The Rationale for the Method of Calculating the Angles of Arrival of Short Radio Waves Taking Into Account the Influence of Regular and Random Inhomogeneities of the Ionosphere Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

Journal of Siberian Federal University. Engineering & Technologies, 2019, 12(5), 573-584

yflK 621.371.33

The Rationale for the Method of Calculating the Angles of Arrival of Short Radio Waves Taking Into Account the Influence of Regular and Random Inhomogeneities of the Ionosphere

Anatoly I. Agaryshev*a and Minh G. Nguyenb

aIrkutsk National Research Technical University 83 Lermontova Str., Irkutsk, 664074, Russia bLe Quy Don Technical University 236 Hoang Quoc Viet Str., Ha Noi, Viet Nam

Received 17.03.2017, received in revised form 01.03.2019, accepted 10.05.2019

The article presents a reasonable method of calculating the angles of elevation of short radio waves with the influence of regular and random inhomogeneities of the ionosphere. The method calculates short radio waves (HF) through the horizontal inhomogeneous scattering ionosphere. The technique is based on application of the law of refraction of Snell's for well-known models of the ionosphere and its evolution in the irregular parts. The description of the program to calculate the angles of radiation and reception HF is presented. The results of calculating the angles of arrival are compared with measurements of angles of arrival of HF. We obtained the best agreement between the experimental and the calculated resultsl of arrival angles of HF than for the regular ionosphere. The use of techniques is discussed in the article.

Keywords: calculation of arrival angles of HF radio waves, radio wave propagation, ionosphere model, optimization of radiation pattern.

Citation: Agaryshev A.I., Nguyen M.G. The rationale for the method of calculating the angles of arrival of short radio waves taking into account the influence of regular and random inhomogeneities of the ionosphere, J. Sib. Fed. Univ. Eng. technol., 2019, 12(5), 573-584. DOI: 10.17516/1999-494X-0157.

© 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: aai.irk@mail.ru

Обоснование методики расчета углов прихода коротких радиоволн с учетом влияния регулярной и случайной неоднородности ионосферы

А.И. Агарышева, М.Ж. Нгуенб

аИркутский национальный исследовательский технический университет

Россия, 664074, Иркутск, ул. Лермонтова, 83 бТехнический универтитет имени Ле Куй Дона Вьетнам, Ханой, ул. Хоанг Куок Вьет, 236

Статья содержит обоснованную методику расчета углов прихода коротких радиоволн с учетом влияния регулярной и случайной неоднородности ионосферы. Представлена методика расчета коротких радиоволн (КВ) через горизонтальную неоднородную рассеивающую ионосферу. Методика основана на применении закона преломления Снеллиуса для известной модели ионосферы и ее развитии в нерегулярной части. Дано описание программы расчета углов излучения и приема КВ. Результаты расчета углов прихода сравниваются с результатами измерений углов прихода КВ. Получено лучшее, чем для регулярной ионосферы, соответствие экспериментальных и расчетных углов места КВ. Обсуждаются вопросы использования методики.

Ключевые слова: расчет углов прихода коротких радиоволн, распространение радиоволн, модель ионосферы, оптимизация диаграмм направленности.

Introduction

Known method of predicting elevation angles is recommended for the practical use by International consultative Committee on radio (CCIR). This method based on the setting of parameters of the ionosphere and the characteristics of the radio waves. It is implemented in the form of a computer program, which provides high speed of calculations of characteristics of short radio waves (HF) [1]. However, the CCIR method does not account for regular (predictable) changes in the ionospheric parameters along the radio links, i.e., does not account for possible differences between average values of angles of radiation and reception of HF in the vertical plane. There are also methods based on numerical integration of the system of radial equations to the ionosphere with changing in vertical and horizontal directions of the electron density N. These methods (for example, we can mention the work of V.I. Sazhin [2]) provide prediction results of the arrival and elevation angles more precisely compared to ones given by CCIR method. However, these methods do not provide high speed of calculating characteristics HF radio waves.

The aim of this work is to develop a more rapid method of calculating the angles of arrival of HF in the horizontally inhomogeneous scattering ionosphere and demonstrate its use on real paths.

