ratio (PAPR) of the DMT signal will distort the system performance. To cope with this problem, discrete Fourier transform spread (DFT-S) precoding realized by multiplying a DFT matrix is proposed [12–17], while the required computational complexity of multiplying a DFT matrix is as high as about O(N2). Thanks to the occurrence of the fast Fourier transform (FFT) algorithm, the required computational complexity is decreased sharply, with about O(Nlog2N), but the implementation of the FFT algorithm needs the payload subcarriers length to satisfy the power of 2, which is difficult to satisfy in many scenarios [14,15]. Equal length multi-band (ELM) DFT-S precoding realized by dividing payload subcarriers into several bands with equal length, has been investigated in a coherent system to reduce the system computational complexity, and the length of each band satisfies the power of 2 [18,19]. For this ELM DFT-S precoding, it is hard to implement for any length of payload subcarriers by using a small number of bands. A realizable method is to reduce the length of each band and then improve the number of bands. However, this method will induce the increment of signal PAPR, which will induce serious distortions in an IM/DD system [5].
In this paper, the unequal length multi-band (ULM) DFT-S precoding with low computational complexity is investigated for the IM/DD system to eliminate the influence of high PAPR. Based on this technique, a 100 Gb/s 32 quadrature amplitude modulation (QAM)-DMT IM/DD system over 2-km single-mode fiber (SMF) using a 10 G-class EML and 4/5-bit digital-to-analog converters (DACs) are experimentally demonstrated. Both pre-equalization and noise shaping (NS) techniques are adopted in such system to reduce the distortions induced by bandwidth limitation and quantization noise, respectively. Various DFT-S precoding schemes, including ELM DFT-S precoding, ULM DFT-S precoding, and traditional DFT-S precoding, are discussed in the aspects of bit-error ratio (BER) performance and computational complexity. The results indicate that the ULM DFT-S precoding scheme with 2-bands (k1 = 256, k2 = 64) outperforms both the traditional DFT-S precoding scheme and ELM DFT-S precoding. Compared with the traditional DFT-S precoding scheme, it only induces about 0.5 dB penalty with the required multiplier ratio and adder ratio decreasing from 1910.4% to 22.69% and from 1317.5% to 23.51%, respectively. Compared with EML DFT-S precoding scheme with 5-bands (k1 = 64, k2 = 64, k3 = 64, k4 = 64, k5 = 64), a 2.5 dB receiver sensitivity improvement can be obtained at the hard-decision forward error correction (HD-FEC) threshold with slightly increased computational complexity. Enabled by ULM DFT-S precoding with 2-bands and NS technique, the BER of 100 Gb/s 32 QAM-DMT signal generated by 5-bit DAC over 2-km SMF transmission can successfully reach the HD-FEC threshold with received optical power (ROP) of -6.5 dBm. Only additional 39.9% multiplier and 33.7% adder are increased.
The rest of this paper is organized as follows. Section 2 introduces the principle of the multi-band DFT-S precoding and NS technique. In Section 3, the required computational complexity of various processes are analyzed. The experimental setup and results are described in Section 4 and Section 5. And Section 6 is the summary of this paper.
2. Principle
2.1 Multi-band DFT-S technique
The high PAPR of the DMT signal, especially the pre-equalized DMT signal, will cause serious quantization noise and nonlinear noise of the signal during digital-to-analog conversion and channel transmission [16]. DFT-S precoding is widely applied in DMT systems to eliminate the distortion induced by high PAPR [14,16]. In DMT system, DFT-S precoding is realized by multiplying the mapped QAM symbols ${\boldsymbol s} = [{s_0},{s_1}, \ldots ,{s_{M - 1}}]$ by a precoding matrix ${\boldsymbol P}$, where M is the number of subcarriers. The precoding matrix ${\boldsymbol P}$ is an orthogonal matrix and can be expressed as [14]:
Then, the pre-coded symbol ${\boldsymbol y} = \left[ {\begin{array}{cccc} {{y_1}}&{{y_2}}& \ldots &{{y_M}} \end{array}} \right]$ can be obtained by the following formula:
DFT-S precoding can reduce the PAPR of the DMT signal by improving the autocorrelation of the input symbols by multiplying the DFT matrix ${\boldsymbol P}$[14]. After multiplying this precoding matrix, Hermitian symmetry is adopted for the pre-encoded symbols, and then the inverse fast Fourier transform (IFFT) is carried out to obtain the DFT-S DMT signal as shown in Fig. 1(a).
