{"id":"https://openalex.org/W4285209104","doi":"https://doi.org/10.1109/twc.2022.3177840","title":"Stochastic Augmented Projected Gradient Methods for the Large-Scale Precoding Matrix Indicator Selection Problem","display_name":"Stochastic Augmented Projected Gradient Methods for the Large-Scale Precoding Matrix Indicator Selection Problem","publication_year":2022,"publication_date":"2022-06-02","ids":{"openalex":"https://openalex.org/W4285209104","doi":"https://doi.org/10.1109/twc.2022.3177840"},"language":"en","primary_location":{"id":"doi:10.1109/twc.2022.3177840","is_oa":false,"landing_page_url":"https://doi.org/10.1109/twc.2022.3177840","pdf_url":null,"source":{"id":"https://openalex.org/S63459445","display_name":"IEEE Transactions on Wireless Communications","issn_l":"1536-1276","issn":["1536-1276","1558-2248"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Wireless Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043426218","display_name":"Jiaqi Zhang","orcid":"https://orcid.org/0000-0001-9039-6843"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jiaqi Zhang","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0001-9039-6843","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100702047","display_name":"Zeyu Jin","orcid":"https://orcid.org/0009-0000-4436-3661"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeyu Jin","raw_affiliation_strings":["School of Mathematical Sciences, Peking University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036799223","display_name":"Bo Jiang","orcid":"https://orcid.org/0000-0001-8232-4604"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Jiang","raw_affiliation_strings":["Key Laboratory for NSLSCS of Jiangsu Province, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-8232-4604","affiliations":[{"raw_affiliation_string":"Key Laboratory for NSLSCS of Jiangsu Province, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006127137","display_name":"Zaiwen Wen","orcid":"https://orcid.org/0000-0003-1762-0671"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zaiwen Wen","raw_affiliation_strings":["Beijing International Center for Mathematical Research, College of Engineering and International Center for Machine Learning Research, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1762-0671","affiliations":[{"raw_affiliation_string":"Beijing International Center for Mathematical Research, College of Engineering and International Center for Machine Learning Research, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043426218"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.1847,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47311033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"21","issue":"11","first_page":"9553","last_page":"9565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9997000098228455,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9997000098228455,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9991999864578247,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/codebook","display_name":"Codebook","score":0.7308143973350525},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.6648114919662476},{"id":"https://openalex.org/keywords/precoding","display_name":"Precoding","score":0.6278016567230225},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6035505533218384},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.595445454120636},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.5551137924194336},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.53276127576828},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.483837753534317},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4798511862754822},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4446377754211426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3727954924106598},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.2646355628967285},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.2022978961467743},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1320682168006897},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07160526514053345}],"concepts":[{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.7308143973350525},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.6648114919662476},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.6278016567230225},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6035505533218384},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.595445454120636},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5551137924194336},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.53276127576828},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.483837753534317},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4798511862754822},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4446377754211426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3727954924106598},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2646355628967285},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.2022978961467743},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1320682168006897},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07160526514053345},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/twc.2022.3177840","is_oa":false,"landing_page_url":"https://doi.org/10.1109/twc.2022.3177840","pdf_url":null,"source":{"id":"https://openalex.org/S63459445","display_name":"IEEE Transactions on Wireless Communications","issn_l":"1536-1276","issn":["1536-1276","1558-2248"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Wireless Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1266523790","display_name":null,"funder_award_id":"11971239","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2030148605","display_name":null,"funder_award_id":"11831002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W114517082","https://openalex.org/W631930523","https://openalex.org/W1511345785","https://openalex.org/W1540764732","https://openalex.org/W1955857676","https://openalex.org/W1984919799","https://openalex.org/W1992591817","https://openalex.org/W2027982384","https://openalex.org/W2076605490","https://openalex.org/W2086953401","https://openalex.org/W2106371135","https://openalex.org/W2107244732","https://openalex.org/W2113593828","https://openalex.org/W2115573600","https://openalex.org/W2132687600","https://openalex.org/W2135029798","https://openalex.org/W2139688603","https://openalex.org/W2139861339","https://openalex.org/W2141461755","https://openalex.org/W2161515500","https://openalex.org/W2167137033","https://openalex.org/W2170569478","https://openalex.org/W2382345871","https://openalex.org/W2601638968","https://openalex.org/W2623630685","https://openalex.org/W2781153464","https://openalex.org/W2901838001","https://openalex.org/W2952235905","https://openalex.org/W2962823402","https://openalex.org/W2963648037","https://openalex.org/W2963704853","https://openalex.org/W2963742264","https://openalex.org/W2965036497","https://openalex.org/W3083845595","https://openalex.org/W3166932924","https://openalex.org/W3168793198","https://openalex.org/W3189345586","https://openalex.org/W6677288282","https://openalex.org/W6680012447","https://openalex.org/W6782767316","https://openalex.org/W6796375350"],"related_works":["https://openalex.org/W2767901536","https://openalex.org/W2939857954","https://openalex.org/W3034758333","https://openalex.org/W2766681470","https://openalex.org/W4310002330","https://openalex.org/W4285209104","https://openalex.org/W4315488731","https://openalex.org/W4288388741","https://openalex.org/W2532768910","https://openalex.org/W2948716505"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,78],"consider":[4],"the":[5,14,24,28,38,64,71,74,96,110,134],"large-scale":[6],"precoding":[7],"matrix":[8,30,40],"indicator":[9],"(PMI)":[10],"selection":[11,20],"problem":[12,75],"at":[13,106],"receiver":[15],"in":[16,31,43,70,99],"wireless":[17],"communications.":[18],"The":[19,35,67],"is":[21,41,113],"based":[22],"on":[23],"channel":[25],"capacity":[26],"of":[27,37],"PMI":[29,39,128],"a":[32,55,80],"pre-designed":[33],"codebook.":[34],"quality":[36],"essential":[42],"achieving":[44],"higher":[45],"spectral":[46],"efficiency.":[47],"We":[48,93],"first":[49],"derive":[50],"two":[51],"novel":[52],"formulations":[53,72],"including":[54],"partial":[56],"permutation-matrix":[57],"model":[58,62],"and":[59,102],"an":[60],"indicator-vector":[61],"for":[63],"original":[65],"problem.":[66],"discrete":[68],"constraints":[69],"make":[73],"NP-hard.":[76],"Then":[77],"propose":[79],"stochastic":[81],"projected":[82],"gradient":[83],"method":[84],"augmented":[85],"by":[86],"block":[87],"coordinate":[88],"descent":[89,105],"under":[90],"various":[91],"strategies.":[92],"show":[94],"that":[95,119],"algorithms":[97,122],"terminate":[98],"finite":[100],"steps":[101],"produce":[103],"sufficient":[104],"each":[107],"iteration":[108],"when":[109],"step":[111],"size":[112],"chosen":[114],"properly.":[115],"Extensive":[116],"experiments":[117],"demonstrate":[118],"our":[120],"proposed":[121],"are":[123],"able":[124],"to":[125,133],"find":[126],"better":[127],"matrices":[129],"more":[130],"efficiently":[131],"compared":[132],"existing":[135],"methods.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}