A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis
A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig's Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, sim...
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| Veröffentlicht in: | IEEE transactions on communications 2020-07, Vol.68 (7), p.4117-4125 |
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| container_title | IEEE transactions on communications |
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| creator | Behnad, Aydin |
| description | A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig's Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig's Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami- m fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami- m fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations. |
| doi_str_mv | 10.1109/TCOMM.2020.2986209 |
| format | Article |
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It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig's Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations.]]></description><identifier>ISSN: 0090-6778</identifier><identifier>EISSN: 1558-0857</identifier><identifier>DOI: 10.1109/TCOMM.2020.2986209</identifier><identifier>CODEN: IECMBT</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Computer simulation ; Craig’s formula ; Diversity reception ; equal-gain combining (EGC) ; Error analysis ; Error probability ; Fading ; Fading channels ; Gaussian distribution ; Modulation ; Nakagami fading ; Performance analysis ; Probability ; Q-function ; Random variables ; Signal to noise ratio</subject><ispartof>IEEE transactions on communications, 2020-07, Vol.68 (7), p.4117-4125</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c295t-51a4ba6026dd7dacf930b5ea2e52868303bc02135bcab8acfd547daf18aaa8e93</citedby><cites>FETCH-LOGICAL-c295t-51a4ba6026dd7dacf930b5ea2e52868303bc02135bcab8acfd547daf18aaa8e93</cites><orcidid>0000-0003-0771-8755</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9058698$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9058698$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Behnad, Aydin</creatorcontrib><title>A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis</title><title>IEEE transactions on communications</title><addtitle>TCOMM</addtitle><description><![CDATA[A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig's Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig's Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations.]]></description><subject>Computer simulation</subject><subject>Craig’s formula</subject><subject>Diversity reception</subject><subject>equal-gain combining (EGC)</subject><subject>Error analysis</subject><subject>Error probability</subject><subject>Fading</subject><subject>Fading channels</subject><subject>Gaussian distribution</subject><subject>Modulation</subject><subject>Nakagami fading</subject><subject>Performance analysis</subject><subject>Probability</subject><subject>Q-function</subject><subject>Random variables</subject><subject>Signal to noise ratio</subject><issn>0090-6778</issn><issn>1558-0857</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1PwzAMhiMEEmPwB-ASiQOnDjdp2uRYyjYmbQykca7cNIWO0o6kRezf032Ik2X7fSzrIeTah5Hvg7pfJcvFYsSAwYgpGTJQJ2TgCyE9kCI6JQMABV4YRfKcXDi3BoAAOB-Qz5g-Nz-mouPf1tSubGraNjSxWL7fOfrqTbpat7vppLFfXYUU65zOWkfjzaYqNe53ZU0fO6y8B4u1_qDjaUJfjC16ou8NjWustq50l-SswMqZq2MdkrfJeJU8efPldJbEc08zJVpP-BhkGAIL8zzKUReKQyYMMiOYDCUHnmlgPheZxkz2-1wEfa7wJSJKo_iQ3B7ubmzz3RnXpuums_0TLmUBC0QgoijoU-yQ0rZxzpoi3djyC-029SHdSU33UtOd1PQotYduDlBpjPkHFAgZKsn_AGCec1k</recordid><startdate>20200701</startdate><enddate>20200701</enddate><creator>Behnad, Aydin</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-0771-8755</orcidid></search><sort><creationdate>20200701</creationdate><title>A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis</title><author>Behnad, Aydin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c295t-51a4ba6026dd7dacf930b5ea2e52868303bc02135bcab8acfd547daf18aaa8e93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer simulation</topic><topic>Craig’s formula</topic><topic>Diversity reception</topic><topic>equal-gain combining (EGC)</topic><topic>Error analysis</topic><topic>Error probability</topic><topic>Fading</topic><topic>Fading channels</topic><topic>Gaussian distribution</topic><topic>Modulation</topic><topic>Nakagami fading</topic><topic>Performance analysis</topic><topic>Probability</topic><topic>Q-function</topic><topic>Random variables</topic><topic>Signal to noise ratio</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Behnad, Aydin</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>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Behnad, Aydin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis</atitle><jtitle>IEEE transactions on communications</jtitle><stitle>TCOMM</stitle><date>2020-07-01</date><risdate>2020</risdate><volume>68</volume><issue>7</issue><spage>4117</spage><epage>4125</epage><pages>4117-4125</pages><issn>0090-6778</issn><eissn>1558-0857</eissn><coden>IECMBT</coden><abstract><![CDATA[A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig's Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig's Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami-<inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations.]]></abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TCOMM.2020.2986209</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0003-0771-8755</orcidid></addata></record> |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Computer simulation Craig’s formula Diversity reception equal-gain combining (EGC) Error analysis Error probability Fading Fading channels Gaussian distribution Modulation Nakagami fading Performance analysis Probability Q-function Random variables Signal to noise ratio |
| title | A Novel Extension to Craig's Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis |
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