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 dual-drive 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 second-stage 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
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 . 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 . 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)) , carrier-less amplitude phase (CAP) modulation  and pulse amplitude modulation (PAM) . 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 . In general, PAM-4 is preferred for short-reach applications due to its simpler implementation and lower power consumption . Moreover, by using Nyquist-pulse shaping, the signal bandwidth is halved with its brick-wall-like spectrum and the efficiency of bandwidth usage is doubled . 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 . Complex modulation or cascaded modulation in , 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 . 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) . 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 .
In this paper, we propose a two-stage HSC construction to cancel the 1st-order and 2nd-order 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 1st-order 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 2nd-order 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
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 :20]:Eq. (2) can be approximated as:Eq. (3), it is observed that the electrical complex signal is linearly converted to optical domain. To approximate this linear conversion, optical modulation index (OMI), where , and 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) . At the receiver side, after the square-law detection by PD, the received electrical signal is:Eq. (4) can be rewritten as:Fig. 2 depicts the first-stage HSC construction which is used to cancel . Then the output of the first-stage HSC is expressed as:Eq. (6), 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 . 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
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 is a baseband DSB signal. After the first-stage HSC, is cancelled while the extra SSBI is introduced. In Eq. (6), the original SSBI product can be calculated and expressed as :Eq. (6), Eq. (7) and Eq. (8) can be rewritten as:
In Eq. (11), the first term is the desired signal , 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, 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 first-stage HSC is not used, only a normal SSLF cannot mitigate the interference from .
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 and 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 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 . When the modulated signal is near the optical carrier and the spectrum distribution is overlapped, the CSPR cannot be estimated accurately . 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 . 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 . 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.
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 exists, while the eye diagram is clearly open due to the linear interference cancellation by the first-stage 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 first-stage HSC. However, it cannot be demodulated without HSC by direct demodulation without any equalization due to the linear interference of its Hilbert transform signal.
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  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.
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.
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. 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 pre-compensation, which also implies that we can enlarge the reach of the system by CD pre-compensation. The BERs without and with CD pre-compensation are 3.02 × 10−3 and 4.46 × 10−4, respectively.
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.
National High Technology Research and Development Program of China (863 Program) (2015AA015501); National Natural Science Foundation of China (NSFC) (No. 61405024, No. 61420106011 and No.61471088); the Fundamental Research Funds for the Central Universities (No. ZYGX2014J004); and the 111 project (B14039).
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