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Abstract
The bandwidth limit of devices and the chromatic dispersion (CD) of optical fiber severely distort the high-speed signal in a passive optical network (PON). In this paper, an efficient equalization scheme is proposed for optical amplified 50-Gb/s PAM4-PON with a 10G-class transmitter. The proposed equalization scheme is based on fast frequency domain equalization (FDE) with circular convolution, an optimized post-filter, and a low-complexity maximum likelihood sequence detector (MLSD), which requires only total 23 real-valued multiplications for each output symbol. Experimental results show that up to 33.2 dB power budget is successfully achieved over 20 km transmission without using any optical CD compensation module in the C-band. Moreover, there is only 0.5 dB penalty of receiver sensitivity compared to optical back to back (BTB) transmission. Therefore, the CD distortion has been nearly compensated for by the proposed equalization scheme. To the best of our knowledge, this is the best performance of an optical amplified 50-Gb/s PAM4-PON system in the C-band.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the rapid increase of bandwidth-thirsty services such as high-definition 4K/8K video, virtual/augment reality (VR/AR) and cloud network, a higher capacity of the passive optical network (PON) for optical access network is demanded [1]. In addition, the mobile front-haul for the fifth generation (5G) mobile communication can also be ideally implemented by PON systems [2, 3]. In the past few years, both IEEE and ITU-T have intensively studied the upgrade roadmap of PON systems [4]. Nowadays, IEEE 802.3ca Task Force is concentrating on the standardization of next-generation 100-Gb/s PON by using either 4×25-Gb/s/λ or 2×50Gb/s/λ scheme [5–9]. Single wavelength 50-Gb/s PON is of great value for saving half of the wavelength resources compared with single wavelength 25-Gb/s PON. Advanced modulation formats such as orthogonal frequency division multiplexing (OFDM), carrierless amplitude phase (CAP), duobinary (DB), and 4-level pulse amplitude modulation (PAM4) along with digital signal processing (DSP) have been proposed for high-speed PON systems [10–13]. Among them, single-carrier modulations such as DB and PAM4 show the benefits of simplicity and low peak-to-average power ratio (PAPR), which are essential characteristics for PON systems. Moreover, compared with DB, PAM4 is of higher spectral efficiency and potentially enable low-cost optical network unit (ONU) design with interleaving architecture [14].
Chromatic dispersion (CD) is one of the key elements affecting transmission performance in high-speed PON systems. Thus, O-band PON systems attracted significant attention owing to its small CD. Recently, 50-Gb/s/λ O-band PAM4-PON systems have been widely investigated and experimentally demonstrated [15–17]. However, PON systems operated at C-band have the advantages of lower fiber loss, mature dense wavelength division multiplexing (DWDM) optics and optical amplifiers such as erbium-doped fiber amplifier (EDFA) [18, 19]. The critical problem for high-speed transmission in C-band is the power fading caused by CD after direct detection, which drastically deteriorates transmission performance. In recent years, CD elimination methods based on direct detection have been widely investigated, including single/vestigial sideband (SSB/VSB) modulation, CD pre-compensation based on IQ modulator or dual-drive Mach-Zehnder modulator (DDMZM), Kramers–Kronig receiver, and so on [20]. However, the cost is still too expensive for short-reach transmission, especially for typical PON systems where transmission distances are less than 20 km. Moreover, it would be attractive if low-cost and mature 10G-class devices can be reused for 50-Gb/s/λ transmission. In this case, however, the bandwidth limit becomes another critical factor which will further degrade system performance.
Electrical equalization based on DSP is an effective method to handle bandwidth limit. Meanwhile, CD tolerance can also be significantly enhanced with appropriate equalization techniques. For instance, Volterra equalizer (VE) and its variants have been investigated to compensate distortions caused by both the CD of fiber and bandwidth limit of devices [21, 22]. Besides, it has been verified that feedforward and decision-feedback equalizer (FFE-DFE) achieves better performance than simple feedforward equalizer (FFE) owing to the introduction of decision-feedback information [23, 24]. Moreover, maximum likelihood sequence detection (MLSD) can be used to improve receiver sensitivity [25]. It is noted the computational complexities of FFE/VE/FFE-DFE are directly related with tap numbers, which means the computational complexities will be extremely high when tap numbers are enormous. As for MLSD, the computational complexity is exponential with its memory length. Since the ONU receivers are cost-sensitive, there is a requirement of low computational complexity for equalization techniques. In this work, we experimentally compare the equalization performance of the above equalization techniques in a 50-Gb/s optical amplified PAM4-PON system. Moreover, in order to achieve a low computational complexity, we propose to replace traditional time domain equalization (TDE) with fast frequency domain equalization (FDE), which dramatically decreases the computational complexity when memory length is long. Afterwards, optimized post-filter with only two taps is proposed to decrease enhanced high-frequency noise, which meanwhile keeps the subsequent MLSD at the shortest memory length, thus having the lowest computational complexity.
