s PAM4 with low-complexity equalizers for next-generation PON systems

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40-Gb/s PAM4 with low-complexity equalizers for next-generation PON systems

T

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Xizi Tanga, Ji Zhoua, Mengqi Guoa, Jia Qia, Fan Hua, Yaojun Qiaoa, , Yueming Lub a

Beijing Key Laboratory of Space-ground Interconnection and Convergence, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China Key Laboratory of Trustworthy Distributed Computing and Service, Ministry of Education, School of Cyberspace Security, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China b

A R T I C L E I N F O

A B S T R A C T

2010 MSC: 00-01 99-00

In this paper, we demonstrate 40-Gb/s four-level pulse amplitude modulation (PAM4) transmission with 10 GHz devices and low-complexity equalizers for next-generation passive optical network (PON) systems. Simple feedforward equalizer (FFE) and decision feedback equalizer (DFE) enable 20 km fiber transmission while highcomplexity Volterra algorithm in combination with FFE and DFE can extend the transmission distance to 40 km. A simplified Volterra algorithm is proposed for reducing computational complexity. Simulation results show that the simplified Volterra algorithm reduces up to ∼75% computational complexity at a relatively low cost of only 0.4 dB power budget. At a forward error correction (FEC) threshold of 10−3 , we achieve 31.2 dB and 30.8 dB power budget over 40 km fiber transmission using traditional FFE-DFE-Volterra and our simplified FFE-DFEVolterra, respectively.

Keywords: Electronic equalizers Volterra algorithm Computational complexity Four-level pulse amplitude modulation (PAM4) Passive optical network (PON)

1. Introduction Next-generation passive optical network (PON) mainly faces two kinds of demand [1]. On one hand, with the rapid growth of bandwidththirsty services such as 4 k/8 k high-definition video, cloud computing and virtual reality, higher capacity of optical access networks will be needed [2,3]. On the other hand, there is also significant requirement of mobile front-haul network for the 5-th generation (5G) of mobile communication systems [4]. The typical front-haul distance is 10 km to 40 km and this can be ideally implemented by PON systems. Low-cost mobile front-haul will become one of the major drivers for PON rates exceeding 10 Gb/s. As a result, the research for single-wavelength 25 Gb/s, 40 Gb/s even 50 Gb/s PON based on low-cost devices has become a hot issue recently [5,6]. In order to achieve high-speed transmission using low-cost devices, spectrally efficient modulation formats such as direct-detection orthogonal frequency division multiplexing (DD-OFDM) modulation, carrier-less amplitude and phase (CAP) modulation and four-level pulse amplitude modulation (PAM4) have been widely studied [7–12]. Among these advanced modulations, PAM4 offers the lowest implementation complexity and can be used in cost-sensitive and power-sensitive PON systems [13–15]. However, advanced modulations are more sensitive to channel impairments compared to traditional non-return to zero (NRZ) modulation. Electronic equalizers based on digital signal processing (DSP) for advanced

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modulations can efficiently mitigate channel distortion without changing the optical infrastructure, which enables a practical low-cost realization of next-generation PON systems [16,17]. In recent years, electronic equalizers for PON systems have been extensively studied. Feed-forward equalizer (FFE) and decision feedback equalizer (DFE) are two kinds of simple equalizers which have been widely investigated in PON systems. For instance, a 29 dB power budget of 25-Gb/s PAM4-PON system without optical amplifier using low-complexity FFE with least mean square algorithm (LMS-FFE) was successfully demonstrated [18]. 40-Gb/s PAM4/Duobinary time division multiplexed PON (TDM-PON) over 10 km standard single-mode fiber (SSMF) using FFE and DFE was experimentally studied [19]. However, in intensity-modulation/direct-detection (IM/DD) systems, the performance of FFE and DFE are fundamentally limited by the decreased fiber dispersion tolerance and the nonlinear distortion [20]. As a result, FFE and DFE can hardly support 40 km transmission in 40-Gb/s PAM4-PON systems. DSP-based signal-signal beat interference (SSBI) mitigation technique was proposed for reducing nonlinear distortions in DD-OFDM systems while Volterra algorithm combined with FFE and DFE has been proved to be a good solution to mitigate nonlinear distortions for single-carrier systems [21,22]. A 40-Gb/s PAM4/Duobinary system using linear and nonlinear equalizers has been deeply studied [23]. The results show that nonlinear equalizers based on Volterra algorithm achieve better performance than simple FFE and DFE.

