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Abstract
With the increasing data rate requirements on short-reach links, the recent standardization of unamplified coherent optical systems is paving the way for a cost and power-effective solution, targeting a massive deployment in the near future. However, unamplified systems are introducing new challenges. Particularly, the performance is highly dependent on the peak-to-average power ratio (PAPR) of the transmitted signal, which puts at question the use of the typical constellation formats. In this work, we use an end-to-end deep learning framework to optimize the geometry of different constellation sizes, ranging from 8- to 128-ary constellations. In general, it is shown that the performance of these systems is maximized with constellations whose outer symbols are disposed in a square shape, owing to the minimization of the real-valued PAPR. Following this premise, we experimentally demonstrate that odd-bit constellations can be significantly optimized for unamplified coherent links, achieving power budget gains in the range of 0.5–3 dB through the geometric optimization of 8-, 32- and 128-ary constellations.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As we advance towards highly demanding networks, such as 6G, increasingly stringent requirements on short-reach links are being imposed, requiring higher data rates. Since the current use of conventional intensity modulation and direct detection (IM-DD) is unable to reach these requirements, coherent systems are now expanding from their typical long-haul deployment to short-reach, owing to their robustness and tunability. However, in order to allow massive coherent short-reach deployments, their power consumption and cost must be reduced. To this end, the 400ZR standardization takes into account link deployments in which no optical amplification is used [1]. These links allow for a decrease in both cost and power consumption, as optical amplifiers are typically the power-hungry Erbium-doped fiber amplifier (EDFA). Furthermore, the removal of such component leads to a decrease in total cost of ownership. Despite its recent standardization, unamplified coherent links still lack investigation. Particularly, the lack of amplification of the optical signal causes impairments that are being uncovered: the system becomes peak-power constrained (PPC) [2], and the peak-to-average power ratio (PAPR) becomes a significant performance-predicting metric, as we have recently shown [3–6]. Moreover, we have shown in [3,4,6] that the typical quadrature and amplitude modulation (QAM) schemes might be unfit for unamplified systems. To this end, geometric constellation shaping (GCS) can be used to provide an optimized solution to these systems.
The optimization of constellations through GCS has been used for a variety of applications and systems. It can be implemented through different methods, including a simulated annealing algorithm [7], the pairwise optimization algorithm [8], lattice-based GCS [9], or using gradient descent [10,11], with [11] focusing on PAPR reduction albeit in multiple fiber spans with hybrid amplification. Recent works make use of autoencoders (AE), which are based on the end-to-end deep learning of the entire optical system, including transmitter, communication channel and receiver [12–19]. Moreover, AE-based GCS has proven to be effective in optical communication systems. AE-based GCS has been implemented in IM-DD systems, improving the performance in a wide range of distances [15], and on amplified coherent communication systems to mitigate nonlinear effects [16], residual phase noise [18], or in an AWGN channel using initialized AEs [12,17] and using GCS together with probabilistic constellation shaping [19]. Recently, GCS has also been used on both amplified and unamplified coherent optical communication systems, improving the optical signal-to-noise ratio (OSNR) in high-order constellations, achieving a 0.55 dB OSNR gain with 128-QAM [14]. In the latter, although unamplified systems are analyzed, a systematic analysis of the implementation on a wide constellation order is still missing.
In this work, we evaluate the best constellation format for unamplified coherent links, for constellation sizes ranging from 8 to 128 symbols. To do so, we implement an autoencoder to optimize the geometry of the constellation for both average and peak power constrained links (APC and PPC, respectively). Furthermore, well-known formats will also be evaluated, such as square or cross QAM, and phase-shift keying (PSK). Following our preliminary results presented in [6], here we significantly extend our work, namely by discussing key concepts in unamplified systems, and by performing deeper comprehensive analysis of both simulated and experimental results.
