Hilbert superposition and modified signal-to - OSA Publishing

Vol. Vol. 25,25, No.No. 1111 | 29 | 29 May May 2017 2017 | OPTICS | OPTICS EXPRESS EXPRESS 12622 1

Hilbert superposition and modified signal-tosignal beating interference cancellation for single side-band optical NPAM-4 directdetection system MINGYUE ZHU,1 JING ZHANG,1,* XINGWEN YI,1 YANG SONG,1 BO XU,1 XIANG LI,2 XINWEI DU,3 AND KUN QIU1 1

Key Laboratory of Optical Fiber Sensing and Communications (Education Ministry of China), School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China 2 State Key Laboratory of Optical Communication Technologies and Networks, Wuhan Research Institute of Posts and Telecommunications, Wuhan 430074, China 3 Department of Electrical and Computer Engineering, National University of Singapore, 117583, Singapore *[email protected]

Abstract: We propose a Hilbert superposition and modified signal-to-signal beating interference (SSBI) cancellation scheme in an optical single side-band (SSB) modulation and direct-detection system. The optical SSB signal is generated by a relatively low-cost dualdrive Mach-Zehnder modulator (DDMZM). The two driving signals are a pair of Hilbert signals with Nyquist pulse-shaped four-level pulse amplitude modulation (NPAM-4). In addition to the transmitted baseband signal, both its Hilbert transform and the SSBI can also be detected by direct-detection, which introduce the interference to the transmitted signal. We use the first-stage Hilbert superposition cancellation (HSC) to cancel the unwanted Hilbert transform signal and a modified single-stage linearization filter which contains the secondstage HSC to deduct the SSBI in the receiver. We experimentally demonstrate that 40 Gb/s optical SSB NPAM-4 signal transmission over 80 km standard single mode fiber (SSMF). © 2017 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2360) Fiber optics links and subsystems.

References and links 1. 2. 3. 4. 5. 6. 7. 8.

X. Zhou, K. Zhong, Y. Gao, Q. Sui, Z. Dong, J. Yuan, L. Wang, K. Long, A. P. T. Lau, and C. Lu, “Polarizationinterleave-multiplexed discrete multi-tone modulation with direct detection utilizing MIMO equalization,” Opt. Express 23(7), 8409–8421 (2015). H. L. Cheng, W. H. Chen, C. C. Wei, and Y. J. Chiu, “Optical single-sideband OFDM transmission based on a two-segment EAM,” Opt. Express 23(2), 982–990 (2015). M. S. Erkılınc, S. Pachnicke, H. Griesser, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Performance Comparison of Single-Sideband Direct Detection Nyquist-Subcarrier Modulation and OFDM,” J. Lightwave Technol. 33(10), 2038–2046 (2015). N. Kikuchi, R. Hirai, and T. Fukui, “Quasi Single-Sideband (SSB) IM/DD Nyquist PAM signaling for highspectral efficiency DWDM transmission,” in Proceedings of Optical Fiber Communication Conference (2016), paper Th2A.41. Q. Zhang, Y. Fang, E. Zhou, T. Zuo, L. Zhang, G. N. Liu, and X. Xu, “C-band 56Gbps transmission over 80-km single mode fiber without chromatic dispersion compensation by using intensity-modulation direct-detection,” in Proceedings of European Conference and Exhibition on Optical Communication (2014), paper P5.19. J. L. Wei, Q. X. Cheng, D. G. Cunningham, R. V. Penty, and I. H. White, “100-Gb/s Hybrid Multiband CAP/QAM Signal Transmission Over a Single Wavelength,” J. Lightwave Technol. 33(2), 415–423 (2015). N. Eiselt, H. Griesser, J. Wei, A. Dochhan, M. H. Eiselt, J.-P. Elbers, J. J. Vegas Olmos, and I. Tafur Monroy, “Real-time evaluation of 26-GBaud PAM-4 intensity modulation and direct detection systems for data-center interconnects,” in Proceedings of Optical Fiber Communication Conference (2016), paper Th1G.3. K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41(12), 2767–2770 (2016).

