On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels With Constant Coefficients
In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper co...
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| Published in: | IEEE transactions on signal processing 2013-05, Vol.61 (9), p.2178-2191 |
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On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels With Constant Coefficients |
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Liu, Tingting Yang, Chenyang |
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Algorithms Antennas Applied sciences Broadcasting Channels Degrees of freedom (DoF) Detection, estimation, filtering, equalization, prediction Electromagnetism Exact sciences and technology Feasibility Information, signal and communications theory Interference interference alignment feasibility interference broadcast channel Jacobi matrix method Jacobian matrices Jacobian matrix Matrix converters MIMO multi-input-multi-output (MIMO) Receiving antennas Signal and communications theory Signal, noise Sparse matrices Streams Studies Telecommunications and information theory |
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In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility. |
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We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. 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We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility.</description><subject>Algorithms</subject><subject>Antennas</subject><subject>Applied sciences</subject><subject>Broadcasting</subject><subject>Channels</subject><subject>Degrees of freedom (DoF)</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Electromagnetism</subject><subject>Exact sciences and technology</subject><subject>Feasibility</subject><subject>Information, signal and communications theory</subject><subject>Interference</subject><subject>interference alignment feasibility</subject><subject>interference broadcast channel</subject><subject>Jacobi matrix method</subject><subject>Jacobian matrices</subject><subject>Jacobian matrix</subject><subject>Matrix converters</subject><subject>MIMO</subject><subject>multi-input-multi-output (MIMO)</subject><subject>Receiving antennas</subject><subject>Signal and communications theory</subject><subject>Signal, noise</subject><subject>Sparse matrices</subject><subject>Streams</subject><subject>Studies</subject><subject>Telecommunications and information theory</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNpdkc2LFDEQxRtRcF29C14CInjpMR-VdPdxbVwdmGUEV_TW1KYrTpaeZE0yyP73ZplhQU9VUL_3eNRrmteCr4Tgw4frb19Xkgu1khJ6zvWT5kwMIFoOnXlad65Vq_vu5_PmRc63nAuAwZw1f7aBlR2xS8Lsb_ziyz2Ljm18IExsHQolR4mCJXax-F9hT6EwFxO7Wl9t_71_TBFni7mwcYch0JLZD192bIwhF6yyMZJz3vpqkV82zxwumV6d5nnz_fLT9fil3Ww_r8eLTWuVhtLOdp5xQNCm4wRiRmXQoNJdD1YZq7Xr8WaWThDHvsMBJJ-1k072IKTCQZ0374--dyn-PlAu095nS8uCgeIhT0IZLerLACr69j_0Nh5SqOkqJY3gnRRdpfiRsinmnMhNd8nvMd1Pgk8PTUy1iemhienURJW8Oxljtri4hMH6_KirWQcNSlTuzZHzRPR4NmAMKFB_AaYekYI</recordid><startdate>20130501</startdate><enddate>20130501</enddate><creator>Liu, Tingting</creator><creator>Yang, Chenyang</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><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>20130501</creationdate><title>On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels With Constant Coefficients</title><author>Liu, Tingting ; Yang, Chenyang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-dcdda9a45670e41da36a6a35784c36c55f8abd2f1e0a87a9420d5f2f284123a93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Antennas</topic><topic>Applied sciences</topic><topic>Broadcasting</topic><topic>Channels</topic><topic>Degrees of freedom (DoF)</topic><topic>Detection, estimation, filtering, equalization, prediction</topic><topic>Electromagnetism</topic><topic>Exact sciences and technology</topic><topic>Feasibility</topic><topic>Information, signal and communications theory</topic><topic>Interference</topic><topic>interference alignment feasibility</topic><topic>interference broadcast channel</topic><topic>Jacobi matrix method</topic><topic>Jacobian matrices</topic><topic>Jacobian matrix</topic><topic>Matrix converters</topic><topic>MIMO</topic><topic>multi-input-multi-output (MIMO)</topic><topic>Receiving antennas</topic><topic>Signal and communications theory</topic><topic>Signal, noise</topic><topic>Sparse matrices</topic><topic>Streams</topic><topic>Studies</topic><topic>Telecommunications and information theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Tingting</creatorcontrib><creatorcontrib>Yang, Chenyang</creatorcontrib><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 signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Tingting</au><au>Yang, Chenyang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels With Constant Coefficients</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2013-05-01</date><risdate>2013</risdate><volume>61</volume><issue>9</issue><spage>2178</spage><epage>2191</epage><pages>2178-2191</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><notes>ObjectType-Article-2</notes><notes>SourceType-Scholarly Journals-1</notes><notes>ObjectType-Feature-1</notes><notes>content type line 23</notes><abstract>In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility for general MIMO-IBC. Except for the proper condition, we find another necessary condition to ensure a kind of irreducible interference to be eliminated. We then prove the necessary and sufficient conditions for a special class of MIMO-IBC, where the numbers of antennas are divisible by the number of data streams per user. Since finding an invertible Jacobian matrix is crucial for the sufficiency proof, we first analyze the impact of sparse structure and repeated structure of the Jacobian matrix. Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix corresponding to the transmit and receive matrices have different repeated structure, we find an invertible Jacobian matrix by constructing the two sub-matrices separately. We show that for the MIMO-IBC where each user has one desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear IA feasibility.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2013.2248005</doi><oa>free_for_read</oa></addata></record> |