An Analytically Tractable Approximation for the Gaussian Q-Function
In this letter we propose an approximation for the Gaussian Q-function that enables simpler evaluation of important communication system performance metrics. The approximation enables derivation of closed-form expressions for metrics such as average symbol, bit and block error probabilities which ar...
Saved in:
Published in | IEEE communications letters Vol. 12; no. 9; pp. 669 - 671 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York, NY
IEEE
01.09.2008
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | In this letter we propose an approximation for the Gaussian Q-function that enables simpler evaluation of important communication system performance metrics. The approximation enables derivation of closed-form expressions for metrics such as average symbol, bit and block error probabilities which are known to be analytically involved as they require computation of the expectation of Q-function and its integer powers, for any m of Nakagami-m fading. The tightness of the approximation is verified by simulations. The usefulness of the approximation is demonstrated by obtaining a simple closed form expression for the average symbol error probability of differentially encoded QPSK in Nakagami-m fading. |
---|---|
AbstractList | In this letter we propose an approximation for the Gaussian Q-function that enables simpler evaluation of important communication system performance metrics. The approximation enables derivation of closed-form expressions for metrics such as average symbol, bit and block error probabilities which are known to be analytically involved as they require computation of the expectation of Q-function and its integer powers, for any m of Nakagami-m fading. The tightness of the approximation is verified by simulations. The usefulness of the approximation is demonstrated by obtaining a simple closed form expression for the average symbol error probability of differentially encoded QPSK in Nakagami-m fading. |
Author | Isukapalli, Yogananda Rao, Bhaskar D. |
Author_xml | – sequence: 1 givenname: Yogananda surname: Isukapalli fullname: Isukapalli, Yogananda email: yoga@ucsd.edu organization: Student Member, IEEE – sequence: 2 givenname: Bhaskar D. surname: Rao fullname: Rao, Bhaskar D. email: brao@ece.ucsd.edu organization: Fellow, IEEE |
BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20646999$$DView record in Pascal Francis |
BookMark | eNp9kEFLwzAUx4NMcJt-APFSBPXUmaRJkxxLcVPYGMI8lyxJsaNLZ9KC-_amduzgwct7D97v_Xn8JmBkG2sAuEVwhhAUz8t8vVrNMIR8BjnkiF6AMaKUxziUUZghFzFjgl-Bifc7GEBM0RjkmY0yK-tjWylZ18do46Rq5bY2UXY4uOa72su2amxUNi5qP020kJ33lbTRezzvrOp31-CylLU3N6c-BR_zl03-Gi_Xi7c8W8aKUNTGkgosmBCl5BBpRlKuiaYYc4UN5YphSbhGPUEVUUzrkpVEb0uc6BRqTpIpeBpyw19fnfFtsa-8MnUtrWk6X3BGIcMIsUA-_ksmhOIkhX3k_R9w13Qu-AhpKWYMpZAHCA2Qco33zpTFwQUt7lggWPT2i1_7RW-_GOyHm4dTsPRBbOmkVZU_H2KYklQIEbi7gauMMec1SXHCGEl-AJv7jaY |
CODEN | ICLEF6 |
CitedBy_id | crossref_primary_10_1109_LWC_2017_2717907 crossref_primary_10_1109_TVT_2011_2138175 crossref_primary_10_1109_LCOMM_2023_3253857 crossref_primary_10_1109_TWC_2021_3052370 crossref_primary_10_1016_j_dsp_2017_03_001 crossref_primary_10_1016_j_optlastec_2023_109990 crossref_primary_10_1109_WCL_2012_080112_120232 crossref_primary_10_1016_j_jfranklin_2021_08_005 crossref_primary_10_1080_15427951_2015_1022626 crossref_primary_10_1109_TCOMM_2010_100510_090258 crossref_primary_10_1109_COMST_2019_2907065 crossref_primary_10_1109_LCOMM_2021_3139372 crossref_primary_10_1109_LCOMM_2013_052413_130690 crossref_primary_10_1109_LCOMM_2011_011011_101964 crossref_primary_10_1109_ACCESS_2020_3015344 crossref_primary_10_1109_TCOMM_2017_2684164 crossref_primary_10_1109_TCSI_2012_2215114 crossref_primary_10_1155_2017_8140487 crossref_primary_10_1109_TCOMM_2021_3113008 crossref_primary_10_1016_j_phycom_2023_102034 crossref_primary_10_1080_09500340_2012_697200 crossref_primary_10_1109_JSYST_2018_2879162 crossref_primary_10_1109_TWC_2012_052512_112063 crossref_primary_10_1109_LCOMM_2010_05_100202 