We experimentally model a VCSEL-based optical
transmitter for high speed intra data center interconnects using
a convolutional neural network digital twin. The device is able to
effectively reproduce the VCSEL linear and nonlinear distortions
on PAM4 signals transmitted at 107.2 Gbps, thus enabling the
optimization of nonlinear VCSEL-MMF digital pre-distorters

Forghieri, Fabrizio

Gaudino, Roberto

Minelli, Leonardo

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

17 October 2023POLITECNICO DI TORINORepository ISTITUZIONALEExperimental VCSEL Digital Twin modeling for net 100 Gb/s/ nonlinear Digital Pre-Distortion / Minelli, Leonardo;Forghieri, Fabrizio; Gaudino, Roberto. - ELETTRONICO. - (2023). (Intervento presentato al convegno Conference onNUmerical Simulation of Optoelectronic Devices (NUSOD) tenutosi a Torino nel 18-21 Settembre 2023).OriginalExperimental VCSEL Digital Twin modeling fornet 100 Gb/s/ nonlinear Digital Pre-DistortionPublisher:PublishedDOI:Terms of use:Publisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2982378 since: 2023-09-21T13:21:59ZIEEEExperimental VCSEL Digital Twin modeling fornet 100 Gb/s/λ nonlinear Digital Pre-DistortionLeonardo MinelliDipartimento di Elettronica e TelecomunicazioniPolitecnico di TorinoTorino, Italyleonardo.minelli@polito.itFabrizio ForghieriCISCO PhotonicsVimercate, ItalyRoberto GaudinoDipartimento di Elettronica e TelecomunicazioniPolitecnico di TorinoTorino, ItalyAbstract—We experimentally model a VCSEL-based opticaltransmitter for high speed intra data center interconnects usinga convolutional neural network digital twin. The device is able toeffectively reproduce the VCSEL linear and nonlinear distortionson PAM4 signals transmitted at 107.2 Gbps, thus enabling theoptimization of nonlinear VCSEL-MMF digital pre-distorters.Index Terms—VCSEL, Neural Networks, Digital Pre-Distortion, Data Center Intra-connectsI. INTRODUCTIONToday’s prevailing solution for short-reach optical intra-DataCenter Inter-Connects (DCI) consists of Intensity-ModulationDirect-Detection (IM-DD) optical links. Specifically, for DCIup to 100 meters, Multi-Mode Fibers (MMF) and Vertical-Cavity Surface-Emitting Lasers (VCSEL) are utilized. As thenext generation of VCSEL-MMF DCI is expected to providea net 100 Gb/s rate per wavelength (λ), these links willdeploy quaternary pulse amplitude modulation (PAM4), usingDigital Signal Processing (DSP) at the transmitter (TX) andthe receiver (RX) side to support the signal reliability [1].The use of nonlinear Digital Pre-Distorters (DPD) has recentlybeen investigated to compensate for bandwidth limitations andnonlinear VCSEL distortions at such high data rates. Figure1 shows the experimental eye-diagrams when transmittinga PAM4 signal at 107.2 Gbps through an 850 nm VCSELwith 22 GHz bandwidth. Without applying DPD (Fig.1.a), theVCSEL exp. setupDigital Twinlossfunction(c)(a) (b)PAM4 nonlinearDPD(d)Fig. 1: Experimental PAM4 107.2 Gbps VCSEL output eye-diagrams (a)without applying DPD; (b) using linear DPD; (c) using nonlinear DPD. (d)DLA scheme for VCSEL DPD optimization.PAM4 eye is fully closed at the VCSEL output, while applyinglinear DPD can compensate for the bandwidth limitations, asshown in Fig.1.b, only nonlinear DPD (Figure 1.c) is alsoable to remove the asymmetric time-domain eye-skew causedby the VCSEL typical nonlinear behaviors (see red dashedline in Fig.1.b). However, nonlinear DPDs for VCSEL-MMFlinks require sophisticated optimization techniques, such asthe Direct Learning Architecture (DLA) [2], [3]. The latterconstists of a convolutional neural network (CNN) made bythe cascade of the DPD and a digital twin