Amplifier-free 4&#x00D7;96 Gb/s PAM8 transmission enabled by modified Volterra equalizer for short-reach applications using directly modulated lasers

Di Li; Lei Deng; Yao Ye; Yucheng Zhang; Haiping Song; Mengfan Cheng; Songnian Fu; Ming Tang; Deming Liu

doi:10.1364/OE.27.017927

1. Introduction

A recent Cisco report predicted that the global datacenter IP traffic would be increased from 6.8 Zettabytes (ZB) in 2016 to 20.6 ZB by the end of 2021, with a compound annual growth rate (CAGR) of 25% [1]. It means that the traffic in metro network is constantly turning to the datacenter. Therefore, massive research efforts are conducted for the standardization of datacenter [2–5]. Generally, the length scale of optical communications for datacenter covers from several hundred meters to beyond a hundred kilometers [2]. The intensity modulation and direct detection (IMDD) scheme is more favorable in short-reach datacenter interconnection since the datacenter is particularly sensitive to the cost and power consumption. Moreover, high capacity is also highly desired in datacenter. Many schemes based on 4-level pulse amplitude modulation (PAM4) modulation have been investigated to achieve a capacity of 400 Gbps in recent years, and PAM4 has been adopted for several distance categories in IEEE 200 GbE and 400 GbE standardization. For example, with the help of high volume manufacturing capable and ridge waveguide platform, 56 Gbit/s PAM4 signal is transmitted over 10 km with strong robustness to temperature fluctuation [6]. Single-λ 112 Gb/s PAM4 signal after 80 km standard single mode fiber (SSMF) transmission with signal-to-signal beat noise cancellation in a DP-I/Q modulator-based system is presented in [4]. Single-wavelength 112 Gb/s PAM4 using 28 GHz directly modulated laser (DML) is transmitted over 40 km with no amplifier [7]. However, all the above schemes are based on either devices with larger bandwidth or complex digital signal processing (DSP) including pre-equalization and nonlinear equalizer. The main reason is that the spectrum efficiency (SE) of PAM4 is still limited in such a bandwidth-hungry era and the highest SE is just 4 bit/s/Hz even if Nyquist shaping is applied [8].

For the specifications of beyond 400 GbE in future, the datacenter continually adopting PAM4 will rely on devices with much larger bandwidth and more complex DSP, which results in dramatic increase of cost and latency. Therefore, PAM8 whose SE is higher than that of PAM4 would have a promising prospect regarding the cost-effective standardization beyond 400 GbE. Up to now, several transmission experiments based on PAM8 have been investigated for long-haul and short-reach application [9–13]. For example, a single-polarization 168 Gbit/s PAM8 is transmitted over 2 km distance based on a transceiver using a high-speed selector power DAC [9]. This transmitter includes a 35-GHz-bandwidth Mach Zehnder modulator (MZM) and a semiconductor laser. A high SE of 4.3 bit/s/Hz is achieved for 107.52 Gbit/s SSB-Nyquist-PAM8 transmission over 80 km SSMF based on an InP-based IQ modulator [10]. The bandwidth of the used DAC is limited to 15 GHz. An 84 Gb/s vestigial sideband (VSB) PAM8 signal based on vertical-cavity surface-emitting laser (VCSEL) transmitter is investigated in fiber-invisible laser light communication, where injection locking scheme is required [11]. 40 GBd Nyquist PAM8 is also successfully transmitted over 2 km SSMF using 10 G-class DAC and photodiode in [12]. However, by considering the cost and power consumption, DML is more preferable in IMDD system than the electro absorption modulated DFB Laser (EML) or MZM. For instance, it states that the proposed method via DML based IMDD system can be thought feasible in the low-cost short reach optical applications in [14]. It also shows that high-level QAM-OFDM can be supported by cost-effective DML, which could be applied in low-cost short reach optical communications in [15]. Moreover, to improve the capacity of the datacenter network, wavelength division multiplexing (WDM) transmission scheme is also demanded. To our knowledge, there are few reports on the transmission of 400 Gbit/s PAM8 signal over longer than 10 km SSMF by using DML without optical amplifier.