A mathematical model of the ionosphere

In a layer with considering random disturbances of trajectories only in the lower part of the layer, the law of refraction is employed for constructing trajectory of HF radio waves. The angle at which

radio wave enters the ionosphe rev (angle of incidence) and the angleat which radio wave comes out of the ionosphere yB are exparlencad random pertuthatione yl, y2 (ecatteeing parameter). Theserandom perturbations have the eamecharacteristtcs, theg diriribate by the normal law.

In order to determine a value of scattering parameter (in degree), we use the method that was presented in work of A.I. Agaryshev [3]. We choose on the Earth's surface segments with le ngth of A and for rays with propagation length of Di, getting in the k-th segment, we calculate the mean values of elevation angles, arrimac aagler and reflection heahtr oa tadio wanae ^ /V, ^cetpectivefy, and we can calculate the standarO neficiion)of tfese aeeeageicr. Ba changing thee aCac na rcaotering narametar to match the measured anh the cahcuSated stanharO dcn1etiono eiows us 3e ds^tct^cale^^ the vnloe od scattering parameter for the snecific cenOifions. The cOaracterirtls r^^le af alstuebanccs.lat OeighVaC 100 km ~ 100 m, whea tOi height increases Vo 3t0 nmehe characteritiictcale Dfditiurbenoes ^creasea to 100 km. The degree of the disturbance effect on the radio trajectory is defined by relation A//s, where Ax = AN/N - a disturbance of the electron concentration, it displays in percent, s - characteristic scale of disturbances. It was knewn ^^at A^ ~e% at hdghf of №0 leai and m g ter/io e- at heighr oa 3ma )tfe, therefore relation Axg at the height af 100 km is over 100 times in compared with the relation A%/s at the height of 300 km.

The method of cmnsVsueeion ai to^jestas^^r HF radio waves is dared onepplicatian o) rhe mof^ifie^ Snell's law for a thicS tener cf the ionosphere. For a thick layer Snell's law is given by formula [4]:

where n, n1 - refraction coefficients of environment at a level of "n" and "1", R, R1 - radius from the Earth's center to the level "n" and "1", y and yl - angles between the path of radio wave and the radius R, R1. The electron densityisdefined inaccordancewiththe ionosphericmodel[5].

According to Fig. 1 trajectory HF radio waves consists of three parts: 1) a direct path between the transmitter and lower boundary of the reflective layer, 2) a curved path in the reflective layer, 3) a direct path between the lower boundary of this layer and the receiver. The method of construction of trajectory HF radio wave at path 2 is to divide it into equal segments, the length of these segments is substantially smaller than the total length of the curved path. Then the law (1) is applied sequentially to each of segments.

n ■ R ■ om(p) = ne Re ■ ompj),

(1)

Fig. 1. The model of "beginning of the ionosphere":l - refraction ray, 2 - reflection ray

h. km

h F 2

"m1 ^

hjY^tj

Nr.

fmE fmF 1 fmF2 f, MHz

Fig. 2. The model of plasma frequencies for the ionospheric layers E, F1, F2 [5]

Then, a description of three-layer model of the ionosphere and mathematical expression of height dependence t2 the riasmo freaueaee oh iaaospheeie ltyers hq Ff, eC2 oce dlaxn iFtg. 2). Aheording to this msdel, Tli^ plasma freRuAycfes of for laRvrs E and F2.

J(h-h E^\2 1 -I-w_ I .

I ymE J

WkR dlO< h R hh) nlUyhr Fl)

fpias(h) ffnE- ( 0.225 + hmF1 -1.225- (E))) - hmE1■

When dmF 1 < h <hmFh llooer F2f. fplas (h ) = F2 2 • - (f^] '

et. mctlind 2on cr^ai^reitctiiej; trajectory HiO radio wave

OWhec Calving it^io acicun) thn nadlent of eluclronie concentration in hooioantal dieeetion oh HF radio waves, the formule ofeefraciif n law cs fotfows:

rhP ) dn

JS№-i) 30

J<s ( Rk ) On

S(R )TE'dS - (2)

S (Rk-1) riH

dn

wRviv--thegradientofrefractive index; dS- theelement hftrajectoryradiowave.

30

The right part of the equation(2)can becalculatedapproximately accordingto aformula:

f(R 5 (.ds « Ên.(s)Rk )-SARkl)) .AS, Js(d.1)30 30 - k d A k- ' 30

where AS = S(Rj) - S(R0) -acalcujation step along trajectorn.

