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Abstract
We experimentally demonstrate a 4 × 10 Gb/s cost-effective coherent ultra-dense wavelength division multiplexing passive optical network (UDWDM-PON) by the use of unequally-spaced 4-level pulse-amplitude modulation (UES-PAM-4) signaling. Because of the advantages of simple architecture and low cost, the simplified coherent receiver (SCR) based on the transmitted signal diversity (TS-D) has been reported, but its receiver sensitivity is constrained by the severe noise arising in the higher level of conventional PAM-4 signals. Here, we first experimentally demonstrate the UES-PAM-4 signaling for the SCR based on the TS-D, by altering the PAM-4 level spacing and the decision threshold through the gradient descent algorithm (GDA). Consequently, we can experimentally achieve −30.1 dBm RS for single wavelength at the bit-error ratio (BER) of 3.8 × 10−3. Compared with the conventional equally-spaced PAM-4 (ES-PAM-4) signaling, 1.3 dB RS enhancement can be secured after the 20-km standard single-mode fiber (SSMF) transmission. Meanwhile, the UES-PAM-4 signaling is experimentally verified for 4 × 10 Gb/s UDWDM-PON. An average RS of −29.6 dBm and 32.6 dB power budget are obtained after the 20-km SSMF transmission. The proposed UES-PAM-4 signaling with the RS enhancement is a promising candidate for the UDWDM-PON by utilizing the existing optical distribution network (ODN).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The explosive development of bandwidth-consuming broadband services including computing network, live broadcasting business, and augmented/virtual reality, stimulate a tremendous increase in bandwidth demand. A passive optical network (PON) can offer a low-cost broadband access option [1,2]. In order to improve the PON capacity, the ITU-T standard of next-generation PON2 (NG-PON2) employs the wavelength division multiplexing (WDM) technique by stacking four or eight wavelengths [3]. According to the ITU-T G.989.1 recommendation, point-to-point WDM systems are widely acknowledged as one of the promising options for next-generation PON [4]. Future PONs with new techniques need to satisfy the co-existence of various PONs. Therefore, WDM-PON are strongly expected to provide high access bandwidth with a low-cost, by utilizing the existing optical distribution network (ODN) for time division multiplexing-PON (TDM-PON).
Broadband optical access based on the coherent ultra-dense WDM (UDWDM) has been verified as a potential scheme to increase both spectral efficiency and downstream capacity [5]. For the implementation of cost-effective UDWDM-PON, many low-cost simplified coherent receivers (SCRs) have been proposed [6–9]. In particular, the polarization independent SCR (PI-SCR) utilizing the 3 × 3 coupler draws global research interests, on account of the unnecessary phase locking and polarization control [7]. The PI-SCR with the TS-D structure has been reported with −51 dBm receiver sensitivity (RS) for 1.25 Gb/s on-off keying (OOK) signal at the bit-error ratio (BER) of 2 × 10−3 [10]. Currently, equally-spaced 4-level pulse-amplitude modulation (ES-PAM-4) has been widely used for the short-reach photonic interconnection, due to its high spectral efficiency and small transmission bandwidth. Recently, we have demonstrated a 8 × 10 Gb/s ES-PAM-4 downstream transmission of UDWDM-PON with a channel spacing of 20 GHz over the C band [11]. Compared with the OOK signals, the ES-PAM-4 signals can double the spectral efficiency, together with excellent PON compatibility. However, traditional ES-PAM-4 signaling with a uniform spacing needs an additional power budget of at least 4.8 dB, in comparison with that of OOK signals at the same BER threshold [12]. Furthermore, the bandwidth constraints from the optoelectronic devices and the fiber nonlinearity will further degrade the transmission performance of traditional ES-PAM-4 signaling [13,14]. Therefore, further enhancing the power budget of the UDWDM-PON, in terms of RS, is challenging. Generally, the power budget of PON is determined by the launch power and the RS. Increasing the launch power is beneficial for the enhancement of the power budget, but fiber nonlinearity will lead a performance penalty for the UDWDM-PON. Optical signals generated by the directly modulated laser (DML) and the chirp managed laser (CML) are more resistant to the highly launch power induced fiber nonlinearity [15]. However, the high launch power indicates the extra power consumption and the use of a costly high-power erbium-doped fiber amplifier (EDFA) for boosting the signal power. Thus, it is expected to improve the power budget of the UDWDM-PON by the RS enhancement, while minimizing the power consumption and cost. The probabilistic shaping (PS) technique has been verified its capability to approach the Shannon capacity and realize a rate-adaptive transmission, under the condition of additive white Gaussian noise channel (AWGN) [16,17]. However, both the complicated coding and the use of