For the traditional DFT-S precoding, the length of payload subcarrier is not always a power of 2, which cannot directly realize precoding by FFT. To solve this problem, multi-band DFT-S precoding is investigated as shown in Fig. 1(b). Different from the traditional DFT-S precoding, the whole payload subcarriers are firstly divided into several bands (k1, k2, $\cdots $, kq), and the length of each band satisfies the power of 2, thus FFT can be implemented. After being divided into several bands, the PAPR of the signal will be increased compared to the signal with traditional DFT-S precoding, but the required computational complexity of multiplier and adder will be decreased sharply. More details will be shown in the following parts.
2.2 Noise shaping technique
Compared with high-resolution DAC, low-resolution DAC with low power consumption and system cost is more suitable for the cost-sensitive intra-DCI [21–23]. However, large quantization noise will be unavoidably induced and distorts the performance of the system. NS technique with low computational complexity and the oversampling ratio is an effective solution for quantization noise elimination [20,21]. And the architecture of the NS technique is shown in Fig. 2. From this architecture, we can get that:
where $X({e^{j\omega }})$, $Y({e^{j\omega }})$, $E({e^{j\omega }})$ represent the input signal, output signal, and quantization noise, respectively. $G({e^{j\omega }})\textrm{ = }{g_1}{e^{ - j\omega }} + {g_2}{e^{ - 2j\omega }} + \cdots + {g_L}{e^{ - Lj\omega }}$ is a linear finite impulse response (FIR) filter that is utilized to minimize the difference between $X({e^{j\omega }})$ and $Y({e^{j\omega }})$. We can get the coefficient of ${\boldsymbol g}\textrm{ = }[{\textrm{g}_1}\textrm{,}{\textrm{g}_2}\textrm{,} \cdots \textrm{,}{\textrm{g}_L}]$ by solving the optimization problem as below:At last, the coefficient of ${\boldsymbol g}$ can be found by solving the optimization problem in Eq. (5) [20]. Generally, the weighting function should be large at the signal band but small at the unused band [20]. In the following experiment, the length of taps of FIR is set as 7, and the weighting within the signal band is 24, while the weighting in the unused band is 1. All of the parameter used for the experiment is optimized by simulation.
3. Required computational complexity of various processes
The generation of the DMT signal is realized by FFT and IFFT algorithms [14]. Assuming the length of FFT is $N$, the FFT algorithm requires $({N{{\log }_2}N} )/2$ complex multipliers and $N{\log _2}N$ complex adders [16,18,19]. Among them, a complex multiplier includes 4 real multipliers and 2 real adders, and a complex adder includes 2 real adders. Therefore, the real multiplier and real adder required to perform the FFT algorithm are $2N{\log _2}N$ and $3N{\log _2}N$, respectively. The computational complexity of IFFT is the same as FFT [16].
For the traditional DMT signal, pre-equalization and post-equalization are utilized to eliminate the influence of the channel [7,16]. For pre-equalization, the process can be described as ${\bar{{\boldsymbol s}}^T} = {\boldsymbol H}_1^{ - 1}{{\boldsymbol s}^T}$, where ${{\boldsymbol H}_1}$ is the M-order real diagonal matrix, and its elements are the obtained amplitude of channel response, ${\boldsymbol H}_1^{ - 1}$ is the inverse matrix of ${{\boldsymbol H}_1}$. Since ${\boldsymbol H}_1^{ - 1}$ is a real matrix, ${{\boldsymbol s}^T}$ is a complex symbol vector. Then, the pre-equalization needs $2M$ real multipliers. For post-equalization at the receiver, the process is the same as pre-equalization, which can be described as ${\bar{{\boldsymbol z}}^T} = {\boldsymbol H}_2^{ - 1}{{\boldsymbol z}^T}$, where ${\boldsymbol H}_2^{ - 1}$ is the inverse matrix of the channel response, and it is an M-order complex diagonal matrix, ${{\boldsymbol z}^T}$ is the received complex symbol vector, then the required real multiplier and adder of the post-equalization are $4M$ and $2M$, respectively.
The traditional DFT-S technique is realized by ${{\boldsymbol y}^T} = {\boldsymbol P}{{\boldsymbol s}^T}$, where ${\boldsymbol P}$ represents the M-order complex matrix, and ${{\boldsymbol s}^T}$ is a complex symbol vector. Therefore, a total of ${M^2}$ complex multipliers and $M(M - 1)$ complex adders are required, then the real multipliers and real adders required for the traditional DFT-S precoding are $4{M^2}$ and $2M(2M - 1)$, respectively [14]. For the multi-band DFT-S technique, the whole payload subcarriers are firstly divided into several bands (k1, k2,⋯, kq), and the length of each band satisfies the power of 2, thus FFT can be implemented. Then the required real multiplexer and adder are $2{k_1}{\log _2}{k_1} + 2{k_2}{\log _2}{k_2} + \cdots 2{k_q}{\log _2}{k_q}$ and $3{k_1}{\log _2}{k_1} + 3{k_2}{\log _2}{k_2} + \cdots 3{k_q}{\log _2}{k_q}$, respectively.
