Analysis of the possibilities of using reflected radiation of ground-based radioelectronic devices from low-orbit Earth satellites

 
Fig. 2. The main lobe of the shadow contour scattering diagram 
The peak of the main lobe of the SD along the direction of 
propagation of the incident wave can be immense. An essential 
feature of bistatic forward scattering is that an intense reflected 
signal can arrive at the receiver even in cases when the "object-
receiver" direction corresponds to the side lobes of the shadow 
field diagram. 
The ESA value when the directions from the diffuser 
coincide with the source of the probing signal and the 
observation point is called a backscattering diagram (BSD). For 
experimental determination, the BSD REM is moved around 
objects and at the same time the field strength of the Е
рх
is 
measured (Fig.3, a). Then the tested object is replaced with a 
reference (usually shaped like a ball) with a known ERA value 
of σ
оэ
and the Е
оэ
field strength is determined. 
Объект
ДОР
РЭ
С
D
Пер
еда
тчик
Прием
ник
Объект
ДР
D
a)
b) 
Fig. 3. Conditions for the experimental determination of 
BSD and SD
. 
In contrast to the considered case of single-position 
(monostatic) REM, the term ESA (effective scattering area) is 
more applicable for two-position (bistatic) REM. To remove 

---

the SD, you can, for example, fix the transmitter and move the 
receiver around the circle around the object (Fig.3, b). 
The possibility of comparing SD and BSD in some cases is 
of interest. So, for simple ideally conducting bodies of 
sufficient smoothness at a small wavelength (strictly speaking, 
tending to zero) and the transmitter—object—receiver angle β 
<180°, the SD is equal to the BSD in the direction of the angle 
bisector β. It follows that the SD does not change if you swap 
the transmitter and receiver. This theorem is clearly incorrect at 
angles β ≈ 180° i.e., near the so-called forward scattering (or 
shadow scattering). 
ERA of two-point objects. Several point objects located 
within the allowed volume form a group object. The simplest 
model of group objects is two-point. 
а)
О
1
О
2
D
1
D
2
D
РЭС
b) 
Е
1
Е
2
Fig. 4. Determining the ERA of two point objects 
It consists of two isotropic reflectors, the distance between 
which is L, and the distance to the REM is D
1
and D
2
(Fig. 4, 
a). Such a model correctly describes complex objects 
containing at least two shiny points. Real objects contain many 
brilliant points, however, using the example of a two-point 
model, it is possible to trace the most important patterns that 
occur when the REM signal is reflected from complex objects. 
The secondary radiation fields of each of the reflectors О
1
and О
2
at the REM are characterized in a complex form by the 
following expressions: 
𝐸
1
𝑒
𝑗𝜔(𝑡−𝑡
31
)
= 𝐸
1
𝑒
−𝑗𝜑
1
𝑒
𝑗𝜔𝑡
, 
𝐸
2
𝑒
𝑗𝜔(𝑡−𝑡
32
)
= 𝐸
2
𝑒
−𝑗𝜑
2
𝑒
𝑗𝜔𝑡
, 
(1.2) 
The fields of individual reflectors at the REM are summed 
up. The total field is represented as 
𝐸̇
𝑝
𝑒
𝑗𝜔𝑡
,
where the complex 
amplitude 
𝐸̇
𝑝
= 𝐸
1
𝑒
−𝑗𝜑
1
+ 𝐸
2
𝑒
−𝑗𝜑
2
.
(1.3) 
Accordingly, the amplitude 
𝐸
𝑝
= |𝐸
1
𝑒
−𝑗𝜑
1
+ 𝐸
2
𝑒
−𝑗𝜑
2
| = √𝐸
1
2
+ 𝐸
2
2
+ 2𝐸
1
𝐸
2
cos 𝜑
1,2
(1.4) 
where is the phase difference of the oscillations from the 
individual reflectors: 
𝜑
1,2
= 𝜑
1
− 𝜑
2
=
2𝜋
𝜆
2(𝐷
2
− 𝐷
1
) =
4𝜋
𝜆
𝐿 sin 𝜃 (1.5) 
A similar result for E
р
can be obtained using the formula of 
an oblique triangle when adding two vectors (Fig. 4, b). 
Applying formula (1.1) and assuming that its primary field 
Е
о
is the same for both objects, we obtain the ERA of two-point 
objects 
𝜎
𝑜
= 4𝜋𝐷
2
𝐸
𝑝
2
𝐸
𝑜
2
= 4𝜋𝐷
2
(
𝐸
1
2
𝐸
𝑜
2
+
𝐸
2
2
𝐸
𝑜
2
+ 2
𝐸
1
𝐸
𝑜
𝐸
2
𝐸
𝑜
cos 𝜑
1,2
) = 
= 𝜎
𝑜1
+ 𝜎
𝑜2
+ 2√𝜎
𝑜1
𝜎
𝑜2
cos 𝜑
1,2
(1.6) 
In particular, for identical objects, when σ
o1
= σ
o2
= σ
o0
, we 
obtain the following expression for BSD: 
𝜎
o
(𝜃) = 2𝜎
o0
[1 + cos (
4𝜋𝐿
𝜆
sin 𝜃)] = 4𝜎
o0
𝑐𝑜𝑠
2
(
2𝜋𝐿
𝜆
sin 𝜃) 
(1.7) 
The analysis of the dependence 
𝜎
o
(𝜃) shows that it is 
multi-petal (Fig.5). The zeros of the function 
𝜎
o
(𝜃) correspond 
to the directions where the secondary oscillations of two objects 
are in antiphase and cancel each other out, and the maximum to 
the directions of in—phase addition, and the resulting ERA 
exceeds four times the ERA of each object. The greater the ratio 
L/λ, the stronger the interference nature of the dependence 
𝜎
o
(𝜃) is manifested. 
If group objects consist of n reflectors, then the resulting 
field 
𝐸
𝑝
= |∑
𝐸
𝑘
𝑒
𝑗𝜑
𝑘
𝑛
𝑘=1
|. 
(1.8) 
Small random movements of objects lead to random 
changes in the phase difference φ
i,k
and, as a result, to 
significant fluctuations in the amplitudes of the reflected 
signals. If the phase difference φ
i,k
is equally probable in the 
range 0–π, then the average value of the cosine cosφ
i,k
=0. 
Therefore, the average value of the ERA 
𝜎
ц
̅̅̅ = ∑
𝜎
ц𝑖
𝑛
𝑖=1
. 
(1.9) 

