Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Transmission of a 112-Gbit/s 16-QAM over a 1440-km SSMF with parallel Kramers-Kronig receivers enabled by an overlap approach and bandwidth compensation

Yuyang Liu, Yan Li, Jingwei Song, Lei Yue, Honghang Zhou, Ming Luo, Zhixue He, Jifang Qiu, Yong Zuo, Wei Li, Xiaobin Hong, Hongxiang Guo, and Jian Wu

Open Access Open Access

Abstract

We investigate the parallelized performance of the conventional Kramers-Kronig (KK) and without the digital up-sampling KK (WDU-KK) receivers in a 112-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) system over a 1440-km standard single-mode fiber (SSMF). A joint overlap approach and bandwidth compensation filter (OLA-BC) architecture is presented to mitigate the edge effect caused by the Hilbert transform and the Gibbs phenomenon induced by the FIR filter, respectively. Moreover, the computational complexity of the OLA-BC based parallelized KK/WDU-KK receiver is also discussed. Parallelized KK/WDU-KK receivers based on the presented OLA-BC architecture can effectively mitigate the edge effect and the Gibbs phenomenon together with more than two orders of magnitude improvement in terms of bit-error-ratio (BER) compared with parallelized KK/WDU-KK receivers without OLA-BC receivers in back-to-back (B2B) case. Finally, we successfully transmit the 16-QAM signals over 960-km SSMF with a BER lower than 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10−3) and 1440-km SSMF with a BER lower than 20% soft-decision FEC (SD-FEC) threshold (2 × 10−2).

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

High-speed and extensible distance fiber transmission with simultaneous demand for lower cost and complexity have become a major trend in short-reach and medium-reach fiber communication systems, e.g. inter-data-center, back-haul and metropolitan applications [1–4]. Wherein, direct-detection (DD), implemented by using a single photo-detector (PD), has long been a major scheme due to its easy implementation, low power consumption and low complexity [5–7]. However, RF power fading induced by chromatic dispersion (CD) and complex field loss during the power detection resulting in a low spectral efficiency (SE) and limited transmission distance in comparison with coherent systems [2,8]. In this regard, single side band (SSB) modulation can be used to solve power fading and double SE [9]. However, a nonlinear effect known as signal-signal beat interference (SSBI) caused by the square-law detection has been a major problem in SSB DD systems all along. Until now, substantial efforts have been proposed to reduce the performance gap between DD and coherent systems, while taking the advantage of the inherent simplicity of DD system [10–14]. Recently, as one of the DD reception methods, Kramers-Kronig (KK) receiver has been proposed that combines the advantages of coherent reception with the simple implementation of DD [15,16]. KK receiver is capable of accurately reconstructing the complete optical complex field as long as the minimum phase condition is satisfied [17,18]. In particular, the intensity and the phase of the received signals are linked by the Hilbert transform. Therefore, numerous advanced DSP technologies developed for traditional coherent detection schemes can also be used after KK field reconstruction algorithm to improve the transmission performance and distance of KK receiver [19–21]. Meanwhile, KK receiver has superior SSBI mitigation ability and enables advanced complex modulation format, such as 16-QAM modulation, which offers a great improvement to the SE [22]. Until now, KK-based experiment systems have reached a maximum transmission distance up to 1440-km with 28-GBaud 16-QAM discrete multi-tone (DMT) system, which shows the increased system performance of KK receiver.

Generally, a high up-sampling rate up to 6 samples-per-symbol (SPS) and a Hilbert transform with high complexity are required for the conventional KK field reconstruction algorithm, which undoubtedly increases the computational complexity and power consumption, and also violates the principle of low complexity and low cost of KK receiver. Therefore, numerous methods have been proposed to solve these problems. In terms of reducing the sampling rate, a typical without digital up-sampling KK (WDU-KK) receiver has been proposed recently, which operates at 2SPS and exhibits similar performance to the conventional KK receiver operates at 6SPS [23–26]. In terms of reducing the complexity of the Hilbert transform, a time-domain Hilbert FIR filter with 16 non-zero coefficients is recently proposed to approximate the Hilbert transform [27].

Although the abovementioned methods have made a great contribution to reducing the complexity of KK receiver and further enable the real-time KK system, the performance of parallelized KK system still needs to be considered. Until now, most of the KK experiments reported with a data rate up to hundreds of Gbit/s or even Tbit/s are based on the offline long frame (LF) validation [16]. In general, sampled signals from real-time digital sampling oscilloscope (DSO) are processed by KK receiver with a long frame, whose length is determined by the actual record length from DSO. Parallel validation after LF validation is extremely necessary since the data rate is several orders of magnitude higher than the clock frequency of state-of-the-art field-programmable gate array (FPGA) or application-specific integrated circuits (ASICs) [28–30]. Wherein, edge effect in time-domain and the Gibbs phenomenon in frequency-domain caused by the Hilbert FIR filter are great challenges along with the parallelized implementation of the KK receiver [15,31].

