=Paper=
{{Paper
|id=Vol-2254/10000237
|storemode=property
|title=Energetic
concealment of low-frequency sattelite communication system with
arbitrary recession of radiointercepting receiver
|pdfUrl=https://ceur-ws.org/Vol-2254/10000237.pdf
|volume=Vol-2254
|authors=Vladimir Pashintsev,Alexander Chipiga,Ivan
Anzin
}}
==Energetic
concealment of low-frequency sattelite communication system with
arbitrary recession of radiointercepting receiver==
https://ceur-ws.org/Vol-2254/10000237.pdf
Energetic concealment of low-frequency sattelite
communication system with arbitrary recession of
radiointercepting receiver
V.P. Pashintsev A.F. Chipiga I.V. Anzin
Stavropol, Russia Stavropol, Russia Stavropol, Russia
pashintsevp@mail.ru chipiga.alexander@gmail.com ianzin@ncfu.ru
North Caucasus Federal University, Stavropol, Russia
Abstract
A method has been developed for evaluation of the energetic conceal-
ment 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 transmit-
ting antenna of an Artificial Earth Satellite with directional pattern
width based on the zeroed radiation level within the state border of
Russia and diversified signal reception with two antennas, with arbi-
trary recession of a radio interception receiver from a ground-based
satellite communication receiver. It has been established that, in such
case, the energetic concealment coefficient value of no lower that 27 dB
is provided.
1 Introduction
It is known [1] that one of the main ways to increase the energetic concealment factor of the satellite commu-
nication system (SCS) is to implement transmitting antennas with a narrow directional pattern (DP). However,
with a radio intelligence receiver placed closely relative to an SCS receiver, when the receivers are within the DP
width of the AES transmitting antenna (service zone), this method of increasing energetic concealment becomes
ineffective.
Contrariwise, a method is known [2-4] to increase energetic concealment of the SCS from radio interception
(RI) of signals by the means of simultaneously reducing the carrier frequency of the signal transmitted from
the AES (down to f0 = 30 . . . 100 MHz) and applying diversified signal reception with several (n = 2 . . . 4)
antennas on an earth-based station. This method allows to provide a significant SCS energetic concealment
value (22 . . . 34dB) with the RI receiver in close proximity (Rd < 10km) to the SCS receiver. The prerequisites
of applying the method are the utilization of a single antenna (nd = 1) and the inability to apply diversified
reception with several (nd = 2 . . . 4) antennas (due to limitations in the mass and dimensional characteristics of
the radio intelligence equipment).
However, in the frequency range of f0 = 30 . . . 100 MHz, it is difficult to implement a narrow DP of the AES
transmitting antenna (for example, helical). Therefore, with a wide DP of the low-frequency SCS on-board
Copyright c by the paper’s authors. Copying permitted for private and academic purposes.
In: Marco Schaerf, Massimo Mecella, Drozdova Viktoria Igorevna, Kalmykov Igor Anatolievich (eds.): Proceedings of REMS 2018
– Russian Federation & Europe Multidisciplinary Symposium on Computer Science and ICT, Stavropol – Dombay, Russia, 15–20
October 2018, published at http://ceur-ws.org
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 (2θ0 ) within the state border is provided in the figure 1.
The purpose of this research is to develop the method for evaluation of energetic concealment for the low-
frequency 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 diversified signal reception with two (n=2) antennas (figure 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 (2θ0 ) 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 = h2alwd G , where G - energetic (systemic) SCS radio link reserve.
Figure 1: Method of providing energetic concealment for the low-frequency SCS with the radio intercepting
receiver located within the state border of Russia Rd ≤ Rb and beyond it Rd > Rb
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 coefficient over the value of one: γec = h2alwd d /h2d > 1.
According to [2, 3], the condition of providing energetic concealment for the SCS can be expressed in detail
as
h2alwd d 1 Gr zd2 Llr Ter h2alwd d
γec = 2 = 2 > 1, (1)
hd Ft (θtd ) Grd z 2 Ll Te h2alwd G
where Ft2 (θtd ) = Gt (θtd )/Gt ≤ 1 - normalized DP of the AES transmitting antenna based on the power in the
direction θtd on the intercepting receiver (RI); Gr and Grd - amplification coefficients of the SCS and RI receiver
antennas; zd and z - length of the radio links between the AES and RI/SCS receivers; Ll r 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 amplification coefficient
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
h2alwd d 1 zd2 h2alwd d
γec = 2 = 2 > 1, (2)
hd Ft (θtd ) z 2 h2alwd G
According to figure 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 θtd < 0.01◦ . Thus, the value Ft2 (θtd ) ≈ 1, the
intelligence radio link length, is almost indistinguishable from the SCS radio link length (zd2 /z 2 ≈ 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 simplified form γec = h2alwd d /h2d ≈ h2alwd d /h2alwd G > 1. The known [3, 4]
method for providing energetic concealment for the SCS with the RI receiver in close proximity is based (figure
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 ∆ϕi = ∆Ni /f0 and by fading of the received signals
that are close to Rayleigh) and implementing diversified 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
(nd = 1) signal reception with Rayleigh fading is h2alwd 2 = h2alwd 1 = 50 dB. In such case, a considerable SCS
energetic concealment coefficient is achieved, which is conditioned by the gains in the signal/noise ratio when
using diversified reception compared to unified [4]:
γec = h2alwd d /h2d ≈ h2alwd 1 /h2alwd 2 = 50 − 28 = 22 dB.