The main restrictions of high speed PAM8 signal transmission by using a DML could be attributed to the severe linear and nonlinear impairments, and the large relative intensity noise (RIN) of DML. The linear equalizer such as feed-forward equalizer (FFE) which is based on least mean square (LMS) algorithm has been successfully used to mitigate the linear distortion [16,17]. In recent years, many nonlinear equalization algorithms have been applied in optical communication to cope with the nonlinear distortion. These nonlinear equalization algorithms include Volterra equalizer [18,19], lookup table (LUT) nonlinear predistortion method [20], clustering algorithms [21], and neural network (NN) algorithms [22,23]. Many experiments have verified the effectiveness of these nonlinear equalization algorithms on the elimination of nonlinear impairments. However, the equalization methods mentioned above would amplify the noise at high frequency, resulting in the decrease of transmission performance. A recent proposed method called NFC can cope with the unwanted impairments and FFE-amplified noise simultaneously as shown in [24,25]. But this algorithm is very complex, and it is composed of equalization, post filtering, and maximum likelihood sequence estimation (MLSE).

In this paper, we extend our previous work in [26] and experimentally demonstrate a transmission of 4 × 96 Gbit/s PAM8 over 15 km SSMF without optical amplifier by using four O-band DMLs for the first time. Meanwhile, the conventional Volterra equalizer is modified to eliminate the enhanced noise at high frequency. In addition, 4 × 64 Gbit/s PAM4 signal transmission is also demonstrated over 30 km SSMF based on the same experimental setup. To be specific, the narrowest 3 dB bandwidth of the used DMLs is 13.5 GHz and no pre-equalization is used at the transmitter. The results show that a power gain of 0.5 dB and 3.3 dB for 4 × 64 Gbit/s PAM4 signal transmission over 30 km SSMF and 4 × 96 Gbit/s PAM8 signal transmission over 15 km SSMF at the HD-FEC limit can be obtained respectively with the help of the modified Volterra equalizer. Furthermore, it is proved that the modified Volterra equalizer can achieve a slightly better BER performance with lower computational complexity compared with the conventional Volterra equalizer, and the reduction in computation complexity is 38%.

2. Principle of the modified Volterra equalizer

Many nonlinear equalizers such as NN-based equalizer and Volterra equalizer have been investigated to combat the linear and nonlinear impairments in the bandwidth-limited system [18–23]. In our scheme, the used DMLs would produce not only the nonlinear chirp effect but also the distortion induced by limited component bandwidth. Therefore, the Volterra equalizer is introduced in our system because the NN-based equalizer is more complex and it requires massive training data symbols. However, the Volterra equalizer can be treated as a kind of FFE which would usually amplify the noise at high frequency. In this way, it is quite harmful to multi-level signals. To solve this problem, the Volterra equalizer is modified in our scheme by jointing a decision feedback process behind the Volterra filter as shown in Fig. 1. The structure of the modified Volterra equalizer resembles the structure of FFE-DFE [27,28], but the FFE is based on nonlinear Volterra series and the decision threshold is modified to adapt the fluctuant signal. For a k-th order discrete modified Volterra equalizer, the input $x (i)$ and the output $y (i)$ signal can be expressed as:

y (i) = \sum_{n = 1}^{k} \sum_{m_{1} = 0}^{l_{1}} \dots \sum_{m_{k} = m_{k - 1}}^{l_{k}} w (m_{1}, \dots, m_{k}) \times x (i - m_{1}) \dots x (i - m_{k}) + \sum_{n = 1}^{q} h (n) d (i - n),

where

w (m_{1}, ..., m_{r})

represents the taps of r^th order Volterra kernel,

l_{i}

is the i^th order memory length,

h (n)

represents the taps of the decision feedback process, and

d (i)

is the decision results of

y (i)

. The first term and the second term of Eq. (1) represent the Volterra filter and decision feedback process, respectively. Generally, the computation complexity of Volterra equalizer is increased with the growth of the number of Volterra kernel and its corresponding memory length, thus 3rd Volterra filter is adopted in our scheme. Consequently, the linear and nonlinear impairments including signal-to-signal beating noise can be mitigated effectively [29]. The enhanced noise at high frequency can be eliminated by the following decision feedback process.

Fig. 1 Schematic diagram of the modified Volterra equalizer. $w_{i}$ : tap coefficients of the 1^st order Volterra kernel, $w_{i j}$ : tap coefficients of the 2^nd order Volterra kernel, $h_{i}$ : tap coefficients of the decision feedback process, $T$ : one symbol delay, $x(i)$ : input signal, $y(i)$ : output signal, and $d(i)$ : decision results of $y(i)$ .