NS is realized by a fixed taps FIR filter, and we suppose the number of taps of the filter is L, then we can get the required real multiplier and real adder of data with length of N are $L \times N$ and $(L\textrm{ - }1) \times N$, respectively [20,21]. Table 1 gives the required computational complexity of various processes.
Table 1. Required computational complexity of various processes.
4. Experimental setup
The experimental setup and DSP algorithm blocks for the transmission of 100 Gb/s 32 QAM-DMT signal over 2-km SMF are shown in Fig. 3. The transmitted signal is generated by MATLAB. At first, the pseudo-random binary sequence (PRBS) is mapped to 32 QAM symbols, and then the serial-to-parallel (S/P) conversion process is executed. After S/P conversion, precoding and pre-equalization techniques are applied to deal with the distortions induced by high PAPR of DMT signal and bandwidth limitation, respectively. Complex conjugate combined with 1024-point IFFT is executed to realize the generation of the DMT signal. In this experiment, the length of payload subcarriers of the DMT signal is 320. A 32-point cyclic prefix (CP) is added in front of the symbol to reduce ISI. After adding CP, the parallel-to-serial (P/S) conversion process is executed. Finally, digital 4/5-bit quantizers combined with NS technique are adopted to emulate 4/5-bit DACs and reshape the quantization noise. After a series of discrete DSP, the quantified discrete digital signal is imported into an 8-bit arbitrary waveform generator (AWG) with a sampling rate of 64 Gsa/s for analog signal generation. Then a 50 GHz electric amplifier (EA) SHF S807 with 23 dB gains combined with an eclectic attenuator is used to adjust the drive amplitude of signal before electric-to-optical conversion by a 10 G-class EML. The generated optical signal is injected into a 2-km SMF. In our experiment, a variable optical attenuator (VOA) is applied to adjust ROP. Then a 40 GHz photodetector (PD) MPRV1332A combined with a trans-impedance amplifier (TIA) is utilized to realize optical-to-electric conversion. The detected signal is captured by an 80 GSa/s oscilloscope with a resolution of 8-bit and a cut-off bandwidth of 36 GHz. At the receiver, the signal is processed in MATLAB by offline DSP, including resampling, synchronization, S/P conversion, time-to-frequency conversion, post-equalization, decoding, P/S conversion, QAM demapping, and BER calculation.
5. Results and discussions
To illustrate the effectiveness of multi-band DFT-S precoding schemes, the BER performance of 100 Gb/s 32 QAM-DMT signal with various multi-band schemes are experimentally tested in optical back-to-back (OBTB), and the results are shown in Figs. 4(a) and 4(b). In this experiment, the number of payload subcarriers is 320. Figure 4(a) gives the BER performance versus ROP with various multi-band DFT-S schemes, we can find that the traditional DFT-S precoding can bring 3.5 receiver sensitivity improvement at the HD-FEC threshold compared to that without precoding, and it gives the best ability for BER improvement among other multi-band DFT-S schemes. However, high computational complexity, about additional 1910.4% multiplier, and 1317.5% adder compared with the scheme without precoding, is required since the length of payload subcarriers is not a power of 2. The performance of multi-band DFT-S schemes is degraded as the number of the band is increased due to the decreased PAPR elimination ability as shown in Fig. 4(b). In contrast, the computational complexity of multi-band DFT-S precoding schemes is decreased sharply, as shown in Table 2. For the case of ULM DFT-S precoding scheme with 2-bands (k1 = 256, k2 = 64), the induced ROP penalty is slight, with only about 0.5 dB, compared with the traditional DFT-S scheme, whereas the required multiplier ratio and adder ratio are decreased from 1910.4% to 22.69% and from 1317.5% to 23.51%, respectively. Compared with the ELM DFT-S precoding scheme with 5-bands (k1 = 64, k2 = 64, k3 = 64, k4 = 64, k5 = 64), about 2.5 dB receiver sensitivity improvement can be observed for ULM DFT-S precoding scheme with 2-bands at the HD-FEC threshold with slightly increased computational complexity. Taking both the BER performance and computational complexity into consideration, ULM DFT-S precoding scheme with 2-bands is the optimal scheme among the aforementioned schemes for this data rate utilized for further experiment tests.
