On Certain Large Random Hermitian Jacobi Matrices With Applications to Wireless Communications
In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular, we are interested in an uplink cellular channel which models mobile users experiencing a soft-handoff situation under joint multice...
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| Veröffentlicht in: | IEEE transactions on information theory 2009-04, Vol.55 (4), p.1534-1554 |
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| creator | Levy, N. Somekh, O. Shamai, S. Zeitouni, O. |
| description | In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular, we are interested in an uplink cellular channel which models mobile users experiencing a soft-handoff situation under joint multicell decoding. Considering rather general fading statistics we provide a closed-form expression for the per-cell sum-rate of this channel in high signal-to-noise ratio (SNR), when an intra-cell time-division multiple-access (TDMA) protocol is employed. Since the matrices of interest are tridiagonal , their eigenvectors can be considered as sequences with second-order linear recurrence. Therefore, the problem is reduced to the study of the exponential growth of products of two-by-two matrices. For the case where K users are simultaneously active in each cell, we obtain a series of lower and upper bound on the high-SNR power offset of the per-cell sum-rate, which are considerably tighter than previously known bounds. |
| doi_str_mv | 10.1109/TIT.2009.2013046 |
| format | Article |
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These matrices are known to describe certain communication setups. In particular, we are interested in an uplink cellular channel which models mobile users experiencing a soft-handoff situation under joint multicell decoding. Considering rather general fading statistics we provide a closed-form expression for the per-cell sum-rate of this channel in high signal-to-noise ratio (SNR), when an intra-cell time-division multiple-access (TDMA) protocol is employed. Since the matrices of interest are tridiagonal , their eigenvectors can be considered as sequences with second-order linear recurrence. Therefore, the problem is reduced to the study of the exponential growth of products of two-by-two matrices. For the case where K users are simultaneously active in each cell, we obtain a series of lower and upper bound on the high-SNR power offset of the per-cell sum-rate, which are considerably tighter than previously known bounds.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2009.2013046</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Channels ; Closed-form solution ; Coding, codes ; Decoding ; Detection, estimation, filtering, equalization, prediction ; Distributed antenna array ; Exact sciences and technology ; Exact solutions ; Fading ; fading channels ; high-signal-to-noise-ratio (SNR) characterization ; Information theory ; Information, signal and communications theory ; Jacobian matrices ; Mathematical analysis ; Matrices ; Matrix methods ; Mobile communication ; multiuser detection ; Protocols ; random matrices ; Signal and communications theory ; Signal to noise ratio ; Signal, noise ; Statistics ; Studies ; sum-rate capacity ; Systems, networks and services of telecommunications ; Telecommunications ; Telecommunications and information theory ; Time Division Multiple Access ; Transmission and modulation (techniques and equipments) ; Wireless communication ; Wireless communications ; Wyner cellular uplink</subject><ispartof>IEEE transactions on information theory, 2009-04, Vol.55 (4), p.1534-1554</ispartof><rights>2009 INIST-CNRS</rights><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Apr 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c383t-c1f8556c92ee36b78c0ba4026f3cd6048557c0bfd7dfc3625bcbd4518d15bbb63</citedby><cites>FETCH-LOGICAL-c383t-c1f8556c92ee36b78c0ba4026f3cd6048557c0bfd7dfc3625bcbd4518d15bbb63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4802316$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4802316$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21471997$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Levy, N.</creatorcontrib><creatorcontrib>Somekh, O.</creatorcontrib><creatorcontrib>Shamai, S.</creatorcontrib><creatorcontrib>Zeitouni, O.