Bit Error Ratio, Caused by Doppler Effect, for Systems of Space Diversity Reception Текст научной статьи по специальности «Компьютерные и информационные науки»

Journal of Siberian Federal University. Engineering & Technologies, 2019, 12(1), 64-71

y^K 621.396.946

Bit Error Ratio, Caused by Doppler Effect, for Systems of Space Diversity Reception

Mikhail G. Polyak*

Academician M.F. Reshetnev Information Satellite Systems 52 Lenin Str., Zheleznogorsk, 662972, Russia

Received 21.06.2018, received in revised form 13.07.2018, accepted 16.07.2018

Today digital data transmission plays a leading role for satellite systems. However, digital data transmission is possible with errors at demodulation, which cause distortion of transmitting information. Errors of digital data transmission are due to three causes. First cause is a low level of signal to noise ratio. Second cause is Doppler Effect. Third cause is symbol-to-symbol interference conditional multipath propagation. Space diversity reception is effective method of bit error resistance.

Doppler Effect is the most significant for bit error probability at satellite communication. Because satellite move very fast in cosmic space. This article show effective of space diversity reception for decrease of bit error probability, which caused by Doppler Effect.

Keywords: satellite communications, bit error ratio, Doppler Effect, space diversity reception.

Citation: Polyak M.G. Bit error ratio, caused by doppler effect, for systems of space diversity reception, J. Sib. Fed. Univ. Eng. technol., 2019, 12(1), 64-71. DOI: 10.17516/1999-494X-0075.

Вероятность ошибки,

вызванной явлением Доплера, в системах

пространственного разнесенного приема

М.Г. Поляк

АО «Информационные спутниковые системы» имени академика М.Ф. Решетнева» Россия, 662972, Железногорск, ул. Ленина, 52

Передача цифровой информации в спутниковых сетях играет в настоящее время ведущую роль. Однако передача цифровой информации вследствие воздействия различных факторов может осуществляться с ошибками при демодуляции, которые приводят к искажению

© 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: [email protected]

переданной информации. Ошибки при передаче цифровой информации возникают по трем причинам: падение уровня отношения сигнал/шум сигнала; действие эффекта Доплера, ввиду межсимвольной интерференции, возникающей по причине многолучевого распространения сигнала. Эффективным методом борьбы с ошибками при приеме цифровых сигналов признан разнесенный прием сигнала.

В связи с космическими объектами одним из наиболее важных факторов, влияющих на вероятность ошибки, является доплеровское смещение частоты, вызванное движением космического аппарата. В данной статье показана эффективность разнесенного приема с точки зрения снижения вероятности ошибки на один бит, возникающей вследствие эффекта Доплера.

Ключевые слова: спутниковая связь, вероятность ошибки на бит, эффект Доплера, пространственный разнесенный прием радиосигналов.

Introduction

Today digital data transmission plays a leading role for satellite systems. Digital signals are very popular, because they allow transmit information more precisely and faster than analog signals. However, digital data transmission is possible with errors at demodulation, which cause distortion of transmitting information.

Modern digital data transmission systems have to provide bit error ratio (BER) not less than 10-5. So special algorithms for processing signals and coding are often using today.

Errors of digital data transmission are due to three causes. First cause is a low level of signal to noise ratio (SNR), when signal transmit through noisy or fading communication channel. Second cause is Doppler Effect. Third cause is symbol-to-symbol interference conditional multipath propagation. Space diversity reception is effective method of bit error resistance.

Doppler Effect is the most significant for bit error probability at satellite communication. Because satellite move very fast in cosmic space. This article show effective of space diversity reception for decrease of bit error probability, which caused by Doppler Effect.

1. Influence of Doppler Effect on bit error ratio for systems of one and two antennas reception

Doppler effect is very significant for BER especially for low-orbiting satellite systems. For example, if satellite rotates on 700 km circular orbit, then its speed is near 7.5 km/s. Time appearance of these satellites is very limited. Satellite's speed is maximal when satellite to turn up horizon. In this moment its Doppler translation is ultimate. If signal frequency is 1.6 GHz, then maximum Doppler translation is near 7 kHz. Thus signal spectrum shift from nominal value. Nominal value of frequency is generated local heterodyne. Demodulation errors eventuate, in view of the fact that carrier received signal frequency is not equal nominal frequency of local heterodyne.