of the VCSEL-based TX, and trained by updating only the DPD coefficients.Figure 1.d shows a the baseline schematics of the DLA-based optimization. Alternative approaches, such as End-to-end (E2E) learning, have been also applied for VCSEL-MMF links [4], [5]. However, both DLA and E2E approachesrequires a digital twin of the TX experimental setup as a key“building block” for optimizing the nonlinear DPD. In thispaper, we obtain this surrogate model from an experimentalVCSEL-MMF TX setup: we train a CNN on the input-outputresponse of a VCSEL-based TX, enabling the optimization ofnonlinear DPDs for net 100 Gbps/λ rate [2].II. DIGITAL TWIN OPTIMIZATION METHODOLOGYWe experimentally model using a CNN the back-to-backVCSEL setup shown in Figure 2. It consists of a 107.2 GSa/sArbitrary Waveform Generator (AWG), driving with 500mVpp an 850 nm probed VCSEL (B3dB=22 GHz), suppliedby 8 mA of DC current. The emitted optical waveforms arethen collimated into 2 meters of MMF, to get then received bya Digital Communication Analyzer: this comprises a PhotoDi-ode (PD), an Electrical Amplifier (EA) and a Digital SamplingOscilloscope (DSO). The CNN is built using a transposed1D convolution layer, followed by ReLU activation functionsalternated to 1D convolution layers. Each hidden convolutionlayer has 30 channels [2], and kernel sizes are designed toget a CNN with a memory equivalent to a Finite ImpulseResponse (FIR) filter with 150 taps. The CNN is trained topredict the output signal y obtained from the experimentalsetup (see Figure 2), given the same input TX signal x.During the training, the TX signal x is a linearly pre-distortedPRBS PAM4 signal at 53.6 GBaud, with periodicity of 216symbols: this allows to model the digital twin in a VCSELdriving condition close to the actual nonlinear DPD signaltransmission. Before optimizing the digital twin, the signaly is processed by the DCA to mitigate the noise impairment,i.e. averaging the RX signal over the PRBS period. It isthen resampled to a 10 samples-per-symbol ratio, to then bealigned with the TX sequence and normalized to zero meanand unitary variance. The training consists of an iterativeprocedure where the CNN predicts the experimental output ŷ :probefibercollimator MMF (2 m)resamplingnormalizationseq. alignmentDCsupplyAWGPAM4 Digital Pre-Distorter2-sps rect. shapingLossPD EADSODCAVCSELConv1dT Conv1dReLU Conv1dReLU Conv1dReLUConvolutional Neural Network Digital TwinBack-to-back VCSEL experimental setupFig. 2: Experimental modeling of a back-to-back VCSEL setup using a Convolutional Neural Network Digital Twin. Conv1d⊤: Transpose 1D convolutionlayer; Conv1d: 1D convolution layerthe Mean Square Error (MSE) between ŷ and y is computed,and the CNN coefficients are updated based on their MSEgradient [2]. This process is performed on a random mini-batch of 1000 symbols of y and repeated for 700 iterations.With the provided methodology, the obtained digital twineffectively models the deterministic response of the VCSELwhen transmitting pre-distorted PAM4 signals at the target107.2 Gbps rate, disregarding random noise impairments: theseare instead efficiently introduced semi-analytically during theDPD optimization as an additive regularization term in the lossfunction [4].III. EXPERIMENTAL RESULTSAfter the optimization of the digital twin, we evaluatethe goodness of the fit with the experimental setup, using adifferent experimental acquisition to prevent overfitting. Thetest TX signal x is a nonlinearly pre-distorted PAM4 signalat 53.6 GBaud, generated from a PRBS different from thetraining one, with periodicity of 216: this also allows toassess the digital twin