In this paper, parallelized performance of KK and WDU-KK receivers are investigated through a 112-Gbit/s 16-QAM transmission experiment. A joint overlap approach and bandwidth compensation filter (OLA-BC) architecture is presented to mitigate the edge effect and the Gibbs phenomenon of the Hilbert FIR filter. Note that this work is extended from our previous work presented in [30], and more detailed analysis is conducted here with experimental results and a more thorough complexity analysis. The experimental results show that parallelized KK (PKK) and parallelized WDU-KK (WDU-PKK) receivers without OLA-BC architecture (PKK/WDU-PKK wo OLA-BC) has three orders of magnitude deterioration compared with LF-KK receiver in terms of BER, while the PKK and WDU-PKK with OLA-BC (PKK/WDU-PKK w OLA-BC) receivers can effectively compensate such deterioration and has a significant BER reduction by more than two orders of magnitude in back-to-back (B2B) case. Moreover, the BER performance versus the tap number of Hilbert FIR filter and the parallel block length are also analyzed. Finally, a Raman amplification fiber link is used to investigate the transmission performance of the parallelized KK receiver. Taking soft-decision forward error correction (SD-FEC) threshold (2 × 10−2) as a reference, PKK/WDU-PKK receivers without OLA-BC can only transmit signals up to 240-km, while the PKK/WDU-PKK receivers with OLA-BC can transmit the same distance as LF-KK receiver, up to 1440-km.

2. Operation principle

2.1. Gibbs phenomenon of Hilbert FIR filter and edge effect in PKK receivers

KK and without digital up-sampling KK (WDU-KK) receivers have been widely studied and compared [23–26]. Wherein, Hilbert transform (HT) is a key process both in KK and WDU-KK receivers, which links the intensity and the phase of the received signal. In order to make Hilbert transform suitable for the parallelized KK receiver, we replace the Hilbert filter with an approximate finite-impulse response (FIR) filter [27,32], which is the inverse discrete Fourier transform of the frequency response H[n] for the index n, and the frequency response is given as follows

$$H[n] = \left\{ \begin{array}{cc} j, &1 \le n < {N_f}/2 \\ - j, &-{N_f}/2 < n < 0 \\ 0, &n \in \{0, -{N_f}/2 \} \end{array} \right.$$
where Nf represents the tap number of the Hilbert FIR filter, and the accuracy of approximation will improve as the Nf increases. Therefore, the phase of the received signals can be obtained by performing the convolution operation as Eq. (2) shows
$$\begin{aligned}{\phi _E}[k] &= \frac{1}{2}\ln \{{I[m]} \}\ast IFFT\{{H[m]} \}= \frac{1}{2}\ln \{{I[m]} \}\ast h[m]\\ &= \frac{1}{2}\sum\nolimits_{m = \max \{{0,k - Nf + 1} \}}^{\min \{{Np - 1,k} \}} {\ln \{{I[m]} \}\cdot h[{k - m} ]} \end{aligned}$$
where k represents the time index in mathematical operation, H[m] and h[m] are a Fourier transform pair and Np is the length of a parallel block. In terms of time-domain convolution as Eq. (2) shows, the response at the edge is obtained by “incomplete” convolution operation. This is because that as k in Eq. (2) becomes closer to the edge of the block, fewer points will be got involved in the calculation of the Hilbert FIR filter output, inducing more serious signal distortion [31]. Since there exist two Hilbert transforms in the WDU-KK receiver, the edge effect and the Gibbs phenomenon caused by the Hilbert FIR filters might be more obvious and we will discuss them in detail as follows [23].

In the offline long frame (LF) KK receiver, phase reconstruction can be implemented by the ideal Hilbert transform or the Hilbert FIR filter [16,27]. Figure 1(a) shows the reconstructed phase of LF-KK receiver with ideal Hilbert transform, Hilbert FIR filter with Nf = 32, and Hilbert FIR filter with Nf = 128, the original phase is used as a reference. It should be noted that the waveform data is obtained by experiment results in section 3 when CSPR=12 dB in back-to-back (B2B) case. Obviously, whether the ideal Hilbert transform or the Hilbert FIR filter is implemented in LF-KK, the reconstructed phase error due to the edge effect is visible at the head and tail of a frame, but it reduces as the distance from the beginning of the frame increases [15,30]. In particular, when the Hilbert FIR filter is implemented in LF-KK receiver, there are some errors in the recovered signals as Fig. 1(a) shows, which can be attributed to the in-band flatness deterioration caused by the Gibbs phenomenon and such errors will further deteriorate the performance of LF-KK receiver [31]. In-band flatness deterioration caused by Gibbs phenomenon can be summarized as follows: due to the limited tap number of Hilbert FIR filter (Nf), the electrical spectrum around the zero-frequency of the Hilbert FIR filter is significantly affected by the Gibbs phenomenon, and further resulting in low-frequency deterioration of the reconstructed phase. Figures 1(b)–1(d) show the electrical spectrums of LF-KK with ideal Hilbert transform (red region), Hilbert FIR filter with Nf = 32 (green region) and Hilbert FIR filter with Nf = 128 (blue region). Note that the sampling rate of the digital sampling oscilloscope (DSO) is 80-GHz, the spectrum range is set from −40-GHz to 40-GHz. Insertions (i) and (ii) of Figs. 1(c) and 1(d) show the low-frequency part of the reconstructed signals, and the effect of the Gibbs phenomenon can easily be observed. It should be noted that although the high-frequency part is also affected by the Gibbs phenomenon, the energy of the high-frequency part is lower than that of the low-frequency part. Therefore, the penalty mainly depends on the frequency content of the signal at the low-frequency part. The blue and green dotted lines are the magnitude-frequency response of Hilbert FIR filter with Nf = 128 and Nf = 32, respectively. Since decreasing the number of Hilbert FIR filter tap (Nf) will worse the magnitude-frequency response, the impact of the Gibbs phenomenon is more obvious with smaller Nf.

 figure: Fig. 1.