digital signal processing (DSP) prevent it to be used for the cost-effective PON. Unequally-spaced PAM-4 (UES-PAM-4) signaling is capable to enhance the PON performance. A 3.5 dB RS improvement has been reported by the UES-PAM-4 generated with hierarchical modulation. However, an interleaved detection is required at the receiver [18]. For the positive intrinsic negative (PIN) receiver together with the semiconductor optical amplifier (SOA), the noise characteristic is power dependent. A 1.5 dB RS enhancement is experimentally reported for the 50 Gb/s UES-PAM-4 TDM-PON [19]. About 2 dB RS enhancement has been obtained by the PAM-4 level optimization for the 100 Gb/s/λ PON [20]. However, the above-mentioned UES-PAM-4 signaling schemes fail to achieve the optimal BER performance, because all optimization strategies assume the equality of the error probability density distribution (PDD) between adjacent levels. Consequently, those UES-PAM-4 signaling schemes achieve a lower BER but not the lowest. Since the noise of TS-D SCR is power dependent [21], to the best of our knowledge, there is no work about the optimization of UES-PAM-4 signaling for the UDWDM-PON application.
In current submission, due to the fact that the higher levels of ES-PAM-4 are affected by more noise from the SCR, we numerically investigate the noise impact on the performance of the TS-D SCR and propose the UES-PAM-4 signaling by employing gradient descent algorithm (GDA), for the sake of improving the power budget of UDWDM-PON. Then, we identify that, the TS-D SCR is the constrained by the power-dependent shot noise. Next, we experimentally demonstrate a UES-PAM-4 scheme for the cost-effective UDWDM-PON, by altering the PAM-4 level spacing and decision threshold based on the GDA. By employing the UES-PAM-4 signaling, −30.3 dBm RS for a single wavelength at the BER of the hard-decision forward error correction (HD-FEC) threshold is achieved. Compared with the conventional ES-PAM-4 signaling, about 1.3 dB RS improvement is obtained over 20-km standard single-mode fiber (SSMF) transmission. Furthermore, we verify the validity of UES-PAM-4 signaling through the 4 × 10 Gb/s PAM-4 UDWDM-PON downstream transmisison, obtaining an average RS of −29.6 dBm and 32.6 dB power budget after the 20-km SSMF transmission.
2. Operation principle and simulation
2.1 Noise of the SCR
Figure 1 shows the schematic of TS-D SCR [11]. The major noise sources of the SCR are thermal noise and shot noise. The random movement of electrons in resistors and other electrical components causes thermal noise, whose the mean-squared value is
where kB is the constant of Boltzmann, T represents the absolute temperature, RL means the load resistance, and $\Delta B$ is the effective bandwidth.The randomness of the photonic-to-electrical converison process arising in a photodiode (PD) produces a fluctuated current with an average value of Iph. The fluctuations are named as shot noise. For a typical PIN receiver, the equation for determining the PD output current in response to a certain optical power is
Here, the mean photocurrent is where Pin represents to the average received optical power, and the PD responsivity is Rd.The mean-squared value of the shot noise is
where q represents the electronic charge and Id means the dark current of the photodiode. ${i_s}(t)$ refers to a fluctuation in electrical current associated to the shot noise. Mathematically, ${i_s}(t)$ obeys the Poisson statistics (often modeled through the Gaussian statistics) [22].As for the TS-D SCR, the LO power PLO can be adjusted, which can be high enough to secure the gain arising in the coherent detection. As a result, the dominated noise is shot noise [22]. In practice, when PLO >> PS is satisfied and the contribution of dark-current to the shot noise is insignificant, $\left\langle {i_s^2} \right\rangle > > \left\langle {i_{th}^2} \right\rangle $ becomes reasonable. Consequently, the mean-squared value of the noise is
Equation (5) indicates that the ES-PAM-4 signal at the higher level is subject to more severe noise. Furthermore, the noise and the signal power are positively correlated. Namely, the degradation of ES-PAM-4 signals at higher levels is more severe, resulting in the frequent occurrence of bit-error.2.2 UES-PAM-4 signaling based on GDA
Two different receivers for the ES-PAM-4 reception is shown in Fig. 2(a). Since the power of received signal is low after the direct detection (DD) with a single PIN-PD, where thermal noise is dominated. Figure 2(c) shows that the noise distributions among four levels are almost uniform. However, as for the SCR, the dominant noise is the shot noise, especially for the case of high output power of LO. Figure 2(d) presents the amplitude probability density (APD) of ES-PAM-4 signals after the TS-D SCR detection. The original APDs are described by those dot lines, which have a good agreement with the solid lines that predicted by the Gaussian PDD. Consequently, the noise PDD at each PAM-4 level is assumed to be Gassian, as shown in Eq. (6).
