Over-the-Air Computation in Correlated Channels

Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	IEEE transactions on signal processing Ročník 69; s. 5739 - 5755
Hlavní autoři:	Frey, Matthias, Bjelakovic, Igor, Stanczak, Slawomir
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Anomalies boosting Channels Combined source-channel coding Computation Correlation distributed computing Distributed databases Fading Fading channels Linear functions Machine learning Noise Norms Random variables robustness Transmitters Wireless communication Wireless sensor networks
ISSN:	1053-587X, 1941-0476
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or even constant) scaling of the communication cost as the number of transmitters grows. In this work, we propose and analyze an analog OTA computation scheme for a class of functions that contains linear functions as well as some nonlinear functions such as <inline-formula><tex-math notation="LaTeX">p</tex-math></inline-formula>-norms of vectors. We prove error bounds that are valid for fast-fading channels and all distributions of fading and noise in the class of sub-Gaussian distributions. This class includes Gaussian distributions, but also many other practically relevant cases such as Class A Middleton noise and fading with dominant line-of-sight components. Moreover, there can be correlations in the fading and noise so that the presented results also apply to, for example, block fading channels and channels with bursty interference. There is no assumption that the distributed function arguments follow a particular probability law; in particular, they do not need to be independent or identically distributed. Our analysis is nonasymptotic and therefore provides error bounds that are valid for a finite number of channel uses. OTA computation has a huge potential for reducing communication cost in applications such as Machine Learning (ML)-based distributed anomaly detection in large wireless sensor networks. We illustrate this potential through extensive numerical simulations.
AbstractList	Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or even constant) scaling of the communication cost as the number of transmitters grows. In this work, we propose and analyze an analog OTA computation scheme for a class of functions that contains linear functions as well as some nonlinear functions such as [Formula Omitted]-norms of vectors. We prove error bounds that are valid for fast-fading channels and all distributions of fading and noise in the class of sub-Gaussian distributions. This class includes Gaussian distributions, but also many other practically relevant cases such as Class A Middleton noise and fading with dominant line-of-sight components. Moreover, there can be correlations in the fading and noise so that the presented results also apply to, for example, block fading channels and channels with bursty interference. There is no assumption that the distributed function arguments follow a particular probability law; in particular, they do not need to be independent or identically distributed. Our analysis is nonasymptotic and therefore provides error bounds that are valid for a finite number of channel uses. OTA computation has a huge potential for reducing communication cost in applications such as Machine Learning (ML)-based distributed anomaly detection in large wireless sensor networks. We illustrate this potential through extensive numerical simulations. Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or even constant) scaling of the communication cost as the number of transmitters grows. In this work, we propose and analyze an analog OTA computation scheme for a class of functions that contains linear functions as well as some nonlinear functions such as <inline-formula><tex-math notation="LaTeX">p</tex-math></inline-formula>-norms of vectors. We prove error bounds that are valid for fast-fading channels and all distributions of fading and noise in the class of sub-Gaussian distributions. This class includes Gaussian distributions, but also many other practically relevant cases such as Class A Middleton noise and fading with dominant line-of-sight components. Moreover, there can be correlations in the fading and noise so that the presented results also apply to, for example, block fading channels and channels with bursty interference. There is no assumption that the distributed function arguments follow a particular probability law; in particular, they do not need to be independent or identically distributed. Our analysis is nonasymptotic and therefore provides error bounds that are valid for a finite number of channel uses. OTA computation has a huge potential for reducing communication cost in applications such as Machine Learning (ML)-based distributed anomaly detection in large wireless sensor networks. We illustrate this potential through extensive numerical simulations.