In this paper, we experimentally demonstrate a 50-Gb/s optical amplified PAM4-PON system with a 10G-class transmitter. An efficient equalization scheme with total 23 real-valued multiplications for each output symbol is proposed, which includes fast FDE, optimized post-filter and low-complexity MLSD. Thanks to the effectiveness of the proposed equalization scheme, up to 33.2 dB power budget is achieved over 20 km fiber transmission in C-band. Moreover, there is only 0.5 dB penalty of receiver sensitivity compared with optical back to back (BTB) transmission. Compared with traditional equalization techniques of FFE/VE/FFE-DFE, the equalization scheme improves 4.2/2.5/2.0 dB receiver sensitivity at the BER threshold of 10−3, respectively. To the best of our knowledge, this is the best performance of 50-Gb/s optical amplified PAM4-PON system in C-band. Therefore, we believe that the proposed equalization scheme is of significant reference value in the next-generation 50-Gb/s PON systems.
2. Principle of equalization scheme
2.1. Fast FDE with circular convolution
Time-domain finite impulse response (FIR) filter has been widely used to handle linear distortion, which can be mathematically expressed as
where x(n) and y(n) are input and output signals, respectively. w(l) represent tap coefficients and L denote tap numbers. The operation theoretically can be replaced by circular convolution for simplicity. However, in order to meet the requirements of fast FDE, further transformation of tap coefficients w(l) ought to be made as follows where N is circular convolution length. The input signal x(n) is also transferred asTo take full use of the simplicity of radix-2 algorithm, N is set to 2k (k = 1, 2, 3, …). Time-domain circular convolution is calculated by using frequency-domain multiplication, which can also be seen as TDE is transformed into FDE. It can be expressed as
In principle, there are plenty of methods to obtain the tap coefficients w(n). For instance, adaptive least mean square (LMS) or recursive least square (RLS) algorithm based on training sequences can be used to initialize tap coefficients [26]. Moreover, the tap coefficients will be maintained basically stable once the algorithm successfully converges. Considering a static FIR filter, the computational complexity of FFT operation for w(n) can be nearly ignored. The computational complexity of circular convolution comes from N-point FFT, N-point IFFT and N-point complex multiplications. Owing to the symmetry of FFT for real-valued signal, the N-point complex multiplications can be simplified as N/2-point complex multiplications. In addition, it is universally acknowledged that one complex multiplication requires four real multiplications when both product terms are complex values. However, a N/2-point complex FFT can be used to calculate N-point FFT of real signal [27]. Therefore, the real multiplications of N-point FFT/IFFT for PAM4 signal is Nlog2N. In conclusion, the total real multiplications for FDE is 2Nlog2N + 2N. For the rest of the paper, the multiplications refer to real multiplications unless otherwise explicitly indicated.
It is noteworthy that traditional TDE for PAM4 signal has continuously serial output, but FDE needs block output. Besides, each output of FDE requires N-point size and each N-point output has the last L − 1 points which are overlapped with the former L − 1 points of the next N-point output. Therefore, there are only N − L + 1 symbols available for each N-point size. In addition, the overlapped parts ought to be added together to obtain the correct signal. Figure 1(a) shows the graphic expression of overlap-add method. The overlap-add process needs extra L − 1 additions but no multiplication. Therefore, the ratio of multiplications between FDE and TDE for each output is (2Nlog2N + 2N)/[(L(N − L + 1)]. In order to intuitively observe the difference of multiplications, Figure 1(b) shows the multiplications ratio of FDE and TDE at different tap numbers. It depicts that FDE has lower computational complexity than TDE when tap numbers are larger than 20. Moreover, FDE has a greater reduction of computational complexity compared with TDE as the tap numbers continuously increase. Different FFT sizes from 64 to 256 are considered. It also shows that the FFT sizes are supposed to larger than double of tap numbers, otherwise the number of output symbols are less efficient.