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The tap coefficients of Volterra filter and decision feedback process can be optimized using adaptive algorithms such as LMS and recursive least square (RLS) [30]. However, the convergence speed of LMS is slower than that of RLS. Therefore, RLS is used in the modified Volterra equalizer. The input vector of the modified Volterra equalizer can be described as:

U (n) = [\underset{1 s t o r d e r i n p u t t e r m s}{\underset{︸}{x (n), x (n - 1), \dots}}, \underset{2 n d o r d e r i n p u t t e r m s}{\underset{︸}{x (n - i) x (n - j), \dots}}, \underset{3 r d o r d e r i n p u t t e r m s}{\underset{︸}{x (n - i) x (n - j) x (n - p), \dots}}, \underset{d e c i s i o n i n p u t t e r m s}{\underset{︸}{d (n - 1), \dots}}] .

Equation (2) is composed of four terms, corresponding to the inputs of the 1^st order kernels, 2^nd order kernels, 3^rd order kernels and the decision feedback process respectively. The tap coefficients of the modified Volterra equalizer can be written as:

W (n) = [\underset{1 s t o r d e r \ker n e l}{\underset{︸}{w_{1}, w_{2}, \dots}}, \underset{2 n d o r d e r \ker n e l}{\underset{︸}{w_{i j}, \dots}}, \underset{3 r d o r d e r \ker n e l}{\underset{︸}{w_{i j p}, \dots}}, \underset{d e c i s i o n f e e d b a c k f i l t e r}{\underset{︸}{h_{1}, h_{2}, \dots}}],

and the tap coefficients are updated by the RLS algorithm as following:

W (n) = W (n - 1) + K (n) \cdot e (n),

π (n) = U (n) \cdot P (n - 1),

K (n) = π^{T} (n) / (λ + π (n) \cdot U^{T} (n)),

P (n) = \frac{1}{λ} (P (n - 1) - K (n) \cdot π (n)),

where

e (n) = d (n) - y (n)

is the error between the decision results

d (n)

and the equalizer outputs

y (n)

, the superscript

T

represents the transposition operation, and the parameter

λ

is a factor that controls the memory span of the adaptive filter.

Generally, training sequences are required to obtain the tap coefficients before the performance test. During the training period, the decision results $d (n)$ can be replaced by the training sequences. In the process of equalizing the receiving data, the decision threshold $t h (n)$ of the decision feedback process is modified as:

t h (n) = t h (n - 1) + μ \cdot \bar{e},

where

μ

is a user-defined scan factor, and

\bar{e}

represents the average of the

z

error values from

e (n - 1)

to

e (n - z)

. For a standard bipolar PAM8 signal,

t h (n)

is [-7, −5, −3, −1, 1, 3, 5, 7]. The modification of decision threshold is useful when the received signal is fluctuant by a low-frequency current signal as shown in [31].

3. Experimental setup

The experimental setup of 4 × 64 Gbps PAM4 and 4 × 96 Gbps PAM8 signal transmissions are shown in Fig. 2(a). At the transmitter, the transmitting data is generated off-line with MATLAB. A pseudorandom bit sequences (PRBS) with length of 2¹⁵-1 is produced and then mapped into PAM4/PAM8 format. After up-sampled by inserting one zero between adjacent symbols, the PAM4/PAM8 signal is pulse-shaped by a root-raised cosine filter with a roll-off of 0.2. Therefore, the over-sampling ratio of the PAM4/PAM8 signal is 2. To obtain four channels of independent PAM4/PAM8 signals, the generated PAM4/PAM8 signal is delayed with different time. It should be noted that no pre-equalization is used in the transmitter as shown in Fig. 2(a). Thus, there is no necessity to obtain the transfer function of the entire system in advance. The generated four channels of PAM4/PAM8 signals are loaded into a four-channel arbitrary waveform generator (AWG, Keysight M8195A) with 3 dB bandwidth of 20 GHz. The sampling rate of this AWG is set to 64 GSa/s, so the data rate of single-lane PAM4 and PAM8 signal are 64 Gbit/s and 96 Gbit/s respectively. The output peak-to-peak voltages of four-channel signals are set to 400 mV, and these signals are then amplified by four electrical amplifiers (EA) with gain of 23 dB. Finally, these four electrical signals are used to drive four O-band DMLs. The photograph of one DML module is shown in the insert of Fig. 2. An integrated circuit board is designed to control the bias current, and the operation wavelength of these four DMLs is 1269.54 nm, 1290.10 nm, 1309.67 nm, and 1329.12 nm respectively. The optical spectrum of the optical signal after MUX is shown in Fig. 2(b). The S21 curves of these four DMLs with the bias current of 46 mA are measured by a vector network analyzer (R&S ZNB40), and they are shown in Fig. 2(c). It could be clearly observed that the 3 dB bandwidth of these four DMLs is 13.5 GHz, 17.1 GHz, 17.5 GHz, and 18.2 GHz respectively. Therefore, the total net rate of four Lanes is 256 Gbit/s (4 × 64 Gbit/s) and 384 Gbit/s (4 × 96 Gbit/s) for PAM4 and PAM8 respectively.