Fig. 1. (a) Reconstructed phase of LF-KK, PKK after ideal Hilbert transform (HT), Hilbert FIR filter with Nf = 32 and with Nf = 128, respectively. The bottom figures are the head of the reconstructed phase, the junction of two blocks and middle of one block. Electric spectrums of LF-KK after (b) ideal Hilbert transform (red region), (c) Hilbert FIR filter with Nf = 32 (green region) and (d) Hilbert FIR filter with Nf = 128 (blue region). (i) and (ii) are the low-frequency part of the reconstructed signals. Green and blue dotted line in (c) and (d) are magnitude-frequency response with Nf = 32 and Nf = 128, respectively.

Download Full Size | PDF

We now switch to analyzing the implementation of the parallelized KK receiver considering the Hilbert FIR filter. Different from LF-KK receiver, the edge effect will be much more serious in the parallelized KK receiver due to the parallel processing pattern. Figure 1(a) also shows the reconstructed phase of PKK receiver with Hilbert FIR filter with Nf = 32, Hilbert FIR filter with Nf = 128, and ideal Hilbert transform, the parallel block length (Np) is 64. It can be observed that unlike LF-KK receiver, the head and tail of each parallel block are affected by the edge effect that cannot be mitigated without overlap approach in PKK receiver. Moreover, increasing the tap number of Hilbert FIR filter (Nf) will aggravate the edge effect since more points are needed to calculate the phase, the error of edge points will be more serious [31]. Furthermore, the same as LF-KK receiver, when Nf is small, the Gibbs phenomenon of the spectrum close to zero-frequency is more obvious in PKK receiver. Thus, the performance of the Hilbert FIR filters with limited tap number in PKK receivers can be summarized in two aspects: (I) with the increasing tap number of Hilbert FIR filter, the edge effect will be more serious and (II) with the decreasing tap number of Hilbert FIR filter, the Gibbs phenomenon will be more serious.

Therefore, it is necessary to determine the length of the edge effect error occurrence region (L) on a parallel block in PKK and WDU-PKK receivers. We calculate the L value by the unbiased estimator and the error between two adjacent points. Equation (3) and Eq. (4) are utilized for the criterion of L value

$$\left| {L_{i + 1}-L_i} \right|^2 \le {\mathop{\textrm{var}}} \left({L_{i + 1},...,L_{end}}\right)$$
$${L_{opti}} = {L_i}$$
where var (.) refers to the unbiased estimator and Li represents the error between the original phase and the recovered phase when L = Li. Here, Eq. (4) is the optimal L (Lopti) value as long as Eq. (3) is satisfied. We verify the influence of the edge effect considering different CSPR, Nf, and Np through a 28-GBaud 16-QAM simulation system, and the roll-factor of raised root cosine (RRC) filter is set to be 0.2, the system noise is dominated by amplifier spontaneous emission (ASE) noise. The simulation results are shown in Figs. 2(a)–2(c). Firstly, as Fig. 2(a) shows, when CSPR is 7 dB and Np increases, the Lopti is almost invariable as the edge effect is only related to Nf, not to Np when CSPR is fixed. Secondly, it can be observed from Fig. 2(b), when Np=64 and CSPR increases from 2 dB to ∼6 dB, Lopti is also increased. Since the minimum phase condition cannot be satisfied under lower CSPR, the deterioration of the system not only depends on edge effect, but also larger nonlinearity called serious SSBI. When CSPR further increases from the optimal value, linear penalty induced by increased carrier-ASE beating will deteriorate the system together with edge effect, resulting in a decreased Lopti [33]. Thus, the longest length of the edge effect appears at the optimal CSPR. Finally, Lopti is almost invariable when Nf>16 and Np=64 as shown in Fig. 2(c), although increasing Nf will lead to a more serious edge effect, it will also reduce the impact of the Gibbs phenomenon as mentioned above.

2.2. Overlap approach and bandwidth compensation of the parallelized KK receiver

We have discussed the edge effect and the Gibbs phenomenon caused by the Hilbert FIR filter as well as the performance analysis of which in KK receiver. Then, edge effect mitigation and bandwidth compensation in PKK receivers will be introduced as follows. Figure 3 shows two different frame architecture diagrams with or without the overlap approach (OLA) of parallelized KK receiver [34,35]. The top panel of Fig. 3(a) shows the waveform of the original phase and the recovered phase by PKK without OLA, the gray window marks the edge effect. The deteriorating points affected by the edge effect are marked as the edge error region (EER) with a length of K in Fig. 3(a). For the PKK without OLA as shown above in Fig. 3(a), the edge effect deteriorates the first and the last K bits of each parallel block (PB) and the number of error bits will increase with parallel processing, further resulting in a deterioration of system performance. In OLA-PKK, as Fig. 3(a) below shows, each frame overlaps 2 K bits, since the edge effect distorts the first K bits and the last K bits of each PB, the phase information of the Np points in the middle of each PB [depicted as PB output in Fig. 3(a)] can be reconstructed correctly. Bandwidth compensation FIR filter can be obtained by making the opposite ripple of its intensity spectrum under the same bandwidth as the original Hilbert FIR filter with a tap number of Nd. Figure 3(b) shows schematic of the improved KK receiver with bandwidth compensation filter and electrical spectrums of each step.

 figure: Fig. 2.