Author	Stanczak, Slawomir Frey, Matthias Bjelakovic, Igor
Author_xml	– sequence: 1 givenname: Matthias orcidid: 0000-0003-3016-2644 surname: Frey fullname: Frey, Matthias email: matthias.frey@tu-berlin.de organization: Network Information Theory Group, Technische Universität Berlin, Berlin, Germany – sequence: 2 givenname: Igor surname: Bjelakovic fullname: Bjelakovic, Igor email: igor.bjelakovic@hhi.fraunhofer.de organization: Fraunhofer Heinrich Hertz Institute, Berlin, Germany – sequence: 3 givenname: Slawomir orcidid: 0000-0003-3829-4668 surname: Stanczak fullname: Stanczak, Slawomir email: stanczak@ieee.org organization: Fraunhofer Heinrich Hertz Institute, Berlin, Germany
BookMark	eNp9kE1LAzEQhoNUsK3eBS8Fz2kz-WpyLItWoVDBCt5C3J2lKdvdmt0K_ntTtnjw4CFMBt5nZnhGZFA3NRJyC2wKwOxs8_oy5YzDVADTAOqCDMFKoEzO9SD9mRJUmfn7FRm17Y4xkNLqIZmtvzDSbot0EeIka_aHY-e70NSTUKc2Rqx8h8Uk2_q6xqq9Jpelr1q8OdcxeXt82GRPdLVePmeLFc25hY5-lHlpBS-hBCtEnjMskWtltTRWQGG4AK-hyFGAMcIzZaQuvCzQ6jkKXogxue_nHmLzecS2c7vmGOu00nFlTXpcm5TSfSqPTdtGLF0e-vO76EPlgLmTHJfkuJMcd5aTQPYHPMSw9_H7P-SuRwIi_satAqs0Fz9w9m-K
CODEN	ITPRED
CitedBy_id	crossref_primary_10_1109_COMST_2023_3264649 crossref_primary_10_1109_TSP_2024_3352405 crossref_primary_10_1016_j_fmre_2024_01_011 crossref_primary_10_1109_TSP_2024_3351469 crossref_primary_10_1109_JIOT_2023_3292882 crossref_primary_10_3390_s23083824 crossref_primary_10_1109_LCSYS_2024_3402123 crossref_primary_10_1109_JSAC_2025_3574622 crossref_primary_10_1109_LCOMM_2022_3187559 crossref_primary_10_1109_TWC_2023_3245304 crossref_primary_10_1109_TWC_2024_3412690 crossref_primary_10_1109_TIT_2025_3542673
Cites_doi	10.1109/TWC.2019.2961673 10.1016/j.csda.2011.04.006 10.1109/TWC.2020.2974748 10.1145/3298981 10.1109/ISIT.2009.5205264 10.1109/COMST.2020.3007787 10.1109/TCOMM.2013.072913.120815 10.1109/18.825799 10.1090/S0002-9939-1982-0652441-4 10.1109/TWC.2020.2993703 10.1109/JIOT.2020.3015489 10.1109/TSP.2005.861896 10.1109/TSP.2013.2272921 10.1109/ICC40277.2020.9148853 10.1109/TIT.2011.2165816 10.1109/TSP.2020.2981904 10.1109/ICC.2016.7510770 10.1109/ISTC.2016.7593132 10.1109/GlobalSIP45357.2019.8969185 10.1109/TSP.2006.887564 10.1109/TSP.2020.2989580 10.1007/978-1-4612-0653-8 10.1109/18.761256 10.1090/mmono/188 10.1109/ALLERTON.2019.8919875 10.1109/SPAWC.2019.8815597 10.1109/TIT.2007.904785 10.1007/3-540-36978-3_11 10.1109/49.233212 10.1109/ISIT.2011.6033876 10.1093/acprof:oso/9780199535255.001.0001 10.1109/TSP.2020.2970338 10.1109/ISIT44484.2020.9174426 10.1002/9780470661291 10.1109/TWC.2019.2946245 10.1109/TIT.2016.2593633 10.1109/PIMRC.2019.8904164 10.1002/sta4.314 10.1109/WCL.2014.022314.140005 10.1109/TWC.2014.2380317
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021
DBID	97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D
DOI	10.1109/TSP.2021.3106115
DatabaseName	IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Xplore CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Technology Research Database
Database_xml	– sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1941-0476
EndPage	5755
ExternalDocumentID	10_1109_TSP_2021_3106115 9519562
Genre	orig-research
GrantInformation_xml	– fundername: Deutsche Forschungsgemeinschaft; German Research Foundation funderid: 10.13039/501100001659 – fundername: Annual Allerton Conference on Communication – fundername: Compressed Sensing in Information Processing – fundername: NVIDIA Corporation grantid: DGX-1 – fundername: Nokia University Donation – fundername: Cyber-Physical Networking grantid: STA 864/7
GroupedDBID	-~X .DC 0R~ 29I 3EH 4.4 53G 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACIWK ACKIV ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AJQPL AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 E.L EBS EJD F5P HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c291t-bfcf932f1f1933cc0efe2659648931d8231a61dce31883a05846da4de967e32d3
IEDL.DBID	RIE
ISICitedReferencesCount	19
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000719561100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1053-587X
IngestDate	Mon Jun 30 10:15:38 EDT 2025 Sat Nov 29 04:10:54 EST 2025 Tue Nov 18 22:22:54 EST 2025 Wed Aug 27 02:27:01 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-c291t-bfcf932f1f1933cc0efe2659648931d8231a61dce31883a05846da4de967e32d3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-3016-2644 0000-0003-3829-4668
PQID	2598259268
PQPubID	85478
PageCount	17
ParticipantIDs	crossref_primary_10_1109_TSP_2021_3106115 ieee_primary_9519562 proquest_journals_2598259268 crossref_citationtrail_10_1109_TSP_2021_3106115
PublicationCentury	2000
PublicationDate	20210000 2021-00-00 20210101
PublicationDateYYYYMMDD	2021-01-01