For a small increment of central angle AO (Fig. 3), we have an afproximate expression:

dx

if* sin( if )=—. (3)

Rkcl

Where dx - an increment of distance by one moving step of radio waves in the ionosphere, Rk-1 -a radius between the central ofthe Earth anda startingpoint of k-th moving step. In order to determine a value of refractive index n, we use a known formula:

fn-

Fig. 3.Calculation ofgeaditni of refractive index with an increment ofcentralanglez)6>

n r„ 1 -

fpla:.

~7

(4)

Where f, fplas - a carrier and a plasma frequencies respectively.

By utine the three-teyer monel (rf ine ronosphere eiml tite expreasktn (4), rhe value of refraction inden ciiir be defind theough tite; critic;^ aretfuehcy, tlie aeight of maiximum iomzatkin, fte semi-thiclines;s£ind n hrighi rcf current point: In tdq layt; r E\

enBht) = t|l -

fBS. f

1-

h-hmE

yJE

^^tdq tayerFi:

nih) =, ¡1 -|f

h -0.225 - hmF1- 1.225 • hmE hmE1- hmE

In thelayer F2:

f„F2 f

1-

h-hnF!

ymF 2

With a very small value of dd, by taking into account the expression (3), we can calculate the gradientofrefractive indrx as folOowind:

dU ~AU dx ' g '

Wh^rn and of?W -lhe values of Ido ratsactroi indax at t)iis beginning and the end o0tlie X-th step oV tie movement or" salio woves, nnthtfgonnice So thn htightr dew and hk.

For each monement step of radio wavet, wc cniculade ihv vvluos of critical frequencies oV the

ionospheric layers E anO d2 (/do A^op and true hhtghl of mhximum ronizatoon hjrf. Ad ght end of the

dr

movement step ne JE^n<e areeicai oi refraction iadex — by formula(5).

Then, by the expression of the Snell's law (2) we can calculate the angle of incidence for a next movementstep ofradin wave:

atn( <Pk) =

nrv A-i "^Pr-O-fl -u® _d0

nk 'Rd

- oei-

2

2

Radio wave is reflected from the ionosphere at the height where the angle of incidence equals to

A calculation program of arrival angles of HF radio waves

The program provides two modes of calculation: the first mode - calculate diurnal variation of arrival angles of considered mode of radio wave in a receiving point. The second mode - predict elevation angles and arrival angles of all modes of HF radio waves that are taken in a given area at a given specific time. Input data as follows: date, time, the average number of sunspot - the Wolf number (W) that corresponds to the given date, geographical coordinates of the transmitter and the receiver, the scattering intensity 5 that can be determined by method in work [3], a minimum and a maximum of elevation angle, step of angle A 6, calculation step along trajectory radiowave AS.

By using the input data, block l deCeomcaer the parnmetets of the ioaoaphere_CeilC, ftnFA, Mt3000S F2 that is close to a t ransmeltc rand a reaeivtiuciaa tabie-natuay paramcteis of vecttcatsoandiag IVSl of the ionosphere, measured in dacs aad hours ot couerimertallon. TCen, we dtOao etie ncoS Selght of the layer F2 of point snftransmission and reception according to the formula developed in [3]:

h 1490 17,

Kb 2 = < =- 176 .

,Jm (t000)2 -1

Unit 2 calculates the length of the route D and the azimuth of A radio link according to the specified geographical coordinates transmission and reception. Unit 3 implements calculations of angles of radiation and reception for each value of the angle of radiation. The values of the radiation angle changes from 0min to dmax in increments of A0. The output from block 3 is a data array of angles of radiation and reception of radio waves received at the point of reception. In block 4, average values of angles of radiation and reception are calculated (n - number of hits). Fig. 5 shows the interface of the program. Unit 6 displays graphical and tabular results of calculations.

Fig. 4. A block-diagram of the program

Файл О программе Помощь Программа моделирования

Рабочая ч Fc (МГц)

Угол излучения(Град)

Параметры слоя Е НтЕ_передат(Км) I110 УтЕ_передат(Км) Р

Максимальный угол |gg Шаг угла

|0.01

Шаг прирашения р

Левый генератор возмущения (Град) От р До [1

Правый генератор возмущения (Град) От р До [1

Широта перед Долгота перед Широта приём Долгота приём Число Волфа

Проп-

:ирОЕ

ание всех модов. приходящих приёмнике

Дета |15.01.201 4 Время |2:00:00

s углов прихода заданного мода Дата 15 1119:?