Fig. 2. Length of edge effect error occurrence region (a) under different Np (b) under different CSPR (c) under different Nf when OSNR are 23 dB, 29 dB and 31 dB, respectively.

Download Full Size | PDF

 figure: Fig. 3.

Fig. 3. Schematic of (a) parallelized KK receiver with or without OLA architecture. (b) Improved KK receiver and electrical spectrums: (i) after Hilbert FIR filter with Nf=32 using OLA, (ii) frequency response of BC filter, (iii) after BC filter, and (iv) after ideal Hilbert transform used as a reference. D(·) refers to the bandwidth compensation FIR filter.

Download Full Size | PDF

2.3. Computational complexity analysis

To further analyze the performance of the parallelized KK/WDU-KK receivers, we calculate the computational complexity of them with or without OLA-BC-based algorithms. Assuming that the oversampling number is M (e.g. M=2 refers to twice the Nyquist sampling rate) and Np is the length of a parallel block. The tap number of Hilbert FIR filter is Nf. Note that the digital up-sampling and down-sampling processes can be implemented with two linear FIR filters with a tap number of Ni. The overlap length is set to be 2 K with a length of Nf/4. The bandwidth compensation (BC) can be implemented by an Nd-tap FIR filter. In order to simplify the hardware complexity, look-up tables (LUTs) are used to implement mathematical operations such as natural logarithm operations [24]. Thus, the complexity of PKK and WDU-PKK with OLA-BC can be represented as the number of multipliers as the following equations show

$${N_m}_{\textrm{(PKK w OLA - BC)}} = ({{N_i} + {N_f}/2 + {N_d} + 2} )\times M \times ({{N_p} + 2K} )+ 2 \times ({{N_p} + 2K} )\times {N_i}$$
$$N_{m \textrm{(WDU-PKK w OLA-BC)}} = \left( {N_f + N_d + 3} \right) \times \left( {N_p + 2K} \right).$$

It should be noted that when Nd = 0, Nm refers to the complexity of PKK and WDU-PKK receivers with OLA algorithm. Moreover, the complexity of PKK and WDU-PKK receivers without OLA-BC algorithm is calculated when Nd=0 and K=0. Figure 4 shows the computational complexity of PKK and WDU-PKK receivers with or without OLA-BC and with OLA under different Np and Nf.

 figure: Fig. 4.

Fig. 4. Complexity of (a) PKK, (b) WDU-PKK receivers with or without OLA-BC and with OLA under different Np and Nf.

Download Full Size | PDF

3. Experimental setup

According to the KK principle, we set up an SSB 16-QAM DD transmission system as Fig. 5 shows. At the transmitter side, a 193.4-THz optical carrier is fed into an IQ modulator (Fujitsu FTM 7961EX/301) biased at its null point. The 28-GBaud 16-QAM electrical signals are generated from a 65-GSa/s arbitrary waveform generator (AWG, Keysight M8195A) with a 3 dB bandwidth of 25-GHz. A pseudo-random bit sequence (PRBS) of length 214−1 is used for the 16-QAM signal generation and the signals are then up-sampled to 2 samples per symbol for the raised root cosine (RRC) shaping with a roll factor of 0.2 so that the signal base bandwidth becomes 16.8-GHz. Then, two 50-GHz linear driving amplifiers (SHF s807) are used to amplify the signal and subsequently send to the I/Q modulator. To satisfy the minimum phase condition, a continuous wave (CW) tone is generated at the left sideband of the signal with a frequency offset of 17-GHz relative to the center of the signal’s spectrum. CSPR can be easily controlled by adjusting the optical power of the CW2 tone (i.e. the output of CW2 in Fig. 5). The optical carrier of the signal and the CW tone are both generated from a 4-channel tunable laser source (Keysight N7714A, linewidth<100-kHz). Before coupling the signal and the CW tone, a polarization-maintaining erbium-doped fiber amplifier (PM-EDFA) is used to amplify the signal to expand the range of CSPR adjustment. Then an EDFA and a variable optical attenuator (VOA) are employed to adjust the optical power launched into the fiber. The fiber link is made up of multi-spans standard single-mode fiber (SSMF) of 80-km with Raman fiber amplifiers (RFA). At the receiver side, the received signal is amplified by another EDFA and then filtered by a tunable optical band-pass filter with a 3 dB bandwidth of 0.4-nm to remove the out-of-band noise and the nonlinear distortion induced by the fiber transmission. At last, the amplified signal is detected by an AC-coupled PD with a bandwidth of 70-GHz, sampled by an 80-GSa/s digital sampling oscilloscope (DSO) with the 36-GHz bandwidth (Lecroy LabMaster 10-36Zi-A), and processed offline in MATLAB.

 figure: Fig. 5.