Today systems of automatic frequency control are very popular for decrease BER caused by Doppler effect. But these systems have lags, which forbid completely except errors. Space diversity reception allow except errors especially when Doppler translation is small. In this case diversity reception allows decrease error probability in two degrees. For example, BER may be decrease from 10-8 to 10-16, sub verbo.

BER, caused by Doppler effect, for DBPSK evaluate by using formula [1-3]:

P =

A.-l-J^.ar.pE.r)) 2-(A+l)

(1)

here p0-rr^i^j^nSKTR;fd [Hz] - maximum value of Doppler frequency shift; J0 (2-n- fd -T) - correlation function in-phaee d and antiphaoed components of complexproc rss shifted on T, which is in Gaussian channel. CorrelaSlen funesion is mopghv-ordes ]eosspl funytion[0];T [s] - bio dpsativn and ddey period of demedulation DBPSK sfgnV.

Diversity reception may be in frequency, in polarization, in angel, in time and in space [1, 5]. Frequency diver sity ae ceptionandtimediversityrece°lionapplyfor navrgatiof systemi,but if sequire additionalfroquencyband orlimrt amouvtofSaanomSrted inyofmatson.Polaelzatsovdiverslty feeeptlon reqbires t\eo recervs0 antsnnoo on have adcitional toss on s dB. S^cu divetshy oooepiionis more beneficeni atid. effitieat mathof ol diverriiy reuupeicn Signals fooies drifereotilrobcstiies antennas are notcorrelatad tfbelween aafefnas (HsSabar u sear ¡^et-s^^i^siL wava knglh.

BER, oouselby Deppler effect, for two antennas reception of DBPSK signals evaluate by using formula [1-3]:

Fig. 1 demonstrated block diagram of one antsnna DBPSK receiver. Fig. 2 demnnstrated block diagramoftwo anteneas DBPiSK aeceimer [l,5f •

Research [nihteneenf Doppler eflkct nn BERwidda eiiferend vdue ofDoppiertranstatianand informationrate.

2. Research ofinfluence ofDoppler effect on bit error ratio

Plot graph of dependence BER from Doppler translation. In case SNR equal 10, information rate equal 32 kb/s and 32 mb/s.

Carry opt asaigza of oStdinkd Sepevgenoe. In caae small DDpelki aranslation somce diversity recepiionaflow decaeaceearor puobabiïityinawo degreases from 10-8 to 10-16. However if value of

(2)

Fig. 1. Block diagram of one antenna DBPSK receiver

Fig. 2. Block diagram of two antennas DBPSK receiver

0.1 Ik ID"3 1k10"; 1*10"7 1k10"?

Pltfd,32 103,10) Ik 10"11 Pï(fâ,32 lü^.io) Ik 10"13 Pi' fd.32- 10s.lo) Ik 10"12 P2(fd,32 104,10) 1*10"1 IkIO"1* ik 10"11 Ik 10" Ik 10"15 IkIO"17 Ik 10"

1 10 100 1x10? 1k104

fa

Fig.3.Dependencebiterror ratiofrom Eoeplerlranslatcon

*tïï

**

. * * HI lr *

* * 1 _ ^

L t* h

* vff n * '

r*

y y +

* ■ *+

*

> *

1 10 100 1x10? ik

fd

Doppler transtetkm w^be incraaaed, thenefficiencyofdiversityreception will be decreased. For example,incase vahre ofD oci^^eri^iiahsomct^]h^yue akHz and irrformttihnrate equal 32 kb/s BER cotirbt c^i;t^i^i^seilies^m iwodegreerrand ifvetuo olDopelar tranelztianequal 7 kHz BER will be decreacod We L5. t^^^i^des, the Vastrr information cate got the vmaflee BER, ceused by Doppler effect. Foroxample, in case one antenna receiving for information rate 32 kb/s and 32 mb/s BER decrease on 6 degreases,and incase twoantennas receiving for information rate 32 kb/s and 32mb/sBER decrease on 12 degreases .

