Hard Fairness Versus Proportional Fairness in Wireless Communications: The Single-Cell Case
We consider a wireless communication system formed by a single cell with one base station and K user terminals. User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path...
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description | We consider a wireless communication system formed by a single cell with one base station and K user terminals. User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path loss. We compare delay-limited systems with variable-rate systems under fairness constraints, in terms of the achieved system spectral efficiency C (bit/s/Hz) versus E b /N 0 . The considered delay-limited systems impose "hard-fairness": every user transmits at its desired rate on all blocks, independently of its fading conditions. The variable-rate system imposes "proportional fairness" via the popular Proportional Fair Scheduling (PFS) algorithm, currently implemented in 3G wireless for data (delay-tolerant) applications. We find simple iterative resource allocation algorithms that converge to the optimal delay-limited throughput for orthogonal (frequency-division multiple access (FDMA)/time-division multiple access (TDMA)) and optimal (superposition/interference cancellation) signaling. In the limit of large K and finite M we find closed-form expressions for C as a function of E b /N 0 . We show that in this limit, the optimal allocation policy consists of letting each user transmit on its best subchannel only. Also, we find a simple closed-form expression for the throughput of PFS in a cellular environment, that holds for any K and M. Finally, we obtain closed-form expressions for C versus E b /N 0 in the low and high spectral efficiency regimes. The conclusions of our analysis in terms of system design guidelines are as follows: a) if hard fairness is a requirement, orthogonal access incurs a large throughput penalty with respect to the optimal (superposition coding) strategy, especially in the regime of high spectral efficiency; b) for high spectral efficiency, PFS does not provide any significant gain and may even perform worse than the optimal delay-limited system, despite the fact that the imposed fairness constraint is laxer; c) for low to moderate spectral efficiency, the stricter hard-fairness constraint incurs in a large throughput penalty with respect to PFS |
doi_str_mv | 10.1109/TIT.2007.892790 |
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User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path loss. We compare delay-limited systems with variable-rate systems under fairness constraints, in terms of the achieved system spectral efficiency C (bit/s/Hz) versus E b /N 0 . The considered delay-limited systems impose "hard-fairness": every user transmits at its desired rate on all blocks, independently of its fading conditions. The variable-rate system imposes "proportional fairness" via the popular Proportional Fair Scheduling (PFS) algorithm, currently implemented in 3G wireless for data (delay-tolerant) applications. We find simple iterative resource allocation algorithms that converge to the optimal delay-limited throughput for orthogonal (frequency-division multiple access (FDMA)/time-division multiple access (TDMA)) and optimal (superposition/interference cancellation) signaling. In the limit of large K and finite M we find closed-form expressions for C as a function of E b /N 0 . We show that in this limit, the optimal allocation policy consists of letting each user transmit on its best subchannel only. Also, we find a simple closed-form expression for the throughput of PFS in a cellular environment, that holds for any K and M. Finally, we obtain closed-form expressions for C versus E b /N 0 in the low and high spectral efficiency regimes. The conclusions of our analysis in terms of system design guidelines are as follows: a) if hard fairness is a requirement, orthogonal access incurs a large throughput penalty with respect to the optimal (superposition coding) strategy, especially in the regime of high spectral efficiency; b) for high spectral efficiency, PFS does not provide any significant gain and may even perform worse than the optimal delay-limited system, despite the fact that the imposed fairness constraint is laxer; c) for low to moderate spectral efficiency, the stricter hard-fairness constraint incurs in a large throughput penalty with respect to PFS</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2007.892790</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithms ; Applied sciences ; Base stations ; Channels ; Closed-form solution ; Code-division multiple access (CDMA) ; Delay systems ; delay- limited capacity ; Digital electronics ; Electrical engineering ; Equipments and installations ; Exact sciences and technology ; Exact solutions ; Fading ; Frequency ; Information theory ; Information, signal and communications theory ; Iterative algorithms ; Mathematical analysis ; Mobile radiocommunication systems ; Multiple access ; Multiplexing ; Optimization ; proportional fair scheduling ; Radiocommunications ; Resource management ; Scheduling algorithm ; Signal and communications theory ; Spectra ; Systems, networks and services of telecommunications ; Telecommunications ; Telecommunications and information theory ; Throughput ; Transmission and modulation (techniques and equipments) ; uplink-downlink duality ; Wireless communication ; Wireless communications</subject><ispartof>IEEE transactions on information theory, 2007-04, Vol.53 (4), p.1366-1385</ispartof><rights>2007 INIST-CNRS</rights><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Apr 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c447t-1804d7771a9d97408f0e5d1b04592da58ef3ae78764a926a30d877681e75259c3</citedby><cites>FETCH-LOGICAL-c447t-1804d7771a9d97408f0e5d1b04592da58ef3ae78764a926a30d877681e75259c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4137874$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27922,27923,54756</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4137874$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18621884$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Caire, G.</creatorcontrib><creatorcontrib>Muller, R.R.</creatorcontrib><creatorcontrib>Knopp, R.</creatorcontrib><title>Hard Fairness Versus Proportional Fairness in Wireless Communications: The Single-Cell Case</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>We consider a wireless communication system formed by a single cell with one base station and K user terminals. User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path loss. We compare delay-limited systems with variable-rate systems under fairness constraints, in terms of the achieved system spectral efficiency C (bit/s/Hz) versus E b /N 0 . The considered delay-limited systems impose "hard-fairness": every user transmits at its desired rate on all blocks, independently of its fading conditions. The variable-rate system imposes "proportional fairness" via the popular Proportional Fair Scheduling (PFS) algorithm, currently implemented in 3G wireless for data (delay-tolerant) applications. We find simple iterative resource allocation algorithms that converge to the optimal delay-limited throughput for orthogonal (frequency-division multiple access (FDMA)/time-division multiple access (TDMA)) and optimal (superposition/interference cancellation) signaling. In the limit of large K and finite M we find closed-form expressions for C as a function of E b /N 0 . We show that in this limit, the optimal allocation policy consists of letting each user transmit on its best subchannel only. Also, we find a simple closed-form expression for the throughput of PFS in a cellular environment, that holds for any K and M. Finally, we obtain closed-form expressions for C versus E b /N 0 in the low and high spectral efficiency regimes. The conclusions of our analysis in terms of system design guidelines are as follows: a) if hard fairness is a requirement, orthogonal access incurs a large throughput penalty with respect to the optimal (superposition coding) strategy, especially in the regime of high spectral efficiency; b) for high spectral efficiency, PFS does not provide any significant gain and may even perform worse than the optimal delay-limited system, despite the fact that the imposed fairness constraint is laxer; c) for low to moderate spectral efficiency, the stricter hard-fairness constraint incurs in a large throughput penalty with respect to PFS</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Base stations</subject><subject>Channels</subject><subject>Closed-form solution</subject><subject>Code-division multiple access (CDMA)</subject><subject>Delay systems</subject><subject>delay- limited capacity</subject><subject>Digital electronics</subject><subject>Electrical engineering</subject><subject>Equipments and installations</subject><subject>Exact sciences and technology</subject><subject>Exact solutions</subject><subject>Fading</subject><subject>Frequency</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Iterative algorithms</subject><subject>Mathematical analysis</subject><subject>Mobile radiocommunication systems</subject><subject>Multiple access</subject><subject>Multiplexing</subject><subject>Optimization</subject><subject>proportional fair scheduling</subject><subject>Radiocommunications</subject><subject>Resource management</subject><subject>Scheduling algorithm</subject><subject>Signal and communications theory</subject><subject>Spectra</subject><subject>Systems, networks and services of telecommunications</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Throughput</subject><subject>Transmission and modulation (techniques and equipments)</subject><subject>uplink-downlink duality</subject><subject>Wireless communication</subject><subject>Wireless communications</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kU1LxDAQhoMouH6cPXgpgnrqOmmTJvEmxVVBUHDVg4cQ26lGuu2a2R7892bZRcGDp5lhnpl5mZexAw5jzsGcTW-m4wxAjbXJlIENNuJSqtQUUmyyEQDXqRFCb7Mdoo9YCsmzEXu5dqFOJs6HDomSJww0UHIf-nkfFr7vXPvb9F3y7AO2y7zsZ7Oh85VbQnSeTN8xefDdW4tpiW2blI5wj201riXcX8dd9ji5nJbX6e3d1U15cZtWQqhFyjWIWinFnamNEqAbQFnzVxDSZLWTGpvcodKqEM5khcuh1koVmqOSmTRVvstOV3vnof8ckBZ25qmKKlyH_UBWKwkyhwIiefIvmQth4qEsgkd_wI9-CPEbZLmJskAaFaGzFVSFnihgY-fBz1z4shzs0hMbPbFLT-zKkzhxvF7rqHJtE1xXefod00XGtRaRO1xxHhF_2oLnUZzIvwEnoJLW</recordid><startdate>20070401</startdate><enddate>20070401</enddate><creator>Caire, G.</creator><creator>Muller, R.R.</creator><creator>Knopp, R.