Мод I*

Время T1 т

R Пек; [v Пак;

графики таблицы

ВремяТг |23;00 00

Fig. 5. Interface of the predietion paorrcm of arrival angles HF radio waves [6]

¡Ml iKO

Distance, km

irn noo

Distance, km

■I 000

Fig. 6. Dependence of elevation angles arel araival angles on distance of mode 1F2 with f=f 8 MHz

Fig- 6 shows prediction results of elevation and arrival angles of HI7 radio waves in the form of graphs. Obviourly, flit elevation angler in thin cate are iees thae the araival engles.

Comparisons with measured results

Examplea of using ihe proeram Sot ealculeting areivol aeijiaSos are prts^^^i^i^cl beiow. On path Khabarovsk - IrOutsktht average valuet otmetoured dela of erriael tpgter fos moths in years [3] were used. We can see on Fig. 7 that, the calculated results (that equal to 8°) of method that is described in work [1] are less agreement with the experiments than the calculated results of presented method. Difference between calculated results of the proposed method and experiment data is caused by differences between prediction results of ionospheric parameters and actual parameters.

As the next example, predictions of arrival angles of HF radio by paths Moscow - Rostov-on-Don and Minsk - Rostov-on-Don are presented. The calculated results are compared with the experimental data of mode 1F2. The description of experiment were presented in [7]. The Wolf number was 72 in November, 90 in December by data in [8]. The calculated results from Fig. 8 have showed that, in the time interval from 5:00 to 6:00 MSK (Moscow standard time) the average value of arrival angles is 35°. The Agreement between the calculated results and experimental data of mode F20 (an ordinary component of mode F2 that is shown by the arrow) is good as shown in Fig. 8.

11

Ji 10

ojj

___ 9

ct3

lO 12 14 16 18

Local time (IRKT), hours

Fig. 7. CabuMed reeuks py metitsodl [1 (tiashed curve) cv£ilcvul^tecl resuks prnjDrse0 meAod (sohd cmrve) and experimental otsults (pocnti wish confiCtnl l^itc^itsS of dependence of arooval onulsn HF radoo wavet on local time m the mMd.eo^cth IChatoeoei. - Irkutskin ()etobet

* j i

2000 -1

1600 -

1200

S00 -

400 -

9 10 II 12 U 14 IS 16 17 13 19 20 21 22 21 2i MSK, hour

0 5 10 15 2025 30 35 40 45 50 55 60 05 70 75 Arrival angle, degree

Ftg. b. The depenhenee 0. arrival annles of HI7 cadio waves on bme by paSh Moscow n Rostov-on-Don lief) and experimentaldistributionof arrivalangles(right),23.11.2013,5:00-6:00MSKf=4.996MHz[7]

MSK, hour

[■TrTTT'TpHTfnTH mmv

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Arrival angle, degree

Fig. 9. Dependence of arrival angles of HF radio waves on time by path Moscow - Rostov-on-Don and experimental distribution of arrival angles, 23.11.2013, 9:00 - 10:00 MSK, f=9.996 MHz [7]

Fig. 9 shows that in the time interval from 9:00 to 10:00 MSK the angles of arrival HF radio vary in the range of 29 to 34° and the average value of arrival angles is 32°. These calculated results have a good agreement with measured results of mode F20 - the ordinary component of mode 1F2 that is presented in the same figure.

It notes that there was not observed mode 2F2 from prediction results in range of 9:00 to 10:00 MSK with transmitting frequency of 9.996 MHz and in range of 5:00 to 6 MSK with transmitting frequency of 4.996 MHz although by experimental data (Fig. 8 and 9, right) this mode was obtained. In order to explain this phenomenon, a maximum usable frequency of mode 2F2 - (MUF) 2F2

