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On the ratio of independent complex Gaussian random variables
In this paper, we derive a closed form equation for the joint probability distribution f R z , Θ z ( r z , θ z ) of the amplitude R z and phase Θ z of the ratio Z = X Y of two independent non-zero mean Complex Gaussian random variables X ∼ C N ( ν x e j ϕ x , σ x 2 ) and Y ∼ C N ( ν y e j ϕ y , σ y...
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| Published in: | Multidimensional systems and signal processing 2018-10, Vol.29 (4), p.1553-1561 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c316t-1b806b6cc34ebf6d7fc6f50576d991adcbf0693cb716e8463850ce7b77dfefd03 |
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| cites | cdi_FETCH-LOGICAL-c316t-1b806b6cc34ebf6d7fc6f50576d991adcbf0693cb716e8463850ce7b77dfefd03 |
| container_end_page | 1561 |
| container_issue | 4 |
| container_start_page | 1553 |
| container_title | Multidimensional systems and signal processing |
| container_volume | 29 |
| creator | Nadimi, E. S. Ramezani, M. H. Blanes-Vidal, V. |
| description | In this paper, we derive a closed form equation for the joint probability distribution
f
R
z
,
Θ
z
(
r
z
,
θ
z
)
of the amplitude
R
z
and phase
Θ
z
of the ratio
Z
=
X
Y
of two independent non-zero mean Complex Gaussian random variables
X
∼
C
N
(
ν
x
e
j
ϕ
x
,
σ
x
2
)
and
Y
∼
C
N
(
ν
y
e
j
ϕ
y
,
σ
y
2
)
. The derived joint probability distribution only contains a confluent hypergeometric function of the first kind
1
F
1
without infinite summations resulting in computational efficiency. We further derive the probability distribution for the ratio of two non-zero mean independent real Rician random variables containing an infinite summation generated by the estimation of the Cauchy product of equivalent series of two modified Bessel functions. |
| doi_str_mv | 10.1007/s11045-017-0519-3 |
| format | article |
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f
R
z
,
Θ
z
(
r
z
,
θ
z
)
of the amplitude
R
z
and phase
Θ
z
of the ratio
Z
=
X
Y
of two independent non-zero mean Complex Gaussian random variables
X
∼
C
N
(
ν
x
e
j
ϕ
x
,
σ
x
2
)
and
Y
∼
C
N
(
ν
y
e
j
ϕ
y
,
σ
y
2
)
. The derived joint probability distribution only contains a confluent hypergeometric function of the first kind
1
F
1
without infinite summations resulting in computational efficiency. We further derive the probability distribution for the ratio of two non-zero mean independent real Rician random variables containing an infinite summation generated by the estimation of the Cauchy product of equivalent series of two modified Bessel functions.</description><identifier>ISSN: 0923-6082</identifier><identifier>EISSN: 1573-0824</identifier><identifier>DOI: 10.1007/s11045-017-0519-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Artificial Intelligence ; Bessel functions ; Circuits and Systems ; Complex variables ; Computing time ; Electrical Engineering ; Engineering ; Hypergeometric functions ; Independent variables ; Probability distribution ; Random variables ; Real variables ; Signal,Image and Speech Processing</subject><ispartof>Multidimensional systems and signal processing, 2018-10, Vol.29 (4), p.1553-1561</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-1b806b6cc34ebf6d7fc6f50576d991adcbf0693cb716e8463850ce7b77dfefd03</citedby><cites>FETCH-LOGICAL-c316t-1b806b6cc34ebf6d7fc6f50576d991adcbf0693cb716e8463850ce7b77dfefd03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782,27907,27908</link.rule.ids></links><search><creatorcontrib>Nadimi, E. S.</creatorcontrib><creatorcontrib>Ramezani, M. H.</creatorcontrib><creatorcontrib>Blanes-Vidal, V.</creatorcontrib><title>On the ratio of independent complex Gaussian random variables</title><title>Multidimensional systems and signal processing</title><addtitle>Multidim Syst Sign Process</addtitle><description>In this paper, we derive a closed form equation for the joint probability distribution
f
R
z
,
Θ
z
(
r
z
,
θ
z
)
of the amplitude
R
z
and phase
Θ
z
of the ratio
Z
=
X
Y
of two independent non-zero mean Complex Gaussian random variables
X
∼
C
N
(
ν
x
e
j
ϕ
x
,
σ
x
2
)
and
Y
∼
C
N
(
ν
y
e
j
ϕ
y
,
σ
y
2
)
. The derived joint probability distribution only contains a confluent hypergeometric function of the first kind
1
F
1