The analysis of figure 1 shows that as the distance (Rd) between the RI receiver and the SCS receiver increases,
the angle (θtd ∼ 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 (θtd ) < 1 and to an increase of the intelligence range zd (θtd ). So, as the intelligence
distance grows (Rd ∼ θtd ) , the energetic concealment coefficient grows consequently (2), which can be expressed
as a function of Rd as
1 zd2 h2alwd d
γec (Rd ) = = P (Rd )∆h2alwd n (Rd )/G > 1. (3)
Ft2 (θtd ) z 2 h2alwd G
Here
1 zd2 (Rd )
P (Rd ) = ≥1 (4)
Ft2 (Rd ) z 2
- SCS spatial concealment coefficient (which grows gradually with recession Rd of the RI receiver from the
SCS receiver)
1, if nd = 1 when Rd ≤ Rb ;
∆h2alwd n (Rd ) = h2alwd dn (Rd )/h2alwd 2 (5)
≤ 1, if nd ≥ 2 when Rd > Rb .
– gains in energetic concealment from utilization of spatially diverse fading signal reception in the low-frequency
SCS, i.e. a constituent of the SCS energetic concealment coefficient, that is conditioned by lowering the carrier
frequency and applying diversified reception with n=2 antennas. According to figure 1, when placing the RI
receiver within the borders (Rd ≤ Rb ) and forcefully utilizing a single (n = 1) antenna, the amount of gains
is ∆h2alwd n (Rd ) = h2alwd 1 (Rd )/h2alwd 2 ≈ 22 dB. When placing the RI receiver beyond the borders (Rd >
Rb ) and willingly utilizing two (n = 2) diversified antennas, such gains are non-existent: ∆h2alwd n (Rd ) =
h2alwd 2 (Rd )/h2alwd 2 = 1 dB (i.e. 0 dB). Therefore, for the considered (figure 1) case, the expression (5) takes
the following form
22, dB if nd = 1 when Rd ≤ Rb ;
∆h2alwd n (Rd ) = h2alwd dn (Rd )/h2alwd 2 (6)
0, dB if nd = 2 when Rd > Rb .
The analysis of figure 1 and the relations (3-6) indicates that the ability to meet the requirements of providing
energetic concealment for the SCS γec (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
diversified 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 coefficient P (Rd ∼ θtd ) , 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 (θtd ∼ Rd ).
To determine the intelligence range zd (Rd ∼ θtd ), let us consider the simplest case (see figure 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, 5αsrv = αd of this distance from the center of Earth with the radius of RE = 6370 km:
αd◦ = Rd /(2πRE /360◦ ) ≈ Rd [km]/111, 2 ≈ 9 · 10−3 Rd [km] (7)
To bind αd to the intelligence direction angle θtd , a consideration should be made for the known [5] dependency
for the AES service zone surveillance angle (βsrv ) of the ground area 2Rd on the angle size of this area from the
center of Earth (αsrv ):
◦ Rd [km] HAES
θtd = 90 − − arctg (8)
222, 4 (2RE + HAES )tg(Rd [km]/222, 4)
The dependence of the specified angles αd and θtd on the RI receiver recession (Rd ) determines the maximum
intelligence range, i.e. the distance between the AES and the location point of the intelligence (radio interception)
receiver
zd (Rd ) = RE · sin αd / sin θtd (9)
The analysis of the expressions (7-9) and figure 1 shows that as the distance Rd between the RI and SCS
receivers increases, the angle of the intelligence receiver direction θtd (Rd ) and the intelligence range zd (θtd ) also
increase. Aside from that, as the AES orbital altitude decreases (HAES ), the angle of the intelligence receiver
direction θtd (Rd , HAES ) and the intelligence range zd (θtd , 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 θtd = ψ(Rd , HAES ) , and the general expression for the DP normalized by the tension of a cylinder
spiral antenna with nc coils [6]
2 sin πnξ
Ft (θtd ) ≈ J0 (ka sin θtd ) cos θtd 2 (10)
πn ξ −1
Here J0 (x) - Bessel function; k = 2π/λ0 - wave number domain; a - spiral radius; ξ = 1 + ka(1 − cos θtd )tgα
- wave velocity factor; α - spiral coil ascent angle. With traditional values α = 12 . . . 14, when ka ≈ 1, the
expression (10) comes down to a more simple form
2 sin πnc ξ
Ft (θtd ) ≈ J0 (sin θtd ) cos θtd 2 (11)
πnc ξ −1
where
ξ = 1 + 0.22 (1 − cos θtd ) tgα (12)
According to [6], when ka ≈ 1 and ξ ≈ 1, the value sin πnc ξ/(ξ 2 − 1) = πnc /2. Thus, with θtd = 0 , we shall
have J0 (sin θtd ) = J0 (0) = 1 and Ft (θtd = 0) = 1. Provided on the figure 2 are the DP of the spiral antenna
normalized by the tension Ft (θtd ) and by the power Ft2 (θtd ), which are structured according to (10, 11) with
nc = 13 and α0 = 5 m (f0 = 60MHz).