Fig. 2 (a) The experimental setup of PAM4/PAM8 signal transmission, (b) the transmitted optical spectrum after MUX, and (c) the measured S21 curves of four DMLs.

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After SSMF propagation without any optical amplifier, the optical signal is wavelength-demultiplexed by a DEMUX at the receiver. The received optical power (ROP) of each Lane signal is controlled by a variable optical attenuator (VOA). Finally, the received signal is detected by a photo-detector (PD) with bandwidth of 22 GHz, and then captured by a digital sampling oscilloscope (DSO, LeCroy LabMaster 10-36Zi-A) operating at 80 GSa/s for offline process. In the receiver, the received signal is first down-sampled to 2 samples per symbol and then synchronized. The modified Volterra equalizer is used to deal with the nonlinear distortion of the system. About $1 \times 10^{5}$ bits are used for BER counting in our experiment.

4. Results and discussion

4.1. 4 × 64 Gbit/s PAM4 signal transmission

Figures 3(a) and 3(b) show the measured BER curves of 4 × 64 Gbit/s PAM4 signals as a function of ROP after optical back-to-back (OBTB) transmission. The conventional Volterra equalizer and the modified Volterra equalizer are both tested in our experiment. In the test, the conventional Volterra equalizer with three kernels and the corresponding memory length of $l_{1}$ , $l_{2}$ , and $l_{3}$ is defined as Volterra ( $l_{1}, l_{2}, l_{3}$ ). The modified Volterra equalizer with the same configuration and a memory length of $q$ for the decision feedback process is defined as the modified Volterra ( $l_{1}, l_{2}, l_{3}, q$ ). The parameters of both equalizers are optimized, and Volterra (51,7,3) and the modified Volterra (51,7,3,4) are used in OBTB case. It can be clearly observed that Lane3 has the best BER performance, and the BER performance of Lane1 is the worst. This could be attributed to the used DML in Lane1 with the narrowest 3 dB bandwidth as shown in Fig. 2(c). When Volterra (51,7,3) is adopted, the receiver sensitivity at the HD-FEC limit (BER of $3.8 \times 10^{- 3}$ ) is −10.7 dBm, −11.1 dBm, −12.3 dBm and −11.4 dBm for Lane1, Lane2, Lane3, and Lane4 respectively. The receiver sensitivity can be improved to −10.9 dBm, −11.4 dBm, −12.4 dBm and −11.6 dBm for Lane1 to Lane4 respectively when the Modified Volterra (51,7,3,4) is used, which brings a power benefit of about 0.2 dB for all these four Lanes due to the elimination of the enhanced noise at high frequency.

Fig. 3 The measured BER curves of 4 × 64 Gbit/s PAM4 signals as a function of ROP after OBTB transmission by using Volterra (51,7,3) and the modified Volterra (51,7,3,4) for (a) Lane 1 and Lane2, (b) Lane3 and Lane4.

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Figure 4(a) presents the BER performance when varying the parameters of Volterra ( $l_{1}, l_{2}, l_{3}$ ) which is abbreviated as V( $l_{1}, l_{2}, l_{3}$ ) at the ROP of −10 dBm after 30 km SSMF transmission for Lane3. For the parameter $l_{1}$ , which corresponds to the 1^st order kernel of Volterra filter, the BER is not improved clearly as the increase of its value from 27 to 63. The memory length of 51 is enough to cope with the linear distortion. By fixing $l_{1}$ at 51, the measured BER value can get a larger improvement when $l_{2}$ is adjusted from 3 to 9, which means that the impairments related to the 2^nd order kernel are eliminated effectively. Moreover, by adding the 3^rd order kernel, the BER performance can be further improved. By considering both the computation complexity and the transmission performance, Volterra (51,7,3) is used in our experiment. The obtained tap coefficients of the trained Volterra (51,7,3) is shown in Fig. 4(b). It can be observed that the tap coefficients of the 2^nd order kernel and the 3rd order kernels are not zero, indicating the residual nonlinear impairments. Based on this optimized Volterra equalizer, the modified Volterra equalizer is designed by jointing a decision feedback process behind.

