[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81543-en":3,"doc-seo-81543-105":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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81543,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Signal Space-Transformed Expectation Propagation for Symbol Detection in ISI Channels","Iterative message passing detection based on expectation propagation (EP) delivers near-optimum performance in many communication scenarios, yet becomes unreliable for strong inter-symbol interference (ISI) when the initial linear minimum mean square error (LMMSE) estimate is inaccurate. An EP-based detector is introduced in a transformed signal space via linear channel shortening. Instead of alternating an LMMSE estimator and a symbol-wise demapper, the approach iterates between a channel-shortening-filter estimator and a reduced-memory trellis-based BCJR detector. A deliberate mismatch in initial messages and covariance accelerates convergence. Results for Proakis-C and measured wireless channels show up to 6 dB gain and better performance–complexity trade-off.","Signal Space-Transformed Expectation Propagation for Symbol Detection in ISI Channels  \nJannis Clausius∗ Luca Schmid† Laurent Schmalen† Stephan ten Brink∗  \n∗ Institute of Telecommunications, Pfaffenwaldring 47, University of Stuttgart, 70569 Stuttgart, Germany † Communications Engineering Lab, Karlsruhe Institute of Technology, 76187 Karlsruhe, Germany  \nEmail: [clausius@inue.uni-stuttgart.de](clausius@inue.uni-stuttgart.de)  \narXiv :2509 . 17735v 3 [ cs .IT] 10 Jul 2026  \nAbstract—Iterative message passing detection based on expectation propagation (EP) has demonstrated near-optimum performance in many signal processing and communication scenarios. The method remains feasible even for channel impulse responses (CIRs), where the optimal Bahl–Cocke–Jelinek–Raviv (BCJR) detector is infeasible. However, significant performance degradation occurs for channels with strong inter-symbol interference (ISI), where the initial linear minimum mean square error (LMMSE) estimate is inaccurate. We propose an EP-based detector that operates in a transformed signal space. Specifically, instead of the conventional approach that iterates between an LMMSE estimator and a non-linear symbol-wise demapper, the proposed method iterates between a linear channel shortening filter-based estimator and a non-linear BCJR detector with reduced memory compared to the actual channel. Additionally, we propose a deliberate mismatch between the initialized messages and the initialized covariance used in the linear estimator in the first iteration for faster convergence. The proposed approach is evaluated for the well-known Proakis-C ISI channel and for CIRs from a wireless measurement campaign. We demonstrate improvements of up to 6 dB at 2 bits per channel use and an improved performance-complexity trade-off over conventional EP-based detection.  \nIndex Terms—Symbol detection, expectation propagation, channel shortening, inter-symbol interference channels  \nI. INTRODUCTION  \nExpectation propagation (EP) is a general framework for approximate Bayesian inference [1] . The product of the likelihood and the prior is approximated with an exponential family distribution, usually a Gaussian, and iteratively refined. The adaptation of EP to the communication scenario over multiple-input multiple-output (MIMO) and inter-symbol interference (ISI) channels [2]–[4] can be interpreted as an iterative message passing algorithm between a linear minimum mean square error (LMMSE) estimator and a symbol-wise demapper. More generally, messages are exchanged between a linear estimator (LE) and a non-linear estimator (NLE) . In many cases, the true posterior can be closely approximated and near-optimal performance is achieved. Moreover, EP-based detection remains feasible for long channel impulse responses (CIRs) where the optimal Bahl–Cocke–Jelinek–Raviv (BCJR) detector [5] is infeasible due to computational complexity.  \nThis work is supported in part from the German Federal Ministry of Research, Technology and Space (BMFTR) within the project Open6GHub (16KISK019, 16KISK010), Open6GHubPlus/FKZ (16KIS2406, 16KIS2405) and in part from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (101001899) .  \nHowever, in the case of discrete priors and a poor initial estimate of the LE, EP may fail to well-approximate the true posterior. Consequently, improvements were proposed, e.g., carefully fine-tuning the hyperparameters [6]–[8], adding neural components [9], or passing messages based on a Gaussian mixture model [10] .  \nHere, we propose the application of EP in a transformed signal space obtained by linear channel shortening [11] . The transformation to this signal space enhances the initialization of the LE and the NLE, which now operate in the transformed space. The resulting transformed system model introduces memory, albeit less than the original channel. To account for the memory, the symbol-wise demapper is replaced b","cbCainmdN8p7EoOV","https://ap.wps.com/l/cbCainmdN8p7EoOV","pdf",373672,2,1,5,"English","en",105,"# Introduction\n# Preliminaries\n## System Model\n## BCJR Detector","[{\"question\":\"Why does expectation propagation detection degrade for channels with strong ISI?\",\"answer\":\"EP relies on approximating the true posterior, and strong ISI combined with an inaccurate initial LMMSE estimate can prevent the posterior from being well-approximated, leading to performance degradation.\"},{\"question\":\"How does the proposed detector differ from conventional EP-based detection?\",\"answer\":\"Conventional EP alternates between an LMMSE estimator and a symbol-wise demapper. The proposed method alternates between a linear estimator based on a channel-shortening filter and a non-linear trellis-based BCJR detector operating on a transformed reduced-memory model.\"},{\"question\":\"What mechanisms are used to improve convergence and control the performance–complexity trade-off?\",\"answer\":\"The method introduces a deliberate mismatch between initialized messages and initialized covariance in the first iteration to speed up convergence. It also uses hyperparameters controlling the transformed-model memory and the number of message passing iterations, enabling fine-granular tuning of performance versus complexity.\"}]",1784174186,13,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"signal-space-transformed-expectation-propagation-for-symbol-detection-in-isi-channels","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/signal-space-transformed-expectation-propagation-for-symbol-detection-in-isi-channels/81543/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does expectation propagation detection degrade for channels with strong ISI?","Question",{"text":75,"@type":76},"EP relies on approximating the true posterior, and strong ISI combined with an inaccurate initial LMMSE estimate can prevent the posterior from being well-approximated, leading to performance degradation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed detector differ from conventional EP-based detection?",{"text":80,"@type":76},"Conventional EP alternates between an LMMSE estimator and a symbol-wise demapper. The proposed method alternates between a linear estimator based on a channel-shortening filter and a non-linear trellis-based BCJR detector operating on a transformed reduced-memory model.",{"name":82,"@type":73,"acceptedAnswer":83},"What mechanisms are used to improve convergence and control the performance–complexity trade-off?",{"text":84,"@type":76},"The method introduces a deliberate mismatch between initialized messages and initialized covariance in the first iteration to speed up convergence. It also uses hyperparameters controlling the transformed-model memory and the number of message passing iterations, enabling fine-granular tuning of performance versus complexity.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,109,114,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":22,"slug":137},19,"General","general"]