We propose an end-to-end learning-based approach for superchannel systems impaired by non-ideal hardware component. Our system achieves up to 60% SER reduction and up to 50% guard band reduction compared with the considered baseline scheme

Graell I Amat, Alexandre

H\ue4ger, Christian

Schr\uf6der, Jochen

Song, Jinxiang

Wymeersch, Henk

English

Chalmers Research

End-to-end Autoencoder for Superchannel Transceivers with HardwareImpairmentsDownloaded from: https://research.chalmers.se, 2022-10-11 19:56 UTCCitation for the original published paper (version of record):Song, J., Häger, C., Schröder, J. et al (2021). End-to-end Autoencoder for Superchannel Transceiverswith Hardware Impairments. Optical Fiber Communications Conference and Exhibition, OFC 2021 -ProceedingsN.B. When citing this work, cite the original published paper.research.chalmers.se offers the possibility of retrieving research publications produced at Chalmers University of Technology.It covers all kind of research output: articles, dissertations, conference papers, reports etc. since 2004.research.chalmers.se is administrated and maintained by Chalmers Library(article starts on next page)End-to-end Autoencoder for SuperchannelTransceivers with Hardware ImpairmentJinxiang Song(1), Christian Häger(1), Jochen Schröder(2),Alexandre Graell i Amat(1), and Henk Wymeersch(1)(1) Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden(2) Department of Microtechnology and Nanoscience, Chalmers University of Technology, Gothenburg, Swedenjinxiang@chalmers.seAbstract: We propose an end-to-end learning-based approach for superchannel systemsimpaired by non-ideal hardware component. Our system achieves up to 60% SER reductionand up to 50% guard band reduction compared with the considered baseline scheme.© 2022 The Author(s)1. IntroductionModern high spectral efficiency (SE) superchannel systems require dense channel spacing (close to the symbolrate) coupled with high-order modulation formats. The narrow channel spacing and high-order modulation for-mats, however, exacerbate performance degradation due to non-ideal hardware components [1, 2]. To compensatefor the hardware impairments, various digital pre-distortion (DPD) algorithms including arcsin [3, 4] and Volterraseries-based pre-compensation [5–8] have been proposed.As an alternative to these conventional approaches, deep learning (DL) techniques using neural networks (NNs)have recently been proposed for hardware impairment compensation in both wireless [9–12] and optical com-munications [13–17], where the main idea is to replace the DPD block with an NN that can be optimized fromdata. In contrast to focusing on a specific functional block (e.g., DPD), end-to-end learning using an autoencoder(AE) optimizes the transmitter and receiver jointly [18]. However, the methods in [9–17] are derived consideringa single-channel setup, thus ignoring inter-channel interference (ICI) with neighboring channels, which can yieldsignificant performance degradation in densely-spaced superchannel systems.In this paper, we propose a novel end-to-end AE for superchannel systems impaired by non-ideal hardwarecomponent, the nonlinear IQ-Modulator (IQM) in particular, that limits ICI. Simulation results show that ourmethod achieves significantly better symbol error rate (SER) performance than a conventional baseline scheme.Moreover, the proposed approach shows great potential to increase the SE of superchannel systems by reducingthe guard band with limited impact on the SER.2. System modelFig. 1 depicts the considered superchannel system. For each channel, messages belonging to the set M ={1, . . . , "} are mapped to constellation points belonging to the set X = {G1, . . . , G" }. The upsampled signals areconvolved with a pulse-shaping (PS) filter, after which a DPD algorithm is applied to pre-compensate for the IQMnonlinearity. The pre-compensated signal is then fed to the digital-to-analog converter (DAC) and amplified bya linear electrical power amplifier (PA) to drive the IQM. Similar to [3, 5, 6], we consider a back-to-back setup,where additive white Gaussian noise (AWGN) with constant power is added to simulate the noise introduced bythe booster amplifier. At