This paper is organized as follows. After this introduction, transmitter-side concepts are presented in section 2, briefly discussing the standardized transmitter [20] as well as the impact of PAPR. Section 3 presents the implemented autoencoder and the used hyper-parameters. In section 4, we analyze the performance of several constellation formats in terms of PAPR, and simulated power budget. Section 5 presents the experimental validation. Finally, in section 6, we draw the main conclusions.
2. Transmitter-side concepts
In unamplified systems, the transmitter is a particularly important component, as any loss will directly impact the launched power, since it is not being compensated by the optical amplifier. In this section, we will give a brief overview on the optical modulator, and discuss the PAPR concept, as it is an important metric for these systems.
2.1 Optical modulator
A key component of the transmitter is the optical modulator that introduces modulation-induced power loss in the system; brief theoretical analysis can be found in [4]. Fig. 1(a) shows a diagram of a dual-polarization (DP) in-phase and quadrature modulator (IQM), in which the electrical sample $k$ of each polarization is identified as $I_{k,p}$ and $Q_{k,p}$, $p = \{x,y\}$, for in-phase and quadrature components, respectively. Note that the samples $I_{k,p}$ and $Q_{k,p}$ are normalized to the range $[-1,\,\,1]$, and are then electrically amplified before being fed to the modulator. The DP-IQM can also introduce severe nonlinearities, depending on its bias point. Its sinusoidal transfer function can be seen in Fig. 1(b) and its expression is given by [4, (7)]. From this figure, we see that it is best to choose a low enough modulation depth in order to define a close-to-linear operating point, while still guaranteeing a good dynamic range to improve the performance. In this work, we have chosen the linear operating point marked with a red triangle, at a modulation depth of 0.3. Nevertheless, the modulation depth could also be optimized for each modulation format, as we have demonstrated in [4] in a probabilistic-shaped unamplified system.
Fig. 1. (a) Transmitter diagram, for systems with or without optical amplification, following the OIF integrated coherent transmit-receive optical sub assembly (IC-TROSA) specifications [20]. (b) Simulated transfer function for the DP-IQM for a 64-QAM signal at 60 Gbaud, with the chosen operating point marked with a red triangle, and $V_\pi$ defining the switching voltage.
2.2 Impact of PAPR
As mentioned in Section 1, the peak-to-average power ratio (PAPR) is an important factor in unamplified systems [2,4–6]. Here, we present a brief theoretical introduction.
The PAPR of a signal is given by
where $S$ can represent either a real-valued or a complex signal, $E\left [.\right ]$ represents the expectation operator, and $|.|$ represents the absolute value. The complex-signal-based PAPR has been widely used in optical communication systems as a useful indicator of modulation-dependent nonlinear interference (NLI) noise, owing to the optical power dependence of Kerr nonlinearity. However, at the transceiver level, the performance should be assessed in terms of the real-valued in-phase (I) and quadrature (Q) components that are actually transmitted and received. Indeed, when no optical amplification is employed, the transmitted optical power will be ultimately constrained by the peak-to-average values of the I and Q components, and therefore the assessment of performance in unamplified links should be driven by the real-valued PAPR as,3. Implementing an end-to-end deep learning algorithm for geometric shaping
In order to optimize the constellation geometry, we have implemented a tensorflow-based symbol-wise autoencoder (AE) with an Adam optimizer, as shown in Fig. 2(a), as proposed in [21]. The AE is composed of two neural networks (NN), one at the encoder, and another at the decoder, an average power or absolute peak normalization layer, corresponding to APC and PPC, and Eqs. (3) and (4), respectively. An additive white Gaussian noise (AWGN) channel model is used to emulate our transmission link. This means that fiber nonlinearities are not taken into account, since there is no optical amplification and the launched power is low; furthermore, we are considering an ideal dispersion compensation at the receiver-side DSP. Note also that, in this work, the pulse shaping is not included in the end-to-end deep learning, since we are considering an optimized RRC solution as shown in [5].