3. Averagrngof ¡influence of Doppler effect on bit error ratio

for racomv glow- orbiïmgsateHiïe'asignals

Fee rerearchefficiencyofspacecheereity reneptiongoingOoaverbgc mfluence of Doppler effect

wiïhdiffcrent prbormation rates. Going to average of momentary value of Doppler translation.

Value of Doppler translatio n:

L =U, (3)

here 1 = y [m] - wave length; c [m/s] - light speed; ur [m/s] - radial velocity of satellite to land.

Research momentary value of radial velocity of satellite to land using Fig. 4.

Duration of communication session depend from duration time of line of sight of satellite on

horizon line. Radial velocity of satellite is maximal at the moment of satellite appearance. Radial

velocityofsatelliteequalnoughtatthemoment offlight vertical relative to land obtainer (dot "O").

- 67 -

Fig.4.Researchof momentary value of radialvelocity

Angle and durationtime of 1 ine of sight of satellite on horizon line depend from satellite orbit height [6]:

^CC^^^R^ ~amm , (4)

here Rf = 6371 [km]i earth radius; h = 700 [km] - satellite orbit height; amm [rad] - minimal operating ang le.

ietoMn^ (5)

a

V

here w =-trad/s]-angular velocityof satel Htemotion.

Rz + h

Orbital velocity of satellite motion [km/s]:

(6)

\Rz + h

0e re Mz = 5,g72- 1024 t -earthmass; G = 6<67 • g ^oi^g 's 2] -orrvitation constant.

In aicorCFtg. 4 moment i/^l^^af rndtal velocity of satellite motion define by angle A. Which is anglebetween vertical lineand satellite direction.

^aF-sieh), (7)

Getanalyticaldependencefordefineangle A fromthat:

1) Direction of satellite velocity is perpendicular for direction to earth center (point C) ZAA'C = n/2;

2)Directionfromearth centertosatellite(vector B) have uniform angular velocity;

3) Angle B move from -p0 top0. Initiatereasoning:

1)Angle A belong totriangleA'VD,when zVA'D = n/2 - A.

2) jungle z. AA' C = sAd consist from angles ¿VA'D+zCA'D. Aesult from that ZCA'D = tz/2 - Z.VA'D= o/e -jz02+t4 =A.

f) Defi ne-ngleO=zCA'D=zCAO depe ndeno e from anglofi=-JB0+® t.

4SWtkmeD Swosidms AA', CO of triangle CA'O and angle between their sides B=zA'CO. Therefore definition of angle A es poieiDle. ^oi" that divide trianglf on tno right-fngled ti^iianijleis C^C)'O oA' O'O by ploe perpendgculor O'O.

5)Length ol1O'O dapeod from sine nf angkt+s 0'0=!z sin(B)=Rz sint-50+ott).

6) Oeegtl of okle CA' fqeO Rz+e.PointO' dlvidestdeCA'on twopartnA'0'having length X and CO' having lengfhX'. SiOe 00' Bependfoem eosine of angle B:X'=Rz cos(B)=Rz cos(-B0+a>t).

7) ThereforeCO'=X=)n- + h-X'=Rz s h-Rzros(lB0+art).

8) Therefore angla = acO'A'O define arctangent division side O'O on CO':

[O'O ]

arc tg A'O' _ = arc/g

Rz ■ sin(-B0 + w-1) Rz+h-Rz-cop(-Be -+(»■0))

(8)

Use formulas(7) and (8) fordefinition ofi^iidi^l^u^loc^^^s of satellitemotion subject to time.Inview of the tectthat obditsonaS Doppletfrequoucy shcft mare nought,when satellite appear on horizon line, and sin(-S0)lessnought, workin multiply (-1):

u (t) = V • (-1) • am

eoc tg

Rz • oin(-B0 + m • t) Rz + h-Rz• cos(-B0 + ® •t)

(9)