Corresponding author. E-mail address: [email protected] (Y. Qiao).

https://doi.org/10.1016/j.yofte.2017.11.015 Received 28 June 2017; Received in revised form 16 November 2017; Accepted 17 November 2017 1068-5200/ © 2017 Elsevier Inc. All rights reserved.

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information of the determined symbols, FFE-DFE generally has a better performance than FFE to eliminate inter-symbol interference (ISI). The FFE-DFE with M forward taps and N feedback taps can be described as follows

However, the Volterra algorithm possesses a relatively high computational complexity. By using the modified Gram-Schmidt method with reorthogonalization techniques, sparse-Volterra was proposed to reduce computational complexity [25,24]. This is a mathematical transformation method to determine the importance of Volterra kernels. In our study, we concentrate on the square terms of Volterra kernels and we find that square terms are the most significant impacting indicators of Volterra kernels. In this paper, we propose a simplified Volterra algorithm in combination with FFE and DFE which has extremely similar performance optimization and only ∼25% computational complexity compared to traditional Volterra algorithm. In addition, we discuss different optimum equalizers for 40-Gb/s PAM4-PON systems over different transmission distances. For 20 km SSMF transmission, we achieve 34.2 dB power budget using simple FFE. For 40 km SSMF transmission, we achieve 31.2 dB and 30.8 dB power budget using traditional FFEDFE-Volterra and our simplified FFE-DFE-Volterra, respectively.

M−1

Y (n) =

∑

N

a (k1) X (n−k1) +

k1= 0

P

Y (n) =

N −1

∑ ∑

N −1

…

∑

hp (k1,…,kp) X (n−k1)…X (n−kp) (3)

kp= 0

where X(n) and Y(n) are input and output signals, respectively. hp is pth-order Volterra kernel. P represents the order of Volterra kernels and N is the memory length. It is noted that nonlinear Volterra equalizer actually becomes linear FFE when P is set to 1. For PON systems, the order of Volterra kernels is usually set to 2 in consideration of computational complexity [23,26]. Thus, the second-order Volterra model can be rewritten as

2.1. The structure of low-complexity equalizers The blue part of Fig. 1 is a schematic of a symbol-spaced FFE structure. An FFE is the simplest structure which can be used in lowcost PON systems. It consists of several delay line filters with corresponding coefficients which are usually updated according to adaptive algorithms, such as least mean square (LMS) algorithm and recursive least square (RLS) algorithm. The FFE with M taps can be expressed as follows

N −1 N −1

Y (n) =

∑ ∑

a (k1,k2) X (n−k1) X (n−k2) (4)

k1= 0 k2= 0

Based on (4), we propose a simplified Volterra algorithm by only considering the square terms of Volterra kernels. The simplified Volterra algorithm combined with FFE can mitigate linear and nonlinear distortion simultaneously. The blue part and green part of Fig. 1 depict an example schematic of simplified Volterra algorithm combined with FFE (simplified FFE-Volterra). The simplified FFE-Volterra can be described as

M−1

∑

(2)

where M and N are the numbers of FFE and DFE taps, respectively. a(k) and b(k) are feed-forward tap coefficients and feed-back tap coefficients, respectively. X(n) and Y(n) represent input and output signals, respectively. Y’(n) represent decision feedback output signals. Volterra algorithm comes from nonlinear Volterra model which has been widely used in coherent optical communication to mitigate nonlinear distortion [24]. Volterra model can be expressed as

2. Principle of equalization

k=0

b (k2) Y ′ (n−k2)

k2= 1

p = 1 k1= 0

Y (n) =

∑

a (k ) X (n−k ) (1)

where X(n) represent input signals, Y(n) represent output signals, a(k) represent tap coefficients, M represents the number of taps. FFE is usually combined with DFE (FFE-DFE) to mitigate the preinterference and post-interference simultaneously. The blue part and red part of Fig. 1 depict a schematic of FFE-DFE with three forward taps and three feedback taps. Thanks to the introduction of the feedback