Fig. 2. Autoencoder system. (a) Diagram of the applied autoencoder, showing the constellation output, $\mathrm {\textbf {C}}$, and the constraint for the system with or without optical amplification, APC and PPC, respectively. (b) Feeding the $M$-AE constellations to the coherent optical system.
The encoder NN has a one-hot-vector of size $M$ as input, followed by one rectified linear unit (ReLU)-activated layer and one linear-activated layer, outputting the in-phase, $I$, and quadrature, $Q$, components of the signal. At the decoder NN, another ReLU-activated layer follows the $I$ and $Q$ input. The final layer includes a softmax activation function, decoding the input back into symbols. The optimization is based on the categorical cross-entropy; i.e., symbol-wise cross-entropy, which is equivalent to optimizing through mutual information (MI) [22].
At the transmitter-side, two different operating modes will be considered: i) a standard optically-amplified coherent transceiver, in which the transmitted optical power is fixed regardless of the modulation-induced loss, thus imposing an APC condition in the system, and ii) an unamplified coherent transceiver, in which the optical power depends on the PAPR of the I/Q components of the transmitted signal, thus introducing a PPC condition in the system. In either case, we consider that the launched power into the fiber link will be sufficiently low to neglect the impact of fiber nonlinearities, so that the link can be emulated through the considered AWGN channel.
As shown in Fig. 2(b), for each $M$, we make $N$ runs of the AE. Because we are using a random noise sequence, albeit with a fixed noise variance, each run leads to different outputs. We store the constellation with the best accuracy, which is then sent to the simulated and experimental coherent optical systems. In this work, we are considering deployment scenarios in which the range of SNR values is small. However, in scenarios with a wider range, it could be beneficial to optimize the constellations for different SNR values (i.e., different noise variance) and switch constellations depending on the current state of the system.
We have trained the AE with a total of $2\times 10^6$ symbols for constellation sizes of $M = \{8,16,32,64,128\}$, for both APC and PPC channels, with $N$=50, and with the parameters identified in Table 1, in which we consider that the total number of symbols is divided into the indicated number of batches.
Table 1. Autoencoder hyper-parameters for each constellation type, $\mathrm {C_{type}}$, and corresponding loss measured as the categorical cross-entropy. Normalization layer for the average power and peak power constraints, where $S$ represents a complex signal vector and $S_{I/Q}$ represents each IQ component of the signal vector.
Note that the complexity of the NN is not the focus of this work since the optimization process is performed offline; however, in [17], an AE with no hidden layers at the transmitter-side is proposed.
4. Analyzing the constellations’ suitability for unamplified coherent systems
As mentioned in Section 3, we analyze constellations with $M = \{8,16,32,64,128\}$. We use AE-optimized constellations ($M$-AE), phase-shift-keying (PSK), and square and cross quadrature amplitude modulation (QAM) constellations. In this section, we will first briefly present our simulation setup and then evaluate the performance of each constellation through simulations.
4.1 Simulation setup
Figure 3 shows the block diagram of the simulated setup. At the transmitter, we define a symbol sequence of length $2^{17}$, for each constellation size, $M$, at a symbol rate of $R_s$ = 60 Gbaud. We then map each symbol into the different constellation geometries: QAM, PSK, AE-APC and AE-PPC. After this, we apply a root-raised cosine (RRC) pulse shaping, with a roll-off factor $\alpha =0.4$. Such roll-off factor has been demonstrated to provide a good trade-off between spectral efficiency and PAPR decrease in systems without stringent bandwidth requirements [5]. The in-phase and quadrature components are then upsampled by a factor of two, and independently normalized at the digital-to-analog converter (DAC). The DP-IQM is emulated by digitally attenuating the signal by 10 dB which is a value close to the optical insertion loss that we experimentally observed and it is also published in literature [23]. An ideal continuous-wave laser is introduced with a power of 15 dBm at 1550 nm wavelength.
The signal is then transmitted through the channel composed of a standard single mode fiber (SSMF). In unamplified coherent systems, the launched power is relatively low so that the nonlinear effects on the fiber are negligible. Because we are considering an ideally dispersion compensated unamplified system, the SSMF can be emulated by an attenuator.
