{"id":"https://openalex.org/W7164060054","doi":"https://doi.org/10.1109/ojcoms.2026.3701935","title":"Orthogonal Time Frequency Space Modulation: A Tutorial View on Delay-Doppler Communications via Zak Transform","display_name":"Orthogonal Time Frequency Space Modulation: A Tutorial View on Delay-Doppler Communications via Zak Transform","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7164060054","doi":"https://doi.org/10.1109/ojcoms.2026.3701935"},"language":"en","primary_location":{"id":"doi:10.1109/ojcoms.2026.3701935","is_oa":true,"landing_page_url":"https://doi.org/10.1109/ojcoms.2026.3701935","pdf_url":null,"source":{"id":"https://openalex.org/S4210202420","display_name":"IEEE Open Journal of the Communications Society","issn_l":"2644-125X","issn":["2644-125X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Open Journal of the Communications Society","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/ojcoms.2026.3701935","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138256053","display_name":"Shuangyang Li","orcid":"https://orcid.org/0000-0002-9503-4865"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Shuangyang Li","raw_affiliation_strings":["Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9503-4865","affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015245862","display_name":"Peter Jung","orcid":"https://orcid.org/0000-0001-7679-9697"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Jung","raw_affiliation_strings":["Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0001-7679-9697","affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138211860","display_name":"Weijie Yuan","orcid":"https://orcid.org/0000-0002-2158-0046"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weijie Yuan","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-2158-0046","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138256780","display_name":"Zhiqiang Wei","orcid":"https://orcid.org/0000-0003-3400-5590"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiqiang Wei","raw_affiliation_strings":["School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China"],"raw_orcid":"https://orcid.org/0000-0003-3400-5590","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138268362","display_name":"Jinhong Yuan","orcid":"https://orcid.org/0000-0002-5794-493X"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Jinhong Yuan","raw_affiliation_strings":["School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia"],"raw_orcid":"https://orcid.org/0000-0002-5794-493X","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063124926","display_name":"Baoming Bai","orcid":"https://orcid.org/0000-0002-6161-5493"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baoming Bai","raw_affiliation_strings":["State Key Laboratory of ISN, Xidian University, Xi&#x2019;an, China"],"raw_orcid":"https://orcid.org/0000-0002-6161-5493","affiliations":[{"raw_affiliation_string":"State Key Laboratory of ISN, Xidian University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5138264936","display_name":"Giuseppe Caire","orcid":"https://orcid.org/0000-0002-7749-1333"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Giuseppe Caire","raw_affiliation_strings":["Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7749-1333","affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1750,"currency":"USD","value_usd":1750},"apc_paid":{"value":1750,"currency":"USD","value_usd":1750},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.68263752,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":"6426","last_page":"6444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11873","display_name":"PAPR reduction in OFDM","score":0.12070000171661377,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11873","display_name":"PAPR reduction in OFDM","score":0.12070000171661377,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.10159999877214432,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10891","display_name":"Radar Systems and Signal Processing","score":0.09049999713897705,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.3962000012397766},{"id":"https://openalex.org/keywords/time\u2013frequency-analysis","display_name":"Time\u2013frequency analysis","score":0.3887999951839447},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.35519999265670776},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.2773999869823456}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.54830002784729},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4007999897003174},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C142433447","wikidata":"https://www.wikidata.org/wiki/Q7806653","display_name":"Time\u2013frequency analysis","level":3,"score":0.3887999951839447},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.35519999265670776},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.34950000047683716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3287000060081482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2815000116825104},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26829999685287476}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ojcoms.2026.3701935","is_oa":true,"landing_page_url":"https://doi.org/10.1109/ojcoms.2026.3701935","pdf_url":null,"source":{"id":"https://openalex.org/S4210202420","display_name":"IEEE Open Journal of the Communications Society","issn_l":"2644-125X","issn":["2644-125X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Open Journal of the Communications Society","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9fa2d79254de4c07952f6dc5d0caa312","is_oa":false,"landing_page_url":"https://doaj.org/article/9fa2d79254de4c07952f6dc5d0caa312","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Open Journal of the Communications Society, Vol 7, Pp 6426-6444 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/ojcoms.2026.3701935","is_oa":true,"landing_page_url":"https://doi.org/10.1109/ojcoms.2026.3701935","pdf_url":null,"source":{"id":"https://openalex.org/S4210202420","display_name":"IEEE Open Journal of the Communications Society","issn_l":"2644-125X","issn":["2644-125X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Open Journal of the Communications Society","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"recently":[1],"proposed":[2],"orthogonal":[3,152],"time":[4,76,113],"frequency":[5,78],"space":[6],"(OTFS)":[7],"modulation,":[8],"a":[9,98,144,177],"representative":[10],"delay-Doppler":[11],"(DD)":[12],"communication":[13],"scheme,":[14],"has":[15],"demonstrated":[16],"appealing":[17,206],"performance":[18,207],"over":[19,213],"doubly-selective":[20,214],"channels.":[21,215],"In":[22,142],"this":[23,173],"paper,":[24],"we":[25,88,175],"present":[26],"the":[27,34,37,55,91,103,120,124,161,167,186,205],"fundamentals":[28],"of":[29,36,106,123,127,163,208],"general":[30,182],"DD":[31,50,93,107,129,135,148,164,183,211],"communications":[32,130,149,165,212],"from":[33,166],"viewpoint":[35],"Zak":[38],"transform":[39],"and":[40,64,77,80,96,114,131,150,202],"explores":[41],"its":[42],"practical":[43,92,112,140,209],"implementation.We":[44],"start":[45],"our":[46,200],"study":[47,146],"by":[48,111],"constructing":[49],"basis":[51,108],"functions":[52,109],"aligning":[53],"with":[54,139],"time-frequency":[56],"(TF)-":[57],"consistency":[58],"condition,":[59],"which":[60,159],"are":[61],"globally":[62],"quasi-periodic":[63],"locally":[65],"twisted-shifted.":[66],"We":[67],"further":[68,203],"reveal":[69],"their":[70,82],"unique":[71],"signal":[72,168],"structures":[73],"in":[74],"both":[75],"domains":[79],"highlight":[81],"benefits":[83],"for":[84,101,181],"effective":[85],"communications.":[86],"Then,":[87],"focus":[89],"on":[90],"pulse":[94,178],"shaping":[95,179,192],"derive":[97],"concise":[99],"formula":[100],"calculating":[102],"ambiguity":[104,125],"function":[105,126],"constructed":[110],"bandlimited":[115],"filters.":[116,141],"This":[117],"analysis":[118],"reveals":[119],"distinct":[121],"properties":[122],"pulse-shaped":[128,210],"shows":[132],"that":[133],"sufficient":[134],"orthogonality":[136],"is":[137,156,194],"achievable":[138],"addition,":[143],"comparative":[145],"between":[147],"conventional":[151],"frequency-division":[153],"multiplexing":[154],"(OFDM)":[155],"also":[157],"presented,":[158],"demonstrates":[160],"superiority":[162],"processing":[169],"viewpoint.":[170],"Building":[171],"upon":[172],"insight,":[174],"establish":[176],"framework":[180],"communications,":[184],"where":[185],"corresponding":[187],"input-output":[188],"relation":[189],"under":[190],"various":[191],"pulses":[193],"derived.":[195],"Our":[196],"numerical":[197],"results":[198],"corroborate":[199],"derivations":[201],"validate":[204]},"counts_by_year":[],"updated_date":"2026-06-18T08:10:14.011955","created_date":"2026-06-10T00:00:00"}
