The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT
The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary inde...
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| Veröffentlicht in: | IEEE transactions on information theory 2012-07, Vol.58 (7), p.4396-4417 |
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| description | The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT. |
| doi_str_mv | 10.1109/TIT.2012.2194270 |
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Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2012.2194270</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Antennas ; Applied sciences ; Degrees of freedom (DoF) ; delayed CSIT ; Detection, estimation, filtering, equalization, prediction ; Electric noise ; Exact sciences and technology ; Fading ; Information theory ; Information, signal and communications theory ; Input output ; Integrated circuits ; Interference ; interference alignment ; MIMO ; MIMO interference channel (IC) ; outer bounds ; Radiocommunications ; Receiving antennas ; Signal and communications theory ; Signal, noise ; Systems, networks and services of telecommunications ; Telecommunications ; Telecommunications and information theory ; Transmission and modulation (techniques and equipments) ; Transmitters ; Transmitters. 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(IEEE) Jul 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c321t-da568739574d83a48d747f927f8807b278147f2d63c8ad94a00ab78d7a6977513</citedby><cites>FETCH-LOGICAL-c321t-da568739574d83a48d747f927f8807b278147f2d63c8ad94a00ab78d7a6977513</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6179997$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54737</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6179997$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26074567$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Vaze, Chinmay S.</creatorcontrib><creatorcontrib>Varanasi, Mahesh K.</creatorcontrib><title>The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.</description><subject>Antennas</subject><subject>Applied sciences</subject><subject>Degrees of freedom (DoF)</subject><subject>delayed CSIT</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Electric noise</subject><subject>Exact sciences and technology</subject><subject>Fading</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Input output</subject><subject>Integrated circuits</subject><subject>Interference</subject><subject>interference alignment</subject><subject>MIMO</subject><subject>MIMO interference channel (IC)</subject><subject>outer bounds</subject><subject>Radiocommunications</subject><subject>Receiving antennas</subject><subject>Signal and communications theory</subject><subject>Signal, noise</subject><subject>Systems, networks and services of telecommunications</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Transmission and modulation (techniques and equipments)</subject><subject>Transmitters</subject><subject>Transmitters. 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(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></search><sort><creationdate>20120701</creationdate><title>The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT</title><author>Vaze, Chinmay S. ; Varanasi, Mahesh K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-da568739574d83a48d747f927f8807b278147f2d63c8ad94a00ab78d7a6977513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Antennas</topic><topic>Applied sciences</topic><topic>Degrees of freedom (DoF)</topic><topic>delayed CSIT</topic><topic>Detection, estimation, filtering, equalization, prediction</topic><topic>Electric noise</topic><topic>Exact sciences and technology</topic><topic>Fading</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Input output</topic><topic>Integrated circuits</topic><topic>Interference</topic><topic>interference alignment</topic><topic>MIMO</topic><topic>MIMO interference channel (IC)</topic><topic>outer bounds</topic><topic>Radiocommunications</topic><topic>Receiving antennas</topic><topic>Signal and communications theory</topic><topic>Signal, noise</topic><topic>Systems, networks and services of telecommunications</topic><topic>Telecommunications</topic><topic>Telecommunications and information theory</topic><topic>Transmission and modulation (techniques and equipments)</topic><topic>Transmitters</topic><topic>Transmitters. Receivers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vaze, Chinmay S.</creatorcontrib><creatorcontrib>Varanasi, Mahesh K.</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><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Vaze, Chinmay S.</au><au>Varanasi, Mahesh K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2012-07-01</date><risdate>2012</risdate><volume>58</volume><issue>7</issue><spage>4396</spage><epage>4417</epage><pages>4396-4417</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2012.2194270</doi><tpages>22</tpages></addata></record> |
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| subjects | Antennas Applied sciences Degrees of freedom (DoF) delayed CSIT Detection, estimation, filtering, equalization, prediction Electric noise Exact sciences and technology Fading Information theory Information, signal and communications theory Input output Integrated circuits Interference interference alignment MIMO MIMO interference channel (IC) outer bounds Radiocommunications Receiving antennas Signal and communications theory Signal, noise Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Transmitters Transmitters. Receivers |
| title | The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT |
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