At the receiver, we emulate the coherent receiver through additive white Gaussian noise (AWGN) with −24 dBm power to account for the receiver sensitivity. An analog-to-digital converter (ADC) downsamples by a factor of two. We employ an RRC matched filter, with the same roll-off, $\alpha =0.4$. The signal is then demapped and decoded.
The performance is analyzed at the symbol level, in terms of mutual information (MI) between transmitted and received symbols (after processing) [24]. In doing so, the focus of our analysis remains on the performance improvement brought by each geometry. Therefore, we are not taking into account the impact of bit labeling, since it is not being optimized here.
4.2 Defining the constellations
First, we start by defining the constellations as shown in Table 2. In this table, the first row presents the typical QAM constellations for each $M$. The second row is composed of PSK constellations, which are characterized by a constant modulus and therefore yield 0 dB complex-signal-based PAPR. Note that the inclusion of PSK constellations into the performance comparison picture serves the purpose of clearly identifying the different nature of complex-signal-based and real-signal-based PAPRs on the optimization of modulation formats for unamplified systems. The third and fourth rows are composed of AE-optimized constellations, with the method presented in Section 3. The third row is optimized for a system with optical amplification: we can see that this optimization led to a Gaussian-like geometry, which has been proven to be the best solution for these systems [14]. By introducing the peak-power constraint (PPC) inherent to unamplified systems, we achieved the constellations shown in the fourth row. First, for 8-AE-PPC, the solution converged to square-QAM [25], thus reducing the real-valued PAPR. Because the 16-AE-PPC constellation converged to the 16-QAM solution, the relationship between each constellation type (16-AE-PPC and 16-PSK, and 16-AE-PPC and 16-AE-APC) becomes a well-known paradigm; as such, we will not show further results. As we increase the constellation size, the higher number of points offers higher optimization freedom, which enables an outer-square point distribution to reduce the PAPR, and since the low amplitude of the inner symbols causes them to be more susceptible to the AWGN noise, we observe a Gaussian-like inner-point distribution.
Table 2. Input constellations for both simulated and experimental systems.
In a general conclusion, the $M$-AE-PPC optimization led to an outer-square/inner-Gaussian geometry, allowing both real-signal-based PAPR reduction and AWGN noise tolerance. With lower-order constellations, this resulted in well-known formats (i.e., square-QAM for 8-ary and 16-ary constellations).
4.3 Constellation PAPR
As we have identified, the PAPR is an important metric to predict the performance in unamplified systems. Table 2 shows each constellation associated with a PAPR value that is obtained as follows. The PAPR is registered using the Monte-Carlo method for 1000 collections of $2^{17}$ symbols. We then define the value of the PAPR so that more than 90% of the collections had a smaller value. This is shown with the cumulative distribution function presented in Fig. 4.
Fig. 4. Cumulative distribution functions (CDF) of the real-signal-based PAPR for (a) M = 8, (b) M = 32, (c) M = 64, (d) M = 128. The intersection points between the CDF curves and the 90% threshold are marked with a star.
Observing both Fig. 4 and Table 2, we see that, for an 8-ary constellation, the typical QAM deployment results in the highest PAPR value with 10.2 dB. Both 8-PSK and 8-AE-APC yielded lower PAPR than 8-QAM, decreasing the PAPR by 1.9 dB and 1.3 dB, respectively. The constellation with the lowest PAPR is the 8-AE-PPC, achieving a 7.1 dB PAPR and yielding a 3.1 dB decrease in PAPR when compared to star 8-QAM, and a 1.2 dB when compared to PSK.
With a 32-ary constellation, the highest PAPR is obtained for a 32-AE-APC constellation, as we increased the number of levels at each IQ component. The 32-AE-PPC constellation yielded a PAPR decrease of 0.7 dB when compared to the typical use of cross 32-QAM.