#291706 Journal © 2017

https://doi.org/10.1364/OE.25.012622 Received 10 Apr 2017; revised 5 May 2017; accepted 9 May 2017; published 19 May 2017


9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Z. Li, M. S. Erkilinc, L. Galdino, K. Shi, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Comparison of digital signal-signal beat interference compensation techniques in direct-detection subcarrier modulation systems,” Opt. Express 24(25), 29176–29189 (2016). L. Zhang, T. Zuo, Q. Zhang, J. Zhou, E. Zhou, and G. N. Liu, “150-Gb/s DMT over 80-km SMF transmission based on Spectrally Efficient SSBI cancellation using guard-band Twin SSB Technique,” in Proceedings of European Conference and Exhibition on Optical Communication (2016), paper 1178. M. S. Erkılınç, Z. Li, S. Pachnicke, H. Griesser, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient WDM Nyquist pulse-shaped 16-QAM subcarrier modulation transmission with direct detection,” J. Lightwave Technol. 33(15), 3147–3155 (2015). N. Kikuchi and R. Hirai, “Intensity-modulated / direct-detection (IM/DD) Nyquist pulse-amplitude modulation (PAM) signaling for 100-Gbit/s/λ optical short-reach transmission,” in Proceedings of European Conference and Exhibition on Optical Communication (2014), paper 4.12. B. Lin, J. Li, H. Yang, Y. Wan, Y. He, and Z. Chen, “Comparison of DSB and SSB transmission for OFDMPON,” in Proceedings of Optical Fiber Communication Conference (2012), paper NTu1J.7. L. Zhang, T. Zuo, Y. Mao, Q. Zhang, E. Zhou, G. N. Liu, and X. Xu, “Beyond 100-Gb/s Transmission Over 80km SMF Using Direct-Detection SSB-DMT at C-Band,” J. Lightwave Technol. 34(2), 723–729 (2016). L. Zhang, E. Zhou, Q. Zhang, X. Xu, G. N. Liu, and T. Zuo, “C-band single wavelength 100-Gb/s IM-DD transmission over 80-km SMF without CD compensation using SSB-DMT,” in Proceedings of Optical Fiber Communication Conference (2015), paper Th4A.2. Q. Zhang, N. Stojanovic, C. Prodaniuc, T. J. Zuo, E. B. Zhou, L. Zhang, F. Karinou, and C. S. Xie, “Demonstration of CD pre-compensated direct detection PAM4 40km transmission in C-band using DDMZM,” in Proceedings of Asia Communications and Photonics Conference (2016), paper ATh3C.2. S. Randel, D. Pilori, S. Chandrasekhar, G. Raybon, and P. Winzer, “100-Gb/s discrete-multitone transmission over 80-km SSMF using single-sideband modulation with novel interference-cancellation scheme,” in Proceedings of European Conference and Exhibition on Optical Communication (2015), paper 0697. X. Li, S. W. Zhou, H. L. Ji, M. Luo, Q. Yang, L. L. Yi, R. Hu, C. Li, S. N. Fu, A. Alphones, W. D. Zhong, and C. Y. Yu, “Transmission of 4×28-Gb/s PAM-4 over 160-km single mode fiber using 10G-Class DML and Photodiode,” in Proceedings of Optical Fiber Communication Conference (2016), paper W1A.5. Q. Zhang, N. Stojanovic, C. Xie, C. Prodaniuc, and P. Laskowski, “Transmission of single lane 128 Gbit/s PAM4 signals over an 80 km SSMF link, enabled by DDMZM aided dispersion pre-compensation,” Opt. Express 24(21), 24580–24591 (2016). M. Erkılınc, M. P. Thakur, S. Pachnicke, H. Griesser, J. Mitchell, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Spectrally efficient WDM Nyquist pulse-shaped subcarrier modulation using a dual-drive Mach–Zehnder Modulator and direct detection,” J. Lightwave Technol. 34(4), 1158–1165 (2016). W. R. Peng, X. X. Wu, V. R. Arbab, K. M. Feng, B. Shamee, L. C. Christen, J. Y. Yang, A. E. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009). H. Y. Chen, C. C. Wei, C. Y. Lin, L. W. Chen, I. C. Lu, and J. Chen, “Frequency- and time-domain nonlinear distortion compensation in high-speed OFDM-IMDD LR-PON with high loss budget,” Opt. Express 25(5), 5044–5056 (2017).