Fig. 2. (a)Traditional direct detection (DD), and (b)simplified coherent detection; The amplitude probability density of received 10 Gb/s PAM-4 signals for (c)the DD and (d) TSD SCR; and (e) The BER schematic.
To identify the optimal UES-PAM-4 signaling for the TS-D SCR, the most important task is to accurately obtain the corresponding noise distribution of each PAM-4 level under a fixed signal power. The noise variance at each level for the received PAM-4 signals is fitted with the Gaussian PDD. Then, the relationship among the noise variances can be obtained as ${\sigma ^2} = k\ast Q + b$. Next, by using Eq. (6) and ${\sigma ^2}(Q)$, the GDA can be implemented to adjust the levels of ${Q_2}$ and ${Q_3}$ for minimizing $\sum\nolimits_{i = 1}^3 {{P_{error\_i}}} $. We define $\sum\nolimits_{i = 1}^3 {{P_{error\_i}}} $ as the objective function of $J({{Q_2},{Q_3}} )$.
Table 1. Optimization based on GDA
2.3 Numerical simulation
As illustrated in Fig. 3, we perform numerical simulation of the UES-PAM-4 signaling for the TS-D. At the transmitter (Tx), a semiconductor laser at 1550 nm is used as light source. A Mach-Zehnder modulator (MZM) driven by an electrical 10 Gb/s PAM-4 signal intends to realize the electrical-to-optical conversion. The length of pseudorandom bit sequence (PRBS) is 216-1. Then, the optical PAM-4 signal with the 1 dBm launch power is introduced into the SSMF. At the receiver (Rx), we choose a tunable semiconductor laser with an output power of 6 dBm as the LO. The linewidth of both semiconductor lasers used at the Tx and Rx is 100 kHz. The SCR is composed of a PBS, a 3 × 3 fiber coupler, and three 10 GHz PDs together with the analog circuit. DSP is unnecessary at the receiver-side. Meanwhile, a 4th Bessel filter with 2.5 GHz 3dB bandwidth is used to recovery the PAM-4 signal.
We first evaluate the impact of shot noise on the performance of 10 Gb/s ES-PAM-4. For the sake of reducing the performance penalty caused by the frequency offset Δf, we set Δf to 6 GHz [11], for a fair comparison under the same heterodyne detection. As shown in Fig. 4, for the case of an ideal PD, the noise distribution of each level of ES-PAM-4 is uniform. However, for the case of real PD (thermal noise = 20 × 10−12 A/Hz1/2 and dark current = 10 nA), the noise at each level for the ES-PAM-4 has an almost linear relationship. A 6.2 dB SNR penalty can be observed, in comparison with the use of an ideal PD.