Figure 2: Normalized directional pattern of the spiral antenna
The analysis of figure 2 shows that the DP width of the given spiral antenna by halved power is 2θ0,5 ≈ 54◦ ,
and by the zeroed radiation level it is θ0 ≈ 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 (θtd ) and (8)
for θtd = ψ(Rd , HAES ). The general expression (4) for the calculation of the SCS spatial concealment coefficient
can be expressed in decibels as the sum of 2 summands:
2
P (Rd )dB = Ft−2 (Rd )dB + [zd (Rd )/HAES ]dB (13)
Provided on figure 3 is the dependency of the SCS spatial concealment (13) P (Rd )dB and its con-
stituents 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 coefficient on recession of the radio interception receiver
The analysis of figure 3 indicates that the graph Ft−2 (Rd )dB (dotted line) takes on the maximum value
(PdB → ∞) when the angle ( θtd ∼ 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 (θtd = θ0 ≈
49◦ ) and Ft2 (θtd = θ0 ) = 0 . Corresponding to this zeroed radiation angle is the intelligence distance that is
equal to the distance to the border (θ0 ∼ 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
γec (Rd )dB = P (Rd )dB + ∆h2alwd 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)
in the SCS receiver, a gain is achieved ∆h2alwd n (θtd ) = 22 dB, which can be considered constant when recessing
the RI receiver up to the borders (Rd ≤ Rb ) . Therefore, the dependency graph ∆h2alwd n (θtd ) with (Rd ≤ Rb )
will have the form of a rectangle with the sides ∆h2alwd n = 22 dB and Rb = 894 km (in cohesion with the AES
altitude HAES = 700 km).
The dependency of the low-frequency SCS energetic concealment coefficient on the RI receiver recession
γec (Rd )dB with the AES altitude of HAES = 700 km, with no radio link energetic reserve (GdB = 0 dB), and
both of its constituents: P (Rd ) and ∆h2alwd n (θtd ) are provided on figure 4. The dependency corresponds to the
one provided on figure 3, and ∆h2alwd n (θtd ) is structured according to (6).
Figure 4: Dependency of the low-frequency SCS energetic concealment coefficient on the radio inter-ception
receiver recession
The analysis of figures 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 diversified recep-
tion of fading signals in the low-frequency SCS and roughly equals to γec (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 γec (Rd )dB ≈ ∆h2alwd n (Rd )dB + P (Rd )dB ≈ 28 dB due to the growth of the spatial concealment coefficient
by P (Rd )dB ≈ 6 dB. When recessing the RI receiver to the border distance Rd = Rb = 894 km, the low-
frequency SCS energetic concealment will be determined by the spatial concealment coefficient, the value of
which γec (Rd )dB ≈ P (Rd )dB → ∞ is conditioned by the zeroed radiation direction of the AES transmitting
antenna that corresponds to (see figure 2) θ0 ≈ 49◦ .
This value θ0 and the known expression for the DP width of the spiral antenna based on the zeroed radiation
level [6]
p p
∆θ0 = 2θ0 ≈ 162 λ0 /Ls = 162 λ0 /Sns (15)
allow to determine the length Ls and the pitch S = Ls /ns of a spiral. Hence, with λ0 = 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 α ≈ λ0 = 5 m. Such an antenna provides the antenna directivity factor of D ≈ 15(Ls /λs ) ≈ 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 diversified 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 coefficient γec (Rd )dB = P (Rd )dB . The least value of this coefficient
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 first side lobe of the AES transmitting antenna DP
(refer to figure 1).
It is worth noting that, according to figure 4, the low-frequency SCS energetic concealment coefficient exceeds
the value γec (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 effect is achieved
mainly by utilizing spatial diversification with two antennas γec (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
γec (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 (figure 1). It is based on the representation of the low-frequency SCS energetic concealment as (3-6) a
product of the spatial concealment coefficient (conditioned by the AES transmitting antenna DP) and the gain
from the application of spatially diversified 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 con-
cealment coefficient 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 diversified reception and lowered frequency according to
the expressions (5-6); 3) determining the dependency γec (Rd ) of the low-frequency SCS energetic concealment
coefficient on the RI receiver recession, according to the expression (14).
The obtained (figure 4) dependency γec (Rd ) points to the ability of providing an exceptionally high energetic
concealment coefficient for the low-frequency SCS (γec (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 diversified 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 figure 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 satisfies 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 coefficient 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 diversified reception and lowered frequency
according to the expressions (5);
5. Determining the dependency γec (Rd ) of the low-frequency SCS energetic concealment coefficient on the RI
receiver recession, according to the expression (14).
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