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22Journal of Siberian Federal University. Engineering & Technologies, 2019, 12(8), 980-986
УДК 621.396.96
Variability of Circular Depolarization Ratio in Radar Sensing of the Medium Filled with Hydrometeors
Evgenii V. Masalov, Nikolay N. Krivin* and Anastasiia S. Rudometova
Tomsk State University of Control Systems and Radioelectronics
40 Lenin, Tomsk, 634050, Russia
Received 25.06.2018, received in revised form 14.11.2019, accepted 05.12.2019
Circularly polarized waves are most sensitive to the influence of the propagation medium factors such as differential phase shift and differential attenuation. The reason of that is a feature of the wave polarization transformation. Such circumstances require consideration during designing radars working with circularly polarized waves. The aim of the study is to develop of approach for estimating the effect of the wave polarization transformation on a value of one of the most informative parameters based on the use of Jones vector component functional dependence on a polarization ellipse orientation angle and ellipticity angle. The task of this work is obtaining the analytical equation for the determination of that polarimetric radar informative parameter. As a result, the solution for the case of wave backscatter by the propagation medium was obtained when the medium basis orientation differs from the radar basis orientation. The estimation of the circular depolarization ratio providing the determination of regions with its raised value was obtained.
Keywords: circular polarization, differential attenuation, differential phase shift, polarization radar.
Citation: Masalov E.V., Krivin N.N., Rudometova A.S. Variability of circular depolarization ratio in radar sensing of the medium filled with hydrometeors, J. Sib. Fed. Univ. Eng. technol., 2019, 12(8), 980-986. DOI: 10.17516/1999-494X-0198.
© Siberian Federal University. All rights reserved
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). Corresponding author E-mail address: freeman46@yandex.ru
Изменчивость кругового деполяризационного отношения при дистанционном зондировании среды, заполненной гидрометеорами
Е.В. Масалов, Н.Н. Кривин, А.С. Рудометова
Томский государственный университет систем управления и радиоэлектроники Россия, 634050, Томск, пр. Ленина, 40
Сигналы с круговой поляризацией в силу специфики трансформации поляризационной структуры сигнала наиболее сильно подвержены воздействию дифференциальных факторов (дифференциального фазового сдвига и дифференциального ослабления) среды распространения. Указанные обстоятельства требуют обязательного учета при проектировании радиолокационных систем, использующих данный вид поляризации. Целью данной работы звязетсябазрьебткапрлбодадлявцзоко влллнияя°рянсфлумацииола^взлщбнной структуры за величину одволоиз оаеНрсее характерзыхунаолезсиучаврадиололанне информативных параметров, основанного на использовании функциональной зависимости компонент вектора Южозсазт^лаэлииптичнслыниу/гоа заклсиалллипсаоебзризиции.Задача данной работы -полуиззие асериmаыx соотношений для определения указанного выше информативного параметра поляризационной радиолокации. Получены расчетные соотношения для случая обратного рассеяния средой, ориентация поляризационного базиса которой отлична от opбУаmлуаоuзмутьmиеиозуо базиса. Выявлены оценки указанного выше информативного параметра, позволяющие определить области с его повышенным значением.
Ключевые слова: круговая поляризация, дифференциальное ослабление, дифференциальный фазовый сдвиг, поляризационная радиолокация.
Introduct i on
The prerequisiteto nheuse for °isplayingandinterpretingthe measurements results of the circulardepolarizationratio(CDR) [1] in pronounceg dependence of ohe errcularly polarized recetvedsirneis ampiinadeon the eiapeoS tic water dropleis.TPe eaniccas It shown in [2-4], is teUepeadeatct ths erientation of ihe tydrometcort atd is test sob]cct On Ohe influence of third party noises. The higher intensity of the rain (in other words, the more water droplets shape differs from the spherical shape), the more differences of a signal received with right and left circular po larizations [5] in the case when the probe signal polarization has one of the pointed above circular polarization states.
Task statement
The character of the differences pointed above is the leading cause of the variability of the circular depolarization ratk) CDR whkch determineuiodecftels (dB)on ohebase aa emphtude measurements wdea thw tvevw with the eighc cireulae rotariaatlon is itansmrtted,a°dtne wave wrth the right circular peptization ls received te. g. EeR), or whrn tha wave with ttie right aircuSar poiaoizaiion is transmitted, onS nhewaoewith ttt Mt circutar poiarieationitreceinedie. 0-ErL)
CDR(z) = 20-lg(|ERR|/|ERL|), (1)
where ERR is the amplitude of the signal transmitted and received with the right circular polarization (the first letter of the index means polarization of the transmitted signal, the second letter of the index means polarization of the received signal); ERL is the amplitude of the signal transmitted with the right circular polarization and received with the left circular polarization.