without infinite summations resulting in computational efficiency. We further derive the probability distribution for the ratio of two non-zero mean independent real Rician random variables containing an infinite summation generated by the estimation of the Cauchy product of equivalent series of two modified Bessel functions.</description><subject>Artificial Intelligence</subject><subject>Bessel functions</subject><subject>Circuits and Systems</subject><subject>Complex variables</subject><subject>Computing time</subject><subject>Electrical Engineering</subject><subject>Engineering</subject><subject>Hypergeometric functions</subject><subject>Independent variables</subject><subject>Probability distribution</subject><subject>Random variables</subject><subject>Real variables</subject><subject>Signal,Image and Speech Processing</subject><issn>0923-6082</issn><issn>1573-0824</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wNuC5-jMZjfZPXiQoq1Q6EXPIZsP3dIma7IV_femrODJywwDz_sOPIRcI9wigLhLiFDVFFBQqLGl7ITMsBaMQlNWp2QGbckoz8c5uUhpC5BTyGfkfuOL8d0WUY19KIIrem_sYPPwY6HDftjZr2KpDin1ymfKm7AvPlXsVbez6ZKcObVL9up3z8nr0-PLYkXXm-Xz4mFNNUM-Uuwa4B3XmlW2c9wIp7mroRbctC0qozsHvGW6E8htU3HW1KCt6IQwzjoDbE5upt4hho-DTaPchkP0-aUsERiUbYM8UzhROoaUonVyiP1exW-JII-W5GRJZkvyaEmynCmnTMqsf7Pxr_n_0A-AgWnZ</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Nadimi, E. S.</creator><creator>Ramezani, M. H.</creator><creator>Blanes-Vidal, V.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20181001</creationdate><title>On the ratio of independent complex Gaussian random variables</title><author>Nadimi, E. S. ; Ramezani, M. H. ; Blanes-Vidal, V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-1b806b6cc34ebf6d7fc6f50576d991adcbf0693cb716e8463850ce7b77dfefd03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Artificial Intelligence</topic><topic>Bessel functions</topic><topic>Circuits and Systems</topic><topic>Complex variables</topic><topic>Computing time</topic><topic>Electrical Engineering</topic><topic>Engineering</topic><topic>Hypergeometric functions</topic><topic>Independent variables</topic><topic>Probability distribution</topic><topic>Random variables</topic><topic>Real variables</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nadimi, E. S.</creatorcontrib><creatorcontrib>Ramezani, M. H.</creatorcontrib><creatorcontrib>Blanes-Vidal, V.</creatorcontrib><collection>CrossRef</collection><jtitle>Multidimensional systems and signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nadimi, E. S.</au><au>Ramezani, M. H.</au><au>Blanes-Vidal, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the ratio of independent complex Gaussian random variables</atitle><jtitle>Multidimensional systems and signal processing</jtitle><stitle>Multidim Syst Sign Process</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>29</volume><issue>4</issue><spage>1553</spage><epage>1561</epage><pages>1553-1561</pages><issn>0923-6082</issn><eissn>1573-0824</eissn><abstract>In this paper, we derive a closed form equation for the joint probability distribution
f
R
z
,
Θ
z
(
r
z
,
θ
z
)
of the amplitude
R
z
and phase
Θ
z
of the ratio
Z
=
X
Y
of two independent non-zero mean Complex Gaussian random variables
X
∼
C
N
(
ν
x
e
j
ϕ
x
,
σ
x
2
)
and
Y
∼
C
N
(
ν
y
e
j
ϕ
y
,
σ
y
2
)
. The derived joint probability distribution only contains a confluent hypergeometric function of the first kind
1
F
1
without infinite summations resulting in computational efficiency. We further derive the probability distribution for the ratio of two non-zero mean independent real Rician random variables containing an infinite summation generated by the estimation of the Cauchy product of equivalent series of two modified Bessel functions.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11045-017-0519-3</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0923-6082 |
| ispartof | Multidimensional systems and signal processing, 2018-10, Vol.29 (4), p.1553-1561 |
| issn | 0923-6082 1573-0824 |
| language | eng |
| recordid | cdi_proquest_journals_2103029816 |
| source | Springer Nature |
| subjects | Artificial Intelligence Bessel functions Circuits and Systems Complex variables Computing time Electrical Engineering Engineering Hypergeometric functions Independent variables Probability distribution Random variables Real variables Signal,Image and Speech Processing |
| title | On the ratio of independent complex Gaussian random variables |
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