was calculated for path Moscow - Ro stov-on-Don by the methodthat te cresected in work [3]. The calculated reculteof (MUFt CW in 5C0 cncC cMSK) are 3W aird 195 MHz recoeo-ivety, at WCh and t0:0n AM (MSK-z- ^]V^UF)2W2are7.45ao-a .3 MHf respectively T-ae calculited lee^t- shon that, theoretically, in the range of 5:00 to 6:00 MSK with transmitting frequency 4.996 MHz modes 2F2 can not be observed and in the range of 9:00 to 10:00 MSK with transmitting frequency 9.996 MHz modes 2F2 ateo can't -e otoooved.Ms55..! o3tiuS[ practical^ °sopagaIsonr odH° radiowitf lransmittina 0requencu lcnltr MUF 2ho are j^octib^i5 0aa we54 5hfwn in Fir. 8, -Z Wy re^src^o of snfluence3 of lhe avndom mC^amag^nec^u^^ ionosphorz. Tlecr arezwetypftod randcm inhimogcneius ionocpeerr: lh t-z random small-scale inhomogeneities (characteristic size < 1 km) that is located lower reflected layer. 2) the random large-scale inhomogeneities (characteristic size >100 km) that is related with traveling rootcpherir clisCurbancus (n-Dse. In o work p], Hie methed "eqnal MpF" is prcrenteC neaC -ce given C°o tcwepataof ]V[esb aFe.

toom the hrapzinFig co, we son oete tiiaC the azetage value o5 arrival angzesof made Ft ie (ho rag^ from lU:Ua to MSK is 3e° Theee resolis are aomisUeat uF2 mezsgrez resutti tiia ordinary component of mode 1F2.

From graph in Fig. 11 (left), the average value of arrival angles from 14:00 to 15:00 MSK can be determivec and h equak to 2r.5e. TWs cdoutoed resuhls more tiian enqterimcntddaov oe ct. wct deviation it cuiteec55plcbeewith considzriee nf rtllsbielty dfdoCermioeng ooiepur

Fig. 10. Variati5ns o0cmIcl znclet cf Ha roaiowamrs ly pcth (^owowz R(tsteo-rn[Dce ani experimcntac oio-tribution of arrival angles, 09.12.2013, 13:00-14:00 MSK, f=14.996 MHz [7]

Fig. 11. Variationsof arrival angles ofHFradiowaves bypath Minsk - Ro stov-on-Don ovd experimental distribution of arrirai angles, 0t.l2.a0Be f4:00Fia:00MSK, f yPOOO MHz[7]

Optimiiation oO antenna diagram

In order to design HF antennas, it is very important to give the angles of arrival of HF radio waves. We can use the proposed program for calculating arrival angles. Let us give an example of design of a horizontal rhombic antenna for path from Khabarovsk to Irkutsk with operating frequency 16.8 MHz. The radiation pattern in the vertical plane of horizontal rhombic antenna is given by an expression [9]:

F(Q) = T—^rCr^^ •sm2 j^r [ - sm® •cos(6-)]] • sm(k • Hp • sin(6m).

1 - sin® • cos(0m ) [ 2 J

k-lp

m) { i

Where 0m - an arrival angle HF radio wave, 4> - a half of obtuse angle of rhombic, lp - a length of sides of rhombic, Hn - a suspension height above ground of antenna.

Using the proposed program, we can determine the radiation pattern for the average angle of arrival on path Khabarovsk-Irkutsk with an operating frequency of 16.8 MHz. In order to solve this problem, firstly, a prediction of arrival angle HF radio on route Khabarovsk - Irkutsk is carried out. Further, by using the calculation results, we can determine the average value of the arrival angles of radio waves in year. The calculated results were shown in Table.

Following the table, the average value of arrival angles of radio waves equals to 11.2° in year. From the handbook [9], we can choose the rhombic antenna RH(65/4)1 with parameters 4> = 65°, l = 4A0, H = 10 with a maximum of the main lobe of the radiation pattern, which corresponds to the calculated arrival angle of mode 1F2 of HF radio waves, the minimum of radiation pattern corresponds to arrival angles of mode 2F2 (Fig. 12).

Conclusions. This article successfully solved the problem of analysis of using the proposed program to solve practical problem, including:

Table. The average values of arrival angles HF (in deg) waves radio by path Khabarovsk - Irkutsk

Months January February March April May June

Pcp 10.2 10 eo.a 11 U(.7 13.2

Months July August September October November December

PcP 13.2 19.7 11.9 9.7 0.4 9.0

10 20 30 to 50 60 70 a,rpCLA Fig. 12. Radiation pattern in the; vertical plane ofantenna RH (65/4)1 [9]

1) Developing the method and building a program to calculate the angles of arrival HF radio waves. The method based on application of modified Snell's law with considering the influence of gradient of refractive index on trajectories HF radio waves in the horizontally inhomogeneous scattering ionosphere.