The differential attenuation Aa [dB/km] and the differential phase shift A® [deg/km] concern to the main factors determining the transformation of the signal polarization structure in the process ofits propagationin the me diumfilled with hndromete ors.These circumstancesdictate the need for searching pfihs to uuaSupte tltt importance ef fise otfeet of thtse Uouters ee the obtained measurement resoles tufl ho detenmpe cht chesmeSoe of she veriabüith sh Üte mrarnre0 itat£^tn^^ee CDR.
The OosR of tltft wte is ogSa^ntncc hm onofytical rohftiioo foe Üio alfluftion sr ete tircular dfhoiarifaCioa retie o n fie Sivls^ cfJvaas vectoc cemponfnS funcüanat nfnnhdfnce oar s polprinstia n ellipre отSfPiaSian mglo 0 md eftipfJcity onglca.
IVteeihioti of determining ehn ^irj-^lae inc-|i i^I in. 1 y^ i tr ^e enVfe
AcreMing to thit; rstuOt of [O-SUe Oncec aectcr en tltKs radan signee fn H;]in^ rineo lür^st oflSe frchahatien mogium ctin tie; represented ucina trigonometric functioac of anales a and] as
jOUT
(z) =
cos ß (z) cos a(z)+ j s(n ((z) zin a(z) - s>i r^ ß(z) cos z(z) -a j cos ß (z) sin a(z)
(2)
where z is the of the signal propagation path in a medium filled with hydrometeors. The
ellipticity angk a and tOe arientatkon atj^e (l rf Ae polarioation elllrese etP the glr^ue^r falr-ietf signal propagating (n the mediumdefinesb0 resulta of i9] as
f 2 . /2-d000z0aisin(0<I>z + 0.Z()\ ,n
a(z) = OtEJ^iocsun -1+z0e|Aaz-¿J, OzZ
nr ( g2-S0°05tazEin(A®a + 0.ne)\ , +i e ...
p(zp = aeazctg(-Z7Z0z°a-( + 0(4)
wXese n= 1, 2,0...
TIp ecmoiex ampHtuds t>f ibe liecisiveci eiicularly a^<ilítrr;t^ad antnal atn iit^n Use Oetermiheel from tire fonawánt ^rt((^a^oi- iateence:
lÉIN(z) (n [t] • iIR(p0)]^z • écut(z), Of
where fit] .r tOe opezztoa h° tie ^(rt;^r)i:^a"lion coirrsíar^t;r eb rfr reaeivah ssignf^l; IRCPoS]"0 p ite operator ot tTs traneitloa frnm ihe mdpium borie ho the measuring basis; p0 - the angle of orientation of the manrurigg bsdr re(atsgn to tliem^dinm bes^.
Forthecaseofreceivingthe signalwiththerightcirculeí polarizniion 0t] defines so
tn = stem j (6)
For thecaseof receiving thesignalwiththeleftcircu lar polarizniion 0t] definesas
iti = hH5 ll j O
The received right circularly polarized signal can then be found by performing multiplication of thematrixesas:
1
VRy
fijNCze = mNee^mf|ig mj|
RRV J r* lor o I
biRO gio r^VtnZ111
;tin V0 aero bO
cce^ ogz- cos aZz- -0 j sin a me Otn a-z-yt s;iD ir(s- cos a(zt D ) coe oin afz-
=( i-j= e^-coo V(f) co^ aCz- oS coo (rfzt oM aCz- -D jCcoo afc- suo ( Cz- D cm afz- suo -(15--]
--Sz
Ccoo0o H otn 0oy-
(8)
Afterthe we fins^l^^yy obltm:
E(rt(zy = -lfei-O ^^^(cos afzy + suo a yvyy.