Fig. 5. The experimental setup of 112-Gbit/s SSB 16-QAM transmission system. DSP, digital signal processing; AWG, arbitrary waveform generator; IQ MZM, IQ Mach-Zehnder modulator; PM-EDFA, polarization-maintaining-erbium-doped fiber amplifier; PMC, polarization-maintaining coupler; VOA, variable optical attenuator; RFA, Raman fiber amplifier; OBPF, optical band-pass filter; PD, photo detector; DSO, digital sampling oscilloscope.

Download Full Size | PDF

The receiver-side DSP configuration is shown in Fig. 5. The detected signals are firstly resampled for long frame (LF) and different parallelized KK/WDU-KK reconstruction schemes. Afterwards, electrical dispersion compensation (EDC) based on the frequency-domain compensation, IQ quadrature imbalance compensation based on the Gram–Schmidt orthogonalization procedure (GSOP) algorithm, clock recovery based on the Gardner algorithm, linear equalization based on the radius-directed algorithm (RDA), frequency offset estimation (FOE) based on the Fast Fourier Transform (FFT) and carrier phase estimation (CPE) based on the Viterbi-Viterbi phase estimation (VVPE) are executed in turn. Finally, BER is calculated using 10 million points after de-mapping and decision.

4. Results and discussions

At first, we investigate the performance of different schemes in back-to-back (B2B) condition. KK receiver and without digital up-sampling KK (WDU-KK) receiver algorithms based on the long frame (LF) and with or without the overlap approach and bandwidth compensation (OLA-BC) architectures are used for comparison and discussion. CSPR is a crucial parameter in KK receiver and Fig. 6(a) shows the BER versus CSPR using different process schemes. The parallel block length of all parallelized KK/WDU-KK receivers is 64 while LF-KK receivers are used as references. For all parallelized and LF KK receivers, BER performance is improved as CSPR increases and tends to be stable when CSPR is greater than 12 dB. Due to the limited bandwidth of the RF cable at the transmitter and 4SPS resampling is used for KK field reconstruction, the demand for CSPR is higher [32]. As expected, the PKK/WDU-PKK receivers without OLA do not work out as the KK phase reconstruction is strongly impaired by edge effect. Moreover, with the help of the OLA-BC architecture, the PKK and the WDU-PKK receivers with OLA-BC outperform the PKK and WDU-PKK receivers without OLA-BC greatly due to its superior edge effect mitigation and bandwidth compensation abilities for the Hilbert FIR filter. However, since there are two Hilbert transforms in WDU-KK receiver, extra errors caused by another Hilbert transform will further deteriorate the BER performance. Figures 6(b)–6(e) show the constellations of different schemes including LF-KK/LF-WDU-KK as well as PKK/WDU-PKK with and without OLA-BC architecture used when CSPR is 12 dB, it is obvious that the distribution of constellation points are less dense for PKK/WDU-PKK receivers without OLA-BC due to strong edge effect and the Gibbs phenomenon.

 figure: Fig. 6.

Fig. 6. (a) CSPR as a function versus CSPR using different schemes. (b) Constellations of PKK and WDU-PKK without OLA-BC (c) Constellations of PKK and WDU-PKK with OLA. (d) Constellations of PKK and WDU-PKK with OLA-BC. (e) Constellations of LF-KK and LF-WDU-KK.

Download Full Size | PDF

Next, the BER performance of different Np for the PKK/WDU-PKK receivers with OLA, PKK/WDU-PKK receivers with OLA-BC and the tap number of the Hilbert FIR filter (Nf) are investigated as shown in Fig. 7. CSPR is kept at 12 dB and Nd remains equal to Nf while Nf and parallel block length Np are changed. Among different Nf values, BER performance is improved as the Np raises, which can be attributed to that the deterioration caused by the edge effect is decreased and consequent improvement of recovery accuracy. Moreover, for the Hilbert FIR filter, increasing Nf value has a negligible impact on the BER performance and the performance of the Hilbert FIR filter tends to be stable when the Nf value is greater than 32 [27]. Furthermore, on the one hand, PKK with OLA-BC at Np=32 and Nf=16 has similar performance to PKK with OLA at Np=256 and Nf=32, as well as Np=64 and Nf=64, while the complexity are reduced by 83% and 49%, respectively, as Fig. 4(a) and Fig. 7(a) show. On the other hand, WDU-PKK with OLA-BC at Np=64 and Nf=16 has similar performance to WDU-PKK with OLA at Np=256 and Nf=64, as well as with Np = 128 and Nf=64, while the complexity are reduced by 81% and 63%, respectively, as Fig. 4(b) and Fig. 7(b) show. Finally, WDU-PKK with OLA-BC at Np=32 and Nf=32 has similar performance to PKK with OLA-BC at Np=32 and Nf=16, and the complexity is further reduced by 67%.

 figure: Fig. 7.

Fig. 7. BER as a function of the different Np and Nf. (a) PKK with OLA and with OLA-BC, (b) WDU-PKK with OLA and with OLA-BC.