Y (n) =

M−1

M−1

∑k1=0 a (k1) X (n−k1) + ∑

a (k1,k1) X (n−k1)2 (5)

k1= 0

Similarly, we can also combine the simplified Volterra algorithm with FFE-DFE. All parts of Fig. 1 depict an example schematic of simplified Volterra algorithm with FFE-DFE (simplified FFE-DFE-Volterra). The simplified FFE-DFE-Volterra can be described as M−1

Y (n) =

∑

N

a (k1) X (n−k1) +

k1= 0

∑

M−1

+

∑

b (k2) Y ′ (n−k2)

k2= 1 N

a (k1,k1) X (n−k1)2 +

k1= 0

∑

b (k2,k2) Y ′ (n−k2)2 (6)

k2= 1

2.2. The computational complexity comparison of equalizers Table I shows the comparison of computational complexity among various equalizers. M and N are the numbers of FFE and DFE taps (also Table I Computational complexity comparison among different equalizers. Equalizers

Additions

Multiplications

FFE FFE-Volterra

M-1

M

M + M2−1 2M −1 M + N-1

M + 2M2 3M M+N

M + M2 + N + N2−1 2 M + 2 N-1

M + N + 2(M2 + N2) 3M+3N

Simplified FFE-Volterra FFE-DFE FFE-DFE-Volterra

Fig. 1. Illustrative diagram of an example FFE/FFE-DFE/simplified FFE-Volterra/simplified FFE-DFE-Volterra with three (M) feedforward taps and three (N) feedback taps.

Simplified FFE-DFE-Volterra

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called filter orders), respectively. For generating each output symbol, M-order FFE and N-order DFE need M + N multiplications and M + N −1 additions (see blue part along with red part of Fig. 1). However, traditional nonlinear Volterra algorithm greatly increases the number of taps by introducing quadratic terms. Moreover, each quadratic term needs two multiplications. Therefore, the Volterra algorithm in combination with M-order FFE and N-order DFE needs M + N + 2(M 2 + N 2) multiplications and M + N + M 2 + N 2−1 additions. Our proposed simplified Volterra algorithm only considers the square terms of Volterra kernels. Thus, the simplified Volterra algorithm combined with M-order FFE and N-order DFE needs only 3M + 3N multiplications and 2M + 2N −1 additions. The number of multiplications is the main factor to measure computational complexity of the algorithm. Table I depicts that the ratio of multiplication numbers between simplified FFE-DFE-Volterra and traditional FFE-DFE3M + 3N Volterra is . For our simplified FFE-DFE-Volterra, an ap2 2 M + N + 2(M + N )

proximately ∼75% reduction of computational complexity (M = 6,N = 5) is achieved. Moreover, it is noted that as the orders of FFE and DFE increase, the reduction degree of computational complexity can be greater.

Fig. 3. Required optical power for a BER of 10−3 with various equalizers versus launch power over 20 km SSMF transmission.

3. Simulations and results FFE and DFE filter orders are set to 6 and 5 unless otherwise explicitly indicated.

3.1. Simulation setup We perform 40-Gb/s PAM4 transmission simulations with 10 GHz devices to investigate low-complexity equalizers for next-generation PON systems. Our proposed system is simulated using VPI Transmission Maker 8.6. Fig. 2 shows the simulation setup. At the transmitter, a 40Gb/s NRZ signal with 231−1 pseudo random binary sequences (PRBS) pattern is mapped to 20 GBaud PAM4 signal. Gray code is used to map the bits onto the PAM4 symbols. In other words, “00” is mapped to “−3”, “01” is mapped to “−1”, “11” is mapped to “1” and “10” is mapped to “3”. 12800 PAM4 symbols are used for once simulation. Then a electrical amplifier is used to amplify PAM4 signal. An external Mach–Zehnder-Modulator (MZM) is used to modulate the optical carrier with the electrical PAM4 signal. Then a pre-amplified Erbium doped fiber amplifier (EDFA) along with a variable optical attenuator (VOA) is employed to adjust optical power into the fiber, thereby possibly increasing system power budget. At the receiver, another VOA is used to adjust received optical power to photo-detector (PD). Then various equalizers are investigated to mitigate channel distortion. Finally, PAM4 decoding and bit error rate (BER) counting are conducted. In our simulations, device bandwidths are limited to 10 GHz, mainly including the bandwidth of MZM and PD. The MZM is biased at the VΠ/2 point to obtain the maximum linear modulation region. The central wavelength of optical signal is 1550 nm corresponding to a fiber loss of 0.2 dB/km, chromatic dispersion of 16.9 ps/km/nm and nonlinear coefficient of 1.32 × 10−3 m−1 w −1. The optical launch power is 12 dBm.