During the optimization of UES-PAM-4 signaling, as shown in Fig. 5(a), the noise distribution can be obtained through the curve fitting after multiple measurements. First, we initially obtain the RS S(0) at the PAM-4 level of Q(0) = [0 1 2 3]. Next, the noise distribution of the PAM-4 signal under the power of S(0) can be obtained accurately. As shown in Fig. 5(b), the noise variance is fitted for each level at a fixed power. Then, based on the GDA with a learning rate of 0.7, the first-round optimization result of UES-PAM-4 signaling is QRX. Figure 5(c) illustrates the optimization flow, with the solid line and the dotted line representing the noise distribution before and after the optimization, respectively. The UES-PAM4 decision thresholds of T = [T1 T2 T3] are acquired by the threshold adaptive decision. According to the correspondence between the transmitter and receiver, the optimal level at the transmitter is updated to Q(1). Next, Q(1) is loaded into the arbitrary waveform generator (AWG) to generate the electrical UES-PAM-4 signals, and then the second round of optimization is performed. After several rounds of optimizations, the iteration is terminated when the condition of abs(S(k)-S(k-1))<0.2 is satisfied. Finally, we can obtain a minimum BER and a RS enhancement by the optimal UES-PAM-4 signaling.
Fig. 5. (a) Flowchart of PAM-4 signaling optimization, Q(k): the signal level, S(k):the RS, (b) the noise variance curve of 10 Gb/s PAM-4, (c) the schematic of PAM-4 level optimization based on GDA.
Next, numerical simulations is performed to evaluate the impact of the state of polarization (SOP) on the performance of 10 Gb/s PAM-4. The received signal, which has a completely arbitrary SOP, will bring the term of 2Δf [11]. Especially, with regard to the situation of $\varphi \textrm{ = }{{n\pi } / 2}\textrm{ + }{\pi / 4}$ (n =0, 1, …), such SOP leads to a severe performance penalty of the TS-D SCR. To better investigate its impact, we set $\varphi \textrm{ = }45^\circ$ and the frequency offset is fixed at 6 GHz. As shown in Fig. 6(a), due to the occurred 2Δf term, the noise variance of each level for the SOP at $\varphi \textrm{ = }45^\circ$ is only slightly larger than that of the SOP at $\varphi \textrm{ = }0^\circ$. For both SOPs, high levels of PAM-4 suffer more serious noise. Consequently, the UES-PAM-4 signaling employing the GDA can effectively provide a performance improvement for all SOPs. The final optimal UES-PAM-4 signaling are Q($\varphi \textrm{ = }0^\circ$) = [0 0.8133 1.7050 3] and Q($\varphi \textrm{ = }45^\circ$)= [0 0.8104 1.6987 3], respectively. In comparison with 10 Gb/s ES-PAM-4 after the B2B transmission, the RS enhancement for the SOP at $\varphi \textrm{ = }0^\circ$ and $\varphi \textrm{ = }45^\circ$ are 2.1 dB and 2.3 dB, respectively, as shown in Fig. 6(b). Figure 6(c) indicates that, when the optimization level of Q($\varphi \textrm{ = }45^\circ$) is implemented, we can acheve 2.1 dB RS enhancement for all SOPs. The GDA-enabled PAM-4 signaling optimization is robust to the polarization fluctuation of received PAM-4 signals.
Fig. 6. (a) Calculated noise variance with respect to each PAM-4 level for different SOPs. (b) Calculated RS gain in regard to the optimization round for different SOPs. (c) Calculated sensitivity gain in regard to the different SOPs by using the optimization level of Q($\varphi \textrm{ = }45^\circ$).
For the sake of investigating the effect of the LO output power on the proposed PAM-4 signaling optimization, we further evaluate the performance of 10 Gb/s UES-PAM-4 by varying the LO output power. The higher output power of LO is helpful for the SCR. During the simulation, 1 dB RS enhancement is observed, when the LO output power varies from 3 dBm to 6 dBm. Under the condition of the fixed BER of 3.8 × 10−3 for both LO powers, the noise distribution curves are almost identical, as shown in Fig. 7(a). The final optimization of UES-PAM-4 levels are Q_6dBm = [0 0.8101 1.6923 3] and Q_3dBm = [0 0.8136 1.6964 3], respectively. Moreover, we can observe that, with the help of PAM-4 signaling optimization, 2.2 dB RS enhancement can be achieved for both cases, as shown in Fig. 7(b). Figure 7(c) indicates that, by the use of the optimal signaling Q_6dBm, more than 2 dB RS enhancement can be secured, when the LO power varies from 0 dBm to 6 dBm. Thus, the proposed signaling optimization is helpful to achieve stable RS enhancement with respect to the LO powers. Since optimizing each level of ES-PAM-4 by the GDA can obtain the sensitivity gain, we chose the UES-PAM4 signaling to carry out experimental verification for UDWDM-PON.