the receiver, the received signals are passed through an analog-to-digital converter (ADC)and then convolved with a matched filter (MF). Finally, the downsampled signals are mapped to estimates of thetransmitted messages.3. AE-based superchannel systemIn principle, the entire transmitter and receiver can be implemented as an AE and optimized by end-to-end learn-ing as proposed in [18]. However, this will lead to i) a black-box solution that can be difficult to interpret andii) potentially high training complexity (a very complex transmitter NN with large memory may be required). Toaddress both issues, we follow a different approach where the transmitter NN is decomposed into a concatenationof simpler NNs, each corresponding to one functional block of a conventional communication system. By doingthis, an additional advantage is that the parameters of these NNs can be initialized such that they initially performTx-N· · ·Tx-2Tx-1Mapper ↑ pulse shaping DPD<: G: G̃: B:NN1 ↑ NN2 NN3<: G: G̃: B:DAClinearPAB̃:IQMMUX +=(C)DEMUXReceiverRx-N· · ·Rx-2Rx-1ADC MF ↓H:De-mapperNN4argmax@ :<̂:<̂:J (\1, \2, \3, \4)Fig. 1. Block diagram showing the end-to-end system model (↑: upsampling, ↓: downsampling). The top branch correspondsto the conventional baseline scheme and the bottom branch to the proposed AE learning-based scheme.close to their conventional counterparts. As a result, the proposed scheme has increased interpretability and de-creased training complexity as compared to a conventional AE. We note that a similar approach has recently beenapplied for nonlinear optical channels in [19], where the transmitter implementation includes a trainable symbolmapper and a trainable PS filter, and it has been show that a PS filter can be trained to compensate the chromaticdispersion and Kerr nonlinearity.3.1. Proposed trainable AEAs shown in the bottom branch of Fig. 1, the AE transmitter is implemented as a concatenation of three NNs.These NNs are denoted by 5\ 1 (·), 5\ 2 (·), 5\ 3 (·), where \1, \2, and \3 are the sets of trainable parameters, and aredefined as follows:• NN1 5\ 1 :M→Cmaps a given message <: ∈M to a constellation point according to G: = 5\ 1 (<: ), wherean average power constraint E{|G: |2} = 1 is enforced by a normalization layer [18].• NN2 5\ 2 : C# → C generates the pulse-shaped signal according to B: = \>2 G̃ : , where G̃ : = [G̃:−# , . . . , G̃: ]>is a sequence of # complex-valued input signals. Note that NN2 only has a single layer applying a linearactivation function, and can be interpreted as a standard finite impulse response filter.• NN3 5\ 3 : C→ C generates the pre-distorted signal according to B̃: = 5\ 3 (B′: ), where 5\ 3 (·) operates sep-arately on the in-phase and quadrature branches, and −1 ≤ <{B′:},={B′:} ≤ 1 is obtained by normalizingB: according to B′: = B:/max{max{|<{B}|},max|={B}|}}, where B is the pulse-shaped signal sequence and|<{B}| and |={B}| return the absolute value of the real and imaginary part of each element in B, respectively.At the receiver, NN4 5\ 4 : C→M maps the downsampled signal H: to an "–dimensional probability vectoraccording to @ : = 5\ 4 (H: ), where \4 is the set of trainable parameters. The transmitted message is estimatedaccording to <̂: = argmax< [@ : ]<, where [G]< returns the <-th element of G .3.2. Optimization procedureThe system is trained in an end-to-end manner by minimizing the cross-entropy loss defined byJCE (\1, \2, \3, \4) = E{log[ 5\ 4 (H: )]<: }, where the dependence of JCE (\1, \2, \3, \4) on \1, \2, \3 is implicitthrough the distribution of the downsampled signal H: , which is a function of the channel input 6( B̃: ), where6(·) denotes the transfer function of the DAC, PA and IQM, and B̃: is dependent on NNs 1–3 as can be seenin the bottom branch of Fig. 1. In practice, JCE can be approximated via Monte Carlo simulation according toĴCE (\1, \2, \3, \4) ≈ 1s∑s:=1 log[ 5\ 4 (H: )]<: , where s is the mini-batch size. For the optimization, in order tohave a faster and more stable convergence, the NNs are first initialized to mimic their model-based counterpartsvia pre-training. Then, the sets of parameters \1, \2, \3, \4 are jointly optimized using the Adam optimizer.4. ResultsWe set " = 64 and consider a 3-channel system where the guard band between the adjacent channels is [ 5b,where [ ≥ 0 and 5b is the symbol rate. The hardware impairment considered in this paper is restricted to theIQM nonlinearity, while it should be noted that the proposed approach can be straightforwardly applied to a moregeneral setup where the other transmitter components are not idealized. As in [3,4], we consider the IQM transferfunction out = sin (in c/2), where in is the driving signal with a peak voltage +p. At the receiver, the ADC isimplemented as a brick-wall filter (i.e., with 2 5b bandwidth) followed by a sampler with rate 2 5b, and the MF isfixed to a root-raised cosine (RRC) filter, which is also used for PS in the baseline. Furthermore, for the baseline,we use a geometrically-shaped constellation set obtained by training a standard AE [18] over the AWGN channelat SNR = 18dB, and apply the arcsin with clipping based DPD [3], according to B̃: = min{+clip,arcsin(B: )}, where+clip is referred to as the clipping factor and arcsin(·) operates separately on in-phase and quadrature branches, tocompensate the IQM nonlinearity. The system performance is evaluated by measuring the achieved SER.Impact of guard band [: We start by investigating a single-channel scenario. Fig. 2 (a) presents the SER of theproposed system when the receiver MF uses 10% roll-off. For a range of considered +p, the proposed approachachieves significantly better performance than the considered baseline. However, by looking at the frequencyresponse of the learned PS filter, as shown with the blue dashed curve in Fig. 2 (b), we observe that compared tothe RRC filter with 10% roll-off, the learned filter has a significant amount of out-of-band (OOB) energy, whichwill introduce significant ICI with narrowly-spaced neighbouring channels and make it unsuitable for superchannelsystems. In contrast, when training the proposed AE in a 3-channel system with [ = 0.05, Fig. 2 (b) shows that thelearned filter restricts the OOB energy and has a narrower frequency response than the RRC filter, indicating thatthe trainable filter learns to limit ICI.SER analysis: We now evaluate the performance of the proposed system setting the receiver MF roll-off factorto 10% and 1%. The achieved SER for the central channel is shown in Fig. 3. As a reference, the SER perfor-mance of the baseline scheme is also shown. We remark that the clipping factor +clip and +p are optimized for thebaseline scheme, while +p is set to 1 in the proposed scheme for simplicity. Potentially, the performance of the0.6 0.7 0.8 0.9 110−610−510−410−310−210−1+psymbolerrorrateW/o compensationBaselineAE(a)−2 −1 0 1 200.511.5Normalized frequency ( 5 / 5b)Frequencyresponse|(5)|RRC filterRRC adj. ch., [ = 0.05Learned filter, [ = 0.05Learned filter, single ch.(b)Fig. 2. (a): SER performance versus +p for the single channel scenario, the blue curve corresponds to the baseline setup butwithout applying DPD; (b): Frequency response of the learned filters when the receiver MF roll-off factor is set to 10%. Thefrequency response of the RRC filter with 10% roll-off is also shown as a reference.4 5 6 7 8 9 10·10−210−410−3[symbolerrorrateBaselineAE w/ fixed NN1, NN2, NN3AE w/ fixed NN1, NN3AE w/ fixed NN1AE(a)single channel4 5 6 7 8 9 10·10−310−3[BaselineAE w/ fixed NN1, NN2, NN3AE w/ fixed NN1, NN3AE w/ fixed NN1AE(b)single channelFig. 3. SER of the central channel of the proposed scheme and the baseline when the receiver MF roll-off factor set to (a)10% roll-off and (b) 1% roll-off. The blue dashed curve corresponds to the SER of the baseline for a single channel scenario.proposed scheme can be further improved by optimizing +p—the optimal performance for the single channel caseis achieved at +p = 0.9 (see Fig. 2 (a)). For roll-off factors of 10% (Fig. 3(a)) and 1% (Fig. 3(b)), the proposedapproach outperforms the baseline scheme over all considered guard bands. More importantly, compared to thebaseline scheme, the guard band for the proposed scheme can be significantly reduced with limited impact on theSER performance—for the target SER where the baseline performance starts to saturate, the guard band can bereduced by around 37% for 