[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119697-en":3,"doc-seo-119697-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119697,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",6,"Technology","FPGA Implementation of Multi-Layer Machine Learning Equalizer with On-Chip Training","Design and implement an adaptive machine-learning equalizer on an FPGA by alternating multiple trainable linear layers with fixed nonlinear Kerr layers. On-chip training is realized through gradient backpropagation, enabling real-time adaptation to time-varying channel impairments in optical fiber links. The model follows a split-step solution of the (inverse) Manakov-PMD equation and uses supervised stochastic gradient descent with mean-squared-error loss on pilot symbols. Numerical chain-rule gradients support backpropagation within the same hardware for continuous adaptation.","FPGA Implementation of Multi-Layer Machine Learning Equalizer with On-Chip Training  \nDownloaded from: [https://research.chalmers.se](https://research.chalmers.se), 2023-09-08 04:45 UTC  \nCitation for the original published paper (version of record):  \nLiu, K., Börjeson, E., Häger, C. et al (2023) . FPGA Implementation of Multi-Layer Machine Learning Equalizer with On-Chip Training. 2023 Optical Fiber Communications Conference and Exhibition, OFC 2023-Proceedings. [http://dx.doi.org/10.23919/OFC49934.2023.10116856](http://dx.doi.org/10.23919/OFC49934.2023.10116856)  \nN. B. When citing this work, cite the original published paper.  \nresearch.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.  \nresearch.chalmers.se is administrated and maintained by Chalmers Library  \n(article starts on next page)  \nFPGA Implementation of Multi-Layer Machine Learning Equalizer with On-Chip Training  \nKeren Liu(1), Erik Brjeson(1), Christian Hger(2), and Per Larsson-Edefors(1)  \n(1) Department of Computer Science and Engineering, Chalmers University of Technology, Gothenburg, Sweden  \n(2) Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden [christian.haeger@chalmers.se](christian.haeger@chalmers.se), [perla@chalmers.se](perla@chalmers.se)  \nAbstract: We design and implement an adaptive machine learning equalizer that alternates multiple linear and nonlinear computational layers on an FPGA. On-chip training via gradient backpropagation is shown to allow for real-time adaptation to time-varying channel impairments. © 2023 The Author(s)  \n1. Introduction  \nOptical fiber channels suffer from both linear and nonlinear impairments that severely affect the transmission performance. Moreover, environmental changes due to temperature or mechanical strains can lead to time-varying effects which require adaptive equalization. Adaptive equalizers are indeed commonplace in optical receivers [1, 2], typically implemented via gradient-descent-based least-mean squares filtering [3] . For example, in coherent systems such equalizers can track the inverse Jones matrix of the channel and may also correct for additional distortions such as residual chromatic dispersion [4] . However, the underlying equalizer structure is linear, which limits the type of functionalities that can be expressed and therefore also the performance that can be achieved.  \nTo overcome the limitations of linear equalizers, a wide variety of machine learning (ML) algorithms have recently been proposed and verified in hardware (HW) . For example, field-programmable gate array (FPGA) implementations of various neural network equalizers were demonstrated for IM/DD links [5], passive optical networks [6], optical interconnects [7], and coherent systems [8] . Moreover, application-specific integrated circuit (ASIC) design of a model-based ML equalizer [9, 10] was studied in [11] . However, all of the previous works in [5–8, 11] consider static nonlinear equalization, i.e., the training is performed offline and only the inference stage is implemented in HW. By contrast, in this paper we implement both the inference and training stage of a model-based ML equalizer on the same FPGA, which allows the equalizer to adapt to time-varying channel impairments. To the best of our knowledge, this is the first paper that studies HW implementation of on-chip gradient backpropagation [12] for nonlinear equalizers. Note that an adaptive equalizer based on unsupervised 􀀠-means clustering was implemented on an FPGA in [13] . However, the corresponding training stage is different (and less complex) compared to the gradient-based training of neural networks.  \n2. Machine Learning Equalizer Model  \nFollowing [14], our ML equalizer is based on the split-step solution of the (inverse) Manakov-PMD equation. T","cbCaintfDh7QuLca","https://ap.wps.com/l/cbCaintfDh7QuLca","pdf",1309933,1,4,"English","en",105,"# Introduction\n# Machine Learning Equalizer Model\n# Hardware (HW) Implementation","[{\"question\":\"What problem does the FPGA-based multi-layer equalizer address?\",\"answer\":\"Optical fiber channels experience linear and nonlinear impairments that can vary over time due to environmental effects, requiring adaptive equalization for improved receiver performance.\"},{\"question\":\"How does the equalizer adapt online on the FPGA?\",\"answer\":\"It performs on-chip training using gradient backpropagation, combining forward propagation for inference with reversed data flow for computing gradients and updating trainable parameters.\"},{\"question\":\"What is the ML equalizer model based on?\",\"answer\":\"The equalizer is based on a split-step solution of the (inverse) Manakov-PMD equation, using alternating trainable linear MIMO-FIR steps and fixed nonlinear Kerr steps, followed by a 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problem does the FPGA-based multi-layer equalizer address?","Question",{"text":75,"@type":76},"Optical fiber channels experience linear and nonlinear impairments that can vary over time due to environmental effects, requiring adaptive equalization for improved receiver performance.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the equalizer adapt online on the FPGA?",{"text":80,"@type":76},"It performs on-chip training using gradient backpropagation, combining forward propagation for inference with reversed data flow for computing gradients and updating trainable parameters.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the ML equalizer model based on?",{"text":84,"@type":76},"The equalizer is based on a split-step solution of the (inverse) Manakov-PMD equation, using alternating trainable linear MIMO-FIR steps and fixed nonlinear Kerr steps, followed by a matched 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