{"id":"https://openalex.org/W2913486660","doi":"https://doi.org/10.1109/tcomm.2019.2899866","title":"Rate Region of the ZF Precoder in a $2\\times2$ Multiuser Optical IM/DD Channel","display_name":"Rate Region of the ZF Precoder in a $2\\times2$ Multiuser Optical IM/DD Channel","publication_year":2019,"publication_date":"2019-02-15","ids":{"openalex":"https://openalex.org/W2913486660","doi":"https://doi.org/10.1109/tcomm.2019.2899866","mag":"2913486660"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2019.2899866","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2019.2899866","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on 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/A5100634165","display_name":"Amit Agarwal","orcid":"https://orcid.org/0000-0002-1259-6839"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Amit Agarwal","raw_affiliation_strings":["Department of Electrical Engineering, IIT Delhi, New Delhi, India"],"raw_orcid":"https://orcid.org/0000-0002-1259-6839","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, IIT Delhi, New Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070481781","display_name":"Saif Khan Mohammed","orcid":"https://orcid.org/0000-0003-3822-2138"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Saif Khan Mohammed","raw_affiliation_strings":["Bharti School of Telecommunication Technology and Management, IIT Delhi, New Delhi, India"],"raw_orcid":"https://orcid.org/0000-0003-3822-2138","affiliations":[{"raw_affiliation_string":"Bharti School of Telecommunication Technology and Management, IIT Delhi, New Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I68891433"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.00814965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"6","first_page":"3936","last_page":"3953"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10851","display_name":"Optical Wireless Communication Technologies","score":1.0,"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/T10851","display_name":"Optical Wireless Communication Technologies","score":1.0,"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/T10767","display_name":"Advanced Photonic Communication Systems","score":0.9980999827384949,"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/T11429","display_name":"Semiconductor Lasers and Optical Devices","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6648270487785339},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5768450498580933},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5469640493392944},{"id":"https://openalex.org/keywords/optical-wireless","display_name":"Optical wireless","score":0.5041555166244507},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5030481219291687},{"id":"https://openalex.org/keywords/optical-power","display_name":"Optical power","score":0.463566392660141},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.43340855836868286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42664024233818054},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4117940068244934},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3939470648765564},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.3669160008430481},{"id":"https://openalex.org/keywords/laser","display_name":"Laser","score":0.31266751885414124},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2798667550086975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27932044863700867},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.21181923151016235},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.19806143641471863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1752455234527588},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.10363739728927612},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09858480095863342},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06796640157699585}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6648270487785339},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5768450498580933},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5469640493392944},{"id":"https://openalex.org/C2781305180","wikidata":"https://www.wikidata.org/wiki/Q7098907","display_name":"Optical wireless","level":3,"score":0.5041555166244507},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5030481219291687},{"id":"https://openalex.org/C191161701","wikidata":"https://www.wikidata.org/wiki/Q559265","display_name":"Optical power","level":3,"score":0.463566392660141},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.43340855836868286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42664024233818054},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4117940068244934},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3939470648765564},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.3669160008430481},{"id":"https://openalex.org/C520434653","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser","level":2,"score":0.31266751885414124},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2798667550086975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27932044863700867},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.21181923151016235},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.19806143641471863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1752455234527588},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.10363739728927612},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09858480095863342},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06796640157699585},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcomm.2019.2899866","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2019.2899866","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325255","display_name":"Ministry of Electronics and Information technology","ror":null},{"id":"https://openalex.org/F4320334971","display_name":"Science and Engineering Research Council","ror":"https://ror.org/00zgdb249"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1472267176","https://openalex.org/W1498440540","https://openalex.org/W1504682046","https://openalex.org/W1673075536","https://openalex.org/W1907092231","https://openalex.org/W1966393174","https://openalex.org/W1999629859","https://openalex.org/W2031724611","https://openalex.org/W2045671658","https://openalex.org/W2063878902","https://openalex.org/W2105935781","https://openalex.org/W2110403488","https://openalex.org/W2116213015","https://openalex.org/W2184140478","https://openalex.org/W2263466419","https://openalex.org/W2289141984","https://openalex.org/W2292520261","https://openalex.org/W2524828424","https://openalex.org/W2584260161","https://openalex.org/W2604605071","https://openalex.org/W3101971347","https://openalex.org/W4235364725"],"related_works":["https://openalex.org/W2183364220","https://openalex.org/W2030697371","https://openalex.org/W2125299588","https://openalex.org/W2022440507","https://openalex.org/W2029884227","https://openalex.org/W4300954526","https://openalex.org/W2095185858","https://openalex.org/W2769147407","https://openalex.org/W1977715751","https://openalex.org/W2911921625"],"abstract_inverted_index":{"We":[0],"derive":[1],"an":[2],"achievable":[3],"rate":[4],"region":[5],"(ARR)":[6],"of":[7,59,108,154],"the":[8,57,60,105,109,118,131,135,138,155,167,170,180,183],"zero-forcing":[9],"precoder":[10],"in":[11,45,91,152],"a":[12,33,71,79],"2":[13,15],"\u00d7":[14],"multi-user":[16],"multiple-input":[17],"single-output":[18],"broadcast":[19],"intensity-modulation/direct-detection":[20],"channel.":[21],"A":[22],"per-light":[23],"emitting":[24],"diode":[25],"(LED)":[26],"peak":[27,73,120],"optical":[28,36,46,74,114,160],"power":[29,37,75,82,116,121,150],"constraint":[30,38,76,83,172,185],"along":[31,77],"with":[32,39,68,78,84,175],"per-LED":[34,72,80,112,119],"average":[35,81,113,158],"inequality":[40],"(Type-I":[41],"constraint)":[42],"generally":[43],"considered":[44,90],"wireless":[47],"communication":[48,94],"systems":[49,95],"is":[50,89,122,137,144],"imposed":[51],"for":[52,96],"which":[53,88],"we":[54,64],"analytically":[55,145],"characterize":[56],"boundary":[58],"proposed":[61],"ARR.":[62],"Then,":[63],"compare":[65],"this":[66],"ARR":[67,132,168,181],"that":[69,103],"under":[70,133,169,182],"equality":[85],"(Type-II":[86],"constraint),":[87],"visible":[92],"light":[93],"constant":[97,174],"illumination":[98],"requirement.":[99],"Our":[100],"analysis":[101],"reveals":[102],"when":[104],"ratio":[106],"(\u03b2)":[107],"maximum":[110],"allowed":[111],"transmit":[115,159],"to":[117,127,147],"less":[123],"than":[124],"or":[125],"equal":[126],"half":[128],"(\u03b2":[129],"\u22641/2),":[130],"both":[134],"constraints":[136],"same.":[139],"However,":[140],"Type-I":[141,171],"constrained":[142],"system":[143],"shown":[146],"be":[148],"more":[149],"efficient":[151],"terms":[153],"required":[156],"total":[157],"power.":[161],"When":[162],"\u03b2":[163,177],">":[164],"1/2":[165],",":[166,178],"remains":[173],"increasing":[176],"whereas":[179],"Type-II":[184],"shrinks.":[186]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}