Download Full Size | PDF

Fiber transmission experiments are carried out using different transmission distances. In KK receiver, lower CSPR will degrade the performance of KK complex field reconstruction since it violates the minimum phase condition, while higher CSPR will induce the fiber nonlinearity and further decrease the system sensitivity. Therefore, it is necessary to obtain an optimal CSPR value to achieve the best fiber transmission performance. Moreover, optical launch power is an extremely important factor for transmission performance as well. Larger launch power will lead to the fiber nonlinearity, while smaller launch power will decrease the signal power and further lead to smaller optical signal-to-noise ratio (OSNR). The results of the joint optimization of CSPR value and launch power over 960 and 1440-km SSMF are shown in Fig. 8. For both PKK/WDU-PKK receivers with OLA-BC, the tap number of interpolation FIR filters and the parallel block length are set to be 64 while the tap number of the Hilbert FIR filter and the BC filter are set to be 32. Different schemes are used to verify the performance in fiber transmission. After 1440-km transmission, the optimal launch power is 6, 7 and 8 dBm when CSPR is 12, 13 and 14 dB, respectively. After 960-km transmission, CSPR and launch power values are all decreased by 1 dB compared with 1440-km transmission. The optimal CSPR and launch power is 13 dB and 7 dBm for 1440-km transmission as well as 12 dB and 6 dBm for 960-km transmission, respectively.

 figure: Fig. 8.

Fig. 8. BER performance versus launch power at different CSPR values using PKK w OLA-BC and WDU-PKK w OLA- BC: (a) after 960-km SSMF. (b) Constellation of PKK w OLA- BC (above) and WDU-PKK w OLA-BC (bottom). (c) After 1440-km SSMF. (d) Constellation of PKK w OLA- BC (above) and WDU-PKK w OLA-BC (bottom).

Download Full Size | PDF

Finally, the BER performance under different transmission distance is analyzed in Fig. 9 to investigate the transmission performance of the parallelized KK receiver. When the transmission distance is up to 960-km, PKK/WDU-PKK receivers without OLA-BC cannot recover the transmitted 16-QAM signal due to the joint large nonlinear noise and strong edge effect. However, the OLA-BC based algorithms have better performance and can lower the BER below the HD-FEC threshold (3.8 × 10−3). When the transmission distance is further increased to 1440-km, the BER of LF-KK is 8.6 x10−3 and the PKK w OLA-BC is 1.44 x10−2 (lower than the SD-FEC threshold of 2 × 10−2). With the help of the OLA-BC based algorithm, parallelized implementation can be realized in any KK receiver.

 figure: Fig. 9.

Fig. 9. BER performance versus transmission distance using different schemes at optimal CSPR and launch power. wo: without OLA-BC.

Download Full Size | PDF

5. Conclusion

We have investigated the parallelized performance of the KK and without digital up-sampling KK (WDU-KK) receivers in a 112-Gbit/s single-polarization (SP) 16-QAM direct detection (DD) transmission system over 1440-km SSMF. A joint overlap approach and bandwidth compensation filter (OLA-BC) architecture is presented to mitigate the edge effect caused by Hilbert transform and the Gibbs phenomenon induced by the FIR filter, respectively. Moreover, the presented OLA-BC based parallelized KK/WDU-KK receivers show a superior ability of edge effect mitigation and bandwidth compensation in B2B case. Besides, a Raman amplification fiber link is used to investigate the transmission performance of the parallelized KK receiver. We successfully transmit the 16-QAM signal over 960-km SSMF with a BER lower than hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10−3 and 1440-km SSMF with a BER lower than soft-decision forward error correction (SD-FEC) threshold of 2 × 10−2. Finally, we also calculate the computational complexity of the PKK/WDU-PKK receivers with or without OLA-BC algorithm. To the best of our knowledge, this is the first time that the parallelized KK algorithm is validated.

Funding

Fundamental Research Funds for the Central Universities; National Natural Science Foundation of China (61875019, 62021005); National Key Research and Development Program of China (2019YFB1803601).

Disclosures

The authors declare no conflicts of interest.

References

1. G. N. Liu, L. Zhang, T. Zuo, and Q. Zhang, “IM/DD Transmission Techniques for Emerging 5G Fronthaul, DCI, and Metro Applications,” J. Lightwave Technol. 36(2), 560–567 (2018). [CrossRef]  

2. P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic Transmission and Networking: The Previous 20 and the Next 20 Years [Invited],” Opt. Express 26(18), 24190–24239 (2018). [CrossRef]  

3. K. Zhong, X. Zhou, Y. Wang, T. Gui, Y. Yang, J. Yuan, L. Wang, W. Chen, H. Zhang, J. Man, L. Zeng, C. Yu, A. Lau, and C. Lu, “Recent advances in short reach systems,” in Proceedings of Optical Fiber Communication Conference (2018), paper Tu2D.7.

4. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. Lau, “Digital signal processing for short reach optical communications: A review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018). [CrossRef]  

5. J. C. Cartledge and A. S. Karar, “100 Gb/s intensity modulation and direct detection,” J. Lightwave Technol. 32(16), 2809–2814 (2014). [CrossRef]  

6. A. Yekani, S. Amiralizadeh, and L. A. Rusch, “Analytical study of optical SSB-DMT with IMDD,” J. Lightwave Technol. 36(3), 666–674 (2018). [CrossRef]  

7. H. Zhou, Y. Li, D. Lu, L. Yue, C. Gao, Y. Liu, R. Hao, Z. Zhao, W. Li, J. Qiu, X. Hong, H. Guo, Y. Zuo, and J. Wu, “Joint clock recovery and feed-forward equalization for PAM4 transmission,” Opt. Express 27(8), 11385–11395 (2019). [CrossRef]  

8. D. Che, Q. Hu, and W. Shieh, “Linearization of direct detection optical channels using self-coherent subsystems,” J. Lightwave Technol. 34(2), 516–524 (2016). [CrossRef]  

9. C. Li, M. Luo, and X. Li, “4 × 128-Gb/s PDM-DMT signal transmission over 1440-km SSMF with high phase noise tolerance,” Opt. Express 26(23), 30901–30910 (2018). [CrossRef]  

10. B. Lin, J. Li, H. Yang, Y. Wan, Y. He, and Z. Chen, “Comparison of DSB and SSB transmission for OFDM-PON,” in Proceedings of National Fiber Optic Engineers Conference (2012), paper NTu1J.7.

