[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83352-en":3,"doc-seo-83352-105":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},83352,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Multiuser Zak-OTFS on the Uplink with Superimposed Spread-Pilots","The paper studies the uplink of a multiuser Zak-OTFS system where users employ heterogeneous delay-Doppler periods and frame sizes. Users are separated in the time-frequency plane via time-frequency shifts, enabling closed-form effective delay-Doppler domain channel expressions for sinc and Gaussian pulse shaping filters. Inter-user interference is shown negligible under the shift-based access, decoupling estimation into independent single-user problems. A superimposed spread-pilot framework supports IOR estimation, using FFT-derived Zadoff–Chu spreading and a DD dictionary iterative scheme for robustness against pilot-data interference. Simulations confirm NMSE/BER close to single-user baselines and highlight spectral-efficiency tradeoffs.","Multiuser Zak-OTFS on the Uplink with Superimposed Spread-Pilots  \nSai Pradeep Muppaneni and Ananthanarayanan Chockalingam Department of ECE, Indian Institute of Science, Bangalore-560012  \narXiv :2607 .08247v 1 [ cs .IT] 9 Jul 2026  \nAbstract—In this paper, we consider the uplink of a multiuser Zak-OTFS system comprising users with heterogeneous delayDoppler (DD) periods/frame sizes. Multiple access is achieved through time-frequency (TF) shifts that place the users in nonoverlapping regions of the TF plane. Closed-form expressions for the effective DD domain channel between each user and the base station are derived for sinc and Gaussian pulse shaping filters. The inter-user interference (IUI) is shown to be negligible under the TF-shift-based multiple access, thereby decoupling the multiuser input-output relation (IOR) estimation problem into independent single-user estimation problems. For IOR estimation, a superimposed spread-pilot framework is employed. The spreadpilot sequence is obtained by applying FFT to a reshaped ZadoffChu sequence. To mitigate the pilot-data interference introduced by the superimposed spread-pilot, a DD dictionary-based IOR estimation scheme that iterates between IOR estimation and data detection is employed. Simulation results for a multiuser Zak-OTFS system demonstrate that the resulting IOR estimates achieve normalized mean-square error (NMSE) and bit error rate (BER) performances that closely match those of the corresponding single-user system. Furthermore, for sinc pulse shaping, the superimposed spread-pilot frame achieves higher spectralefficiency compared to embedded pilot frame across a wide range of inter-user power ratios. For Gaussian pulse shaping, however, the embedded pilot frame achieves a higher spectral efficiency due to the combined effects of residual IUI and significant pilot-data interference in the case of superimposed spread-pilot. The robustness of the estimation framework to variations in channel power-delay profile and maximum Doppler shift is also demonstrated.  \nIndex Terms—Zak-OTFS, multiuser uplink, delay-Doppler domain, superimposed spread-pilot, IOR estimation, spectral efficiency.  \nI. INTRODUCTION  \nNext-generation wireless communication networks are expected to support diverse and highly mobile scenarios, including non-terrestrial networks, high-speed train and vehicular communications, and aircraft-to-ground links. Such environments are characterized by channels with significant delay and Doppler spreads [1] . Orthogonal frequency division multiple access (OFDMA), which underpins current 4G and 5G systems, performs well in low/medium-mobility environments where the input-output relation (IOR) can beefficiently acquired. However, in high-mobility channels, the IOR in OFDMA becomes difficult to estimate and track. Acquiring the channel response across all subcarriers simultaneously is challenging in the presence of significant Doppler spreads (which is typical in high-mobility channels), resulting in increased pilot overhead and degraded performance [2] . Furthermore, OFDMA requires all users to operate with a  \ncommon subcarrier spacing. Consequently, the presence of a single high-mobility user necessitates a larger subcarrier spacing for all users, leading to increased cyclic-prefix (CP) overhead and reduced spectral efficiency [3] .  \nZak transform based OTFS modulation [4], [5], referred to as Zak-OTFS, offers a promising alternative. Unlike multicarrier OTFS (MC-OTFS) [6] - [14], which builds upon the existing OFDM-based framework, Zak-OTFS uses inverse Zak transform [15], [16] to directly convert information symbols embedded in the DD domain into a continuous time domain (TD) signal. In Zak-OTFS, information symbols are carried by quasi-periodic pulses in the DD domain, whose TD realizations are pulse trains modulated by tones, referred to as pulsones. The IOR of Zak-OTFS is predictable and nonfading when the delay period exceeds the delay spread of the effective chann","cbCaikUUrb0vDVVF","https://ap.wps.com/l/cbCaikUUrb0vDVVF","pdf",1066237,1,14,"English","en",105,"# Introduction\n## Motivation from high-mobility channels\n## Zak-OTFS modulation and crystallization\n## Prior work on IOR estimation and pilot designs","[{\"question\":\"How is multiuser access achieved in the uplink Zak-OTFS system?\",\"answer\":\"Multiuser access is implemented through time-frequency (TF) shifts that place users into nonoverlapping regions of the TF plane.\"},{\"question\":\"Why can inter-user interference be treated as negligible?\",\"answer\":\"With TF-shift-based multiple access, the inter-user interference is shown to be negligible, which decouples the multiuser input-output relation estimation into independent single-user estimation problems.\"},{\"question\":\"What is the role of the superimposed spread-pilot in IOR estimation?\",\"answer\":\"The superimposed spread-pilot is generated by applying FFT to a reshaped Zadoff–Chu sequence, and a DD dictionary-based iterative scheme alternates between IOR estimation and data detection to mitigate pilot-data interference.\"}]",1784186948,35,{"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},"multiuser-zak-otfs-on-the-uplink-with-superimposed-spread-pilots","",{"@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/multiuser-zak-otfs-on-the-uplink-with-superimposed-spread-pilots/83352/",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 multiuser access achieved in the uplink Zak-OTFS system?","Question",{"text":75,"@type":76},"Multiuser access is implemented through time-frequency (TF) shifts that place users into nonoverlapping regions of the TF plane.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why can inter-user interference be treated as negligible?",{"text":80,"@type":76},"With TF-shift-based multiple access, the inter-user interference is shown to be negligible, which decouples the multiuser input-output relation estimation into independent single-user estimation problems.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the role of the superimposed spread-pilot in IOR estimation?",{"text":84,"@type":76},"The superimposed spread-pilot is generated by applying FFT to a reshaped Zadoff–Chu sequence, and a DD dictionary-based iterative scheme alternates between IOR estimation and data detection to mitigate pilot-data 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