On Distributed Estimation in Hierarchical Power Constrained Wireless Sensor Networks

We consider distributed estimation of a random source in a hierarchical power constrained wireless sensor network. Sensors within each cluster send their measurements to a cluster head (CH). CHs optimally fuse the received signals and transmit to the fusion center (FC) over orthogonal fading channel...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on signal and information processing over networks Vol. 6; pp. 442 - 459
Main Authors Shirazi, Mojtaba, Vosoughi, Azadeh
Format Journal Article
LanguageEnglish
Published Piscataway IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Online AccessGet full text
ISSN2373-776X
2373-7778
DOI10.1109/TSIPN.2020.2995046

Cover

Abstract We consider distributed estimation of a random source in a hierarchical power constrained wireless sensor network. Sensors within each cluster send their measurements to a cluster head (CH). CHs optimally fuse the received signals and transmit to the fusion center (FC) over orthogonal fading channels. To enable channel estimation at the FC, CHs send pilots, prior to data transmission. We derive the mean square error (MSE) corresponding to the linear minimum mean square error (LMMSE) estimator of the source at the FC, and obtain the Bayesian Cramér-Rao bound (CRB). Our goal is to find (i) the optimal training power, (ii) the optimal power that sensors in a cluster spend to transmit their amplified measurements to their CH, and (iii) the optimal weight vector employed by each CH for its linear signal fusion, such that the MSE is minimized, subject to a network power constraint. To untangle the performance gain that optimizing each set of these variables provide, we also analyze three special cases of the original problem, where in each special case, only two sets of variables are optimized across clusters. We define three factors that allow us to quantify the effectiveness of each power allocation scheme in achieving an MSE-power tradeoff that is close to that of the Bayesian CRB. Combining the information gained from the factors and Bayesian CRB with our computational complexity analysis provides the system designer with quantitative complexity-versus-MSE improvement tradeoffs offered by different power allocation schemes.
AbstractList We consider distributed estimation of a random source in a hierarchical power constrained wireless sensor network. Sensors within each cluster send their measurements to a cluster head (CH). CHs optimally fuse the received signals and transmit to the fusion center (FC) over orthogonal fading channels. To enable channel estimation at the FC, CHs send pilots, prior to data transmission. We derive the mean square error (MSE) corresponding to the linear minimum mean square error (LMMSE) estimator of the source at the FC, and obtain the Bayesian Cramér-Rao bound (CRB). Our goal is to find (i) the optimal training power, (ii) the optimal power that sensors in a cluster spend to transmit their amplified measurements to their CH, and (iii) the optimal weight vector employed by each CH for its linear signal fusion, such that the MSE is minimized, subject to a network power constraint. To untangle the performance gain that optimizing each set of these variables provide, we also analyze three special cases of the original problem, where in each special case, only two sets of variables are optimized across clusters. We define three factors that allow us to quantify the effectiveness of each power allocation scheme in achieving an MSE-power tradeoff that is close to that of the Bayesian CRB. Combining the information gained from the factors and Bayesian CRB with our computational complexity analysis provides the system designer with quantitative complexity-versus-MSE improvement tradeoffs offered by different power allocation schemes.