As we further increase the constellation size to $M$ = 64, AE-APC continues to be the geometry with the highest PAPR. From Table 2, we see that AE-PPC has a geometry close to that of QAM, which justifies the small PAPR decrease of 0.1 dB.
In the largest evaluated constellation size, $M$ = 128, the AE-PPC now yields a PAPR decrease of 0.5 dB, owing to the largely sub-optimal geometry of cross 128-QAM.
In general terms, it can be concluded that AE-optimized constellations for unamplified (PPC) systems tend to yield a geometry in which the outer symbols are organized in a square shape, which leads to the optimum balance between the minimization of PAPR and the maximization of Euclidean distance, for all constellation sizes. As a consequence, in cases for which the number of bits of the constellation size is even, the AE-based optimization shows little improvement over standard square QAM formats. Therefore, it can be concluded that square QAM formats are nearly optimal (or even strictly optimal, as in the case of 4- and 16-QAM) for unamplified systems. In contrast, for odd-bit constellations, we have observed a significant PAPR decrease in AE-based optimization over cross QAM formats. Thus, the geometry of odd-bit QAM constellations should be improved for unamplified systems, leading to a significant reduction of PAPR, even when compared with the respective AE-optimized constellations for amplified (APC) systems. For that reason, for the remaining of this paper we shall focus our attention on the optimization of the geometry of odd-bit constellation formats for unamplified optical links.
4.4 How PAPR impacts power gains
As previously discussed, in unamplified systems, the system performance is expected to increase as the PAPR decreases. Figure 5 shows the simulated power budget (i.e., supported link loss) for each $M$ and constellation type.
For the 8-ary constellations presented in Fig. 5(a), we see that 8-AE-PPC outperforms other geometries, exceeding the power budget of 8-QAM by 3 dB at a mutual information (MI) of 2.7 bits/symbol (i.e., power budget gain of 3 dB). Both 8-PSK and 8-AE-APC yield a somewhat similar performance; the 8-AE-PPC gain over these constellations is 2 dB and 1.6 dB, respectively, at a MI of 2.7 bits/symbol. Note that, as expected, these power budget gains are within the same range as the PAPR reduction observed in the previous section, since there is no optical amplification, and therefore a peak power reduction leads to a proportional increase in average power.
For 32-ary constellations, shown in Fig. 5(b), and contrary to what was observed for 8-ary constellations, PSK is now largely outperformed by all the other geometries, as the reduction of the Euclidean distance between points in the 32-PSK constellation becomes a significant impairment, cancelling out the PAPR decrease that was previously observed. Using the cross 32-QAM as a benchmark, we observe that the optimized 32-AE-PPC constellation enables a power budget gain of roughly 0.5 dB, which is in good agreement with the respective PAPR reduction observed in Fig. 4. It is also worth noting that the optimization of 32-ary constellations following an APC condition (i.e., assuming an optically-amplified system) actually leads to a performance penalty over the baseline cross 32-QAM. This clearly showcases the possible pitfalls of applying to unamplified systems the same traditional constellation design rules that have been inherited from traditional amplified links.
In the 64-ary constellations, in Fig. 5(c), the 64-QAM and 64-AE-PPC solutions achieve similar performance, despite their different geometry. However, this was an expected result, since the 64-AE-PPC PAPR reduction was only 0.1 dB when compared to 64-QAM. This provides further confirmation to our previous observation that square QAM is nearly optimal for unamplified links, and therefore it will not be subject of further studies in this work.
Further increasing the constellation size to $M$ = 128, as showed in Fig. 5(d), 128-AE-PPC now yields a power budget gain of 0.5 dB at an MI of 6.3 bits/symbol when compared to cross 128-QAM, which again matched quite well with the PAPR decrease.
Through these figures, we can also observe that the gain is dependent on the MI at which the performance is evaluated. For this reason, Fig. 6 shows the $M$-AE-PPC gain over QAM, PSK and $M$-AE-APC, evaluated at different values of threshold MI, $\mathrm {MI}_{th}$ and for $M = \{8,32,128\}$.