</creatorcontrib><title>On Certain Large Random Hermitian Jacobi Matrices With Applications to Wireless Communications</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular, we are interested in an uplink cellular channel which models mobile users experiencing a soft-handoff situation under joint multicell decoding. Considering rather general fading statistics we provide a closed-form expression for the per-cell sum-rate of this channel in high signal-to-noise ratio (SNR), when an intra-cell time-division multiple-access (TDMA) protocol is employed. Since the matrices of interest are tridiagonal , their eigenvectors can be considered as sequences with second-order linear recurrence. Therefore, the problem is reduced to the study of the exponential growth of products of two-by-two matrices. For the case where K users are simultaneously active in each cell, we obtain a series of lower and upper bound on the high-SNR power offset of the per-cell sum-rate, which are considerably tighter than previously known bounds.</description><subject>Applied sciences</subject><subject>Channels</subject><subject>Closed-form solution</subject><subject>Coding, codes</subject><subject>Decoding</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Distributed antenna array</subject><subject>Exact sciences and technology</subject><subject>Exact solutions</subject><subject>Fading</subject><subject>fading channels</subject><subject>high-signal-to-noise-ratio (SNR) characterization</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Jacobian matrices</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Matrix methods</subject><subject>Mobile communication</subject><subject>multiuser detection</subject><subject>Protocols</subject><subject>random matrices</subject><subject>Signal and communications theory</subject><subject>Signal to noise ratio</subject><subject>Signal, noise</subject><subject>Statistics</subject><subject>Studies</subject><subject>sum-rate capacity</subject><subject>Systems, networks and services of telecommunications</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Time Division Multiple Access</subject><subject>Transmission and modulation (techniques and equipments)</subject><subject>Wireless communication</subject><subject>Wireless communications</subject><subject>Wyner cellular uplink</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kUtLAzEUhYMoWKt7wU0Q1NVoMnlMspTio1IpSMWdIZPJaGQmqcl04b83pdWFCzcJuee7hxwOAMcYXWKM5NViurgsEZL5wARRvgNGmLGqkJzRXTBCCItCUir2wUFKH_lJGS5H4HXu4cTGQTsPZzq-WfikfRN6eG9j7wanPXzQJtQOPuohOmMTfHHDO7xeLjtn9OCCT3AIeRhtZ1OCk9D3K_8jHYK9VnfJHm3vMXi-vVlM7ovZ_G46uZ4VhggyFAa3gjFuZGkt4XUlDKo1RSVviWk4olms8qhtqqY1hJesNnWTA4gGs7quORmDi43vMobPlU2D6l0ytuu0t2GVlMQyh2eVyOT5vyShnJQVwRk8_QN-hFX0OYXCkknChFy7oQ1kYkgp2lYto-t1_FIYqXUvKvei1r2obS955Wzrq5PRXRu1Ny797pWYVvmzVeZONpyz1v7KVKCSYE6-AYrSld4</recordid><startdate>20090401</startdate><enddate>20090401</enddate><creator>Levy, N.</creator><creator>Somekh, O.</creator><creator>Shamai, S.</creator><creator>Zeitouni, O.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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These matrices are known to describe certain communication setups. In particular, we are interested in an uplink cellular channel which models mobile users experiencing a soft-handoff situation under joint multicell decoding. Considering rather general fading statistics we provide a closed-form expression for the per-cell sum-rate of this channel in high signal-to-noise ratio (SNR), when an intra-cell time-division multiple-access (TDMA) protocol is employed. Since the matrices of interest are tridiagonal , their eigenvectors can be considered as sequences with second-order linear recurrence. Therefore, the problem is reduced to the study of the exponential growth of products of two-by-two matrices. 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| subjects | Applied sciences Channels Closed-form solution Coding, codes Decoding Detection, estimation, filtering, equalization, prediction Distributed antenna array Exact sciences and technology Exact solutions Fading fading channels high-signal-to-noise-ratio (SNR) characterization Information theory Information, signal and communications theory Jacobian matrices Mathematical analysis Matrices Matrix methods Mobile communication multiuser detection Protocols random matrices Signal and communications theory Signal to noise ratio Signal, noise Statistics Studies sum-rate capacity Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Time Division Multiple Access Transmission and modulation (techniques and equipments) Wireless communication Wireless communications Wyner cellular uplink |
| title | On Certain Large Random Hermitian Jacobi Matrices With Applications to Wireless Communications |
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