11. Z. Li, M. S. Erkilinc, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, B. Bayvel, and R. I. Killey, “Reach enhancement for WDM direct-detection subcarrier modulation using low-complexity two-stage signal-signal beat interference cancellation,” in Proceedings of European Conference on Optical Communications (2016), paper M.2.B.1.

12. 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). [CrossRef]  

13. Z. Li, M. S. Erkilinc, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “SSBI Mitigation and the Kramers-Kronig Scheme in Single-Sideband Direct-Detection Transmission With Receiver-Based Electronic Dispersion Compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017). [CrossRef]  

14. Z. Li, M. S. Erkilinc, R. Maher, L. Galdino, K. Shi, B. C. Thomsen, B. Bayvel, and R. I. Killey, “Two-stage linearization filter for direct-detection subcarrier modulation,” IEEE Photonics Technol. Lett. 28(24), 2838–2841 (2016). [CrossRef]  

15. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]  

16. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig receivers,” Adv. Opt. Photonics 11(3), 480–517 (2019). [CrossRef]  

17. A. Mecozzi, “Retrieving the full optical response from amplitude data by Hilbert transform,” Opt. Commun. 282(20), 4183–4187 (2009). [CrossRef]  

18. A. Mecozzi, “A necessary and sufficient condition for minimum phase and implications for phase retrieval,” arXiv: 1606.04861. Oct. 2016.

19. L. Shu, J. Li, Z. Wan, Z. Yu, X. Li, M. Luo, S. Fu, and K. Xu, “Single-photodiode 112-Gbit/s 16-QAM transmission over 960-km SSMF enabled by Kramers-Kronig detection and sparse I/Q Volterra filter,” Opt. Express 26(19), 24564–24576 (2018). [CrossRef]  

20. S. An, Q. Zhu, J. Li, Y. Ling, and Y. Su, “112-Gb/s SSB 16-QAM signal transmission over 120-km SMF with direct detection using a MIMO-ANN nonlinear equalizer,” Opt. Express 27(9), 12794–12805 (2019). [CrossRef]  

21. T. Gui, L. Yi, C. Guo, C. Lu, and A. Lau, “120 Gbaud PAM-4 transmission over 80-km SSMF using optical band interleaving and Kramers-Kronig detection,” Opt. Express 26(20), 25934–25943 (2018). [CrossRef]  

22. Y. Liu, Y. Li, H. Zhou, Z. Zhao, L. Yue, H. Guo, J. Qiu, X. Hong, W. Li, Y. Zuo, and J. Wu, “Performance Analysis of Extended Kalman Filter in Kramers-Kronig Receiver,” in Proceedings of Opto Electronics and Communications Conference (2019), paper ThC3.

23. T. Bo and H. Kim, “Toward practical Kramers-Kronig receiver: resampling, performance, and implementation,” J. Lightwave Technol. 37(2), 461–469 (2019). [CrossRef]  

24. T. Bo, R. Deng, J. He, and H. Kim, “On the hardware complexity of Kramers-Kronig receiver,” in Proceedings of Conference on Lasers and Electro-Optics/Pacific Rim (2018), paper Tu2I.2.

25. T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” Opt. Express 26(11), 13810–13818 (2018). [CrossRef]  

26. T. Bo and H. Kim, “Kramers-Kronig receiver operable without digital upsampling,” in Proceedings of Optical Fiber Communication Conference (2018), paper W4E.2.

27. C. Fullner, S. Wolf, J. N. Kemal, J. Lutz, L. Altenhain, R. Schmid, W. Freude, C. Koos, and S. Randel, “Transmission of 80-GBd 16-QAM over 300 km and Kramers-Kronig reception using a low-complexity FIR Hilbert filter approximation,” in Proceedings of Optical Fiber Communication Conference (2018), paper W4E.3.

28. M. Chen, J. He, Z. Cao, J. Tang, L. Chen, and X. Wu, “Symbol synchronization and sampling frequency synchronization techniques in real-time DDO-OFDM systems,” Opt. Commun. 326(1), 80–87 (2014). [CrossRef]  

29. M. Chen, J. He, and L. Chen, “Real-time optical OFDM long-reach PON system over 100-km SSMF using a directly modulated DFB laser,” J. Opt. Commun. Netw. 6(1), 18–25 (2014). [CrossRef]  

30. Y. Liu, Y. Li, J. Song, H. Zhou, L. Yue, X. Li, M. Luo, and J. Wu, “Parallel implementation of KK receiver enabled by heading-frame architecture and bandwidth compensation,” in Proceedings of Optical Fiber Communication Conference (2020), paper M3J.5.

31. J. G. Proakis and D. G. Manolakis, “Digital Signal Processing: Principles, Algorithms, and Applications,” 4th Edition, Pearson Education, Inc., New Delhi, 2007.