1. Introduction Driven by the bandwidth hungry applications, the traffic of data center and short-reach applications has been exponentially increased. Cost, spectral efficiency (SE) and power consumption are the main factors to be considered in short-reach communications. Although coherent detection systems can achieve high performance in long haul transmissions, it requires complex hardware, i.e., local oscillator, hybrid, which causes high costs [1]. In contrast, direct-detection (DD) systems only need one single-ended photodiode (PD) in the receiver with the advantages of low cost, relaxed laser linewidth requirement and simplicity which are more attractive in short-reach applications [2]. A variety of advanced modulation formats have been proposed to achieve higher SE [3,4], including subcarrier modulation (SCM) (e.g., Nyquist subcarrier modulation (NSCM) and orthogonal frequency division multiplexing (OFDM)) [5], carrier-less amplitude phase (CAP) modulation [6] and pulse amplitude modulation (PAM) [7]. SCM formats can use a guard band between optical carrier and signal to avoid the SSBI, or the guard band can be removed by the complex SSBI mitigation schemes [8,9]. OFDM signals have a higher peak-to-average power ratio (PAPR) which limits the transmission performance [10,11]. The CAP signal is sensitive to timing jitter at the receiver side [6]. In general, PAM-4 is preferred for short-reach applications due to its simpler implementation and lower power consumption [7]. Moreover, by using Nyquistpulse shaping, the signal bandwidth is halved with its brick-wall-like spectrum and the


efficiency of bandwidth usage is doubled [12]. Even though PAM-4 only needs a simple architecture, its transmission distance is limited by dispersion-introduced power fading. To alleviate the power fading without using dispersion compensating fiber (DCF), the single side-band (SSB) technique has been proposed [13]. Complex modulation or cascaded modulation in [2], and vestigial sideband filtering (VSB), have been proposed to generate a SSB signal. Considering the cost and a high roll-off factor requirement of the optical filter, complex modulation with a pair of Hilbert transform signals is preferred to generate the SSB signal. It also enables electrical dispersion pre-compensation at the transmitter side compared with the cascaded modulators. A dual-drive Mach-Zehnder modulator (DDMZM) is an alternative to an optical IQ modulator with a lower cost and simpler bias control, for complex modulation to generate the optical SSB signal [14,15]. Meanwhile, the phase rotation method also can be used for SSB modulation with DDMZM [16]. After fiber transmission, the chromatic dispersion (CD) aggravates the influence of SSBI with square-law detection. Recently, a number of digital SSBI mitigation techniques have been proposed. Generally, two main methods, one is to estimate and calculate the SSBI based on the received signal [9,17], the other one is the using of the nonlinear equalizer, such as Volterra based nonlinear equalizer (VNLE) [18]. The two common methods mainly focus on the 2nd-order SSBI mitigation. However, the received signal has a blurry eye diagram in back-to-back (B2B) as the 1st-order interference resulted from the Hilbert transform term is also detected by PD [19]. In this paper, we propose a two-stage HSC construction to cancel the 1st-order and 2ndorder interference, respectively. In the transmitter, an optical SSB signal is generated by DDMZM with two small NPAM-4 driving signals with a phase difference of π/2. At the receiver side, in addition to the transmitted baseband NPAM-4 signal, its Hilbert transform signal and the SSBI are also detected. Hence, the first-stage HSC is used to cancel the 1storder interference of the unwanted Hilbert transform term and the second-stage HSC is applied to implement a modified single-stage linearization filter (SSLF) to mitigate the 2ndorder nonlinear distortion. Least mean squares (LMS) based feed forward equalizer (FFE) is also used to compensate for the inter symbol interference (ISI). We show that the transmission performance is improved about one order of magnitude after the first-stage HSC and the modified SSLF processing. 2. Principle of Hilbert superposition cancellation and modified single-stage linearization filter 2.1 Principle of Hilbert superposition cancellation

Fig. 1. Generation of an optical SSB signal based on DDMZM

Figure 1 shows the generation of an optical SSB signal based on a DDMZM, which contains two parallel phase modulators (PMs) with independent radio frequency (RF) and DC bias ports. The input-output relationship of DDMZM is given by [19]:

Eout (t ) =

 VRF 1 + Vbias1   VRF 2 + Vbias 2   Ein (t )  exp  jπ  + exp  jπ  2  Vπ Vπ     

(1)


where Ein (t ) is the input optical field, VRF 1 and VRF 2 are two driving electrical signals, Vbias1 and Vbias 2 are the DC bias voltages of two PMs and Vπ is the half-wave voltage of the two electrodes to provide a π phase-shift between the two waveguides of the PM. To generate the optical SSB signal, the DDMZM is biased at the quadrature point, Vbias1 = −Vπ / 2 and Vbias 2 = 0 , the baseband NPAM-4 electrical signal s(t ) and its Hilbert transform term sˆ(t ) are used to drive two PMs, VRF 1 = s(t ) , VRF 2 = sˆ(t ) . The output of DDMZM can be expressed as [20]:

 s (t ) − Vπ / 2   sˆ(t )   Ein (t )  exp  jπ  + exp  jπ  Vπ Vπ   2    

Eout (t ) =

(2)

when s(t ) and sˆ(t ) are small signals, Eq. (2) can be approximated as:

Eout (t ) ≈

  Ein (t )   jπ jπ s(t )  + 1 + sˆ(t )   − j 1 + 2   Vπ Vπ  

(3)

 E (t )  π = in 1 − j + ( s(t ) + jsˆ(t ) )  2  Vπ 

In Eq. (3), it is observed that the electrical complex signal Tx = s(t ) + jsˆ(t ) is linearly converted to optical domain. To approximate this linear conversion, optical modulation index (OMI), where OMI = (VRF ) RMS / Vπ , and (VRF ) RMS is the root-mean-square (RMS) amplitude of the electrical input to DDMZM, has been optimized by adjusting the amplitude of driving signals to achieve the optimum carrier to signal power ratio (CSPR) [21]. At the receiver side, after the square-law detection by PD, the received electrical signal is:

r (t ) = Eout (t ) =

Ein (t ) 2

2

2

+

π Ein (t ) 2Vπ

2

[ s(t ) − sˆ(t )] +

π 2 Ein (t ) 4Vπ

2

(4)

2

 s 2 (t ) + sˆ 2 (t ) 

The first term is the DC component, the second term is the desired signal s(t ) and the unwanted Hilbert transform term sˆ(t ) , and the third term is the nonlinear distortion of SSBI. At the receiver side, after DC blocking and normalization, Eq. (4) can be rewritten as:

r (t ) = A [ s(t ) − sˆ(t )] + B  s 2 (t ) + sˆ2 (t )  2

(5) 2

where A is proportional to π Ein (t ) / (2Vπ ) , B is directly proportional to π 2 Ein (t ) / (4Vπ 2 ) , as Vπ is normally larger than π , hence B is smaller compared with A. To cancel sˆ(t ) , we utilize the characteristic of the Hilbert transform, H [ sˆ(t )] = − s(t ) , to build a HSC

construction. H [ ] means Hilbert transform. The inset (a) in Fig. 2 depicts the first-stage HSC construction which is used to cancel sˆ(t ) . Then the output of the first-stage HSC is expressed as:


r (t ) = r (t ) + H [ r (t ) ]

{

}

= A [ s(t ) − sˆ(t ) ] + B  s 2 (t ) + sˆ 2 (t )  + H A [ s (t ) − sˆ(t ) ] + B  s 2 (t ) + sˆ 2 (t ) 

{

}

(6)

= 2 A ⋅ s(t ) + B s 2 (t ) + sˆ 2 (t ) + H  s 2 (t ) + sˆ 2 (t ) 

In Eq. (6), sˆ(t ) has been cancelled by the first-stage HSC, the first term is the desired signal and the second term is the 2nd-order nonlinear distortion including the original SSBI in Eq. (4), and its Hilbert transform, i.e., the extra SSBI, which cannot be mitigated by the normal SSLF [17]. In the following section, a modified SSLF with the second-stage HSC is proposed to compensate for the whole 2nd-order distortion. 2.2 Modified single-stage linearization filter

Fig. 2. DSP with HSC and modified single-stage linearization filter.