3.2. Optimization of optical launch power Fig. 3 displays the optical power sensitivity versus different launch power with different equalizers over 20 km SSMF transmission. The results depict that 12 dBm is the optimum launch power on the condition that FFE or FFE-DFE is used. When launch power is beyond 12 dBm, the high launch power leads to significant system nonlinear penalty. For instance, 1.4 dB penalty is observed at 16 dBm launch power, which rapidly increases with continually increasing launch power. However, nonlinear Volterra algorithm can reduce nonlinear distortion to a certain extent. The optimum launch power can be improved to around 16 dBm which indicates that nonlinear Volterra algorithm can potentially increase system total power budget if larger launch power could be used in the future. In the following simulations, launch power is set to 12 dBm for a relatively fair comparison among different equalizers. 3.3. Analysis of equalizers performance In this part, we firstly discuss the equalization contribution of reducing inter symbol interference (ISI) caused by limited system bandwidth for the back to back (BTB) transmission. Next, various equalizers with different taps are investigated for reducing linear and nonlinear Fig. 2. Simulation configuration of 40-Gb/s PAM4 transmission system.

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taps. In our simulation results, FFE-DFE(12,10) achieves slightly better performance than FFE-DFE(6,5). However, FFE-DFE(16,15) almost has the same performance with FFE-DFE(12,10). It displays that only increasing the tap numbers cannot significantly improve the transmission performance. The results show that both of FFE and FFE-DFE fail to support 40 km SSMF transmission. This is because the performance of FFE and FFE-DFE are fundamentally limited by the decreased fiber dispersion tolerance and the nonlinear distortion. Fortunately, FFEDFE-Volterra(42,30) successfully achieves 40 km SSMF transmission at a received optical power sensitivity of −19.2 dBm. The reasons can be analysed as: 1) the nonlinear Volterra algorithm achieves higher dispersion tolerance; 2) the nonlinear Volterra algorithm effectively mitigates the signal-signal nonlinear distortion owing to fiber chromatic dispersion and square-law detection of photo-detector. In conclusion, Volterra algorithm can support longer transmission distance by not only mitigating nonlinear distortion but also improving dispersion tolerance. However, FFE-DFE-Volterra(42,30) possesses high computational complexity for introducing large numbers of quadratic terms. Therefore, a simplified Volterra algorithm is proposed to reduce computational complexity. The simplified FFE-DFE-Volterra only considers the square terms of the Volterra kernels, reducing tap numbers from (42,30) to (12,10). As depicted in Fig. 5, the simplified FFE-DFE-Volterra(12,10) can also achieve extremely similar performance optimization with traditional FFE-DFE-Volterra(42,30). As discussed in Section 2.2, each linear term needs one multiplication while each quadratic term needs two multiplications. Consequently, traditional FFE-DFEVolterra(42,30) needs in total 72 taps, including 6 + 5 = 11 taps with one multiplication and 36 + 25 = 61 taps with two multiplications. However, simplified FFE-DFE-Volterra(12,10) only needs in total 22 taps, including 6 + 5 = 11 taps with one multiplication and 6 + 5 = 11 taps with two multiplications. Thence, the ratio of multiplication numbers between simplified FFE-DFE-Volterra(12,10) and traditional 11 + 11 × 2 FFE-DFE-Volterra(42,30) is 11 + 61 × 2 × 100% = 24.8%. Moreover, it can be implied from Fig. 6 that as the numbers of FFE taps and DFE taps increase, the degree of computational complexity reduction can be greater. In Fig. 7, the absolute values of second-order kernels in traditional Volterra algorithm are depicted for 40 km SSMF transmission. It shows that only the kernels along the diagonal have relatively higher values, while the other kernels are nearly zero and could be excluded. The result reveals that square terms are the most significant impacting indicators of Volterra kernels. It is the principle for reducing the computational complexity of Volterra algorithm.