Author Vosoughi, Azadeh
Shirazi, Mojtaba
Author_xml – sequence: 1
  givenname: Mojtaba
  orcidid: 0000-0003-2947-2370
  surname: Shirazi
  fullname: Shirazi, Mojtaba
  email: mojsh@knights.ucf.edu
  organization: Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL, USA
– sequence: 2
  givenname: Azadeh
  orcidid: 0000-0002-1937-2838
  surname: Vosoughi
  fullname: Vosoughi, Azadeh
  email: azadeh@ucf.edu
  organization: Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL, USA
BookMark eNp9kM1PwkAQxTcGExH5B_TSxDO4H22XPRpEISFAAkZvTTs7jYt1F3dLiP-95SMcPHiYzBzem5f3uyYt6ywScstonzGqHlbLyWLW55TTPlcqoXF6QdpcSNGTUg5a5zt9vyLdENaUUpbIWCrVJqu5jZ5MqL0ptjXqaBRq85XXxtnI2Ghs0OcePgzkVbRwO_TR0NlGnRvbiN-MxwpDiJZog_PRDOud85_hhlyWeRWwe9od8vo8Wg3Hven8ZTJ8nPaAq6TuFYUqkpIykQLIUtNBqnlaNAMAiZZa0xIw1nEsGCiUVAMHQF4oiiC0ANEh98e_G---txjqbO223jaRGY-ZjHmaSNqo-FEF3oXgscw2vunofzJGsz3A7AAw2wPMTgAb0-CPCUx94LIvX_1vvTtaDSKesxRViVBC_AKCZoJq
CODEN ITSIBW
CitedBy_id crossref_primary_10_1109_JSEN_2023_3312733
crossref_primary_10_1109_TGCN_2022_3146868
crossref_primary_10_1080_00207721_2021_1897707
crossref_primary_10_1109_TWC_2022_3199415
crossref_primary_10_1109_TSIPN_2021_3074882
crossref_primary_10_1109_TCNS_2023_3314582
crossref_primary_10_1109_TGCN_2021_3087456
crossref_primary_10_1109_TSIPN_2021_3054981
crossref_primary_10_1109_TCCN_2021_3056691
crossref_primary_10_1109_TIM_2023_3315396
crossref_primary_10_1109_TSIPN_2022_3161827
crossref_primary_10_1109_TSIPN_2024_3352271
crossref_primary_10_1109_JAS_2021_1004308
Cites_doi 10.1109/TSP.2015.2417508
10.1017/S0308210511001648
10.1109/9780470544198
10.1016/S0167-6377(99)00074-7
10.1109/TSP.2012.2229993
10.1109/TSP.2007.896019
10.1109/TWC.2009.081438
10.1109/TWC.2016.2607703
10.1109/TSIPN.2019.2928093
10.1109/JSAC.2006.879350
10.1109/TSP.2005.861898
10.1049/iet-spr.2011.0199
10.1017/CBO9780511804441
10.1109/TSP.2011.2177264
10.1109/TSP.2018.2824279
10.1109/TWC.2011.120810.101465
10.1080/10556789908805730
10.1109/TVT.2018.2847300
10.1109/TSP.2008.2005090
10.1109/TSP.2016.2552504
10.1109/TSP.2009.2028196
10.1109/TSIPN.2019.2901198
10.1109/TWC.2013.050613.111959
10.1109/TIT.2003.810631
10.1186/1687-6180-2011-92
10.1109/TSP.2005.861774
10.1109/JSAC.2005.843539
10.1109/LSP.2013.2246514
10.1109/SURV.2012.062612.00084
10.1109/TSP.2005.863031
10.1016/j.sigpro.2010.10.002
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020
DBID 97E
RIA
RIE
AAYXX
CITATION
7SP
8FD
L7M
DOI 10.1109/TSIPN.2020.2995046
DatabaseName IEEE All-Society Periodicals Package (ASPP) 2005–Present
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Electronics & Communications Abstracts
Technology Research Database
Advanced Technologies Database with Aerospace
DatabaseTitle CrossRef
Technology Research Database
Advanced Technologies Database with Aerospace
Electronics & Communications Abstracts
DatabaseTitleList
Technology Research Database
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2373-7778
EndPage 459
ExternalDocumentID 10_1109_TSIPN_2020_2995046
9095393
Genre orig-research
GrantInformation_xml – fundername: NSF
  grantid: CCF-1341966; CCF-1319770
GroupedDBID 0R~
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABQJQ
ABVLG
ACGFS
AGQYO
AGSQL
AHBIQ
AKJIK
AKQYR
ALMA_UNASSIGNED_HOLDINGS
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
EBS
EJD
IFIPE
IPLJI
JAVBF
M43
O9-
OCL
RIA
RIE
AAYXX
CITATION
7SP
8FD
L7M
ID FETCH-LOGICAL-c295t-bb9b5f0136cc7fd086d26bd26ccc5d7dd0fce4d4431c9e70dc2cce2b90ec3d3c3
IEDL.DBID RIE
ISSN 2373-776X
IngestDate Mon Jun 30 06:18:56 EDT 2025
Thu Apr 24 23:11:11 EDT 2025
Wed Oct 01 02:19:32 EDT 2025