Digital signal processing (DSP) with the first-stage HSC and the modified SSLF is shown in Fig. 2. After direct-detection, the received electrical signal r (t ) is a baseband DSB signal. After the first-stage HSC, sˆ(t ) is cancelled while the extra SSBI is introduced. In Eq. (6), the original SSBI product can be calculated and expressed as [17]:

VSSBI (t ) = r (t ) + jH ( r (t ) )

2

(7)

where r (t ) + jH ( r (t ) ) has single side-band spectral components and is used to generate the original SSBI by restoring the signal-to-signal beating process. However, VSSBI (t ) is only a part of the whole SSBI, thus the second-stage HSC in modified SSLF aims to calculate the whole SSBI and the SSBI is deducted from the output, r (t ) , after the first-stage HSC. To mitigate the 2nd-order nonlinear distortion, we use the second-stage HSC to construct the whole SSBI. The output of the modified SSLF can be written as:

rLin (t ) = r (t ) − η {VSSBI (t ) + H [VSSBI (t )]}

(8)

where η is the optimized positive real-valued scaling factor. We define N (t ) = s 2 (t ) + sˆ 2 (t ) , thus, Eq. (6), Eq. (7) and Eq. (8) can be rewritten as:

r (t ) = 2 A ⋅ s(t ) + B { N (t ) + H [ N (t )]} VSSBI (t ) = r (t ) + jH (r (t ))

(9)

2

{

}

= 2 A ⋅ s(t ) + B  N (t ) + Nˆ (t )  + jH 2 A ⋅ s (t ) + B  N (t ) + Nˆ (t ) 

(

)

2

(

)

= 4 A2 N (t ) + 2 B 2  N 2 (t ) + Nˆ 2 (t )  + 4 AB  s(t ) N (t ) + Nˆ (t ) + sˆ(t ) Nˆ (t ) − N (t )    (10)


rLin (t ) = 2 A ⋅ s(t ) + B  N (t ) + Nˆ (t )  

(



)

{

}

2 −4η A N (t ) + Nˆ (t ) − 2η B 2 N 2 (t ) + Nˆ (t ) + H  N 2 (t ) + Nˆ 2 (t ) 

2

{

(

)



(

)



(

)

(

)}

−4η AB s(t ) N (t ) + Nˆ (t ) + sˆ(t ) Nˆ (t ) − N (t ) + H  s(t ) N (t ) + Nˆ (t ) + sˆ(t ) Nˆ (t ) − N (t )  

(11) In Eq. (11), the first term is the desired signal s(t ) , the second term (the original SSBI and the extra SSBI) is the 2nd-order nonlinear distortion which can be eliminated by the third term with an optimized η. Furthermore, since the fourth-order (SSBI-to-SSBI beating) and the fifth-order (signal-to-SSBI beating) terms are relatively small due to the input are small signals, and their coefficients are relatively small as A and B are smaller than 1, we can neglect their influences. Finally, sˆ(t ) is cancelled by the first-stage HSC. The whole SSBI after the first-stage HSC is mitigated by modified SSLF. According to the Eq. (4), if the firststage HSC is not used, only a normal SSLF cannot mitigate the interference from sˆ(t ) . 3. Experimental verification and results

