The Probability Distribution of the Amplitude of a Constant Vector Plus a Rayleigh-Distributed Vector

Norton, Kenneth A.; Vogler, L. E.; Mansfield, W. V.; Short, P. J.

doi:10.1109/jrproc.1955.277948

Cited by 97 publications

(39 citation statements)

References 5 publications

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“…On the other hand, if SI= sl = 4 s, but a~O, then (15) reduces to the N akagam i-Rice di stribution (17) a distribution derived by Rice [1944 and 2 and further analyzed, e.g., by Norton et al [1955], and Zuhrt [1957]. The distribution (17) R ayleigh nctor , for the x a nd y co mponents of th e sum will t hen obviously be di stribu ted normally…”

Section: Nonuniform Phase Distributionsmentioning

confidence: 96%

Rayleigh distribution and its generalizations

Beckmann¹

1964

J. RES. NATL. BUR. STAN. SECT. D. RAD. SCI.

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Department of Ele ctric al Enginee ring, University of C olor ado, Boulde r, C olo.(R eceived D eccmber 7, ] 963) Th e Rayleigh d istribu tion is the di stribution of thc sum of a large num be r of coplanar (or t im c) vectors \\'ith r andom. amplitudes alld Ull ifO rlllly distributed phases. As s uch, it is the lim iti ng case of di stributions a~soci at('d II ith 111 0re gl'IlPral v pctor surn s t hat arise i n practical problems. S uch cases arC' til(' folloll' ing: (a) 'I'll(' p hasC' distribu tions of the vec tor tC'rms are not uni fo rm , e.g., in the case of scatt l' ring fro m rough surface'S; (b) One or more vector tcrms predominaLP, their nwan sq uare va lue' not I>l'illg neglig;ble co m pared to th e m ean square valup of Uw SU Ill , c.g., in tJle ea~e of sigl als propagat ed in eil i (,'. ll1<'teor-scatter, and atmosplwrie noi se; (0) Th e numiJer of \'('ctO I' t('r n ' j~ small, ('.g., in rada r ret ur ns from several clo",(' targets; (d) '1'110 Jlumi)('r of vector le l'm o is ilsl'H randolll , e.g., in at mosp her ic t u rbuh'nce, m ekor-scatter and atm ~pl'(' .. ic noise'. The ('('suI ting distributio ns for t hese cases and their deviatio ns from the R ayleig h distr ibution will be co nsidered.

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Section: Nonuniform Phase Distributionsmentioning

confidence: 96%

Rayleigh distribution and its generalizations

Beckmann¹

1964

J. RES. NATL. BUR. STAN. SECT. D. RAD. SCI.

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“…These four qu an ti ties togeth er with th e interdecile r ange of R are shown as fun ctions of J{ in figure 1. The m edian and in terdecile range ar e taken from the p aper by Norton et al [1955].…”

Section: Calculation Of Rand (Jrmentioning

confidence: 99%

Some statistical parameters related to the Nakagami-rice probability distribution

Burns¹

1964

J. RES. NATL. BUR. STAN. SECT. D. RAD. SCI.

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Formulas and tables a re given for t he m ean and stand a rd dev iat ion of R = 20 loglo r wh er e t h e r a ndom va ria ble 1· h as t h e N akagami-Rice distribu t ion. This d ist ri b ut ion is of inter est in conn ection wit h t he s hort -te rm fadin g cha racteristics of som c recci ved rad io fi eld s. A p a rt icula rl y simple formu la f or t he m ean of R is obtained in te rm s of th e well -kn own ex po nential in tegral function -Ei ( -x) . Addi t ion al inform at ion co ncernin g t he m ed ia ll a nd in te rd ecil e r a nge of If is a lso gi ve n.

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“…The sum of a direct wave and a wave reflected \ from a randomly rough surface will b e considered to b e composed of a constant component and a Rayleigh-distributed component, and can be separated into these two components by a consideration of the slop e of the cumulative distribution of the received signal strength over discr ete intervals of distance along the path [15,16]. The probability distrib ution of the amplitude (1") of the sum of a constant vector pl us a Rayleigh distributed vector was considered by Norton, Vogler , Mansfield , and Short [16 ], based on the expansion of a probability distribution derived by Rice [17] in the analysis of random noise:…”

Section: 2 Characteristic Effects Of Specular and Random Reflectionsmentioning

confidence: 99%

“…The probability distrib ution of the amplitude (1") of the sum of a constant vector pl us a Rayleigh distributed vector was considered by Norton, Vogler , Mansfield , and Short [16 ], based on the expansion of a probability distribution derived by Rice [17] in the analysis of random noise:…”

Section: 2 Characteristic Effects Of Specular and Random Reflectionsmentioning

confidence: 99%

Study at 1046 megacycles per second of the reflection coefficient of irregular terrain at grazing angles

McGavin¹,

Maloney²

1959

J. RES. NATL. BUR. STAN. SECT. D. RAD. PROP.

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An experimental d etermination of the reflection coefficient over rough te rrain is r epo rted . The reflected signal received over rough terrain is considered to be mad e up oft wo components, one that is a specular component and the other a R ayleigh-distr ibuted componen t. Where one term inal is low, the Rayleigh component is considered to be small with respect to the sp.ecular component ?lIt increas:s in relative magnitude as the height of the lower te rJl?ln almcreases. A tenmnal h eIght IS reached where the specular component is no longe r ~Hgl11~Cant, and the refl ected energy is esse ntia lly Rayleigh-distributed . A t erm inal height I S qUickly reached a,?ove which the m ea n valu e of the reflected energy is relatively constant, of a low value, a nd md epend ent of the g razing angle.

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The Probability Distribution of the Amplitude of a Constant Vector Plus a Rayleigh-Distributed Vector

Cited by 97 publications

References 5 publications

Rayleigh distribution and its generalizations

Rayleigh distribution and its generalizations

Some statistical parameters related to the Nakagami-rice probability distribution

Study at 1046 megacycles per second of the reflection coefficient of irregular terrain at grazing angles

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