Wed Aug 27 02:38:22 EDT 2025
IsPeerReviewed true
IsScholarly true
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
https://doi.org/10.15223/policy-029
https://doi.org/10.15223/policy-037
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c295t-bb9b5f0136cc7fd086d26bd26ccc5d7dd0fce4d4431c9e70dc2cce2b90ec3d3c3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-1937-2838
0000-0003-2947-2370
PQID 2417426570
PQPubID 4437207
PageCount 18
ParticipantIDs ieee_primary_9095393
proquest_journals_2417426570
crossref_primary_10_1109_TSIPN_2020_2995046
crossref_citationtrail_10_1109_TSIPN_2020_2995046
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 20200000
2020-00-00
20200101
PublicationDateYYYYMMDD 2020-01-01
PublicationDate_xml – year: 2020
  text: 20200000
PublicationDecade 2020
PublicationPlace Piscataway
PublicationPlace_xml – name: Piscataway
PublicationTitle IEEE transactions on signal and information processing over networks
PublicationTitleAbbrev TSIPN
PublicationYear 2020
Publisher IEEE
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml – name: IEEE
– name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References ref35
ref13
ref34
ref12
ref37
ref15
ref36
ref14
ref31
ref30
ref32
ref10
ref1
ref17
ref38
ref16
ref19
luenberger (ref33) 2015
ref18
cui (ref11) 2007; 55
proakis (ref22) 2007
shirazi (ref3) 2014
ref24
ref23
ref26
ref20
ref21
ref28
ref29
ref8
ref7
ref9
ref4
ref6
ref5
shirazi (ref2) 2014
kay (ref25) 1993
meyer (ref27) 2001
References_xml – ident: ref13
  doi: 10.1109/TSP.2015.2417508
– ident: ref34
  doi: 10.1017/S0308210511001648
– start-page: 712
  year: 2014
  ident: ref2
  article-title: Bayesian Cramer-Rao bound for distributed vector estimation with linear observation model
  publication-title: Proc IEEE Int Symp Pers Indoor Mobile Radio Commun
– year: 2015
  ident: ref33
  publication-title: Linear and Nonlinear Programming
– ident: ref28
  doi: 10.1109/9780470544198
– ident: ref36
  doi: 10.1016/S0167-6377(99)00074-7
– ident: ref8
  doi: 10.1109/TSP.2012.2229993
– volume: 55
  start-page: 4683
  year: 2007
  ident: ref11
  article-title: Estimation diversity and energy efficiency in distributed sensing
  publication-title: IEEE Trans Signal Process
  doi: 10.1109/TSP.2007.896019
– ident: ref6
  doi: 10.1109/TWC.2009.081438
– start-page: 1484
  year: 2014
  ident: ref3
  article-title: Bayesian Cramer-Rao bound for distributed estimation of correlated data with non-linear observation model
  publication-title: Proc Asilomar Conf Signals Syst Comput
– ident: ref12
  doi: 10.1109/TWC.2016.2607703
– ident: ref1
  doi: 10.1109/TSIPN.2019.2928093
– ident: ref31
  doi: 10.1109/JSAC.2006.879350
– ident: ref38
  doi: 10.1109/TSP.2005.861898
– ident: ref7
  doi: 10.1049/iet-spr.2011.0199
– ident: ref32
  doi: 10.1017/CBO9780511804441
– ident: ref37
  doi: 10.1109/TSP.2011.2177264
– ident: ref5
  doi: 10.1109/TSP.2018.2824279
– ident: ref26
  doi: 10.1109/TWC.2011.120810.101465
– ident: ref35
  doi: 10.1080/10556789908805730
– start-page: 124
  year: 2001
  ident: ref27
  publication-title: Matrix Analysis and Applied Linear Algebra
– start-page: 63
  year: 2007
  ident: ref22
  publication-title: Digital Communications
– ident: ref16
  doi: 10.1109/TVT.2018.2847300
– year: 1993
  ident: ref25
  publication-title: Fundamentals of Statistical Signal Processing Estimation Theory
– ident: ref19
  doi: 10.1109/TSP.2008.2005090
– ident: ref4
  doi: 10.1109/TSP.2016.2552504
– ident: ref17
  doi: 10.1109/TSP.2009.2028196
– ident: ref9
  doi: 10.1109/TSIPN.2019.2901198
– ident: ref15