Fig. 7. (a) Calculated the noise variance at each level with respect to the LO output power. (b) Calculated the sensitivity gain with respect to the optimization round for different LO output powers. (c) Calculated the sensitivity gain with respect to the different LO power by using the optimization level of Q_6dBm.
3. Experimental results and discussions
As shown in Fig. 8, four distributed feedback lasers (DFBs), whose central wavelengths are 1550.000 nm, 1550.020 nm, 1550.040 nm, and 1550.060 nm, respectively, are divided into odd and even groups with a channel spacing of 25 GHz. At the OLT, two 2 × 1 couplers are used to combine the odd and even channels, respectively. 215-1 PRBS is chosen for the generation of electrical PAM-4 signal. For the purpose of de-correlation between adjacent channels, two MZMs are independently modulated with 10 Gb/s ES-PAM-4 or UES-PAM4 signaling. After the wavelength division multiplexing by another 50:50 coupler, 4 × 10 Gb/s PAM-4 optical signals are introduced into the SSMF. Then, the optical signals are attenuated by a variable optical attenuator (VOA) to simulate the power loss of the installed ODN for the TDM-PON. At the ONU, a TS-D receiver based on 3 × 3 polarization maintaining (PM) optical coupler is used. In order to select the corresponding channel, another tunable DFB is utilized as the LO source. After the coherent mixing, three 10 GHz PIN-PDs, together with the TIA, are used for the optical-to-electrical conversion. Finally, three PD outputs are sampled by a Lecroy Labmaster oscilloscope operated 40 GSa/s, in order to emulate the DSP-free signal processing.
3.1 Single wavelength 10Gb/s PAM4 optimization
First, we evaluate the B2B performance of single channel 10 Gb/s ES-PAM-4 signal at 1550nm. The output power of tunable LO laser is fixed at 6 dBm. As shown in Fig. 9, the lower BER appears, when the range of frequency offset is from 4.6 GHz to 7.5 GHz. A larger frequency offset is helpful to obtain a better transmission performance. Thus, during next experimental verification, the frequency offset is chosen to be 6 GHz.
During the optimization of UES-PAM-4 signaling, the most important task is to accurately obtain the corresponding noise distribution of each PAM-4 level under a fixed signal power. Please note that, the optimization must be valid for all SOPs, especially for the worst case of a specific SOP. Thus, we focus on the fitting of noise distribution for the worst SOP case under conditions of $\varphi \textrm{ = }{{n\pi } / 2}\textrm{ + }{\pi / 4}$ (n =0, 1, …) by managing the polarization controller. Based on the GDA with a learning rate of 0.7, the first-round optimal receiver levels of UES-PAM-4 are QRX = [0.146 0.853 1.787 2.904]. According to the correspondence between the transmitter and receiver, the transmitter's optimal levels are Q(1) [0 0.891 1.815 3 ]. Next, Q(1) is loaded into the AWG to generate the electrical UES-PAM-4 signals, and then the second round of optimization is performed. After four-rounds optimizations, the condition of abs(S(k)-S(k-1))<0.2 is satisfied, leading to the termination of iteration. After the B2B transmission, the final optimal PAM-4 signaling are QB2B = [0 0.870 1.789 3]. As depicted in Fig. 10(a), for the 10 Gb/s ES-PAM-4 and UES-PAM-4 at the BER of 3.8 × 10−3, RSs of −28.8 dBm and −30.1 dBm are achieved, respectively. For the case of 20-km SSMF transmission, the optimization scheme is also effective. The final optimization levels are Q20km = [0 0.867 1.772 3]. Compared with the 10 Gb/s ES-PAM-4 signal, the RS of −30.1 dBm is obtained, leading to a 1.3 dB RS enhancement. Since generalized mutual information (GMI) indicates the maximum achievable information rate (AIR) that can be achieved by ideal binary FEC, we also identify the capability of our proposed PAM-4 signaling to realize the optimal GMI enhancement. Please note that, during the PAM-4 signaling optimization, once the output power of the Tx laser is fixed, the launched optical power may vary, due to the variable level of UES-PAM-4 signals to be loaded into AWG. During the experimental verification, the launched optical power is fixed at 3 dBm. We investigate the RS and power budget of 10 Gb/s PAM-4 after the SSMF transmission of 20 km, with multi-round optimization based on the GDA. As shown in Fig. 10(b), the UDWDM-PON downstream transmission can reach the minimum RS of −30.1 dBm after the three-round optimization. Further increasing the number of optimization rounds may not be helpful to enhance the RS. Moreover, in comparision with simulation results, the RS improvement can be degraded, due to the non-uniform response of three commercial PDs. Given the launched optical power of 3 dBm, a power budget of 33.1 dB is secured after 20 km SSMF transmission.