The experimental setup of the optical SSB NPAM-4 system is shown in Fig. 3. At the transmitter side, a pseudo random bit sequence (PRBS) with 218 bits is used for PAM-4 modulation and up-sampled to 2 sample-per-symbol. The Nyquist filter with a roll-off factor of 0.01 is applied to generate NPAM-4 sequence and its Hilbert term is generated by Hilbert transform. The output sequence is down-sampled to m sample-per-symbol (m = 1.5 or m = 1.25) to achieve higher bit rate. AWG700002A is used to generate s(t ) and sˆ(t ) at its highest sample rate of 25 GS/s. Hence, the signal bit rates are 25 Gb/s (m = 2), 34 Gb/s (m = 1.5) and 40 Gb/s (m = 1.25), respectively. A DDMZM with Vπ = 3.8 V is used to generate optical SSB signal. The upper branch is biased at −1.9 V and the lower branch is grounded. For a DD system, the CSPR is also an important parameter to optimize the system performance. If the modulated signal is far away from the optical carrier, the CSPR can be estimated by calculating the integration in the corresponding range of the spectrum trace [19]. When the modulated signal is near the optical carrier and the spectrum distribution is overlapped, the CSPR cannot be estimated accurately [19]. In optical SSB system, the optimized CSPR is mainly limited by the nonlinearity of DDMZM. Therefore, it can be adjusted by changing the bias condition or the driving amplitude [21]. In our experiment, a pair of attenuators is used between AWG and DDMZM to adjust the OMI for optimal CSPR. According to the numerical calculation and experimental test, the optimal OMI is set at 0.13. An optical source at output optical power of 12 dBm at 1550 nm wavelength with a claimed laser linewidth below 10 MHz is fed into the DDMZM, and the output optical signal at 0 dBm is launched into 80 km SSMF with an attenuation coefficient of 0.2 dB/km. At the receiver side, an Erbium-doped optical fiber amplifier (EDFA) and an optical band-pass filter (OBPF) are used to compensate for the fiber loss and suppress the noise before PD. A variable optical attenuator (VOA) is employed to change the received optical power (ROP). Note that our efforts are focused on interference and dispersion mitigation. The EDFA, OBPF, and VOA can be skipped for practical applications with a careful power budget, e.g., by reducing the DDMZM’s insertion loss and increasing the laser’s output power. The optical signal is detected by a commercial PD with 10 GHz bandwidth and sampled by a DPO72504D operating at 50 GS/s. Then, the received electrical signal is processed offline. The received signal is firstly processed by the first-stage HSC to remove sˆ(t ) . After that, a modified SSLF


with the second-stage HSC is used to compensate for the whole SSBI. The performance of normal SSLF and VNLE are also assessed in offline DSP, respectively.

Fig. 3. Experimental setup of optical SSB PAM-4 system.

3.1 Optical back-to-back performance of Hilbert superposition

The spectrum of the optical SSB NPAM-4 signal with 0.03 nm resolution is shown in Fig. 4 (a), whose sideband power is 10 dB higher than the unmodulated laser source. The inset in Fig. 4 (a) is the frequency spectrum in the DPO of the NPAM-4 signal. The signal bandwidth is halved with its brick-wall-like spectrum and the bandwidth is about 6.3 GHz. The eye diagrams of NPAM-4 signal without and with HSC without SSBI cancellation in B2B case are shown in Fig. 4 (b). The eye diagram is blurry without HSC since the sˆ(t ) exists, while the eye diagram is clearly open due to the linear interference cancellation by the first-stage HSC.

Fig. 4. (a) Spectrum of laser source and DDMZM output optical signal with NPAM-4; (b) The eye diagram without and with HSC.

At B2B case, we directly demodulate the received electrical NPAM-4 signal at 25 Gb/s without any equalization processing. Figure 5 (a) shows the BER versus ROP without and with the first-stage HSC, respectively. The inset in Fig. 5 (a) is the eye diagram with HSC under ROP of −8 dBm before FFE. According to Eq. (5) and Eq. (6), the 1st-order interference will be mitigated and the signal level can be recognized clearly as depicted in Fig. 4 (b) after HSC. Obviously, the received signal can be directly demodulated after firststage HSC. However, it cannot be demodulated without HSC by direct demodulation without any equalization due to the linear interference of its Hilbert transform signal.


Fig. 5. (a) Experimental BER of direct demodulation versus ROP with and without HSC; (b) BER with FFE versus ROP with and without HSC.

To further study the transmission performance, T-spaced LMS-based FFE with 9 taps is used to recover the received signal at B2B case. Figure 5 (b) depicts the experimental BER performance with FFE at different ROPs without and with the first-stage HSC at 25 Gb/s. The BERs with HSC are also lower than that without HSC, as the linear interference can be fundamentally cancelled by HSC. The insets of Fig. 5 (b) are the eye diagrams after FFE. The eye diagram is clearer with HSC than that without HS after FFE because the first-order interference is partly mitigated by FFE without HSC. Meanwhile, the receiver sensitivity is improved about 1 dB at the 7% hard-decision forward error correction (HD-FEC) threshold (BER = 3.8 × 10−3). Figures 5(a) and 5(b) show that the HSC improves the system performance due to the linear interference cancellation. 3.2 Optical fiber transmission performance of modified SSLF