Plot ithe; grafh radial velocity of nalellite deeendencc on time (9), using amm =3-[rad] ^nd.

getting fa = 0,3dA [rad], At = "750,41 [s5]n c = 1,0(54 • 10n [rad/s], 180

Average i)f iofluence of Doppko affeit oeBER for sessio n timeout by using formuLa (9). Avaraga BER get as inleoral on Oarmulai (1) or i2) acoording to onoand fwo aeOeanas, inplaoe ofDoppler frequency ohtfl usaformule (°) , ier place of radial velocity use formula (9), getting expression average to time:

Po ■

P1 = -If

At0

1 - J„

V ■ ( -1) ■ sin

2 ■n-

arc 'g

Rz • sin(-B0 + m ■') Rz + h - Rz ■ cos(-B0 +m ■ ')

\\

A

■T

2 ■(Po +1)

-d',

]10)

0,25 •

P2 = -if

Ait „

1 - J„

V • ( -1) • sin

2 •n-

arc tg

Rz • sin(—B0 + a • t ) Rz + h-Rz• cos(—B( + a •t)

2

•T

2 + J

V^ (—1>sm

2 • n -

arc tg

Rz • sin(—B0 + a • t) Rz + h— Rz • cos (—B(( +a• t) 2

• T

dt

(11)

Fig. 5. The graph of the radial velocity ofthe satellite

100 lxio3 1*104 1x10s lxio6 IkIO7 Ik 10s Fig. 6. Average biterror ratio dependenceon information rate forone or two antennas receiving

Plot the graph average BER dependence on information rate fS =— on formulas (10), (11).

Carryout analyze ofobtaineddependence. In case information rateequal 1 mb/s tpace chversity receptionallowdecrease avarageBERmSwo frcm 10a to 10"4. Ao. m dase information

i^^ta^tl^arimb/a ipace diversity reception allow decrease average BER in two degreases from 10 5 to lO"10.

Summary and Conclusions

Doppler effect increases number of errors at demodulation. In this paper consider efficiency of dcoeeaoas number af errors at domoudlatiou°y o sing gystem rf tpasedinershyreoepikin. For example ^^^duant^ode\i^^pt^t^n towtortiitingsaCelHSe eommumcrtionsysaem. aatrlHteorbit hefght tain taken 7e0]^m, tppr ofoignal mpOulaeia—wactokenDBPOK.

i- 70 —

Fig. 3 was showing by using formula (1) and (2) that space diversity reception allow decrease BER in two degrees from 10-8 to 10-16 for small value of Doppler frequency shift. And if value of Doppler translation equal 7 kHz BER will be decreased in 1.5.

Besides in this paper was average influence of Doppler effect on BER for session timeout and was getting formulas (10) and (11). In case information rate equal 32 mb/s space diversity reception allow decrease average BER in two degreases from 10-5 to 10-10.

References

[1] William C. Jakes. Microwave mobile communications. 1974

[2] Voelker H.B. Phase-Shift Keying in Fading Channels, Proc. IEEE, 107, Part B, January 1960, 31

[3] Bello P. A. and Nelin B.D. The Influence of Fading Spectrum on the Binary Error Probabilities of Incoherent and Differentially Coherent Matched Filter Receivers. IRE Trans. Comm, Systems, June 1962, 160-168.

[4] Rice S.O. Mahematical Analysis of Random Noise, Bell System Tech. J. 23, July 1944, 282332; 24, January 1945, 46-156.

[5] Rice S.O. Statistical Properies of a Sine Wave Plus Rendom Noise», Bell System Tech. J. 27, January 1948, 109-157.

[6] Bernard Sklar. Digital Communications. Fundamentals and Applications. Second edition.: Perevod s angliyskogo. Moscow: Izdatelskiy dom «Villiams», 2003. 1104.

[7] Бордовицына Т.В. Технологии глобального позиционирования (GPS / ГЛОНАСС). Электронное учебное пособие. Томск, 2007. [Bordovitsina T.V. Global Positioning Technology (GPS / GLONASS). E-learning tool Tomsk, 2007. (in Russian)]