10% roll-off and around 50% for 1% roll-off.Ablation study: In order to quantify the origin of the performance gains, we carry out an ablation study by firstfreezing all the pre-trained NNs and individually unfreezing the NNs in the order of NN4, NN2, NN3, and NN1.Fig. 3 shows that the SER performance of proposed system improves every time one more NN is made trainable,indicating that the performance improvement of the proposed system can be attributed to the joint optimization ofthe mapper, the PS filter, the nonlinearity compensator (i.e., the DPD), and the de-mapper.5. ConclusionWe have proposed an approach for high SE superchannel systems using an AE, where the transmitter networkdesign follows the architecture of conventional systems. The resulting system achieves significantly better perfor-mance than the considered baseline scheme, and allows to increase the SE of superchannel systems by reducingthe channel spacing without SER performance degradation.Acknowledgements: This work was supported by the Knut and Alice Wallenberg Foundation, grant No. 2018.0090, and the Swedish ResearchCouncil under grant No. 2018-0370.References1. G. Bosco et al., “Investigation on the robustness of a nyquist-WDM terabit superchannel to transmitter and receiver non-idealities,” in Proc. ECOC, 2010.2. C. Liu et al., “Joint digital signal processing for superchannel coherent optical communication systems,” Optics Express, vol. 21, no. 7, pp. 8342–8356, 2013.3. V. Curri et al., “Optimization of DSP-based nyquist-WDM PM-16QAM transmitter,” in Proc. ECOC, 2012.4. Y. Tang et al., “Coherent optical OFDM transmitter design employing predistortion,” IEEE Photon. Technol. Lett., vol. 20, no. 11, pp. 954–956, 2008.5. G. Khanna et al., “A robust adaptive pre-distortion method for optical communication transmitters,” Photon. Technol. Lett., vol. 28, no. 7, pp. 752–755, 2015.6. P. W. Berenguer et al., “Nonlinear digital pre-distortion of transmitter components,” J. light. technol., vol. 34, no. 8, pp. 1739–1745, 2015.7. R. Elschner et al., “Improving achievable information rates of 64-GBd PDM-64QAM by nonlinear transmitter predistortion,” in Proc. OFC, 2018.8. Y. Yoffe et al., “Low-resolution digital pre-compensation enabled by digital resolution enhancer,” J. Light. Technol., vol. 37, no. 6, pp. 1543–1551, 2019.9. N. Benvenuto et al., “A neural network approach to data predistortion with memory in digital radio systems,” in Proc. ICC. IEEE, 1993, pp. 232–236.10. C. Tarver et al., “Design and implementation of a neural network based predistorter for enhanced mobile broadband,” in Proc. SiPS, 2019, pp. 296–301.11. T. Gotthans et al., “Digital predistortion with advance/delay neural network and comparison with volterra derived models,” in Proc. PIMRC, 2014, pp. 811–815.12. C. Tarver et al., “Neural network DPD via backpropagation through a neural network model of the pa,” in Proc. ACSSC. IEEE, 2019, pp. 358–362.13. G. Paryanti et al., “Recurrent neural network for pre-distortion of combined nonlinear optical transmitter impairments with memory,” in Proc. SPPCom, 2018.14. M. Schaedler et al., “AI-based digital predistortion for IQ mach-zehnder modulators,” in Proc. ACP, 2019.15. M. Abu-Romoh et al., “Neural-network-based pre-distortion method to compensate for low resolution DAC nonlinearity,” in Proc. ECOC, 2019.16. G. Paryanti et al., “A direct learning approach for neural network based pre-distortion for coherent nonlinear optical transmitter,” J. Light. Technol., 2020.17. V. Bajaj et al., “Single-channel 1.61 Tb/s optical coherent transmission enabled by neural network-based digital pre-distortion,” in Proc. ECOC, 2020.18. T. O’Shea et al., “An introduction to deep learning for the physical layer,” Trans. on Cogn. Commun. and Netw., vol. 3, no. 4, pp. 563–575, 2017.19. T. Uhlemann et al., “Deep-learning autoencoder for coherent and nonlinear optical communication,” in 21th ITG-Symposium on Photonic Networks, 2020.

End-to-end Autoencoder for Superchannel Transceivers with Hardware Impairments

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End-to-end Autoencoder for Superchannel Transceivers with Hardware Impairments

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