Fig. 4 (a) The measured BER values as a function of the parameters of Volterra ( $l_{1}, l_{2}, l_{3}$ ) at the ROP of −10 dBm after 30 km SSMF transmission for Lane3, (b) tap coefficients of the trained Volterra (51,7,3).

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By using the optimized parameters in both Volterra equalizer and the modified Volterra equalizer, the BER performance of 4 × 64 Gbit/s PAM4 signals after 30 km SSMF transmission is measured and displayed in Figs. 5(a) and 5(b). Volterra (51,7,3) and the modified Volterra (51,7,3,4) are used in this test. It could be observed that the receiver sensitivity at the HD-FEC limit is −8.8 dBm, −11.1 dBm, −12.2 dBm and −12.0 dBm for Lane1, Lane2, Lane3, and Lane4 respectively when Volterra (51,7,3) is used. Negligible power penalty induced by fiber transmission can be observed for Lane2 and Lane3 because the chromatic dispersion (CD) is low when the wavelength is close to 1310 nm. Power penalty of 1.9 dB and −0.6 dB are observed for Lane1 and Lane4 respectively, compared with the OBTB case. And this could be attributed to the interaction of DML-induced frequency chirp and CD [32]. When the modified Volterra (51,7,3,4) is applied, the receiver sensitivity can be improved to −9.3 dBm, −11.4 dBm, −12.4 dBm and −12.2 dBm for Lane1 to Lane4 respectively. A power gain of 0.5 dB is observed for Lane1 because the bandwidth of the used DML is the lowest.

Fig. 5 The measured BER curves of 4 × 64 Gbit/s PAM4 signals as a function of ROP after 30 km SSMF transmission by using Volterra (51,7,3) and the modified Volterra (51,7,3,4) for (a) Lane 1 and Lane2, (b) Lane3 and Lane4.

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To verify the validity of the modified Volterra equalizer on the elimination of the enhanced noise at high frequency, a white Gaussian noise is generated and then passed through the Volterra (51,7,3) and the modified Volterra (51,7,3,4) equalizer used in Fig. 5. Figure 6(a) shows the spectrum of the generated white Gaussian noise. The frequency is normalized to 1, and the white Gaussian noise has a uniform distribution in the frequency domain. After the Volterra (51,7,3) equalizer, the noise at the region of high frequency is enhanced as presented in Fig. 6(b). However, when the modified Volterra (51,7,3,4) equalizer is used, the noise at the region of high frequency is effectively suppressed as shown in Fig. 6(c). Therefore, the modified Volterra equalizer could not only equalize the impaired signal but also suppress the enhanced noise at high frequency.

Fig. 6 Normalized spectrum of white Gaussian noise (a) before equalizers, (b) after the Volterra (51,7,3), and (c) after modified Volterra (51,7,3,4). Red curves: the envelope of the corresponding spectrum.

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4.2. 4 × 96 Gbit/s PAM8 signal transmission

Figures 7(a) and 7(b) show the measured BER curves of 4 × 96 Gbit/s PAM8 signals as a function of ROP after OBTB transmission. Volterra (51,7,3) and the modified Volterra (51,7,3,6) are used in this test. The receiver sensitivity at the HD-FEC limit is −4.5 dBm, −6.0 dBm, −7.2 dBm and −6.6 dBm for Lane1, Lane2, Lane3 and Lane4 respectively when Volterra (51,7,3) is applied. However, the receiver sensitivity is altered to −5.6 dBm, −6.7 dBm, −7.8 dBm and −7.1 dBm for Lane1 to Lane4 respectively as the modified Volterra (51,7,3,6) is used. Thus, there are power gain of 1.1 dB, 0.7 dB, 0.6 dB, and 0.5 dB for Lane1 to Lane4 respectively thanks to the elimination of the enhanced noise at high frequency. It can be clearly observed that the power gain caused by the modified Volterra equalizer is larger compared with the PAM4 case in Fig. 3. The power gain of Lane1 is still the largest one in accordance with the results of PAM4 transmission.