PublicationDate_xml	– year: 2021 text: 20210000
PublicationDecade	2020
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	IEEE transactions on signal processing
PublicationTitleAbbrev	TSP
PublicationYear	2021
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	kone?n? (ref21) 2016 ref13 ref12 mohri (ref45) 2012 ref15 ref14 yin (ref35) 2016 bhatia (ref51) 1989 ref52 ref11 ref10 ref17 ref16 ref19 ref18 buck (ref29) 1976 steinwart (ref43) 2008 pedregosa (ref47) 2011; 12 ref50 ref46 ref48 ref42 ref41 ref44 kolmogorov (ref30) 1957; 114 ref49 ref8 ref7 middleton (ref32) 1993; 2 ref9 ref4 ref3 ref6 ref5 ref40 wainwright (ref37) 2019 ref34 ref36 ref31 ref33 ref2 ref1 ref39 vershynin (ref38) 2018; 47 mcmahan (ref20) 2017 ref24 ref23 ref26 ref25 ref22 ref28 ref27
References_xml	– ident: ref24 doi: 10.1109/TWC.2019.2961673 – ident: ref44 doi: 10.1016/j.csda.2011.04.006 – year: 2008 ident: ref43 publication-title: Support Vector Machines Ser Information Science and Statistics – ident: ref23 doi: 10.1109/TWC.2020.2974748 – ident: ref40 doi: 10.1145/3298981 – year: 2016 ident: ref21 article-title: Federated learning: Strategies for improving communication efficiency publication-title: Proc NIPS Workshop Private Multi-Party Mach Learn – ident: ref9 doi: 10.1109/ISIT.2009.5205264 – start-page: 1273 year: 2017 ident: ref20 article-title: Communication-efficient learning of deep networks from decentralized data publication-title: Proc 20th Int Conf Artif Intell Statist – ident: ref3 doi: 10.1109/COMST.2020.3007787 – ident: ref6 doi: 10.1109/TCOMM.2013.072913.120815 – ident: ref2 doi: 10.1109/18.825799 – year: 1976 ident: ref29 article-title: Approximate complexity and functional representation publication-title: Wisconsin Univ-Madison Mathematics Research Center Tech Rep – ident: ref31 doi: 10.1090/S0002-9939-1982-0652441-4 – ident: ref16 doi: 10.1109/TWC.2020.2993703 – ident: ref52 doi: 10.1109/JIOT.2020.3015489 – ident: ref41 doi: 10.1109/TSP.2005.861896 – volume: 2 start-page: 137 year: 1993 ident: ref32 article-title: Elements of weak signal detection in non-gaussian noise environments publication-title: Proc Adv Stat Signal Process – start-page: 151 year: 1989 ident: ref51 article-title: Comparing a matrix to its off-diagonal part publication-title: The Gohberg Anniversary Collection – ident: ref7 doi: 10.1109/TSP.2013.2272921 – ident: ref26 doi: 10.1109/ICC40277.2020.9148853 – ident: ref11 doi: 10.1109/TIT.2011.2165816 – ident: ref18 doi: 10.1109/TSP.2020.2981904 – volume: 114 start-page: 953 year: 1957 ident: ref30 article-title: On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition publication-title: Dokl Akad Nauk SSSR – ident: ref15 doi: 10.1109/ICC.2016.7510770 – ident: ref13 doi: 10.1109/ISTC.2016.7593132 – ident: ref28 doi: 10.1109/GlobalSIP45357.2019.8969185 – year: 2012 ident: ref45 publication-title: Foundations of Machine Learning Ser Adaptive Computation and Machine Learning – ident: ref42 doi: 10.1109/TSP.2006.887564 – ident: ref25 doi: 10.1109/TSP.2020.2989580 – ident: ref49 doi: 10.1007/978-1-4612-0653-8 – ident: ref34 doi: 10.1109/18.761256 – volume: 47 year: 2018 ident: ref38 publication-title: High Dimensional Probability An Introduction with Applications in Data Science ser Cambridge Series in Statistical and Probabilistic Mathematics – ident: ref36 doi: 10.1090/mmono/188 – ident: ref1 doi: 10.1109/ALLERTON.2019.8919875 – ident: ref46 doi: 10.1109/SPAWC.2019.8815597 – ident: ref4 doi: 10.1109/TIT.2007.904785 – year: 2016 ident: ref35 publication-title: Propagation channel characterization parameter estimation and modeling for wireless communications – ident: ref5 doi: 10.1007/3-540-36978-3_11 – ident: ref33 doi: 10.1109/49.233212 – ident: ref10 doi: 10.1109/ISIT.2011.6033876 – ident: ref50 doi: 10.1093/acprof:oso/9780199535255.001.0001 – ident: ref17 doi: 10.1109/TSP.2020.2970338 – ident: ref27 doi: 10.1109/ISIT44484.2020.9174426 – ident: ref48 doi: 10.1002/9780470661291 – year: 2019 ident: ref37 publication-title: High-Dimensional Statistics A Non-Asymptotic Viewpoint ser Cambridge Series in Statistical and Probabilistic Mathematics – ident: ref22 doi: 10.1109/TWC.2019.2946245 – ident: ref12 doi: 10.1109/TIT.2016.2593633 – ident: ref19 doi: 10.1109/PIMRC.2019.8904164 – ident: ref39 doi: 10.1002/sta4.314 – volume: 12 start-page: 2825 year: 2011 ident: ref47 article-title: Scikit-learn: Machine learning in Python publication-title: J Mach Learn Res – ident: ref14 doi: 10.1109/WCL.2014.022314.140005 – ident: ref8 doi: 10.1109/TWC.2014.2380317
SSID	ssj0014496
Score	2.4442356
Snippet	Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By...