Fig. 1 (a) Graphic expression of overlap-add method. (b) Ratio of multiplications between FDE and TDE.
2.2. Optimized post-filter and MLSD
For a system with severe inter-symbol interference (ISI), maximum likelihood detection or maximum a-posteriori probability (MAP) detection has better performance than the hard decision [28]. However, it is hard to obtain extremely accurate channel information in a real transmission system. One way is to estimate the total probability density function (PDF) of the signal and obtain the optimal survival path. However, it takes a large number of training symbols to do the channel estimation [29]. Another way is to shape the unknown channel response into a known intermediate state with a post-filter, and then feed the output symbols after post-filter to a short-memory MLSD. The function of post-filter includes two parts: 1) suppress the enhanced noise by the previous linear equalizer; 2) shape the signal with a known channel response. There are many ways to obtain the parameters of post-filter, such as Yule-Walker equations and partial response shaping. In this work, the z-transform of post-filter is given as
The adopted post-filter has advantages in two aspects: 1) the tap numbers of post-filter is only two, which means the subsequent MLSD has the shortest memory length of two as well; 2) the impulse response of post-filter can be adjusted by the factor β. When β is set to 1, the post-filter can be seen as an ideal duo-binary filter. Then, the signal after post-filter is fed to MLSD based on the Viterbi algorithm. The target of MLSD is to select the maximum survival path, in which has the minimum accumulative metrics (AM). The AM is the sum of each distance metric (DM), which is given as follows
where Yk represents the signal after post-filter, Hpostfilter • X denote the product of post-filter coefficient matrix H and original signal X. The product of H and X can be calculated at the initialization period because the tap coefficients and the original signal are already known. Moreover, it is noted that the calculation method of DM is the absolute method instead of the traditional square method, since both methods have little difference on the final selection of survival. However, the absolute method shows lower computational complexity [30]. As a result, it can be found that there is no multiplication during the update of the survival path. Figure 2 shows the process of Viterbi decoding. In order to select the optimal survival path, it takes 32 additions and 12 comparisons for each output symbol. In Fig. 2, the solid lines indicate the selected paths and the other dashed lines refer to the paths which are discarded. At last, only one survival path with the minimum AM is saved. Due to the limited hardware memory of electronic chip, it is impossible to store the ever increasing symbols for selecting one survival path. Therefore, it is generally to make decisions after a fixed storage length. In our offline processing, the storage length is fixed as same as the output block length of FDE. By this means, the delay can be shared by FDE and MLSD.3. Experimental setup
Figure 3 shows the experimental setup of 50-Gb/s optical amplified PAM4-PON. At the transmitter, 51200 pseudo-random binary sequences (PRBS) with the seed number of 30 are mapped into PAM4 symbols for each frame. Afterwards, the up-sampling is employed and a digital root-raised cosine (RRC) filter is used as a pulse-shaping filter. Different pulse-shaping factors from 0 to 1 are considered to obtain the optimal performance, which will be further analyzed in the next section. The shaped signal is resampled to match the DAC sampling rate. Then, the data is sent to a 64-GSa/s digital to analog converter (DAC) with ∼15 GHz bandwidth and 8-bit resolution. The generated PAM4 signal is amplified by an electrical amplifier (EA), and the peak-to-peak voltage is ∼ 4V. The laser is operated at 1550.12 nm and the maximum output power can be set to 18 dBm. A ~ 10 GHz Mach-Zehnder modulator (MZM) is employed to modulate the electrical signal to the optical domain. The bias voltage is adjusted to make the modulated signal at the linear region of MZM. The insertion loss of MZM is ~7 dB. Thanks to the high output power of the laser, the launch power into the fiber can be set to 8 dBm without any optical amplifier at the transmitter. For transmission link, a typical fiber length of 20 km for PON application is employed. In addition, a variable optical attenuator (VOA) is applied to emulate the optical splitter in PON systems. The receiver includes a pre-amplified EDFA, an optical bandpass filter (OBPF) with the bandwidth of 0.4 nm, and a photo-detector (PD) with the bandwidth of ~ 20 GHz. Finally, the signal is sampled by a 100-GSa/s digital phosphor oscilloscope (DPO). The offline process of DSP is done by MATLAB, which mainly includes resampling, matched filtering, equalization, PAM4 demapping and bit error rate (BER) calculation.