Fig. 4. BER performance of 40-Gb/s PAM4 transmission with and without equalizers for BTB transmission.

damage over 40 km SSMF transmission. Finally, we discuss the reduction of computational complexity in our proposed simplified Volterra algorithm. Fig. 4 shows the BER performance for BTB transmission. Due to the limited system bandwidth of 10 GHz, 40-Gb/s PAM4 transmission suffers from severe ISI. As a result, the black performance curve without any equalizer can not reach the FEC threshold of 10−3 . However, FFE and FFE-DFE successfully reach the FEC threshold at the received optical power of −23.2 dBm and −23.5 dBm, respectively. FFE-DFE achieves slightly better performance than FFE thanks to the introduction of the feedback information of the determined symbols. The results indicate that FFE and FFE-DFE effectively mitigate ISI caused by limited system bandwidth. In order to mitigate the damage of limited system bandwidth, FFE and FFE-DFE are included in nonlinear FFE-Volterra and FFE-DFE-Volterra, respectively. Fig. 5 reveals the BER performance over 40 km SSMF transmission using different equalizers. In the presentation of Fig. 5, the numbers after equalizers are feed-forward tap numbers and feedback tap numbers which can also reflect computational complexity. For instance, FFE-DFE(6,5) means FFE-DFE with 6 feed-forward taps and 5 feedback

3.4. Trade-off between power budget and computational complexity Fig. 8 depicts the received optical power sensitivity of 40-Gb/s PAM4 system over different fiber lengths with different equalizers. For 20 km SSMF transmission, a link power budget of 34.2 dB (launch power is 12 dBm) can be achieved by FFE. Since the achieved power budget is extremely similar to other equalizers, FFE is the optimum equalizer at the lowest computational complexity. For 40 km SSMF transmission, Volterra algorithm in combination with FFE and DFE achieves an obviously better performance than simple FFE-DFE owing to nonlinear compensation and higher dispersion tolerance. The traditional FFE-DFE-Volterra achieves 31.2 dB power budget while a simplified FFE-DFE-Volterra achieves 30.8 dB power budget. This results demonstrate that a simplified FFE-DFE-Volterra has a similar performance compared to a traditional FFE-DFE-Volterra. However, simplified FFE-DFE-Volterra has only ∼25% computational complexity compared to traditional FFE-DFE-Volterra. Consequently, we believe that our proposed simplified FFE-DFE-Volterra is the optimum equalizer when transmission distance reaches 40 km.

Fig. 5. BER performance of 40-Gb/s PAM4 transmission with different equalizers over 40 km SSMF transmission.

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Fig. 6. The ratio of multiplication numbers between simplified and traditional Volterra algorithms with different FFE taps and DFE taps.

Fig. 8. Received optical power sensitivity for a BER of 10−3 versus transmission distance with different equalizers.

Fig. 7. The absolute values of the second-order kernels in traditional Volterra algorithm for 40 km SSMF transmission.

Acknowledgments 4. Conclusion

This work was supported in part by the National Natural Science Foundation of China under Grant 61427813 and Grant 61331010, in part by the National Key Research and Development Program under Grant 2016YFB0800302.

Electronic equalizers play an important role in conducting highspeed and low-cost next-generation PON systems. In this paper, we investigated various low-complexity equalizers for 40-Gb/s PAM4-PON systems. Considering performance and computational complexity, there are different optimum equalizers for different transmission distances. For 20 km transmission, we achieved 34.2 dB power budget with FFE. For 40 km transmission, we achieved 31.2 dB and 30.8 dB power budget with FFE-DFE-Volterra and our proposed simplified FFE-DFE-Volterra, respectively. Moreover, simplified FFE-DFE-Volterra significantly reduces up to ∼75% computational complexity and achieves similar performance compared to traditional FFE-DFE-Volterra. The results have an important guiding significance to trade off performance and cost in next-generation PON systems.

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