Fig. 7 The measured BER curves of 4 × 96 Gbit/s PAM8 signals as a function of ROP after OBTB transmission by using Volterra (51,7,3) and the modified Volterra (51,7,3,6) for (a) Lane 1 and Lane2, (b) Lane3 and Lane4.

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Figures 8(a) and 8(b) show the measured BER curves of 4 × 96 Gbit/s PAM8 signals as a function of ROP after 15 km SSMF transmission. In this case Volterra (51,7,3) and the modified Volterra (51,7,3,6) are used. It can be observed that the BER performance of Lane1 is still the worst, testifying the influence of limited bandwidth. When Volterra (51,7,3) is used, the receiver sensitivity of Lane1 to Lane4 at the HD-FEC limit is −0.3 dBm, −5.4 dBm, −7.2 dBm and −6.5 dBm respectively. Compared with the OBTB transmission, we can conclude that there is the power penalty of 4.2 dB, 0.6 dB, 0 dB and 0.1 dB for Lane1, Lane2, Lane3 and Lane4 respectively. The difference of power penalty could be attributed to the results of interplay between chirp and chromatic dispersion. When the modified Volterra (51,7,3,6) is applied, the receiver sensitivity can be improved to −3.6 dBm, −6.0 dBm, −7.8 dBm and −7.0 dBm, resulting in a power gain of 3.3 dB, 0.6 dB, 0.6 dB and 0.5 dB for Lane1 to Lane4 respectively. The largest power gain of Lane1 confirms that the modified Volterra is suitable for bandwidth-limited application.

Fig. 8 The measured BER curves of 4 × 96 Gbit/s PAM8 signals as a function of ROP after 15 km SSMF transmission by using Volterra (51,7,3) and the modified Volterra (51,7,3,6) for (a) Lane 1 and Lane2, (b) Lane3 and Lane4.

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Figure 9 presents the effect of the modified Volterra equalizer on the enhanced noise elimination and the equalized PAM8 symbols after 15 km SSMF with different equalizers. The same white Gaussian noise as shown in Fig. 6(a) is used in this case. The noise spectrum after Volterra (51,7,3,6) is displayed in Fig. 9(a). It can be seen that noise at the region of high frequency is effectively suppressed. However, the noise at the region of high frequency is enhanced when Volterra (51,7,3) is used as shown in Fig. 9(b). The equalized PAM8 symbols with the modified Volterra (51,7,3,6) and Volterra (51,7,3) at the ROP of 1 dBm for Lane1 is displayed in Figs. 9(c) and 9(d) respectively. It can be observed that the equalized PAM8 signal by using the modified Volterra is clearer, corresponding to a better BER value. Compared with the power gain caused by the modified Volterra in the PAM4 case, the power benefit in PAM8 case is larger since PAM8 signal is more sensitive to the noise.

Fig. 9 Normalized spectrum of white Gaussian noise after (a) modified Volterra equalizer (51,7,3,6), and (b) the conventional Volterra equalizer (51,7,3). The equalized PAM8 symbols by using (c) the modified Volterra equalizer (51,7,3,6), and (d) the conventional Volterra equalizer (51,7,3) at the ROP of 1 dBm for Lane1. Red curves: the envelope of the corresponding spectrum.

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4.3. The computation complexity of the modified Volterra equalizer

Considering the higher cost of a multiplier compared with that of an adder, the computational complexity of the modified Volterra equalizers can be calculated in terms of the required number of the real-valued multiplications per symbol. As shown in Fig. 1, the modified Volterra equalizer is composed of a conventional Volterra filter and a decision feedback process. It should be noted that the complexity of the training process is not considered because it is no longer needed once the obtained equalizer is converged stably. By considering the generation of i-th order inputs term, the number of the real-valued multiplier of Volterra ( $l_{1}, l_{2}, l_{3}$ ) can be calculated as:

C_{1} = l_{1} + l_{2} \cdot (l_{2} + 1) + \frac{3}{2} \cdot (1 \cdot (1 + 1) + 2 \cdot (2 + 1) + \dots + l_{3} \cdot (l_{3} + 1)) .

