SCIENTIFIC ABSTRACT ALEKSANDROV, M. S. - ALEKSANDROV, N.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000100830002-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 5, 2000
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

6.4400, 6.9000 77(948
SOV/1-09-5-3-2/26
AUTHORs Alcksandrov, M. 3.
TITM DlstribuFI7773'"~, Bangle Oscillations in the
Aggregate of Fluctuat.ing Signal, Noise, and Correlated
Noise lnterferenc~e,
PERIODICALi Radiotelchnika I elektronika, JL960, Vol 5, Nr 3, PP
36o-365 (USSR)
ABSTRAM The article deals with theoretical de-7elcipment and
analysis of differential and integral lawq of
probability of phase angle dIstribution In the
aggregate of fluctuating a signal, wh:Lte noise,
and correlated interference noise. It is demonstrated
that In pre8ence of correlatedn)lse the mean value
of phase angle between the resulting oscillations
of signal, white noise, and Interference Is different
from the phase angle of received signE..1s. , Introduc-
tion. The problem wa,,, solved for sigi':als with a
Card 1/ 16 constant amplitude by V. V. Tsvetnov (Statistical

Distribution of Pha-,e Angle 0scIllatI()n,9 77948
in the Aggregate of Fluctuating Signal, SOV/.109-5-3-2/26
Noise, and Correlated Noise Interference
Properties of Signals arid Noises In Two)-Channel
Phase Systems, Radio teldinika, 1957, 12, 5), but
the separate relations were given before by V. I.
Bunimovich (Fluctuation Processes in Radio-Receiving
Devices, Publ. Sovetskoye Radio, 1951). Due to the
nonuniforinitY of propmaLion conditlon3, the magnitude
of the radio signal usually fluctuates at the receiver.
Therefore, a more complete statistical characteristic
of the radionavigation system mus 't take the fluctua-
tions of signal intensity Into consideration. The
computation Of Droba-bility density and the integral
law of probability distribution of pha:3e angles In
the aggrefate of signal, noises, and the nonnal
correlated interference nolso for two-.,.Igiial
reception, ~Ailftekl in phase, are given below. (1)
InItIal Assumptions. (a) Slgnal cmiplitudes fluctuato
per Rayleight
Card 2/ 16 Z)

Distribution of Phaov Angle MY,48
In the Aggregate of Fluctuating Signal, 801V1001-5-3-2/26
Noise, and Correlated Noise Interference
where
4-
is the ratio signal -to-stunmary noise by powe r level;
'/l is ratio signal-to-interference per power level;
2 2
GL= CF. / (T is ratio noise-to-signal-to-inter-
n/ I
ference per power level. Signal attenuation occurs
simultaneously in both channels. (b) Noises in both
channels are normal, noncorrelated; Interferences are
normal, correlated, the analogous square components
only being correlated. The mutual co:rrelation co-
efficient of analoggous square components of the
interference proper in.different channels is pl;
that of the summary interference (noi~3e, + correlated
Card 3/ 16 interference) is p = p, (1 + CL). (c) Oscillation

Distribution of Phase Angle Oscillations
In the A,r.rgregate of Fluctuating Slf.,I'!~Ll,
Noise, and Correlated Noise Interference
77948
SOVIA109-5-3-2/26
phase of summary interference in the first of the
channels with relation to the Tscillation phase of
signal In the sEune channel is of random value and
uniformly distributed withia limits 0 to 2
In this diagram nott.,,tlons LI-Ile phase angle of
signal oscillations In two cha4iels; - = unknown
phase angle of resulting o:3cil-----..-.f (2)
Mathematical Formulation of Problem. The normal
distribution law of probability derisitY for square
components of summary interfcrence Is (per S. 0.
Rice): 1-4 1-4k
N1 V Mq."
W (XI *.*3 2; X'J; X') J-1
where the determinant of the matrix of second
moments Ist
Card It/ 16 !

