Energetic concealment of low-frequency sattelite communication system with arbitrary recession of radiointercepting receiver

Abstract

A method has been developed for evaluation of the energetic concealment factor of a satellite communication system that utilizes lowered carrier frequency down to 30. . . 100 MHz (such that wave propagation is followed by scattering on the ionospheric inhomogeneities), a transmitting antenna of an Arti cial Earth Satellite with directional pattern width based on the zeroed radiation level within the state border of Russia and diversi ed signal reception with two antennas, with arbitrary recession of a radio interception receiver from a ground-based satellite communication receiver. It has been established that, in such case, the energetic concealment coe cient value of no lower that 27 dB is provided.

Introduction

Copyright c by the paper's authors. Copying permitted for private and academic purposes. transmitter, the service zone can be vast to such an extent that the RI receiver may be placed beyond the borders of Russia, where it (and the SCS receiver) is capable of using several (nd = 2 : : : 4) antennas. It presents itself as self-evident that in this case, it is possible to provide high energetic concealment for the low-frequency SCS by the means of choosing the AES transmitting antenna parameters in a way which ensures that its DP width based on the zeroed radiation level does not exceed the state border of Russia. The suggested method of providing energetic concealment for the low-frequency SCS with the arbitrarily recessed radio intercepting receiver by the means of choosing the DP width of the AES transmitting antenna based on the zeroed radiation level (2 0) within the state border is provided in the gure 1.

The purpose of this research is to develop the method for evaluation of energetic concealment for the lowfrequency satellite communication system with the choice of the AES transmitting antenna directional pattern width based on the zeroed radiation level within the borders of Russia and with arbitrary recession of the radio intercepting receiver. 2

Energetic concealment evaluation technique

Let us analyze the capabilities of the known [2-4] method of improving energetic concealment of the SCS by lowering the carrier frequency of the on-board SCS transmitter (TSM) signal (down to f0 = 30 : : : 100 MHz) and applying diversi ed signal reception with two (n=2) antennas ( gure 1) for two cases: 1) utilizing one (n=1) antenna in the RI receiver (RCV) when it is recessed by the distance Rd within the state border (BD) (Rd Rb); 2) recessing the RI receiver which utilizes two (nd = 2) antennas by the distance Rd that exceeds the distance to the border (Rd > Rb). Herewith, the DP width of the AES receiving antenna based on the zeroed radiation level (2 0) does not exceed the state border.

It is known [2-4] that the condition of providing noise immunity for the SCS is expressed in the actual signal/noise ratio h2 exceeding the allowed value h2alwd (with which the achieved error probability value equals the value allowed in the SCS Perr = Perr alwd = 10 5). This condition h2 > h2alwd can be rewritten as the expression h2 = h2alwdG , where G - energetic (systemic) SCS radio link reserve.

The condition of providing energetic concealment for the SCS is expressed as non-exceedance of the actual signal/noise ratio on the RI receiver input h2d over the allowed value h2alwd d. This condition (h2d < h2alwd d) can be expressed as exceedance of the energetic concealment coe cient over the value of one: ec = halwd d=h2d > 1. 2 as

According to [2, 3], the condition of providing energetic concealment for the SCS can be expressed in detail 2 ec = halwd d =

1 Gr zd2 Llr Ter h2alwd d > 1;

Ft2( td) Grd z2 Ll Te h2alwdG h2

d where Ft2( td) = Gt( td)=Gt 1 - normalized DP of the AES transmitting antenna based on the power in the direction td on the intercepting receiver (RI); Gr and Grd - ampli cation coe cients of the SCS and RI receiver antennas; zd and z - length of the radio links between the AES and RI/SCS receivers; Llr and Ll - transmission losses due to wave absorption in the intelligence (radio interception) and communication radio link medium; Ter and Te - equivalent noise temperatures of the receiving radio interception systems and the ground-based station.

Hereinafter, we shall suppose that in the RI receiver, the noise temperature and the ampli cation coe cient values are ensured to be approximately the same as in the SCS receiver (i.e. Ter=Te 1 and Gr=Grd 1). It can be shown [2] that the transmission losses due to wave absorption in the radio link intelligence and the communication medium (ionosphere) are small and are approximately equal (Llr=Ll 1). Then, the condition ( 1 ) of providing energetic concealment for the SCS comes down to an approximate form

2 ec = halwd d =

1 zd2 h2alwd d > 1;

