[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84919-en":3,"doc-seo-84919-105":29,"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":13,"seo_description":14,"update_tm":27,"read_time":28},84919,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Constrained Capacity Analysis for Faster-than-Nyquist Signaling","This paper studies constrained-capacity performance of precoded faster-than-Nyquist (FTN) signaling under finite-alphabet inputs, addressing the unclear fundamental rate limit under practical modulation constraints. By adding cyclic prefix and cyclic suffix, the FTN channel is decomposed into parallel eigenchannels via the DFT matrix, enabling a constrained-capacity derivation. Findings show time acceleration increases spectral efficiency over Nyquist even with fixed modulation order. In low/moderate SNR, a smaller constellation with stronger acceleration can outperform a larger constellation with weaker acceleration. As acceleration approaches zero, constrained capacity is shown to be limited by constellation size, and channel mismatch is analyzed using a mismatched achievable information rate. Adaptive bit loading across eigenchannels further exploits higher-quality modes.","Constrained Capacity Analysis for Faster-than-Nyquist Signaling  \nZichao Zhang, Student Member, IEEE, Melda Yuksel, Senior Member, IEEE, Gokhan M. Guvensen, Member, IEEE, Halim Yanikomeroglu, Fellow, IEEE  \narXiv :2607 .06496v 1 [ cs .IT] 7 Jul 2026  \nAbstract—This paper studies the constrained-capacity for precoded faster-than-Nyquist (FTN) signaling with finite-alphabet inputs. Despite the promise of accelerated transmission, the fundamental rate limit of precoded FTN signaling under practical finite-alphabet constraints remains unclear. By introducing cyclic prefix (CP) and cyclic suffix (CS), the FTN channel is decomposed into a set of parallel eigenchannels by the discrete Fourier transform (DFT) matrix, based on which the constrained capacity is derived. The results demonstrate that time acceleration can improve spectral efficiency over Nyquist signaling even when a fixed modulation order is employed. Moreover, in the low and moderate signal-to-noise ratio (SNR) regimes, a smaller constellation combined with stronger time acceleration can outperform a larger constellation with weaker acceleration. Next, the asymptotic behavior of the constrained capacity is analyzed as the acceleration factor tends to zero under both fixed transmitSNR and fixed receive-SNR definitions. It is shown that the constrained capacity for DFT-precoded FTN is fundamentally limited by the constellation size. In addition, the constrained capacity under channel mismatch is studied and a mismatched achievable information rate (AIR) formulation is developed to show the effects of practical constraints on the performance degradation. Finally, adaptive bit loading across eigenchannels is investigated to exploit the higher-quality eigenchannels.  \nIndex Terms—Constrained capacity, faster-than-Nyquist, achievable information rate, channel mismatch, adaptive bit loading.  \nI. INTRODUCTION  \nThe rapid growth of modern communication demands is unprecedented. As the number of connected devices continues to increase, radio spectrum is becoming an increasingly scarce resource. Early vision documents for sixth-generation (6G) wireless systems describe future service requirements in terms of immersive communication, global broadband, omnipresent IoT, spatio-temporal services, critical services, and computeAI services [1] . These use cases imply a dramatic increase in traffic volume. Consequently, new transmission techniques with higher spectral efficiency are required so that limited spectrum resources can support substantially higher communication rates.  \nThis work was funded in part by the Scientific and Technological Research Council of Turkey, TUBITAK, under grant 122E248, and in part by a Discovery Grant awarded by the Natural Sciences and Engineering Research Council of Canada (NSERC) .  \nZ. Zhang and H. Yanikomeroglu are with the Department of Systems and Computer Engineering at Carleton University, Ottawa, ON, K1S 5B6, Canada e-mail: zichaozhang@cmail.carleton.ca, halim@sce.carleton.ca.  \nM. Yuksel and G. Guvensen are with the Department of Electrical and Electronics Engineering, Middle East Technical University, Ankara, 06800, Turkey, e-mail: ymelda, [guvensen@metu.edu.tr](guvensen@metu.edu.tr).  \nFaster-than-Nyquist (FTN) signaling has emerged as a promising technique for improving spectral efficiency by increasing the transmission rate without expanding the occupied bandwidth. Interest in FTN signaling can be traced back to Mazo’s seminal work [2], which showed that symbols can be transmitted faster than the Nyquist rate without compromising the error rate performance. Specifically, FTN increases the symbol rate by accelerating the symbol interval. If T denotes the Nyquist symbol interval, then FTN sends symbols every δT seconds, where δ ∈ (0 , 1] is the acceleration factor. A key advantage of FTN is that this rate increase is achieved without requiring additional bandwidth, since the pulse shape itself is unchanged and only the signaling rate is incr","cbCailY0ORCgsjeh","https://ap.wps.com/l/cbCailY0ORCgsjeh","pdf",1063662,1,13,"English","en",105,"# Introduction\n## Background and motivation\n# Constrained-capacity formulation\n## CP/CS based channel decomposition\n## DFT eigenchannel capacity derivation\n# Performance analysis\n## Spectral efficiency vs. Nyquist\n## Low/moderate SNR constellation tradeoffs\n## Asymptotic behavior as acceleration factor decreases\n# Practical considerations\n## Channel mismatch and mismatched AIR\n## Adaptive bit loading across eigenchannels","[{\"question\":\"How is the constrained capacity of DFT-precoded FTN signaling derived?\",\"answer\":\"The paper introduces cyclic prefix and cyclic suffix so the FTN channel can be decomposed into parallel eigenchannels using the DFT matrix. Constrained capacity is then derived based on this eigenchannel representation.\"},{\"question\":\"What effect does time acceleration have on spectral efficiency compared with Nyquist signaling?\",\"answer\":\"Time acceleration improves spectral efficiency over Nyquist signaling even when using a fixed modulation order, despite the presence of intentionally introduced intersymbol interference.\"},{\"question\":\"What fundamentally limits constrained capacity as the acceleration factor tends to zero?\",\"answer\":\"As the acceleration factor approaches zero under fixed transmit-SNR or fixed receive-SNR definitions, the constrained capacity for DFT-precoded FTN is fundamentally limited by the constellation size.\"}]",1784199342,33,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"constrained-capacity-analysis-for-faster-than-nyquist-signaling","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/constrained-capacity-analysis-for-faster-than-nyquist-signaling/84919/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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},"How is the constrained capacity of DFT-precoded FTN signaling derived?","Question",{"text":75,"@type":76},"The paper introduces cyclic prefix and cyclic suffix so the FTN channel can be decomposed into parallel eigenchannels using the DFT matrix. Constrained capacity is then derived based on this eigenchannel representation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What effect does time acceleration have on spectral efficiency compared with Nyquist signaling?",{"text":80,"@type":76},"Time acceleration improves spectral efficiency over Nyquist signaling even when using a fixed modulation order, despite the presence of intentionally introduced intersymbol interference.",{"name":82,"@type":73,"acceptedAnswer":83},"What fundamentally limits constrained capacity as the acceleration factor tends to zero?",{"text":84,"@type":76},"As the acceleration factor approaches zero under fixed transmit-SNR or fixed receive-SNR definitions, the constrained capacity for DFT-precoded FTN is fundamentally limited by the constellation size.","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":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]