Distribution of' Phase Angle 0-,3cillatiocko 77)4 8
C:, C)
in the Aggregate of Flue tua UnEI Sl~gnal, Ij '1/109-5-3-2/2-6
Noise, and Correlated Noise lnterfc~vence
but the minors of' this determinant, wl-ilch are Included
in the exponent, are:
Pj, 0 - - I,`)
Changing, to polar coordij:iates and com-oletely
cumbersome mathematical calculationZ3, the sought
distribution of' probability densitieo of phase angles
for the aggregate oscillations of signal, noise, and
correlated interferences is:
+ 4 0 F) I R di!.R
whe re
1) ms, Y + I
'I I-C Cos 0 <
Card 5/16

Distribution of Phase Angle Oscillations T(948
in the Aggregate of F2uctuatllng Signal, SOIr/109-5-3-2/26
Noise, and Correlated Noise Interference
Equation (4) is valid for conditionE..
tP1 < 1, T r/= -, (5)
which always exist. (3) Characteri:3tic Nculiarities
of the Distribution of Phase Angle -Oscillations
for the Aggregate of Fluctuating Stmal, Noises
and Correlated Normal Interference., Equation (4)
proves that the probability density w(y) is an
even function of S(( Designating /31= are coo
(-s) in (4), it -fo:L ows that:
where s Ay
a 21a Ay 9 - (po, yo I
1-1-7 g
Card 7/16 P + 7

DI.s.tribution of Phaoe Anp,,,lo 0.,icillall-lonO 77 911
In the Aggregmte or Fluctuating, Signial, S 0 V/ 10 93 - 2 /~-, 6
Noise, and Correlated Noise Interference
The phase(p 0 has the physical meanJng of mean value
of' a random phase angle(P . An Interesting case-
is when 7T, '/ = p., when the presence of a
signal de~ ~
-, orrelates the interference, and the
phase angle d1stribution of receIVE-d signals is
uniform despite the pre,,-,ence of signal and correlated
interferences, thus making impossible the measurement
of the signal phase angle. The mean value of
TO
phase angle of signal, noise, and correlated inter-
ference oscillations together does not equal the
signal phase angle ~. Denoting If
after some transformations:
P Fill E
A~l arc, tg T~- I, C-()i~,
Card 8/16 wherefrom it followo that ITO I < I I

Distribution of Phase Angle Oscillatlatis 77 (1-1118
in the Aggregate of Fluctuating Signal, SOV/109-5-3-2p-6
Noise, and Correlated Noise Interf'erence
Caption to Fig. 2
Fig. 2. Probability density distribi%tion w (? )'Of
phase angle(p of remilting signal and, summary inter-
ference oscillations for summary interference
correlation coefficient p = 0.9. Sif;nal oscillation
phase angle equals for (a) 90'; (b) 0'; (c) 1800.
The presence of correlation between interferences
acting in two channels of the phase :,adionavigation
system, or appearance of noise correlation in two
channels, which can be caused by cha::~acteristics of the
system construction, leads to a systomatic mistake
in phase measuremerits of the received signals.
Card 11/ .16

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AlYM 0 MU&MU-11khonovigh; BLUOV, Aleksandr Aleksandrovich;
LITOVALITSEV, Fe-Cr ~Vedo~ovich; YANISON, Tamara Ale'coandrovna[deceased];
BORISHCHNVA, M.M., red.; CHICBERIN, A.W., tekhn.red.
[Preparatory operations and printing on four-page rotation machines]
Podgotovitellnye operataii i pechatanie na chetyrekhlistnoi rotatsionnoi
mashine. Mosk7a, Goa.izd-vo "Iskusstvo," 1957. 30 P. (MIRA 10:12)
(Printing)

_AL3g�k j red.; BIMKIN, N.A.. red.; KAPITONOV. A.G.. red.; 3
jf L
STRAKHOVA, N.I., red.; KOZHUNII(OVA, V.A., red.; (:HXRZHIBOV, N.Y.,
tokhn.red.
[Kuybyshev Province; its history and econoaT] Kulbyshevskaia oblast';
istoriko-ekonomicheakii ocherk. [Kuibyshevj Khibyshevskoe knizhnoe
ltd-vo, 1957. 494 p, (MIRA 11:4)
(Kuybyshev Province)

Doe Med Sci
ALEKSANDROV, M. V.
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23/6/50
Aced Med Sci USSR
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