Ft2( td) z2 h2alwdG h2

d

According to gure 1, with the RI receiver being in close proximity to the SCS receiver (for example, Rd 10 km) and with the AES orbital altitude having any value HAES = z = 700 : : : 40000 km, the surveillance angle of the intelligence receiver from the AES is extremely small td < 0:01 . Thus, the value Ft2( td) 1, the intelligence radio link length, is almost indistinguishable from the SCS radio link length (zd2=z2 1). Thereat, the condition of providing energetic concealment for the SCS ( 2 ) with the RI receiver RCV in close proximity (Rd 10 km) comes down to a simpli ed form ec = h2alwd d=h2d h2alwd d=h2alwdG > 1. The known [3, 4] method for providing energetic concealment for the SCS with the RI receiver in close proximity is based ( gure 1) on lowering the carrier frequency of the signal transmitted from the AES down to f0 = 30 : : : 100 MHz (with which radio wave propagation is followed by dissipation in the ionospheric inhomogeneities Ni, by the appearance of relative phasic shifts of the received beams 'i = Ni=f0 and by fading of the received signals that are close to Rayleigh) and implementing diversi ed signal reception with several (for example, n = 2) antennas. In this case, the actual signal/noise ratio on the RI receiver input (h2d) is almost equal (when G = 1) to the allowed signal/noise ratio on the SCS receiver input, which, with Perr alwd = 10 5 and with diverse n=2 antennas, may be h2alwd 2 28 dB. The allowed signal/noise ratio on the RI receiver input with single antenna 2 2 (nd = 1) signal reception with Rayleigh fading is halwd 2 = halwd 1 = 50 dB. In such case, a considerable SCS energetic concealment coe cient is achieved, which is conditioned by the gains in the signal/noise ratio when using diversi ed reception compared to uni ed [4]: ec = halwd d=h2d 2 halwd 1=h2alwd 2 = 50 2 28 = 22 dB:

The analysis of gure 1 shows that as the distance (Rd) between the RI receiver and the SCS receiver increases, the angle ( td Rd) between the AES and SCS intelligence receivers surveillance direction increases as well. This, in turn, leads to a decrease in the normalized DP of the SCS transmitting antenna in the direction of the intelligence receiver Ft2( td) < 1 and to an increase of the intelligence range zd( td). So, as the intelligence distance grows (Rd td) , the energetic concealment coe cient grows consequently ( 2 ), which can be expressed as a function of Rd as

Here ec(Rd) =

1 zd2 h2alwd d = P (Rd) h2alwd n(Rd)=G > 1: Ft2( td) z2 h2alwdG

P (Rd) =

1 Ft2(Rd) zd2(Rd) z2 1 ( 1 ) ( 2 ) ( 3 ) ( 4 ) halwd n(Rd) = halwd dn(Rd)=h2alwd 2 2 2

The analysis of gure 1 and the relations ( 3-6 ) indicates that the ability to meet the requirements of providing energetic concealment for the SCS ec(Rd) = P (Rd) h2alwd n(Rd)=G > 1 when the RI receiver is placed beyond the borders (Rd Rb) is determined by the increase in spatial concealment P (Rd) 1, and when it is placed in close proximity to the SCS receiver RCV (Rd Rb) - by the increase in the second constituent of h2alwd n(Rd) = h2alwd 1(Rd)=h2alwd 2 1 , that is conditioned by the decrease in the SCS frequency and the application of diversi ed reception with two (n = 2) antennas when the RI receiver has only one (n = 1) antenna. According to ( 4 ), to determine the SCS spatial concealment coe cient P (Rd td) , it is required to establish the dependencies on the intelligence distance Rd , normalized intelligence range zd(Rd)=z = zd(Rd)=HAES and the normalized AES antenna DP Ft2( td Rd).

To determine the intelligence range zd(Rd td), let us consider the simplest case (see gure 1), when the AES transmitting antenna aiming point matches the under-satellite point (z = HAES) where the SCS receiver is located, and the RI receiver is recessed by Rd. The intelligence distance Rd corresponds to one half of the surveillance angle 0; 5 srv = d of this distance from the center of Earth with the radius of RE = 6370 km:

Here J0(x) - Bessel function; k = 2 = 0 - wave number domain; a - spiral radius; = 1 + ka(1 cos td)tg - wave velocity factor; - spiral coil ascent angle. With traditional values = 12 : : : 14, when ka 1, the expression (10) comes down to a more simple form

zd(Rd) = RE sin d= sin td

The analysis of the expressions (7-9) and gure 1 shows that as the distance Rd between the RI and SCS receivers increases, the angle of the intelligence receiver direction td(Rd) and the intelligence range zd( td) also increase. Aside from that, as the AES orbital altitude decreases (HAES), the angle of the intelligence receiver direction td(Rd; HAES) and the intelligence range zd( td; HAES) increase. To determine the second constituent of spatial concealment of the SCS (10) P (Rd) 1=Ft2(Rd), let us apply the expression (8), which establishes the connection td = (Rd; HAES) , and the general expression for the DP normalized by the tension of a cylinder spiral antenna with nc coils [6]

