[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82241-en":3,"doc-seo-82241-105":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},82241,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Inter-Frame Channel Prediction for Zak-OTFS","Zak-Orthogonal Time Frequency Space (Zak-OTFS) modulation offers robustness to Doppler spread in high-mobility scenarios versus OFDM by enabling accurate estimation of a carrier’s channel response from another carrier within the same frame. This work addresses whether channel response can be predicted across frames, not just within a frame. The paper shows deterministic variation of effective DD-domain channel filter coefficients and subspace invariance across consecutive frames, enabling a deterministic ESPRIT-type method to forecast future and frequency-separated channels using training frames. ","Inter-frame Channel Prediction for Zak-OTFS  \nMuhammad Ubadah∗ and Saif Khan Mohammed∗†  \n∗Department of Electrical Engineering, Indian Institute of Technology Delhi, India  \n†Cohere Technologies Inc., San Jose, CA, USA  \narXiv :2607 .09184v1 [ ee ss . SP] 10 Jul 2026  \nAbstract—Zak-Orthogonal Time Frequency Space (OTFS) modulation is known to be robust to Doppler spread in high mobility scenarios when compared to Orthogonal Frequency Division Multiplexing (OFDM). This is due to the fact that the channel response to a Zak-OTFS carrier within a frame can be accurately estimated from the channel response to another carrier within the same frame. However, an important open problem and question is whether inter-frame channel prediction is possible with Zak-OTFS, i.e., is it possible to accurately predict the channel response to a Zak-OTFS carrier in a frame based on knowledge of the channel response to some Zak-OTFS carrier in another frame (i.e., not the same frame).  \nIn this paper we show that indeed inter-frame channel prediction is possible. We show that the effective DD domain channel filter coefficients vary in a deterministic manner as we move from current to future frames in time and frequency. We also show that the subspace spanned by channel filter coefficients of consecutive frames in time/frequency is invariant to discrete shiftsin time and frequency. We exploit the deterministic variation and subspace invariance to propose a novel deterministic ESPIRITtype method which uses the effective DD domain channel filter taps/coefficients estimated in training frames (i.e., current/past frames in time and frequency having both pilot and data carriers) to predict the effective DD domain channel filter for frames which are several tens of frames in future and several tens of frames away in frequency.  \nExhaustive numerical simulations for the Vehicular-A channel reveal that even for a high Doppler spread of 2 kHz, the normalized prediction error for a frame 120 ms into future and 432 MHz away is roughly −14 .2 dB when the pilot power to noise power ratio is 15 dB in the training frame. An application of the proposed prediction is to reduce the pilot overhead since the prediction frames (for which channel is predicted) do not need dedicated pilot. Simulation of coded Zak-OTFS frames reveal that for a Doppler spread of 2 kHz and total transmit power to noise power ratio of 15 dB, the effective spectral efficiency (SE) for a prediction frame 60 ms in future and 216 MHz away is infact 30 percent higher than the SE of traditional frames which have both pilot and data.  \nIndex Terms—Zak-OTFS, prediction, pilot, training.  \nI. INTRODUCTION  \nNext generation communication systems are expected to deploy Artificial Intelligence (AI) and Machine Learning (ML) to achieve significant improvements in network performance (spectral and energy efficiency, latency, reliability and scalability) [1], [2] . These improvements are achieved through integration of AI into the protocol stack thereby enabling smart resource allocation, predictive traffic management, dynamic beamforming, interference management, smart sensing [4],  \nM. Ubadah and S. K. Mohammed are with the Department of Electrical Engineering, Indian Institute of Technology Delhi, India (E-mail: [eez198356@ee.iitd.ac.in](eez198356@ee.iitd.ac.in), [saifkmohammed@gmail.com](saifkmohammed@gmail.com)). S. K. Mohammed is currently with Cohere Technologies Inc., CA, USA, on extra-ordinary leave from I.I.T. Delhi.  \n[5] . Wireless channels in 6G and beyond are expected to be highly time and frequency selective due to scenarios where the channel delay and Doppler spread can be high [3] . Some examples include, satellite based non-terrestrial networks, high speed train, Vehicle-to-everything communication,(V2X), Unmanned Aerial Vehicle (UAV) communication, High-AltitudePlatform-Stations (HAPS) communication, Aircraft to Ground communication.  \nFast time-and frequency domain variations of the com","cbCaibpb6lCBJfFj","https://ap.wps.com/l/cbCaibpb6lCBJfFj","pdf",2387714,1,15,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What problem does the paper address about Zak-OTFS channel estimation?\",\"answer\":\"It investigates whether inter-frame channel prediction is possible with Zak-OTFS, meaning predicting a carrier’s channel response in one frame using channel information from Zak-OTFS carriers in different frames rather than the same frame.\"},{\"question\":\"How does the proposed method enable inter-frame prediction?\",\"answer\":\"It leverages deterministic variation of effective DD-domain channel filter coefficients across time/frequency and invariance of the subspace spanned by coefficients for consecutive frames, enabling a deterministic ESPRIT-type prediction method from training frames.\"},{\"question\":\"What benefits are demonstrated for vehicular channels and coded frames?\",\"answer\":\"Numerical simulations show low normalized prediction error for channels far into the future and separated in frequency, and coded Zak-OTFS frames achieve higher effective spectral efficiency while reducing pilot overhead because prediction frames need no dedicated pilots.\"}]",1784179077,38,{"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},"inter-frame-channel-prediction-for-zak-otfs","",{"@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/inter-frame-channel-prediction-for-zak-otfs/82241/",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},"What problem does the paper address about Zak-OTFS channel estimation?","Question",{"text":75,"@type":76},"It investigates whether inter-frame channel prediction is possible with Zak-OTFS, meaning predicting a carrier’s channel response in one frame using channel information from Zak-OTFS carriers in different frames rather than the same frame.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method enable inter-frame prediction?",{"text":80,"@type":76},"It leverages deterministic variation of effective DD-domain channel filter coefficients across time/frequency and invariance of the subspace spanned by coefficients for consecutive frames, enabling a deterministic ESPRIT-type prediction method from training frames.",{"name":82,"@type":73,"acceptedAnswer":83},"What benefits are demonstrated for vehicular channels and coded frames?",{"text":84,"@type":76},"Numerical simulations show low normalized prediction error for channels far into the future and separated in frequency, and coded Zak-OTFS frames achieve higher effective spectral efficiency while reducing pilot overhead because prediction frames need no dedicated pilots.","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 & 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