{"id":"https://openalex.org/W7123335150","doi":"https://doi.org/10.1109/access.2026.3651811","title":"Physics-Informed Deep Learning for 2-D Phased Array Beamforming With Imperfection Tolerance","display_name":"Physics-Informed Deep Learning for 2-D Phased Array Beamforming With Imperfection Tolerance","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7123335150","doi":"https://doi.org/10.1109/access.2026.3651811"},"language":null,"primary_location":{"id":"doi:10.1109/access.2026.3651811","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3651811","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","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/access.2026.3651811","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068617124","display_name":"Tarek Sallam","orcid":"https://orcid.org/0000-0003-3485-7988"},"institutions":[{"id":"https://openalex.org/I4210103733","display_name":"Shandong Xiehe University","ror":"https://ror.org/01bx4e159","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210103733"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tarek Sallam","raw_affiliation_strings":["School of Computer Science and Technology, Shandong Xiehe University, Jinan, Shandong, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Shandong Xiehe University, Jinan, Shandong, China","institution_ids":["https://openalex.org/I4210103733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077834762","display_name":"A. M. Attiya","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156128","display_name":"Electronics Research Institute","ror":"https://ror.org/0532wcf75","country_code":"EG","type":"facility","lineage":["https://openalex.org/I4210094263","https://openalex.org/I4210156128"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed M. Attiya","raw_affiliation_strings":["Microwave Engineering Department, Electronics Research Institute (ERI), Cairo, Egypt"],"affiliations":[{"raw_affiliation_string":"Microwave Engineering Department, Electronics Research Institute (ERI), Cairo, Egypt","institution_ids":["https://openalex.org/I4210156128"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068617124"],"corresponding_institution_ids":["https://openalex.org/I4210103733"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1487988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":null,"first_page":"7841","last_page":"7849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11946","display_name":"Antenna Design and Optimization","score":0.39640000462532043,"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"}},"topics":[{"id":"https://openalex.org/T11946","display_name":"Antenna Design and Optimization","score":0.39640000462532043,"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/T10860","display_name":"Speech and Audio Processing","score":0.18379999697208405,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.1624000072479248,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/beamforming","display_name":"Beamforming","score":0.8892999887466431},{"id":"https://openalex.org/keywords/phased-array","display_name":"Phased array","score":0.7335000038146973},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7329999804496765},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5667999982833862},{"id":"https://openalex.org/keywords/antenna-array","display_name":"Antenna array","score":0.5253999829292297},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.45910000801086426},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.4505999982357025},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.43709999322891235}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8892999887466431},{"id":"https://openalex.org/C55494473","wikidata":"https://www.wikidata.org/wiki/Q727898","display_name":"Phased array","level":3,"score":0.7335000038146973},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7329999804496765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7067000269889832},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5667999982833862},{"id":"https://openalex.org/C62191587","wikidata":"https://www.wikidata.org/wiki/Q4771249","display_name":"Antenna array","level":3,"score":0.5253999829292297},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.45910000801086426},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.45669999718666077},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.4505999982357025},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44600000977516174},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C143635782","wikidata":"https://www.wikidata.org/wiki/Q1187868","display_name":"Smart antenna","level":4,"score":0.4056999981403351},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.36880001425743103},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33390000462532043},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C33378366","wikidata":"https://www.wikidata.org/wiki/Q4680719","display_name":"Adaptive beamformer","level":3,"score":0.27649998664855957}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/access.2026.3651811","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3651811","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/access.2026.3651811","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2026.3651811","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1892947258","https://openalex.org/W1989000345","https://openalex.org/W2001434454","https://openalex.org/W2109974986","https://openalex.org/W2121415284","https://openalex.org/W2166181226","https://openalex.org/W2182236020","https://openalex.org/W2346498921","https://openalex.org/W2497191323","https://openalex.org/W2608333666","https://openalex.org/W2809254203","https://openalex.org/W2897361856","https://openalex.org/W2899283552","https://openalex.org/W2900440316","https://openalex.org/W3011009558","https://openalex.org/W3182453992","https://openalex.org/W3200673624","https://openalex.org/W3202714406","https://openalex.org/W3213136017","https://openalex.org/W4226457169","https://openalex.org/W4309717547","https://openalex.org/W4316013522","https://openalex.org/W4327740189","https://openalex.org/W4366245904","https://openalex.org/W4367315342","https://openalex.org/W4381662810","https://openalex.org/W4393115925","https://openalex.org/W4395661779","https://openalex.org/W4399601245","https://openalex.org/W4400028688","https://openalex.org/W4403295160","https://openalex.org/W4407199456","https://openalex.org/W4410295030"],"related_works":[],"abstract_inverted_index":{"Designing":[0],"efficient":[1],"and":[2,65,97,154],"reliable":[3],"two-dimensional":[4],"(2D)":[5],"beamforming":[6,29,71],"for":[7],"phased":[8],"array":[9,63,152],"antennas":[10],"(PAAs)":[11],"remains":[12],"a":[13,28,33,51,66,101,110,124],"significant":[14],"challenge":[15],"because":[16],"of":[17,134],"the":[18,47,57,62,75,81,89,113,119,132,142],"heavy":[19],"computational":[20,160],"demands":[21],"involved.":[22],"In":[23],"this":[24,156],"study,":[25],"we":[26],"introduce":[27],"framework":[30],"that":[31,141],"adopts":[32],"physics-informed":[34],"deep":[35],"neural":[36,107,115],"network":[37,108,116],"(PIDNN).":[38],"The":[39,70],"proposed":[40],"model":[41],"incorporates":[42],"physical":[43],"principles":[44],"directly":[45],"into":[46],"training":[48],"process":[49],"through":[50],"customized":[52],"loss":[53],"function,":[54],"which":[55],"minimizes":[56],"mean":[58],"squared":[59],"error":[60],"between":[61],"response":[64],"target":[67],"reference":[68],"signal.":[69],"weights":[72,147],"produced":[73],"by":[74],"PIDNN":[76,120,143],"are":[77],"systematically":[78],"evaluated":[79,98],"against":[80,99],"theoretically":[82],"optimal":[83],"Wiener":[84],"solution.":[85],"To":[86],"assess":[87,128],"robustness,":[88],"method":[90],"is":[91,121],"implemented":[92],"on":[93],"an":[94],"8\u00d78":[95],"PAA":[96,126],"both":[100],"shallow":[102],"architecture\u2014the":[103],"radial":[104],"basis":[105],"function":[106],"(RBFNN)\u2014and":[109],"deeper":[111],"model,":[112],"convolutional":[114],"(CNN).":[117],"Moreover,":[118],"applied":[122],"to":[123,127,151],"large":[125],"its":[129],"performance":[130],"when":[131],"number":[133],"antenna":[135],"elements":[136],"increases.":[137],"Experimental":[138],"results":[139],"demonstrate":[140],"closely":[144],"approximates":[145],"Wiener-optimal":[146],"while":[148],"maintaining":[149],"robustness":[150],"imperfections":[153],"achieving":[155],"with":[157],"markedly":[158],"reduced":[159],"cost.":[161]},"counts_by_year":[],"updated_date":"2026-01-20T17:24:06.736184","created_date":"2026-01-14T00:00:00"}