Ft( td) 2 sin n n J0(ka sin td) cos td 2 1 Ft( td) 2 nc

To bind d to the intelligence direction angle td, a consideration should be made for the known [5] dependency for the AES service zone surveillance angle ( srv ) of the ground area 2Rd on the angle size of this area from the center of Earth ( srv):

According to [6], when ka 1 and 1, the value sin nc =( 2 1) = nc=2. Thus, with td = 0 , we shall have J0(sin td) = J0(0) = 1 and Ft( td = 0) = 1. Provided on the gure 2 are the DP of the spiral antenna normalized by the tension Ft( td) and by the power Ft2( td), which are structured according to (10, 11) with nc = 13 and 0 = 5 m (f0 = 60MHz).

The analysis of gure 2 shows that the DP width of the given spiral antenna by halved power is 2 0;5 54 , and by the zeroed radiation level it is 0 2 49 = 98 . The sought dependency Ft2(Rd) of the normalized DP of the spiral antenna on recession of the RI receiver is determined by the expressions (11) for Ft2( td) and (8) for td = (Rd; HAES). The general expression ( 4 ) for the calculation of the SCS spatial concealment coe cient can be expressed in decibels as the sum of 2 summands:

Provided on gure 3 is the dependency of the SCS spatial concealment (13) P (Rd)dB and its constituents Ft 2(Rd)dB and (zd(Rd)=HAES)2 on recession of the RI receiver (Rd) with low AES orbital altitude HAES = 700 km.

Figure 3: Dependency of the SCS spatial concealment coe cient on recession of the radio interception receiver

The analysis of gure 3 indicates that the graph Ft 2(Rd)dB (dotted line) takes on the maximum value (PdB ! 1) when the angle ( td Rd ) between the RI receiver direction and the SCS receiver is equal to one half of the DP width based on the zeroed radiation level of the AES transmitting antenna ( td = 0 49 ) and Ft2( td = 0) = 0 . Corresponding to this zeroed radiation angle is the intelligence distance that is equal to the distance to the border ( 0 Rd = Rb), which, with the AES altitude of HAES = 700 km, is Rb = 894 km. The contribution of the second summand is much less prominent, and with Rb = 894 km it is just (zd(Rd)=HAES)2dB 6 dB. With the RI receiver recessed to the distance that exceeds the boundaries Rd > Rb, the SCS spatial concealment shall be considerable: PdB > 28 dB.

The general expression for the calculation of energetic concealment of the SCS can be expressed in decibels as 3 summands ec(Rd)dB = P (Rd)dB +

2 halwd n(Rd)dB

GdB (14)

According to the expression ( 6 ), when using one antenna (n = 1) in the RI receiver and dual reception (n = 2) itwnhieltlhRheaISvrCeecStehireveecfroeiruvmpero,tofaatghareeincbtioasrndageclehrsiwe(viRtehdd thheR2asbliw)dde.snT(hthedr2a)elw=fodr2en2,=tdhB2e2,dwdehBpiecanhndcdeanRncybb=egrca8op9nh4sikdmehr2ae(ldiwndcocnon(hstetadsni)otnwwiwthhietnh(RrtedhceesAsRiEnbSg) altitude HAES = 700 km).

The dependency of the low-frequency SCS energetic concealment coe cient on the RI receiver recession ec(Rd)dB with the AES altitude of HAES = 700 km, with no radio link energetic reserve (GdB = 0 dB), and obnoethporofvitidsecdonosntitugeunrtes:3,Pa(nRdd) ahn2adlwd nh(2alwtdd) nis( sttdr)uacrteurperdovaicdceodrdoinng gtour(e6)4.. The dependency corresponds to the

The analysis of gures 4 and 1 shows that when deploying the single-antenna (nd = 1) RI receiver in close proximity (Rd < 10 km) to the SCS receiver with lowered frequencies and two (n = 2) antennas, the energetic concealment of the SCS is determined by the gains provided by the application of spatially diversi ed reception of fading signals in the low-frequency SCS and roughly equals to ec(Rd)dB h2alwd n(Rd)dB 22 dB. When recessing the RI receiver to the distance of Rd 430 km, energetic concealment of the SCS increases to ec(Rd)dB h2alwd n(Rd)dB + P (Rd)dB 28 dB due to the growth of the spatial concealment coe cient by P (Rd)dB 6 dB. When recessing the RI receiver to the border distance Rd = Rb = 894 km, the lowfrequency SCS energetic concealment will be determined by the spatial concealment coe cient, the value of which ec(Rd)dB P (Rd)dB ! 1 is conditioned by the zeroed radiation direction of the AES transmitting antenna that corresponds to (see gure 2) 0 49 .