Fig. 10. (a) BER versus received power for 10 Gb/s ES-PAM-4 and UES-PAM-4 signal. (b) Power budget and sensitivity in regard to the optimization round of 10 Gb/s UES-PAM-4 signal.
3.2 Experimental results of 4 × 10Gb/s UES-PAM-4 WDM-PON
For a UDWDM-PON system, two factors that contribute to the impairment, including both the linear and nonlinear crosstalk from adjacent channels. Since a wide channel spacing is ideally desired to achieve a better RS, a channel spacing of 25 GHz is set. Meanwhile, increasing the launched optical power is profitable for the improvement of the power budget [23]. However, the fiber nonlinearity may degrade system performances [24]. Therefore, we fix the launch power at 3 dBm per wavelength channel. First, the optical spectrum before and after the 20 km SSMF transmission is shown in Fig. 11. Compared with four-channel PAM-4 signals, the power of four-wave mixing (FWM) components is decreased by 47.5 dB. Thus, the FWM effect can be negligible [23].
Next, for each ONU, the LO laser operating wavelength is modified to achieve a frequency offset of 6 GHz with regard to the corresponding downstream channel. In the case of B2B transmission of 4 × 10 Gb/s ES-PAM-4, four channels RSs are −28.8 dBm, −29.0 dBm, −28.7 dBm, and −28.8 dBm, respectively. Using the UES-PAM-4 signal with QB2B, four channels RSs become −30.1 dBm, −30.1 dBm, −30.0 dBm, and −29.8 dBm, respectively, as demonstrated in Fig. 12(a). An average RS enhancement of 1.1 dB is achieved by utilizing the UES-PAM-4 signaling. After the 20-km SSMF transmission, with the help of UES-PAM-4 signal with Q20km, four channels RSs are −29.7 dBm, −29.7 dBm, −29.5 dBm, and −29.5 dBm, respectively, as shown in Fig. 12(b). The RS enhancements of four channels are 1.1 dB, 1.1 dB, 1.0 dB, and 1.0 dB, respectively, in comparison with that of 10 Gb/s ES-PAM-4 UDWDM-PON transmission. Consequently, the average RS of −29.6 dBm can be achieved at the BER of 3.8 × 10−3. Considering that the launch power is 3 dBm, over 32.6 dB power budget can be realized for 4 × 10 Gb/s UES-PAM-4 signals over 20 km SSMF transmission.
Fig. 12. Receiver sensitivities of four wavelength channels for 10 Gb/s ES-PAM-4 and UES-PAM-4, (a) B2B transmission, and (b) 20 km SSMF transmission.
4. Conclusions
We experimentally demonstrate 4 × 10 Gb/s UES-PAM-4 downstream transmission for the low-cost coherent UDWDM-PON with a channel spacing of 25 GHz. By altering the PAM-4 level spacing and the decision threshold based on the GDA, −30.1 dBm RS is achieved for a single wavelength at the HD-FEC threshold. Compared with the conventional ES-PAM-4 signal after the 20-km SSMF transmission, 1.3 dB RS enhancement is secured. For 4 × 10 Gb/s PAM-4 signals under the 20-km SSMF transmisison, a power budget of 32.6 dB is achieved at an average RS of −29.6 dBm for four channels. The experimental results verify the UES-PAM-4 signaling for the UDWDM-PON, with advantages of RS enhancement, spectrum efficiency improvement, and the reuse of installed ODN.
Funding
National Key Research and Development Program of China (2018YFB1801301); National Natural Science Foundation of China (62025502).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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