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20070401</creationdate><title>Hard Fairness Versus Proportional Fairness in Wireless Communications: The Single-Cell Case</title><author>Caire, G. ; Muller, R.R. ; Knopp, R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c447t-1804d7771a9d97408f0e5d1b04592da58ef3ae78764a926a30d877681e75259c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Base stations</topic><topic>Channels</topic><topic>Closed-form solution</topic><topic>Code-division multiple access (CDMA)</topic><topic>Delay systems</topic><topic>delay- limited capacity</topic><topic>Digital electronics</topic><topic>Electrical engineering</topic><topic>Equipments and installations</topic><topic>Exact sciences and technology</topic><topic>Exact solutions</topic><topic>Fading</topic><topic>Frequency</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Iterative algorithms</topic><topic>Mathematical analysis</topic><topic>Mobile radiocommunication systems</topic><topic>Multiple access</topic><topic>Multiplexing</topic><topic>Optimization</topic><topic>proportional fair scheduling</topic><topic>Radiocommunications</topic><topic>Resource management</topic><topic>Scheduling algorithm</topic><topic>Signal and communications theory</topic><topic>Spectra</topic><topic>Systems, networks and services of telecommunications</topic><topic>Telecommunications</topic><topic>Telecommunications and information theory</topic><topic>Throughput</topic><topic>Transmission and modulation (techniques and equipments)</topic><topic>uplink-downlink duality</topic><topic>Wireless communication</topic><topic>Wireless communications</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Caire, G.</creatorcontrib><creatorcontrib>Muller, R.R.</creatorcontrib><creatorcontrib>Knopp, R.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Caire, G.</au><au>Muller, R.R.</au><au>Knopp, R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hard Fairness Versus Proportional Fairness in Wireless Communications: The Single-Cell Case</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2007-04-01</date><risdate>2007</risdate><volume>53</volume><issue>4</issue><spage>1366</spage><epage>1385</epage><pages>1366-1385</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>We consider a wireless communication system formed by a single cell with one base station and K user terminals. User channels are characterized by frequency-selective fading due to small-scale effects, modeled as a set of M parallel block-fading channels, and a frequency-flat distance-dependent path loss. We compare delay-limited systems with variable-rate systems under fairness constraints, in terms of the achieved system spectral efficiency C (bit/s/Hz) versus E b /N 0 . The considered delay-limited systems impose "hard-fairness": every user transmits at its desired rate on all blocks, independently of its fading conditions. The variable-rate system imposes "proportional fairness" via the popular Proportional Fair Scheduling (PFS) algorithm, currently implemented in 3G wireless for data (delay-tolerant) applications. We find simple iterative resource allocation algorithms that converge to the optimal delay-limited throughput for orthogonal (frequency-division multiple access (FDMA)/time-division multiple access (TDMA)) and optimal (superposition/interference cancellation) signaling. In the limit of large K and finite M we find closed-form expressions for C as a function of E b /N 0 . We show that in this limit, the optimal allocation policy consists of letting each user transmit on its best subchannel only. Also, we find a simple closed-form expression for the throughput of PFS in a cellular environment, that holds for any K and M. Finally, we obtain closed-form expressions for C versus E b /N 0 in the low and high spectral efficiency regimes. The conclusions of our analysis in terms of system design guidelines are as follows: a) if hard fairness is a requirement, orthogonal access incurs a large throughput penalty with respect to the optimal (superposition coding) strategy, especially in the regime of high spectral efficiency; b) for high spectral efficiency, PFS does not provide any significant gain and may even perform worse than the optimal delay-limited system, despite the fact that the imposed fairness constraint is laxer; c) for low to moderate spectral efficiency, the stricter hard-fairness constraint incurs in a large throughput penalty with respect to PFS</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2007.892790</doi><tpages>20</tpages></addata></record> |
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subjects | Algorithms Applied sciences Base stations Channels Closed-form solution Code-division multiple access (CDMA) Delay systems delay- limited capacity Digital electronics Electrical engineering Equipments and installations Exact sciences and technology Exact solutions Fading Frequency Information theory Information, signal and communications theory Iterative algorithms Mathematical analysis Mobile radiocommunication systems Multiple access Multiplexing Optimization proportional fair scheduling Radiocommunications Resource management Scheduling algorithm Signal and communications theory Spectra Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Throughput Transmission and modulation (techniques and equipments) uplink-downlink duality Wireless communication Wireless communications |
title | Hard Fairness Versus Proportional Fairness in Wireless Communications: The Single-Cell Case |
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