This value 0 and the known expression for the DP width of the spiral antenna based on the zeroed radiation level [6] allow to determine the length Ls and the pitch S = Ls=ns of a spiral. Hence, with 0 = 5 m, the required spiral antenna will have the length of Ls = 13:7 m, the pitch of S = Ls=ns 1:05 m and the coil length of ls = S= sin 0 = 5 m. Such an antenna provides the antenna directivity factor of D 15(Ls= s) 41 (i.e. 16 dB).

When deploying the RI receiver beyond the state border (Rd > Rb = 894 km) and utilizing two (n = 2) antennas, the gains from the application of spatially diversi ed reception with two (n = 2) antennas in the RI receiver are not evident ( h2alwd n(Rd)dB = 0 dB) and the SCS energetic concealment is totally (with G = 0) determined by the spatial concealment coe cient ec(Rd)dB = P (Rd)dB. The least value of this coe cient P (Rd)dB = 28 dB is observed when recessing the RI receiver RCV to the distance of Rd 1250 km, which corresponds to the direction of maximal radiation of the rst side lobe of the AES transmitting antenna DP (refer to gure 1).

It is worth noting that, according to gure 4, the low-frequency SCS energetic concealment coe cient exceeds the value ec(Rd)dB > 28 dB when recessing the RI receiver to the distance of Rd > 430 km both with one (n = 1) and two (n = 2) antennas. However, with the recession of Rd = 430 : : : 740 km, this e ect is achieved mainly by utilizing spatial diversi cation with two antennas ec(Rd)dB h2alwd n(Rd)dB > 28 dB, and with the recession of Rd > 740 rm { by the ability of the AES on-board antenna to provide spatial concealment ec(Rd)dB P (Rd)dB > 28 dB.

CONCLUSIONS In the research, the method has been developed for evaluation of the suggested technique for providing energetic concealment for the low-frequency SCS when choosing the AES transmitting antenna directional pattern width based on the zeroed radiation level within the state border and with arbitrary recession of the radio interception receiver ( gure 1). It is based on the representation of the low-frequency SCS energetic concealment as ( 3-6 ) a product of the spatial concealment coe cient (conditioned by the AES transmitting antenna DP) and the gain from the application of spatially diversi ed reception and lowered frequency.

In contrast to the known methods, applicable only in near or far location of the radio interception receiver, the method allows to evaluate the energy stealth low-frequency SCS at an arbitrary location of the radio receiver.

The method consists of three main stages: 1) determining the dependency P (Rd) of the SCS spatial concealment coe cient on the RI receiver recession, according to the expressions (7-9) and (11-13); 2) determining the gain h2alwd n from the application of spatially diversi ed reception and lowered frequency according to the expressions ( 5-6 ); 3) determining the dependency ec(Rd) of the low-frequency SCS energetic concealment coe cient on the RI receiver recession, according to the expression (14).

The obtained ( gure 4) dependency ec(Rd) points to the ability of providing an exceptionally high energetic concealment coe cient for the low-frequency SCS ( ec(Rd) > 28 dB) with arbitrary recession of the radio interception receiver. Besides, with the RI receiver in close proximity, high values of energetic concealment for the low-frequency SCS are provided by the means of spatially diversi ed fading signal reception, and with the recession distance of Rd > 740 km { by the means of spatial concealment of the AES transmitting antenna radiation.

Provided on gure 4 is the dependency of the energetic concealment for the low-frequency SCS, in which a dual reception is used at a carrier frequency of f0 = 60 MHz at an orbit altitude of HAES = 700 km.

The algorithm for applying the developed methodology for an arbitrary case consists of the following steps: 1. Obtaining characteristics of SCS, such as orbit height, distance from receiver to boundary, carrier frequency; 2. The choice of an antenna that satis es the requirement of the direction of the the zeroed radiation level within the state border (Ft(Rb) = 0);

3. determining the dependency P (Rd) of the SCS spatial concealment coe cient on the RI receiver recession, according to the expressions (7-9) and (11-13);

4. Determining the gain h2alwd n from the application of spatially diversi ed reception and lowered frequency according to the expressions ( 5 );

5. Determining the dependency ec(Rd) of the low-frequency SCS energetic concealment coe cient on the RI receiver recession, according to the expression (14).

References

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