32. C. Fullner, M. H. Adib, S. Wolf, J. N. Kemal, W. Freude, C. Koos, and S. Randel, “Complexity Analysis of the Kramers–Kronig Receiver,” J. Lightwave Technol. 37(17), 4295–4307 (2019). [CrossRef]  

33. Z. Li, M. S. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. C. Thomsen, P. Bayvel, and R. I. Killey, “Joint Optimisation of Resampling Rate and Carrier-to-Signal Power Ratio in Direct-Detection Kramers-Kronig Receivers,” in Proceedings of European Conference on Optical Communications (2017), paper W.2.D.3.

34. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009). [CrossRef]  

35. S. Muramatsu and H. Kiya, “Extended overlap-add and-save methods for multirate signal processing,” IEEE Trans. Signal Process. 45(9), 2376–2380 (1997). [CrossRef]  

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)
Fig. 1.
Fig. 1. (a) Reconstructed phase of LF-KK, PKK after ideal Hilbert transform (HT), Hilbert FIR filter with Nf = 32 and with Nf = 128, respectively. The bottom figures are the head of the reconstructed phase, the junction of two blocks and middle of one block. Electric spectrums of LF-KK after (b) ideal Hilbert transform (red region), (c) Hilbert FIR filter with Nf = 32 (green region) and (d) Hilbert FIR filter with Nf = 128 (blue region). (i) and (ii) are the low-frequency part of the reconstructed signals. Green and blue dotted line in (c) and (d) are magnitude-frequency response with Nf = 32 and Nf = 128, respectively.

View in Article | Download Full Size | PDF

Fig. 2.
Fig. 2. Length of edge effect error occurrence region (a) under different Np (b) under different CSPR (c) under different Nf when OSNR are 23 dB, 29 dB and 31 dB, respectively.

View in Article | Download Full Size | PDF

Fig. 3.
Fig. 3. Schematic of (a) parallelized KK receiver with or without OLA architecture. (b) Improved KK receiver and electrical spectrums: (i) after Hilbert FIR filter with Nf=32 using OLA, (ii) frequency response of BC filter, (iii) after BC filter, and (iv) after ideal Hilbert transform used as a reference. D(·) refers to the bandwidth compensation FIR filter.

View in Article | Download Full Size | PDF

Fig. 4.
Fig. 4. Complexity of (a) PKK, (b) WDU-PKK receivers with or without OLA-BC and with OLA under different Np and Nf.

View in Article | Download Full Size | PDF

Fig. 5.
Fig. 5. The experimental setup of 112-Gbit/s SSB 16-QAM transmission system. DSP, digital signal processing; AWG, arbitrary waveform generator; IQ MZM, IQ Mach-Zehnder modulator; PM-EDFA, polarization-maintaining-erbium-doped fiber amplifier; PMC, polarization-maintaining coupler; VOA, variable optical attenuator; RFA, Raman fiber amplifier; OBPF, optical band-pass filter; PD, photo detector; DSO, digital sampling oscilloscope.

View in Article | Download Full Size | PDF

Fig. 6.
Fig. 6. (a) CSPR as a function versus CSPR using different schemes. (b) Constellations of PKK and WDU-PKK without OLA-BC (c) Constellations of PKK and WDU-PKK with OLA. (d) Constellations of PKK and WDU-PKK with OLA-BC. (e) Constellations of LF-KK and LF-WDU-KK.

View in Article | Download Full Size | PDF

Fig. 7.
Fig. 7. BER as a function of the different Np and Nf. (a) PKK with OLA and with OLA-BC, (b) WDU-PKK with OLA and with OLA-BC.

View in Article | Download Full Size | PDF

Fig. 8.
Fig. 8. BER performance versus launch power at different CSPR values using PKK w OLA-BC and WDU-PKK w OLA- BC: (a) after 960-km SSMF. (b) Constellation of PKK w OLA- BC (above) and WDU-PKK w OLA-BC (bottom). (c) After 1440-km SSMF. (d) Constellation of PKK w OLA- BC (above) and WDU-PKK w OLA-BC (bottom).

View in Article | Download Full Size | PDF

Fig. 9.
Fig. 9. BER performance versus transmission distance using different schemes at optimal CSPR and launch power. wo: without OLA-BC.

View in Article | Download Full Size | PDF

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

H [ n ] = { j , 1 ≤ n < N f / 2 − j , − N f / 2 < n < 0 0 , n ∈ { 0 , − N f / 2 }
ϕ E [ k ] = 1 2 ln ⁡ { I [ m ] } ∗ I F F T { H [ m ] } = 1 2 ln ⁡ { I [ m ] } ∗ h [ m ] = 1 2 ∑ m = max { 0 , k − N f + 1 } min { N p − 1 , k } ln ⁡ { I [ m ] } ⋅ h [ k − m ]
| L i + 1 − L i | 2 ≤ var ( L i + 1 , . . . , L e n d )
L o p t i = L i
N m (PKK w OLA - BC) = ( N i + N f / 2 + N d + 2 ) × M × ( N p + 2 K ) + 2 × ( N p + 2 K ) × N i
N m (WDU-PKK w OLA-BC) = ( N f + N d + 3 ) × ( N p + 2 K ) .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use