crossref_primary_10_1007_s11276_020_02488_9 crossref_primary_10_1002_dac_4162 crossref_primary_10_1155_2010_193183 crossref_primary_10_1109_OJCOMS_2023_3332838 crossref_primary_10_1109_LCOMM_2011_032111_102440 crossref_primary_10_1007_s12046_022_01944_w crossref_primary_10_1049_iet_com_2012_0597 crossref_primary_10_1109_LCOMM_2016_2615300 crossref_primary_10_1109_TWC_2011_101711_100901 crossref_primary_10_1016_j_aeue_2020_153101 crossref_primary_10_1109_LCOMM_2021_3052257 crossref_primary_10_1109_OJCOMS_2022_3205346 crossref_primary_10_1007_s10957_012_0217_0 crossref_primary_10_1080_00207217_2012_713024 crossref_primary_10_1002_wcm_2347 crossref_primary_10_1109_TCOMM_2011_072011_100049 crossref_primary_10_4218_etrij_10_0209_0352 crossref_primary_10_1109_LSP_2010_2092427 crossref_primary_10_1109_TCOMM_2011_012711_100105 crossref_primary_10_1016_j_dsp_2022_103800 crossref_primary_10_1109_TCOMM_2020_3006902 crossref_primary_10_1109_LCOMM_2012_120612_122130 crossref_primary_10_1007_s12243_021_00864_w crossref_primary_10_1109_TSP_2010_2040667 crossref_primary_10_1109_TIFS_2010_2103061 crossref_primary_10_1016_j_aeue_2021_153963 crossref_primary_10_1109_LCOMM_2009_081754 crossref_primary_10_1016_j_amc_2017_10_019 |
Cites_doi | 10.1002/0471200697 10.1109/26.35381 10.1109/TWC.2003.814350 10.1109/LCOMM.2008.080009 10.1109/TCOM.1979.1094433 10.1109/26.843116 10.1109/LCOMM.2007.070470 |
ContentType | Journal Article |
Copyright | 2008 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008 |
Copyright_xml | – notice: 2008 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008 |
DBID | 97E RIA RIE IQODW AAYXX CITATION 7SP 8FD L7M F28 FR3 |
DOI | 10.1109/LCOMM.2008.080815 |
DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005-present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Xplore Pascal-Francis CrossRef Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
DatabaseTitle | CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
DatabaseTitleList | Engineering Research Database Engineering Research Database |
Database_xml | – sequence: 1 dbid: RIE name: IEEE Xplore url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Engineering Applied Sciences |
EISSN | 1558-2558 |
EndPage | 671 |
ExternalDocumentID | 2325388701 10_1109_LCOMM_2008_080815 20646999 4623774 |
Genre | orig-research |
GroupedDBID | -~X 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AASAJ AAYOK ABQJQ ABVLG ACGFO ACIWK AENEX AETIX AI. AIBXA AKJIK ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV AZLTO BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD HZ~ H~9 IES IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RIG RNS TN5 VH1 XFK IQODW VOH AAYXX CITATION 7SP 8FD L7M F28 FR3 |
ID | FETCH-LOGICAL-c451t-a5929799fa801d7468d4d5228c2e58c72a48d197995c4c7ddf7f4dbf23d60d843 |
IEDL.DBID | RIE |
ISSN | 1089-7798 |
IngestDate | Sat Aug 17 00:59:51 EDT 2024 Fri Aug 16 23:30:37 EDT 2024 Thu Oct 10 20:31:36 EDT 2024 Fri Aug 23 02:11:48 EDT 2024 Sun Oct 22 16:08:26 EDT 2023 Wed Jun 26 19:26:56 EDT 2024 |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 9 |
Keywords | Performance evaluation Gaussian Q-function Bit error rate Gaussian approximation Quadrature phase shift keying Nakagami fading Gaussian process Simulation Nakagami-m fading Telecommunication system Metric Differential method Symbol error rate |
Language | English |
License | CC BY 4.0 |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-c451t-a5929799fa801d7468d4d5228c2e58c72a48d197995c4c7ddf7f4dbf23d60d843 |
Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
PQID | 862771608 |
PQPubID | 23500 |
PageCount | 3 |
ParticipantIDs | proquest_journals_862771608 crossref_primary_10_1109_LCOMM_2008_080815 ieee_primary_4623774 pascalfrancis_primary_20646999 proquest_miscellaneous_875072117 proquest_miscellaneous_34523604 |
PublicationCentury | 2000 |
PublicationDate | 2008-09-01 |
PublicationDateYYYYMMDD | 2008-09-01 |
PublicationDate_xml | – month: 09 year: 2008 text: 2008-09-01 day: 01 |
PublicationDecade | 2000 |
PublicationPlace | New York, NY |