Fig. 6. Simulated power budget gain of $M$-AE-PPC over QAM, PSK and $M$-AE-APC, for (a) M = 8, (b) M = 32, (c) M = 128.
In Fig. 6(a), we see that 8-AE-PPC gain over 8-QAM exceeds 2.9 dB for all the $\mathrm {MI}_{th}$ values. The 8-AE-PPC gain over 8-PSK increases with $\mathrm {MI}_{th}$, since the performance requirements become more stringent, and the Euclidean distance between constellation points in the 8-PSK is smaller than that of 8-AE-PPC. The AE-PPC gain over AE-APC has an inversely-similar behavior, as AE-APC increased the Euclidean distance between points by avoiding the outer square shape imposed by AE-PPC.
Figure 6(b) shows the AE-PPC gain for $M$ = 32. From this figure, and as expected, the gain over PSK rapidly increases due to the short Euclidean distance. The gain over both AE-APC and QAM, however, is much more stable; for example, the gain over QAM is kept between 0.6 and 0.4 dB.
The AE-PPC gain over QAM in 128-ary constellations, shown in Fig. 6(c), is also kept fairly constant for a wide range of $\mathrm {MI}_{th}$ values, exceeding 0.4 dB of power budget gain. The AE-PPC gain over AE-APC, however, is constant for small $\mathrm {MI}_{th}$ values, increasing near the saturation MI, achieving up to 2.1 dB gain at a saturated MI, which would correspond to a practical system with very low FEC overhead. Note that the 128-AE-PPC gain over 128-PSK is too high to be represented here, but it can be computed from Fig. 5(d): for example, at an MI of 5 bits/symbol, the 128-AE-PPC power budget surpasses that of 128-PSK by 8 dB.
5. Experimental validation
In this section, we start by describing the experimental setup and then present experimentally-obtained results. We show results for 8, 32 and 128-ary constellations, as these have demonstrated a higher optimization potential. Note that, due to our laboratory and equipment limitations, the particular case of 128-ary constellations is here analyzed at a reduced baudrate of 30 Gbaud.
5.1 Experimental setup
A block diagram and photos of our experimental setup are depicted in Fig. 7. At the transmitter-side digital signal processing (DSP) block, the bits are generated, and mapped into one of the constellations of Table 2. A root-raised cosine (RRC) pulse shaping is applied, with a roll-off factor of $\alpha = 0.4$ [5]. The signal is sent to the 120 GSa/s arbitrary waveform generator (AWG) with 8-bit resolution. Four radio-frequency (RF) drivers then electrically amplify the signal by 23 dB and feed it to the DP-IQM which has a bandwidth of 35 GHz and is being fed by a tunable laser source (TLS) operating at 1554 nm and 13 dBm with 100 kHz linewidth. A variable optical attenuator (VOA) enables the power budget evaluation. At the receiver, a tunable laser source (TLS) local oscillator (LO) at 1554 nm with 100 kHz linewidth and 13 dBm feeds the coherent receiver that has a 40 GHz bandwidth. The signal is then digitized at 200 GSa/s by the four 70 GHz-bandwidth oscilloscopes. At the receiver-side data-aided DSP, we apply a Gram-Schmidt orthonormalization, followed by a constant modulus algorithm (CMA) equalizer. A first stage of carrier phase estimation (CPE) with 101 taps is used to aid in the convergence of the real-valued $4\times 4$ least mean squares (LMS) equalizer, and a final CPE stage with 51 taps mitigates any residual frequency offset. Because we are operating in an AWGN channel, the AE decision boundaries converged to a minimum Euclidean distance demapper, which is here implemented.
Fig. 7. Diagram of the experimental setup and optical spectra for 8-and 32-QAM constellations at 60 Gbaud, and 128-QAM at 30 Gbaud.