In Fig. 4, various multi-band DFT-S schemes are compared based on the implementation of the pre-equalization technique, which can effectively prevent the signal-to-noise ratio (SNR) unflatness, thereby avoiding BER performance distortion. As we know, besides PAPR elimination, the DFT-S technique can eliminate the influence of SNR unbalanced distortion to some extent, then the performance of ULM DFT-S technique is studied in the case without the pre-equalization technique, as shown in Fig. 5. From these results, we can find that in the HD-FEC threshold, obvious improvement can still be found when 2-bands DFT-S is utilized, and the difference between traditional DFT-S and ULM DFT-S technique is slight, but there is about 0.3 dB penalty compared with the case using the pre-equalization technique, which is caused by the unbalanced SNR between various bands. Based on DFT-S precoding, pre-equalization can bring about 1.5 dB receiver sensitivity improvement by avoiding noise amplification during post-equalization. The constellations of received DMT signal without pre-equalization with various precoding schemes are shown in Figs. 5(i), 5(ii), and 5(iii), respectively. The constellation becomes more clear when the precoding is applied, and the difference between traditional DFT-S and 2-bands DFT-S technique is small.
Fig. 4. (a) BER performance versus ROP with various multi-band DFT-S precoding schemes. (b)The PAPR of DMT signal with various multi-band DFT-S precoding schemes.
Table 2. The computational complexity of various multi-band DFT-S precoding schemes.
Fig. 5. BER versus ROP of signal with various techniques. The constellations of received DMT signal without pre-equalization (i) without precoding (ii) with 2-bands DFT-S precoding scheme (iii) with traditional DFT-S precoding scheme.
Low-resolution DAC is a feasible solution to reduce the system cost, which is more suitable for low-cost intra-DCI, but plenty of quantization noise will seriously distort the system performance. In this experiment, to accommodate this problem, the low-complexity NS technique realized by a 7-taps linear FIR filter is adopted to eliminate the influence quantization noise. Based on pre-equalization, precoding, and NS techniques, signals generated by 4/5-bit DACs have been experimentally studied over OBTB and 2-km SMF transmission, and the results are shown in Figs. 6(a) and 6(b). Signals generated by 4/5-bit DACs combined with NS technique have a great performance improvement compared to signals generated by 4/5-bit DACs without NS technique, but it still exists about 1.7 dB penalty for the 4-bit with NS technique compared with the case signal generated by 8-bit DAC. Based on low-resolution DAC and NS technique, the difference between traditional DFT-S precoding and 2-bands DFT-S technique is still slight. The BER performance slightly degrades compared with OBTB due to fiber dispersion. Signal generated by 4-bit DAC and NS technique using traditional DFT-S precoding can reach the HD-FEC threshold, but the required computational complexity is high since FFT algorithm can not be used. Signal generated by 5-bit DAC and NS technique using 2-bands ULM DFT-S precoding with low computational complexity can also reach the HD-FEC threshold with about 1.4 dB receiver sensitivity improvement compared with signal generated by 4-bit DAC and NS technique using traditional DFT-S precoding. Both the required computational complexity and their increased ratio of 2-bands UML DFT-S and NS techniques are shown in Table 3. We can find that the required multiplier and adder increased ratio of both 2-bands UML DFT-S and NS techniques are 39.9% and 33.7%, which is much lower than the case of using the traditional DFT-S precoding, as about 1910.4% and 1317.5%, respectively. Therefore, 100 Gb/s 2-bands ULM DFT-S 32 QAM-DMT signal generated by 5-bit DAC combined with NS technique using 10G-class EML modulator is a potential scheme for 2-km intra-DCI.
Fig. 6. BER versus ROP of signal generated by 4/5/8-bit DAC in (a) OBTB and (b) 2-km SMF transmission.
Table 3. Required computational complexity of 2-bands DFT-S and NS techniques.
6. Conclusion
A low-cost 100 Gb/s short-haul intra-DCI using 10 G-class EML and 4/5-bit DACs is experimentally demonstrated in this work. Low computational complexity ULM DFT-S technique with 2-bands (k1 = 256, k2 = 64) is utilized to reduce the distortions induced by high PAPR of pre-equalized 100 Gb/s 32 QAM-DMT signal. NS technique realized by 7-taps FIR filter is applied to suppress high quantization noise of signal generated by 4/5-bit DACs. Based on the abovementioned techniques, the BER of 100 Gb/s 2-bands ULM DFT-S 32 QAM-DMT signal generated by 5-bit DAC can successfully reach the HD-FEC threshold with ROP of -6.5 dBm. Only additional 39.9% multiplier and 33.7% adder are increased.
Funding
National Key Research and Development Program of China (2018YFB1800902); Local Innovation and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X121); Fundamental and Applied Basic Research Project of Guangzhou City under Grant (202002030326); Open Fund of IPOC (BUPT) (IPOC2020A010); National Natural Science Foundation of China (61871408).
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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