SourceID	proquest crossref ieee
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	5739
SubjectTerms	Anomalies boosting Channels Combined source-channel coding Computation Correlation distributed computing Distributed databases Fading Fading channels Linear functions Machine learning Noise Norms Random variables robustness Transmitters Wireless communication Wireless sensor networks
Title	Over-the-Air Computation in Correlated Channels
URI	https://ieeexplore.ieee.org/document/9519562 https://www.proquest.com/docview/2598259268
Volume	69
WOSCitedRecordID	wos000719561100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1941-0476 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014496 issn: 1053-587X databaseCode: RIE dateStart: 19910101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3dS8MwED_m8EEf_JridEoffBGMbfqRNI9DHD7NgRP2VtrkAgPppOv8-03SrgwUwbcWklDu0tzv7nL3A7hLuTRANUkITwpOYoZIRMEUYcrYN4pacSod2QSfTtPFQsx68NDVwiCiu3yGj_bR5fLVSm5sqMwXthWKPXD3OGdNrVaXMYhjx8Vl4EJEkpQvtinJQPjzt5lxBENq_FNjvSwB7o4JcpwqPw5iZ10mx__7rhM4alGkN27Ufgo9LM_gcKe34AD8V7NJiYF3ZLysvIa8wWnBW5bmtXJFLKg8W15QGgN5Du-T5_nTC2nZEYgMBa1JoaU24EtTbTBYJGWAGkOWCGbbyVBl03s5o0raIGca5YFFGiqPFQrGMQpVdAH9clXiJXgsZTLiiupCGwAnVWrWoioPmM4VxxiH4G8Flsm2dbhlsPjInAsRiMyIOLMizloRD-G-m_HZtM34Y-zAirQb10pzCKOtTrL2v1pnoe03mIiQpVe_z7qGA7t2EyQZQb-uNngD-_KrXq6rW7dlvgFBuL0M
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3dS8MwED_GFNQHv6Y4ndoHXwTjmn4kzeMQx8Q5B07YW2mTCwykk33495tkXRkogm8tJG25S3O_u8vdD-Am4dIA1TgmPM45iRgiETlThClj3yhqxal0ZBN8MEjGYzGswV1VC4OI7vAZ3ttLl8tXU7m0obK2sK1Q7Ia7ZZmzymqtKmcQRY6NywCGkMQJH6-Tkr5oj96GxhUMqPFQjf2yFLgbRsixqvzYip196R7878sOYb_EkV5npfgjqGFxDHsb3QUb0H41y5QYgEc6k5m3om9wevAmhbmduTIWVJ4tMCiMiTyB9-7j6KFHSn4EIgNBFyTXUhv4pak2KCyU0keNAYsFsw1lqLIJvoxRJW2YMwkz32INlUUKBeMYBio8hXoxLfAMPJYwGXJFda4NhJMqMc-iKvOZzhTHCJvQXgsslWXzcMth8ZE6J8IXqRFxakWcliJuwm0143PVOOOPsQ0r0mpcKc0mtNY6Scs_a54GtuNgLAKWnP8-6xp2eqOXftp_GjxfwK59zypk0oL6YrbES9iWX4vJfHblls83Sk7AVQ
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=Over-the-Air+Computation+in+Correlated+Channels&rft.jtitle=IEEE+transactions+on+signal+processing&rft.au=Frey%2C+Matthias&rft.au=Bjelakovic%2C+Igor&rft.au=Stanczak%2C+Slawomir&rft.date=2021&rft.issn=1053-587X&rft.eissn=1941-0476&rft.volume=69&rft.spage=5739&rft.epage=5755&rft_id=info:doi/10.1109%2FTSP.2021.3106115&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TSP_2021_3106115
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1053-587X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1053-587X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1053-587X&client=summon