  doi: 10.1109/TWC.2013.050613.111959
– ident: ref10
  doi: 10.1109/TIT.2003.810631
– ident: ref18
  doi: 10.1186/1687-6180-2011-92
– ident: ref30
  doi: 10.1109/TSP.2005.861774
– ident: ref23
  doi: 10.1109/JSAC.2005.843539
– ident: ref14
  doi: 10.1109/LSP.2013.2246514
– ident: ref24
  doi: 10.1186/1687-6180-2011-92
– ident: ref21
  doi: 10.1109/SURV.2012.062612.00084
– ident: ref29
  doi: 10.1109/TSP.2005.863031
– ident: ref20
  doi: 10.1016/j.sigpro.2010.10.002
SSID ssj0001574799
Score 2.2668772
Snippet We consider distributed estimation of a random source in a hierarchical power constrained wireless sensor network. Sensors within each cluster send their...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 442
SubjectTerms Bayesian analysis
Bayesian Cramér-Rao bound
Channel estimation
Clusters
Complexity
Constraints
Data communication
Data transmission
Distributed estimation
Electric power distribution
Fading channels
hierarchical power constrained WSN
linear fusion
LMMSE estimator
Mean square errors
MSE-power tradeoff
Optimization
random source
Resource management
Sensors
Tradeoffs
Training
transmit power optimization
Wireless networks
Wireless sensor networks
Title On Distributed Estimation in Hierarchical Power Constrained Wireless Sensor Networks
URI https://ieeexplore.ieee.org/document/9095393
https://www.proquest.com/docview/2417426570
Volume 6
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Electronic Library (IEL)
  customDbUrl:
  eissn: 2373-7778
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001574799
  issn: 2373-776X
  databaseCode: RIE
  dateStart: 20150101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3PS8MwFH5sO-nB3-J0Sg7etFuWtc1yFJ1MwTnYhN1K85KCODrR7eJfb17azaEiHgqFJiXk5cf3kve-D-BcS5FmImsH2OVpEFqhAoUqDjKu3f4aC-O-U7TFIO4_hfeTaFKBy1UujLXWB5_ZJr36u3wzwwUdlbUUkaOpThWqUqoiV-vrPCVywFipZV4MV63x6G44cB6g4E235kacMO7a3uPFVH6swH5bud2Gh2WDimiSl-Zirpv48Y2r8b8t3oGtEl-yq2JA7ELF5nuwucY6uA_jx5zdEF8uSV1Zw3pulhcJjOw5Z_1nSkn2CilTNiQNNUainl5KwhWmaNmpWx3ZyPm_szc2KMLI3w_g6bY3vu4HpbhCgEJF80BrpaOMGNsQZWacZ2NErN2DiJGRxvAMbWhCBzBQWckNCkQrtOIWO6aDnUOo5bPcHgFD4pCJpMRQ2LCdpTpLU250GHed-5F2TR3ay25PsGQep1ZPE--BcJV4UyVkqqQ0VR0uVnVeC96NP0vvU9-vSpbdXofG0rpJOTXfEwdZpIMlkeTHv9c6gQ36d3HO0oDa_G1hTx3ymOszP-Q-AV2p2Fc
linkProvider IEEE
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1NTxsxEB0BPQAHKF9qKG194AYbHGe9jo9VAYUCAYkgcVutx14parRBkFz66zvj3aQIUNXDSiutrbU8_nhjz7wHcOiMKkpVdhLsySJJg7KJRZslpXS0v2bK03eOthhk_fv054N-WILjRS5MCCEGn4U2v8a7fD_BGR-VnVgmR7PdZfigyaswdbbW3xMVTdDY2nlmjLQnw7uL2wH5gEq2adXVklHui90nyqm8WYPjxnK-CdfzJtXxJL_as6lr4-9XbI3_2-aPsNEgTPG9HhJbsBSqbVh_wTu4A8ObSpwyYy6LXQUvzmie1ymMYlSJ_oiTkqNGyljcsoqaYFnPKCZBhTledkzro7gjD3jyJAZ1IPnzLtyfnw1_9JNGXiFBZfU0cc46XTJnG6IpPfk2XmWOHkTU3ngvSwypTwlioA1GelSIQTkrA3Z9F7t7sFJNqvAJBDKLjDYGUxXSTlm4siikd2nWIwek6PkWdObdnmPDPc6tHufRB5E2j6bK2VR5Y6oWHC3qPNbMG_8svcN9vyjZdHsLDubWzZvJ-ZwTaDEETLSR--_X-gar_eH1VX51Mbj8DGv8n_rU5QBWpk-z8IVwyNR9jcPvD-ED26g
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=On+Distributed+Estimation+in+Hierarchical+Power+Constrained+Wireless+Sensor+Networks&rft.jtitle=IEEE+transactions+on+signal+and+information+processing+over+networks&rft.au=Shirazi%2C+Mojtaba&rft.au=Vosoughi%2C+Azadeh&rft.date=2020&rft.pub=IEEE&rft.eissn=2373-7778&rft.volume=6&rft.spage=442&rft.epage=459&rft_id=info:doi/10.1109%2FTSIPN.2020.2995046&rft.externalDocID=9095393
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2373-776X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2373-776X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2373-776X&client=summon