PublicationPlace_xml | – name: New York, NY – name: New York |
PublicationTitle | IEEE communications letters |
PublicationTitleAbbrev | COML |
PublicationYear | 2008 |
Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
References | ref8 ref7 ref4 ref3 ref6 simon (ref1) 2002 ref5 ref2 gradshteyn (ref9) 1980 |
References_xml | – ident: ref2 doi: 10.1002/0471200697 – ident: ref4 doi: 10.1109/26.35381 – ident: ref6 doi: 10.1109/TWC.2003.814350 – ident: ref8 doi: 10.1109/LCOMM.2008.080009 – ident: ref3 doi: 10.1109/TCOM.1979.1094433 – year: 1980 ident: ref9 publication-title: Table of Integrals Series and Products Corrected and Enlarged Edition contributor: fullname: gradshteyn – ident: ref5 doi: 10.1109/26.843116 – ident: ref7 doi: 10.1109/LCOMM.2007.070470 – year: 2002 ident: ref1 publication-title: Probability Distributions Involving Gaussian Random Variables A Handbook for Engineers and Scientists contributor: fullname: simon |
SSID | ssj0008251 |
Score | 2.290398 |
Snippet | In this letter we propose an approximation for the Gaussian Q-function that enables simpler evaluation of important communication system performance metrics.... |
SourceID | proquest crossref pascalfrancis ieee |
SourceType | Aggregation Database Index Database Publisher |
StartPage | 669 |
SubjectTerms | Applied sciences Approximation Blocking Closed-form solution Computational modeling Derivation Error probability Exact sciences and technology Exact solutions Fading Gaussian Gaussian approximation Mathematical analysis Measurement Nakagami distribution Nakagami-m fading Performance analysis Q-function Quadrature phase shift keying Rayleigh channels Symbols Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) |
Title | An Analytically Tractable Approximation for the Gaussian Q-Function |
URI | https://ieeexplore.ieee.org/document/4623774 https://www.proquest.com/docview/862771608 https://search.proquest.com/docview/34523604 https://search.proquest.com/docview/875072117 |
Volume | 12 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3dS8MwED_UJ33wW6zTmQefxG5pm7bJ4xhOEacIDvZWunyAKJ24FdS_3kvaFT_Bt0JCm94lud8l97sDODExj5RGT9VwYXxmosjnQlJf4I6ZJNQEEbPk5OFNcjliV-N4vARnDRdGa-2Cz3THPrq7fDWVpT0q6zK01QhXlmGZ07DiajW7rqVgVsH0AhGj4PUNZkBF97p_OxzWYZO20ET8xQa5oio2JDKfoVRMVc7ix87szM1gA4aLgVZRJo-dcj7pyPdvORz_-yebsF7jTtKrJsoWLOliG9Y-ZSPcgX6vIC5HiTvefnoj95ZBZalVpGczj78-VDRHgjiXIG4kF3k5sxxMcucP0Dzatl0YDc7v-5d-XWPBlywO5n4eIz5KhTA5miqVsoQrphCTcRnqmMs0zBlXge0RSyZTpUxqmJqYMFIJVZxFe7BSTAu9DyRIsAVfJPBvGdMIHYUKTYgeSZrLSCkPThdSz56rVBqZc0GoyJyK6pKYTkUe7FipNR1rgXnQ_qKnpj1EaJUg2PWgtVBcVq_GWYZeW4p-IeUeHDetuIzs3Uhe6Gk5yyKGHnlC8QPkjx7o2NlcckF68PvQWrC6iCWhwSGszF9KfYSAZT5pu5n6ATJw500 |
link.rule.ids | 315,786,790,802,27955,27956,55107 |
linkProvider | IEEE |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3fT9swED4x9sB4gA2GCDDwA0_TUpzEie3HqqIU1oCQisRblPqHhJjSaW2kwV_P2UkjYEziLZKtxLmzfd_Z990BHNtUJNqgp2qFtCGzSRIKqWgoccfMMmqjhDlycn6ZjW7YxW16uwI_Oi6MMcYHn5mee_R3-XqmandUdsLQViNc-QAf0c5T3rC1un3XkTCbcHqJmFGK9g4zovJkPLjK8zZw0pWaSF9YIV9WxQVFlnOUi20KWvyzN3uDM9yEfDnUJs7kvlcvpj31-CqL43v_5TNstMiT9Jup8gVWTLUF68_yEW7DoF8Rn6XEH3D_eiATx6Fy5CrSd7nH_941REeCSJcgciRnZT13LExyHQ7RQLq2r3AzPJ0MRmFbZSFULI0WYZkiQuJS2hKNleYsE5ppRGVCxSYVisclEzpyPVLFFNfacsv01MaJzqgWLNmB1WpWmV0gUYYt-CKJf8uYQfAodWxj9El4qRKtA_i-lHrxu0mmUXgnhMrCq6gtiulVFMC2k1rXsRVYAIcv9NS1xwiuMoS7AewvFVe063FeoN_G0TOkIoCjrhUXkrsdKSszq-dFwtAnzyh-gPynB7p2LptcxPfeHtoRrI0m-bgYn1_-3IdPy8gSGh3A6uJPbb4hfFlMD_2sfQKGC-qh |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Analytically+Tractable+Approximation+for+the+Gaussian+Q-Function&rft.jtitle=IEEE+communications+letters&rft.au=Isukapalli%2C+Yogananda&rft.au=Rao%2C+Bhaskar+D.&rft.date=2008-09-01&rft.pub=IEEE&rft.issn=1089-7798&rft.eissn=1558-2558&rft.volume=12&rft.issue=9&rft.spage=669&rft.epage=671&rft_id=info:doi/10.1109%2FLCOMM.2008.080815&rft.externalDocID=4623774 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1089-7798&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1089-7798&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1089-7798&client=summon |