4. Experimental results and discussions
4.1. Optimized pulse shaping at optical BTB transmission
Pulse shaping with different factor α makes the signal have different bandwidth, which can be expressed as , where W is signal bandwidth and Rs is baud rate. In principle, the pulse-shaping factor α can be set from 0 to 1 according to the requirements of shaping filter. When the pulse-shaping factor is set to 0, it means the ideal Nyquist pulse shaping. Apart from signal bandwidth, however, the change of pulse-shaping factor also leads to the difference of PAPR, which is directly related to modulation efficiency. Figure 4(a) shows the PAPR curve versus pulse-shaping factor α. It depicts that the PAPR of ideal Nyquist pulse shaping is ~9.5 dB while the PAPRs with pulse-shaping factor α from 0.4 to 1.0 are reduced to ~6 dB. Figure 4(b) depicts the relationship of BER with pulse-shaping factor α at optical BTB transmission, with the help of linear equalization of 51 taps. The results reveal that pulse shaping with α = 0.4 achieves the lowest BER. This is an optimal result after a comprehensive consideration of signal PAPR and bandwidth, because the signal with high bandwidth suffers from severe high-frequency distortions while the signal with high PAPR has a low modulation efficiency.
4.2. Equalization performance
In this section, the transmission performances with different equalizations are analyzed and compared. First of all, the performance of FDE is investigated. In order to do the circular convolution for FDE, the tap coefficients should be initiated firstly. In this work, RLS algorithm is adopted owing to its quick convergence. Figure 5(a) shows the convergence curve of RLS algorithm and less than 100 symbols are enough for the convergence. Thus, the overhead for coefficients initialization is almost negligible. As a matter of fact, the coefficients can be obtained before the system operation. Afterwards, once the tap coefficients are successfully obtained, the equalizer is switched to circular convolution mode for FDE. The equalization performance with different tap numbers for 20 km transmission are compared in Fig. 5(b). It can be observed that the performance is improved with the increase of tap numbers. In order to find the appropriate tap number, the reference received optical power (ROP) is set to -25/-24/-23 dBm, respectively. In this work, the top priority is the equalization performance (the achieved BER) instead of computational complexity. As a result, we try our best to obtain an optimal BER performance. When the BER performances are very close (e.g. difference <1%), we select the minor tap number. Therefore, taking performance and computational complexity into consideration comprehensively, the optimized tap numbers of 51 is adopted. However, the performance of linear equalization is limited and it cannot achieve the threshold at a BER of 10−3. The result shows the poor equalization performance of linear equalization for distortions caused by both CD and bandwidth limit. Moreover, it is noted that traditional FFE has the same performance as FDE, since FDE is essentially a quick algorithm for FFE by replacing linear convolution with circular convolution. However, the computational complexity can be significantly reduced.
Fig. 5 (a) Square errors versus the number of iterations for RLS algorithm. (b) BER versus the number of taps at different received optical power (ROP).
Afterwards, a post-filter is employed to decrease the enhanced noise by FDE thus improving transmission performance. In order to keep a low computational complexity, as mentioned above, the tap number of post-filter is only two in the form of [1 β]. The frequency response of post-filter with different coefficient β is analyzed in Fig. 6(a). It can be found that the increase of coefficient β makes the frequency response curve of post-filter steeper. The β = 0 means the all-pass filter while the β = 1 means the ideal duobinary filter. Then, the subsequent MLSD is employed to recover PAM4 symbols. Figure 6(b) shows the BER performance with different β at the ROP of -25/-24/-23 dBm, respectively. The results reveal that β = 0 achieves the worst performance, which is the same as the equalization performance achieved by FDE, because in this case the post-filter has no effect and MLSD has no memory length to use as well. However, the performance are significantly improved with the increase of coefficient β. For all of the three ROPs, the best performance are achieved in the case of β = 0.6. This is because the post-filter is supposed to match the channel response as far as possible. The β-factor may be varied in different transmission systems. Moreover, it can be seen that all of the BERs at the three ROPs are reduced to below the threshold of 10−3. The result shows the excellent equalization performance achieved by FDE+post-filter+MLSD scheme.