2) The comparisons with measured results by paths Khabarovsk - Irkutsk, Moscow - Rostov-on-Don, Minsk - Rostov-on-Don were carried out. As a result, our calculation agrees much better with measured data, compared to calculations from other methods based on the horizontal homogeneous ionosphere.

3) Showing that the proposed program allows designing radiation pattern of HF antenna with the main lobe that corresponds to mode 1F2 and the minimum corresponds to mode 2F2.

The causes of deviations between the calculation results of arrival angles of HF radio waves and the measured results are obvious. The first deviation can be reduced by taking into account the extraordinary components of radio waves, the second deviation is relates to using a more efficient method for calculating MUF 2F2 that was known as reception of hops with equal MUF [3]. In our future works, we will work on improving the performances of the program and the proposed method to reduce the deviations.

References

[1] А simple HF propagation method forMUF and field strength: Document CCIR 6/288.- CCIRXVI-th Plenary Assembly. Dubrovnik, 1986. 34 p.

[2] Afanasiev N.T., Tinin M.V., Sazhin V.I. et al. Effects of large-scale clouds of ionospheric irreqularites on the propagation of high-frequency radio waves. J. Of Atmospheric and Solar- teorestrial physics. Pergamon, London, 1998, 60, 1687-1694.

[3] Агарышев А.И., Агарышев В.А., Алиев П.М., Труднев К.И. Системы коротковолновой радиосвязи с подавлением многолучевости сигнала: монография. Под ред. А.И. Агарышева. Иркутск: Изд-во ИрГТУ, 2009. 160 с. ^garysev А.! et al. Systems of shortwave radio with the suppression of multipath signal. Irkutsk: Publishing House of Irkutsk state technical University, 2009. 160 p. (in Russian)]

[4] Дэвис К. Радиоволны в ионосфере. М.: Мир, 1973. 502 с. [Davis K. Radio waves in the ionosphere. M.: Mir, 1973. 502 p. (in Russian)]

[5] Bradley P. A., Dudeney J.R. A simple model of the vertical distribution of electron concentration in the ionosphere. J. Atmos. Terr. Phys. 1973, 35(12), 2131-2146.

[6] Агарышев А.И., Жанг Н.М. Прогнозирование характеристик декаметровых радиоволн на неоднородной рассеивающей ионосфере. Свидетельство о государственной регистрации программы для ЭВМ№° 2015610215, заявка J№ 2014661368 от 10 ноября 2014 г., дата гос. регистрации Реестре программ для 12 января 2015 г. [Agaryshev A.I., Giang N.M. Forecasting characteristics of decameter radio waves on inhomogeneous scattering ionosphere. Certificate of state registration for program of the computer No. 2015610215, application number 2014661368 dated 10 November 2014, the date of the state. Registration Program Register on January 12, 2015 (in Russian)]

[7] Чайка Е.Г., Вертоградов Г.Г. Использование данных текущей диагностики ионосферы в задаче КВ-пеленгации и однопозиционного места определения. Распространение радиоволн: c6. докл. XXIVВсерос. науч. конф. (Иркутск, 29 июня - 5 июля, 2014 г.): в 4 Т. Под ред. Д.С. Лукина

[и др.]. Иркутск: ИСЗФ СОРАН, 2014, 2, 41-44 [Chaika E.G. Using current diagnostic data of the ionosphere in the problem HF-direction finding and single point positioning. Chaika E.G., Vertogradov G.G. XXIV All-Russian Scientific.Conf. "Radio propagation", June 29-July 5, 2014 [Collec. rep] to 4 Vol. Eds.: D.S Lukin [et al.]. Irkutsk: ISTP SB RAS, 2014, 2, 41-44 (in Russian)]

[8] Solar Physics. National Aeronautics and Space Administration [Electronic resource] Access: http://solarscience.msfc.nasa.gov/.

[9] Айзенберг Г.З. Коротковолновые антенны. M.: Связьиздат, 1962. 815 с. [Eisenberg G.Z. Shortwave antennas. M.: Svyaz'izdat, 1962. 815 p. (in Russian)]