Thus, the computation complexity of the modified Volterra ( $l_{1}, l_{2}, l_{3}, q$ ) after jointing a decision feedback process behind the conventional Volterra filter can be expressed as:

C_{2} = C_{1} + q = l_{1} + l_{2} \cdot (l_{2} + 1) + \frac{3}{2} \cdot (1 \cdot (1 + 1) + 2 \cdot (2 + 1) + \dots + l_{3} \cdot (l_{3} + 1)) + q .

Obviously, the computation complexity of the modified Volterra equalizer is higher than the conventional Volterra filter, even if it has advantages in the elimination of the enhanced noises at high frequency.

To fairly compare the computation complexity of the modified Volterra equalizer and the conventional Volterra equalizer, the required multiplication per symbol and the achieved BER value of 96 Gbit/s PAM8 signal transmission over 15 km SSMF at the ROP of 1 dBm for Lane1 is measured and displayed in Fig. 10. The modified Volterra ( $l_{1}, l_{2}, l_{3}, q$ ) and Volterra ( $l_{1}, l_{2}, l_{3}$ ) are abbreviated as ( $l_{1}, l_{2}, l_{3}, q$ ) and ( $l_{1}, l_{2}, l_{3}$ ) respectively for convenience. (51,7,3) which is used in our experiment mentioned above is chosen as the reference. More complex Volterra equalizer (51,11,5) could be used to significantly improve the BER performance, but the required multiplication per symbol is also increased by more than twofold. However, with the help of the modified Volterra equalizer, the required taps of 2nd order and 3rd Volterra kernel can be effectively decreased. Meanwhile, the better BER performance could be achieved, contributing to the decrease of the computation complexity. Obviously, the used parameters of (51,7,3,6) in our experiment can achieve a much better BER performance than the reference of (51,7,3) at the same computation complexity level. Moreover, (51,5,1,1) can achieve a slightly better BER performance with lower computation complexity, thus it may be the best choice by comprehensively considering both the required computation complexity and the achieved BER performance. The required multiplication per symbol of (51,5,1,1) is 85 while it is 137 for (51,7,3), corresponding to a reduction of 38% ( $\frac{137 - 85}{137} = 38 %$ ). Therefore, the modified Volterra equalizer cannot only effectively eliminate the enhanced noise but also decrease the required computation complexity.

Fig. 10 The measured BER performance and the required computation complexity of different equalizers at the ROP of 1 dBm for Lane1 with 96 Gbit/s PAM8 signal transmission over 15 km SSMF.

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5. Conclusion

In our experiment, 4 × 64 Gbit/s PAM4 and 4 × 96 Gbit/s PAM8 signals are successfully transmitted over 30 km SSMF and 15 km SSMF without any optical amplifiers in a DMLs-based IMDD system. The narrowest 3 dB bandwidth of the used DMLs is only 13.5 GHz, and the wavelength is 1269.54 nm, 1290.10 nm, 1309.67 nm, and 1329.12 nm respectively. The Volterra equalizer is modified to eliminate the enhanced noise at high frequency in our scheme. The experimental results show that the modified Volterra equalizer can suppress the enhanced noise effectively, and about 0.2 dB and 0.5 dB power gain can be achieved after OBTB and 30 km SSMF transmission in the PAM4 case respectively. For 4 × 96 Gbit/s PAM8 signal transmission, the power gain after OBTB and 15 km SSMF transmission is improved to around 0.6 dB and 3.3 dB respectively. Furthermore, the modified Volterra equalizer has been proved to reach a slightly better BER value with a lower computational complexity compared with the conventional Volterra equalizer, and a reduction of 38% in computation complexity can be achieved. The obtained results predict that the DML-modulated PAM8 may have a promise prospect in the future cost-effective standardization beyond 400 GbE.

Funding

National “863” Program of China (2015AA016904); National Natural Science Foundation of China (NSFC) (61675083, 61505061); Fundamental Research Funds for the Central Universities HUST (2017KFKJXX010); Key project of R&D Program of Hubei Province (2017AAA046).

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Amplifier-free 4×96 Gb/s PAM8 transmission enabled by modified Volterra equalizer for short-reach applications using directly modulated lasers

Abstract

1. Introduction

2. Principle of the modified Volterra equalizer

3. Experimental setup

4. Results and discussion

4.1. 4 × 64 Gbit/s PAM4 signal transmission

4.2. 4 × 96 Gbit/s PAM8 signal transmission

4.3. The computation complexity of the modified Volterra equalizer

5. Conclusion

Funding

References

Cited By

Figures (10)

Equations (10)

Optics Express