(9)
Aa ian b s tm )ti fro m ies sbi (rafjii'^ tsion fo)t tCe ^rinjil.i-t^^ir of tbs siliigniiil rid e fived whlr right circular pnlatiaatio n ft
z ErR (zy I = -( (cOf afzy D SUO C)()zi)). t|i]hii pbere oli tie tiignvl ^ii;(-i;iisieti wzi0 ritCC circular polrnization it
<)rr(z) no E = 0( a a Rzy . hi lifii) caoe vi (e ae as—n a spsn)h w=eh leS( u^^t^iiiap) polt(l]C) zntren] we lane
^nro = Or1-).^ eg. ^-n
^nW - ol i5^)g(-c ^OSia(o
cos (Oozi cos csij^a -)s j sin (Z(zy sin aCzy — sip 0(iD cos afzy D) scs aSia sin dOz- '
Bp f)^t]]'orhi^iig lie transfoiorrtksn similar to the previous one, we obtain the expression for the received signal wlzhleft eir-ula- polarization:
(10)
(11)
(12)
URNL(zy = -U^^M
(zos (xfzy — stai a(zyy(
(13)
-lUiW - Ld
Tllsn tlie omttHsMe o!- tltesiIinfi c1-!!)^«^«! m llz) willbe
|ERNL(zy| =i -((аoаaаzа-аtnafzУУ. (14)
Tte phese o1 tha iigne1 liir^ifiedd wlthMt ci^cular polirizationis
)R^Kiiei = - -V N 0-M0 (15)
To otdsin iecied ^xjir^ssioss Ioo SPo eirculaa bepdla-znofn satin] a ns Vepna li^o» nalue at the 'pICcI oT lopasCtilmic recoiver as
CD R(aZzy) = ^C( - z EElRRCD)|/|ERLy))|) - (16)
Afterthesubstituting(10)and(14)expression(16)canbewrittenas
CDR(afzZ) - zo^i-0™)0--"™^). R z — ° Vtosafiytsinafiy/
(17)
Results analysis
Fig. 1-3 show the plots of the CDR as a function of the observation distance z calculated according to (17) for several values of the rain intensity. Differential attenuation Aa and differential phase shift
- 983 -
Distance (km)
Fig. 2. CDR as a function of observationdistancezfor therainintensityR = 50 mm/h
Distance (km)
Fig. 3. CDR as a function of observationdistance z for therainintensityR = 150 mm/h
ДФ values measured for the three-centimeter distance signals have used in the calculations. For the different values of the rain intensity R, these values were [9]: (a) Да = 0.02 dB/km, ДФ = 1 deg/km for R = 12.5 mm/h; (b) Да = 0.1 dB/km, ДФ = 4 deg/km for R =50 mm/h; (с) Да = 0= dB/km, A<I>=14deg/km for R = 150 mm/h.
Theacalysis of the calculaOe d rucves cmite CDR (see Fig.0-30a/short Oietcnces z(/orthe 0ront boundary о/ tie metearolocscdl formotion)showo a sobolanliai in fhe mile v^fee which at
z = S 0m isfbout d=d0 0)o it =12.5 mmih, SOdB Cor I. = 50mm/h, 40 0BfoeR / l/Cmm/h respectively.
In this case, starting with the precipitates intensity of 50 mm/h, areas of positive values of the CDRevaluotion appear. For R = 50 mm/h, the maximum of the CDR in the positive region is 12.5 dB, and for R = 150 mm/h is 6...7 dB. In the last two cases, CDR equals zero at a distance of 22.5 km (for R = 50 mm/h) and has four zerovalues atthe distances of 6.45; 19.3; 32.15 and 45 km (for R= h50mm/h).
Cnnchision
TbeanalyOicrlsolutkinfor the evaluation of the circular depolarization ratio CDR on the base of Jones vectoeoomponeof functicnaMnpondenee оn a pokirizaikmell^nee.enkalionan^e /(u)akd el-)iftic/tp nccle аф wayobtarncO.
A s it seen from (17), the characteristic feature of CDR is its dependence only on the vari-abilityof (he eliitoecity ongle a(c/. Io tic case, bhe ra/lo i s CnCrpenContof Шс yrien/ftюn angle P(z) changing.
The magnitude of the circular depolarization ratio CDR as it follows from (3) and (17) depends on diffosentM characteristics of propagation medium - differential attenuation Да and differential phase вЫйДФ;
Thcvcombiliyo of /Ueoctio has apшnounosechuraclсy ^пСзс^О^зФпС^пС Ciffereocoe lo/tceo dB) at thauhortkibtonc esgz 12 km(eram Шс frc^nfyoc^c^^syc^i^ ^Ite melekreSoclenifosmation.
CDR y)gn cOance is an undoubted indication of high-intensity precipitates presence in the sensed meteorological formation.
The procedure of high-intensity precipitation meteorological formations determining can be per-foomed wi)h (he uee of (he algoniuhm )see above) for She bDd eeofoaSm1 uasek сп Сгопоф.ооюп and receptkm it о^по/о with clrco/ar (^с/^зп^^^С^^с^п (|Err| оп) |Erl|). In this case, the appearance of the positive ratio can indicate the meteorological formation with a high rain intensity.o
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