The optical spectra are evaluated at the output of the DP-IQM using an optical spectrum analyzer (OSA). In the inset of Fig. 7, we see that we have a 29 dB optical signal-to-noise ratio (OSNR) for both 8- and 32-QAM.
5.2 Performance evaluation
Table 3 shows the experimentally-received constellations in an optical back-to-back configuration, providing a qualitative performance evaluation of the system. We see that the symbols can be generally differentiated, except for 32-PSK and 128-PSK and 128-AE-APC due to their reduced symbol distance. Overall, we can also see from these constellations that the system is maintained at a linear region.
Table 3. Experimentally received constellations in optical back-to-back.
Figure 8 shows the power budget for different constellations. Particularly, for $M$ = 8, shown in Fig. 8(a), we confirm that 8-AE-PPC outperforms the other geometries, achieving a power budget gain of 2.6 dB and 2.1 dB relatively to cross 8-QAM and 8-PSK, respectively, at an MI of 2.7 bits/symbol. We achieve similar gains to what was observed in our simulations, in Fig. 5.
In 32-ary constellations, showed in Fig. 8(b), the 32-PSK performance is severely affected: we can only reach an MI of 3.5 bits/symbol at very low attenuation values, which was not observed in our simulated results. This is because our simulation was kept ideal, and impairments such as a finite effective number of bits (ENOB) were not included. In fact, we can see from Table 3 that, even in optical back-to-back (OB2B), we cannot easily distinguish between symbols. Nonetheless, the interplay between constellation types was maintained: 32-AE-PPC achieves the best performance, and 32-QAM outperforms 32-AE-APC. At an MI of 4 bits/symbol, 32-AE-PPC surpasses 32-QAM by 1 dB, and 32-AE-APC by 1.8 dB.
With $M$ = 128, shown in Fig. 8(c), the interplay observed in the simulations is not affected. The 128-PSK constellation reaches a maximum MI of 4.3 bits/symbol, and 128-AE-PPC and 128-QAM reach 5.8 bits/symbol and 5.6 bits/symbol, respectively. The 128-AE-PPC power budget gain over 128-QAM is 1.2 dB at an MI of 5.5 bit/symbol. Overall, the interplay between each constellation geometry is kept in these experimental power budgets, validating the simulated-achieved results.
Figure 9 shows the experimental power budget gain of AE-PPC over QAM, PSK and AE-APC, similarly to Fig. 6. For an 8-ary constellation, shown in Fig. 9(a), we see the same behavior as in Fig. 6(a). The 8-AE-PPC gain over 8-QAM is kept above 2.5 dB, reaching up to 3.5 dB at an MI of 2 bits/symbol, proving that the typical use of cross 8-QAM is indeed a largely sub-optimal geometry for unamplified systems. We validate the behavior observed in Fig. 6(a). Figure 9(b) shows the AE-PPC gain for 32-ary constellations. Compared to Fig. 6(b), the 32-AE-PPC gain over both QAM and AE-APC now increases with the MI: the increased symbol distance within the inner symbols benefited the performance of 32-AE-PPC. The 32-AE-PPC exceeds 0.5 dB power budget gain over 32-QAM, for all MI values, in accordance to the PAPR reduction and simulated power budget gain. Similarly, the 128-AE-PPC gain over both QAM and AE-APC, shown in Fig. 9(c), has increased in our experimental campaign when compared to the simulation, once again owing to the inner-symbol increased distance and Gaussian distribution, capable of tackling the AWGN channel. The 128-AE-PPC constellation surpasses the performance of 128-QAM by at least 0.9 dB in power budget, and achieving a 1.5 dB power budget gain at an MI of 5.3 bit/symbol.
Fig. 9. Experimental power budget gain of $M$-AE-PPC over QAM, PSK and $M$-AE-APC, for (a) M = 8, (b) M = 32, and (c) M = 128.