---

1
2
3
0
о
90
о
180
о
270
о
а)
1
2
3
4
0
о
90
о
180
о
270
о
b) 
Fig. 5. BSD of two-point objects 
For n=2, this directly follows from the fact that, for 
𝜑
1,2
= 𝜋,: 
𝜎
o
̅̅̅ = (𝜎
o 𝑚𝑎𝑥
+ 𝜎
o 𝑚𝑖𝑛
). (1.10) 
The power of reflected radiation depends on the ESA σ of 
objects, which depends on the main reflective properties of 
objects, such as the size of the object (the projection area of the 
body on a plane perpendicular to the direction of the REM), 
configuration, surface material, the wavelength of the REM, its 
polarization, the direction of irradiation. The power of the 
reflected signal in the receiving antenna is given by the 
equation: 
𝑃
𝑟
=
𝑃
𝑡
𝐺
𝑡
𝐺
𝑟
𝜆
2
𝜎
(4𝜋)
3
𝑅
𝑡
2
𝑅
𝑟
2
𝐿
(1.11) 
This equation establishes the relationship between the 
received signal power 
𝑃
𝑟
and the radiation power 𝑃
𝑡
. From the 
formula (1.11) it can be seen that with increasing distance to 
objects, the power of the received signal decreases very 
quickly-inversely proportional to the 4th degree of range. In this 
regard, the power of the received signal will be small, and the 
signal itself is random. The low power of the reflected signal is 
explained by the large distance to objects in near-Earth orbits 
and the absorption of signal energy during its propagation.
Using 
the 
MATLAB 
Radar 
Equation 
Calculator 
application, it is possible to determine the required signal 
strength of the transmitter according to the formula (1.11) 
(Fig.6). It is necessary to enter data such as wavelength, pulse 
width, system losses in dB, noise temperature and effective 
scattering area of objects, gain of transmitting and receiving 
antennas, signal/interference ratio on the receiving antenna 
(probability of detection, probability of false alarm, number of 
pulses) and distance to objects. When performing the 
calculation for the radio communication system under 
consideration, the parameters given in Table 1 were used. 
TABLE I.
S
YSTEM 
P
ARAMETERS