The equalization performance of traditional FFE-DFE and VE with different taps are investigated to do a comparative analysis. Figure 7(a) shows the BER performance versus FFE-DFE tap numbers at the ROP of −23 dBm. It can be found that the optimal tap numbers for FFE-DFE are (31, 11), which means the FFE needs 31 taps and DFE needs 11 taps. Similarly, the BER performance with different memory lengths for VE are analyzed. The kernels of VE higher than two are ignored due to the dramatically increased complexity. Figure 7(b) shows that the first memory length of 31 and the second memory length of 13 are enough to achieve an optimal equalization performance. Considering the crossed terms of VE, the first order has 31 taps and the second order has (13 + 13 × 13)/2 = 91 taps, which can be expressed as VE (31, 91).
Fig. 7 (a) BER performance versus FFE tap numbers and DFE tap numbers at the ROP of -23dBm. (b) BER performance versus memory length for VE at the ROP of −23dBm.
Figure 8 shows the performance comparison for BTB/20 km transmission with the above-mentioned equalizations, including FDE, VE, FFE-DFE, and FDE+post-filter+MLSD. For BTB transmission, it can be seen that the four equalizations achieve similar BER performance and the receiver sensitivity is -25.7 dBm. This is because the bandwidth limit is the key factor at BTB transmission, and the distortion of bandwidth limit is approximately considered as linear distortion. As a result, linear and nonlinear equalizations have similar performance. However, CD is another key factor at 20 km transmission for up to 50-Gb/s PAM4 signal in C-band. At this time, different equalizations achieve different CD tolerance. The linear equalization of FDE (51) has the worst performance and it cannot achieve the BER threshold of 10−3 when the ROP is no more than −21 dBm. FFE-DFE (31, 11) and VE (31, 91) achieve better performance than FDE (51), and the receiver sensitivity can reach −23.2 dBm and −22.7 dBm, respectively. The best performance is achieved by FDE+post-filter+MLSD. The receiver sensitivity reaches −25.2 dBm, corresponding to 33.2 dB link power budget since the launch power is 8 dBm. Besides, it only has 0.5 dB penalty compared with −25.7 dBm receiver sensitivity at optical BTB transmission. It can be analyzed that the CD of fiber has almost been compensated. Moreover, there is a low computational complexity for the equalization scheme of FDE, post-filter and MLSD. We take the multiplications per output symbol as the reference standard. In this work, the tap number of 51 and circular convolution length of 256 are adopted for FDE. Therefore, FDE (51) has (2 × 256 × 9)/(256 − 51 + 1)≈ 22 multiplications for each output symbol. As for post-filter and MLSD, the preceding post-filter needs one multiplication and the MLSD requires no multiplication but additions and comparisons. Therefore, it can be concluded that FDE+post-filter+MLSD achieves the best performance at total 23 multiplications for each output symbol.
5. Conclusion
We have experimentally demonstrated a C-band 50-Gb/s optical amplified PAM4-PON system with up to 33.2 dB link power budget, which theoretically supports more than 1 : 512 optical power splitter. At the transmitter, the pulse shaping was optimized to achieve an optimal performance after a comprehensive consideration of signal bandwidth and PAPR. At the receiver, an efficient equalization scheme consisting of FDE, post-filter and MLSD was proposed to eliminate channel distortions caused by both CD of fiber and bandwidth limit of devices. Experimental results reveal that the proposed equalization scheme achieves excellent equalization performance for C-band 50-Gb/s PAM4 signal over 20 km transmission, and the receiver sensitivity penalty is only 0.5 dB compared with optical BTB transmission. We believe that the equalization scheme is of great potential in the next 50-Gb/s PON systems.
Funding
National Key R&D Program of China (2016YFB0800302); National Natural Science Foundation of China (61771062, 61331010); Fund of State Key Laboratory of IPOC (BUPT) (No. IPOC2018ZT08), P. R. China; BUPT Excellent Ph.D. Students Foundation (CX2018202).
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