6. Conclusion
As a way of meeting the increasing data rate demands in the cost-stringent short-reach applications, unamplified coherent optical systems have been recently standardized. However, the removal of the optical amplifier brings new challenges. Particularly, these systems are severely affected by the signal’s peak-power, becoming peak-power constrained (PPC). In these conditions, the use of traditional constellation design rules can be sub-optimal.
In this paper, we have implemented an autoencoder-based geometry constellation shaping technique to address the specific impairments of these unamplified systems. We briefly discussed the PAPR measurement, highlighting the need for a real-valued measurement in order to provide a good estimator for performance outcomes in unamplified systems. We have presented the autoencoder implementation and hyper-parameters. The offline constellation optimization is then loaded into our transmitter-side digital signal processing block, which provides performance gains without increasing the system’s complexity. We have found that, as a general rule, the AE optimization process led to a square distribution of the outer symbols in order to reduce the PAPR, and a Gaussian-like distribution of the inner symbols to mitigate the impact of the AWGN channel. We have analyzed the AE-enabled PAPR reduction, which we have then shown to be converted into both simulated and experimental power budget gains.
We have demonstrated experimentally-achieved power budget gains of PPC over QAM exceeding 2.5 dB in a wide operation range, for the case of 8-ary constellations. In the particular case of 16-ary constellations, the AE solution converges to 16-QAM, due to the low optimization freedom inherent to the low inner-symbol density. This is not the case of 64-ary constellations: here, the AE optimization converged to the outer-square/inner-Gaussian symbol distribution. This is also the case for both 32- and 128-ary constellations, in which we exceeded 0.5 dB and 0.9 dB power budget gain over QAM, respectively.
We have also implemented an AE optimization tailored to an optically-amplified coherent system, which is regulated by an average power constraint (APC), to assess the performance of both AE-optimized PPC and APC constellations. As expected, the AE-APC constellations converged to a Gaussian-like distribution. The AE-PPC constellations have consistently surpassed the AE-APC performance, exceeding 1.1 dB, 0.4 dB and 1.9 dB for 8, 32 and 128-ary constellations, respectively. Furthermore, the QAM geometry generally outperforms AE-APC constellations, due to the inherently lower real-valued PAPR.
With this work, we have demonstrated how an autoencoder-optimized unamplified coherent system can be deployed, without affecting the system’s complexity and yielding power budget gains in the range of 0.5–3 dB, depending on the constellation size. This can enable a link reach increase of 2.5–15 km in an unamplified SSMF link.
As future work, the autoencoder could include the full DSP required for coherent systems. Recently, a step towards implementing the CPE has been made [26]. A smaller step would be to implement bit labeling to this approach, and pulse shaping could be implemented to tailor not only the roll-off but also the filter function itself. Furthermore, the impact of the nonlinearity of the optical modulator should also be analyzed. And finally, probabilistic constellation shaping could also be included in the autoencoder to achieve joint optimization of the constellation geometry and its probability mass function.
Funding
H2020 Marie Skłodowska-Curie Actions (10100828); Programa Operacional Regional do Centro (CENTRO-01-0145-FEDER-022141, POCI-01-0145-FEDER-031527); “la Caixa” Foundation (LCF/BQ/PR20/11770015); Fundação para a Ciência e a Tecnologia (SFRH/BD/143498/2019, UI/BD/151328/2021, UIDB/EEA/50008/2020).
Acknowledgments
This work was partially supported by FEDER, through the CENTRO 2020 programme, project ORCIP (CENTRO-01-0145-FEDER-022141), LANDMARK (POCI-01-0145-FEDER-031527), and MSCA RISE programme through project DIOR (grant agreement no.10100828), and FCT/MCTES through project FreeComm-B5G (UIDB/EEA/50008/2020), and PhD grants SFRH/BD/143498/2019 and UI/BD/151328/2021. Fernando P. Guiomar acknowledges a fellowship from “la Caixa” Foundation (ID 100010434), code LCF/BQ/PR20/11770015.
Disclosures
The authors declare no conflicts of interest.
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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