In order to study the transmission performance, we use normal SSLF, modified SSLF and conventional VNLE [22] to mitigate the 2nd-order nonlinear distortion and compare their effects. At 25 Gb/s, 21 taps are used for FFE after 80 km transmission. Figure 6 shows the experimental BER performance over 80 km at 25 Gb/s under different processing methods. As shown in Fig. 6, the BER performance is poor only with FFE without HSC because FFE is not sufficient as the interaction of the chromatic dispersion and the square-law detection. Even the transmission performance is slightly improved after HSC due to the 1st-order interference cancellation, the 2nd-order interference limits the transmission performance. Therefore, we use a normal SSLF to mitigate the SSBI effect. However, the transmission performance is still limited due to the residual 1st-order interference without HS or the extra SSBI products introduced by HSC, which cannot be mitigated by normal SSLF. We also use a conventional VNLE with the memory length of (21, 11, 5) to compensate for the nonlinear distortion, which has similar performance as normal SSLF. It is because VNLE is effective to compensate for the nonlinear distortion, however, it cannot effectively mitigate the 1st-order interference. According to Eqs. (6) and (11), we first use HSC to cancel the 1st-order interference and then use the modified SSLF to compensate for the whole SSBI. As shown in Fig. 6, the transmission performance is improved about one order of magnitude. The insets (a) and (b) depict the eye diagrams after normal and modified SSLF at ROP of −6 dBm, respectively. The eye diagram with HSC and modified SSLF is clearer.


Fig. 6. Experimental BER performance at 25 Gb/s.

As the sample rate of AWG700002A is limited at 25 GS/s, we apply down-sampling the output electrical NPAM-4 signal from m = 2 to m = 1.5 and m = 1.25 to increase the bit rate from 25 Gb/s to 34 Gb/s and 40 Gb/s with signal noise ratio (SNR) penalty, respectively. Figures 7 (a) and (b) show the transmission performance of 34 Gb/s and 40 Gb/s, respectively. For 34 Gb/s and 40 Gb/s transmissions, 31 and 51 taps are used for FFE, respectively. As shown in Fig. 7, the transmission performance is poor without or with HSC only with FFE. This is because a linear FFE is not sufficient when chromatic dispersion is combined with the square-law detection. The higher symbol rate aggravates the nonlinear distortion and the SNR penalty decreases the cancellation effect of the 1st-order interference of HSC. Similar as the Fig. 6, the mentioned three methods have similar performance and cannot reach the 7% HD-FEC threshold due to the residual linear interference or the extra SSBI. After HSC and modified SSLF, the BERs for both 34 Gb/s and 40 Gb/s decrease significantly and are lower than the 7% HD-FEC threshold.

Fig. 7. BER performance (a) at 34 Gb/s and (b) at 40 Gb/s.

The dispersion is a main limiting factor in direct-detection systems. The optical SSB signal is generated by DDMZM with complex modulation in our experiment, which enables digital electrical dispersion pre-compensation due to the complex field modulation capability.

Vol. Vol. 25, 25, No. No. 1111 | 29 | 29 May May 2017 2017 | OPTICS | OPTICS EXPRESS EXPRESS 12631 10

Figure 8 shows the system performance with and without CD pre-compensation with HSC and modified SSLF at 40 Gb/s over 80 km SSMF transmission. As shown in Fig. 8, the receiver sensitivity has improved about 8 dB at the 7% HD-FEC threshold after CD precompensation, which also implies that we can enlarge the reach of the system by CD precompensation. The BERs without and with CD pre-compensation are 3.02 × 10−3 and 4.46 × 10−4, respectively.

Fig. 8. BER performance with and without CD pre-compensation at 40 Gb/s over 80 km SSMF.

4. Conclusion

We have proposed and demonstrated a HSC and modified SSLF scheme to mitigate the interference resulted from the Hilbert transform signal and the SSBI in an optical NPAM-4 SSB system. The experimental results show that HSC and modified SSLF can improve the transmission performance about one order of magnitude. We have experimentally demonstrated a 40 Gb/s optical NPAM-4 SSB signal transmission over 80 km SSMF with BERs at 3.02 × 10−3 and 4.46 × 10−4 without and with the CD pre-compensation, respectively. Funding

National High Technology Research and Development Program of China (863 Program) (2015AA015501); NSFC (No. 61405024, No. 61420106011 and No.61471088); the Fundamental Research Funds for the Central Universities (No. ZYGX2014J004); and the 111 project (B14039).