{"id":"https://openalex.org/W7161281505","doi":"https://doi.org/10.48550/arxiv.2605.14451","title":"CP-OFDM Achieves Lower Ranging CRB Than Frequency-Spread Waveforms in the Large-Sample Regime","display_name":"CP-OFDM Achieves Lower Ranging CRB Than Frequency-Spread Waveforms in the Large-Sample Regime","publication_year":2026,"publication_date":"2026-05-14","ids":{"openalex":"https://openalex.org/W7161281505","doi":"https://doi.org/10.48550/arxiv.2605.14451"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.14451","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.14451","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.14451","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136220818","display_name":"Fan Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Fan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136240714","display_name":"Yifeng Xiong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiong, Yifeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136229488","display_name":"Ya-Feng Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ya-Feng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136220974","display_name":"Jie Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Jie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136206402","display_name":"Christos Masouros","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masouros, Christos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136237748","display_name":"Shi Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Shi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.33500000834465027,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.33500000834465027,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.27790001034736633,"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"}},{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.2198999971151352,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ranging","display_name":"Ranging","score":0.7458000183105469},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5839999914169312},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48559999465942383},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.4796999990940094},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.45509999990463257},{"id":"https://openalex.org/keywords/demodulation","display_name":"Demodulation","score":0.3801000118255615},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.3610999882221222},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.36070001125335693},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.3578000068664551},{"id":"https://openalex.org/keywords/quadrature-amplitude-modulation","display_name":"Quadrature amplitude modulation","score":0.35199999809265137}],"concepts":[{"id":"https://openalex.org/C115051666","wikidata":"https://www.wikidata.org/wiki/Q6522493","display_name":"Ranging","level":2,"score":0.7458000183105469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.61080002784729},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5839999914169312},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49129998683929443},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48559999465942383},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.45509999990463257},{"id":"https://openalex.org/C195251586","wikidata":"https://www.wikidata.org/wiki/Q1185939","display_name":"Demodulation","level":3,"score":0.3801000118255615},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3610999882221222},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.36070001125335693},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.3578000068664551},{"id":"https://openalex.org/C32409245","wikidata":"https://www.wikidata.org/wiki/Q749753","display_name":"Quadrature amplitude modulation","level":4,"score":0.35199999809265137},{"id":"https://openalex.org/C40409654","wikidata":"https://www.wikidata.org/wiki/Q375889","display_name":"Orthogonal frequency-division multiplexing","level":3,"score":0.33079999685287476},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.3102000057697296},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C129997835","wikidata":"https://www.wikidata.org/wiki/Q806263","display_name":"Bandlimiting","level":3,"score":0.2944999933242798},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29190000891685486},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.28450000286102295},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.2703999876976013},{"id":"https://openalex.org/C59030546","wikidata":"https://www.wikidata.org/wiki/Q7265371","display_name":"QAM","level":5,"score":0.2694999873638153},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C31243852","wikidata":"https://www.wikidata.org/wiki/Q1666739","display_name":"Stochastic geometry","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.14451","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.14451","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.14451","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.14451","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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":[0,210],"inherent":[1],"randomness":[2,37],"of":[3,82,97,144,154,200],"communication":[4,30],"symbols":[5,156],"creates":[6],"a":[7,49,79,115,162,216],"fundamental":[8],"tension":[9],"in":[10],"Integrated":[11],"Sensing":[12],"and":[13,134,148,189,222,249],"Communications":[14],"(ISAC).":[15],"On":[16,32],"the":[17,33,58,62,83,94,98,102,109,121,145,152,172,176,197,201,207],"one":[18],"hand,":[19,35],"they":[20],"enable":[21],"data":[22,71,110],"transmission":[23],"while":[24],"allowing":[25],"sensing":[26,44,68],"to":[27,186],"fully":[28],"reuse":[29],"resources.":[31],"other":[34],"their":[36],"induces":[38],"waveform-dependent":[39],"fluctuations":[40],"that":[41,213,241],"directly":[42],"affect":[43,61],"accuracy.":[45],"This":[46,112,181],"paper":[47],"investigates":[48],"foundational":[50],"question":[51,76],"arising":[52],"from":[53,101],"this":[54,75],"tradeoff:":[55],"\\textit{How":[56],"does":[57],"modulation":[59],"waveform":[60,170],"ranging":[63,164],"Cram\u00e9r--Rao":[64],"Bound":[65],"(CRB)":[66],"when":[67,151],"reuses":[69],"random":[70,103,177],"symbols?}":[72],"We":[73,194],"address":[74],"by":[77,108,127],"revealing":[78],"structural":[80],"factorization":[81],"Fisher":[84],"information":[85],"matrix":[86],"(FIM)":[87],"for":[88,219,229],"joint":[89,191],"delay-amplitude":[90,192],"estimation,":[91],"which":[92,123],"separates":[93],"deterministic":[95],"Jacobian":[96],"target":[99],"geometry":[100,199],"frequency-domain":[104],"signal":[105],"power":[106],"induced":[107],"symbols.":[111],"structure":[113],"yields":[114],"Jensen-type":[116],"universal":[117],"lower":[118,163],"bound":[119],"on":[120],"CRB,":[122],"is":[124,179,183,215,226],"exactly":[125],"attained":[126],"CP-OFDM":[128,160,214],"under":[129],"PSK":[130],"constellations.":[131],"For":[132],"QAM":[133],"broader":[135],"sub-Gaussian":[136],"constellations,":[137],"we":[138],"develop":[139],"an":[140],"asymptotic":[141,235],"perturbation":[142],"analysis":[143,211],"inverse":[146],"FIM":[147,178],"prove":[149],"that,":[150],"number":[153],"transmitted":[155],"$N$":[157],"grows":[158],"large,":[159],"achieves":[161],"CRB":[165,203],"than":[166],"any":[167],"frequency-spread":[168],"orthogonal":[169],"over":[171,206],"almost-sure":[173],"event":[174],"where":[175],"invertible.":[180],"superiority":[182],"further":[184],"extended":[185],"amplitude":[187],"estimation":[188],"full":[190],"estimation.":[193],"also":[195],"characterize":[196],"local":[198,236],"stochastic":[202],"minimization":[204],"problem":[205],"unitary":[208],"group.":[209],"reveals":[212],"stationary":[217],"point":[218],"finite":[220],"$N$,":[221,232],"its":[223,234],"Riemannian":[224],"Hessian":[225],"positive":[227],"semidefinite":[228],"sufficiently":[230],"large":[231],"establishing":[233],"optimality.":[237],"Numerical":[238],"results":[239],"confirm":[240],"OFDM":[242],"outperforms":[243],"representative":[244],"waveforms":[245],"including":[246],"SC,":[247],"OTFS,":[248],"AFDM.":[250]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-16T00:00:00"}