reliability in the target optimal VCSELdriving condition (i.e., as in Figure1.c). To evaluate also theimprovements induced by the nonlinear model, we compare itsfit performance with a linear FIR filter digital twin, with thesame memory of the CNN. The predicted output eyediagramsfor the two surrogate models are shown in Figures 3.a and 3.b.Noticeably, the FIR filter digital twin shows an inverse time-(a) (b)(c)Fig. 3: Simulated VCSEL output (a) eye-diagram using FIR digital twin; (b)eye-diagram using CNN digital twin. (c) Time-domain comparison betweensimulated and actual VCSEL outputdomain eye-skew (see magenta-dashed line in Fig.3.a): thisis due to the inability of the FIR to synthesize the VCSELnonlinear effect, thus mantaining the pre-compensated skewinduced by the nonlinear DPD. The CNN digital twin isinstead able to fully reproduce the VCSEL behavior. Figure 3.cthen compares the two digital twins predictions with the actualexperimental output: the CNN digital twin clearly shows tobetter fit the real signal than the FIR filter. In order to quantifythe model accuracies, we report in Table I the normalized rootMSE (NRMSE) between ŷ and y both in dB and in terms offit percentage, expressed as follows:fitness (%) = 100 ·(1− ||y − ŷ||||y − E[y]||)(1)TABLE I:Digital Twin Architecture NRMSEfitness (%)NRMSE[db]Linear FIR filter 88.9 % -19.1 dBConvolutional Neural Network 93.7 % -24.0 dBAs shown in the Table, the CNN shows to accuratelymodel the VCSEL TX, with a NRMSE equal to -24 dB. Italso significantly outperforms the FIR digital twin, with again of 4.9 dB in terms of NRMSE and a 4.8 % of fitnessimprovement.IV. CONCLUSIONIn this paper, we experimentally demonstrate a CNN able toreliably emulate the VCSEL linear and nonlinear distortionson PAM4 signals at 107.2 Gbps. The effective optimizationdefinitively enables a reliable nonlinear DPD optimization forVCSEL-MMF optical links.ACKNOWLEDGEMENTSThis work was carried out under a research contract with Cisco Pho-tonics. We also acknowledge the PhotoNext Center at Politecnico di Torino(http://www.photonext.polito.it/) and Cisco Optical GmbH at Nuremberg.REFERENCES[1] “IEEE Standard for Ethernet - Amendment 3: Physical Layer Specifi-cations and Management Parameters for 100 Gb/s, 200 Gb/s, and 400Gb/s Operation over Optical Fiber using 100 Gb/s Signaling,” in IEEEStd 802.3db-2022, pp.1-73, 2022.[2] L. Minelli, F. Forghieri, T. Shao, A. Shahpari and R. Gaudino, “Net 100Gb/s/λ VCSEL+MMF nonlinear Digital Pre-Distortion using Convolu-tional Neural Networks,” 2023 Optical Fiber Communications Confer-ence and Exhibition (OFC), San Diego, CA, USA, 2023, pp. 1-3[3] G. Paryanti, H. Faig, L. Rokach and D. Sadot, “A Direct Learning Ap-proach for Neural Network Based Pre-Distortion for Coherent NonlinearOptical Transmitter,” in Journal of Lightwave Technology, vol. 38, no.15, pp. 3883-3896, 2020[4] L. Minelli, F. Forghieri, A. Nespola, S. Straullu and R. Gaudino, “AMulti-Rate Approach for Nonlinear Pre-Distortion Using End-to-EndDeep Learning in IM-DD Systems” in Journal of Lightwave Technology,vol. 41, no. 2, pp. 420-431, 2023[5] L. Minelli, F. Forghieri and R. Gaudino, “Nonlinear Pre-distortionthrough a Multi-rate End-to-end Learning Approach over VCSEL-MMF IM-DD Optical Links,” 2022 European Conference on OpticalCommunication (ECOC), Basel, Switzerland, 2022, pp. 1-4.

Experimental VCSEL Digital Twin modeling for
net 100 Gb/s/λ nonlinear Digital Pre-Distortion

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Experimental VCSEL Digital Twin modeling for net 100 Gb/s/λ nonlinear Digital Pre-Distortion

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