Aerospace and Electronic Systems Magazine November 2017 - 37
Osechas et al.
Figure 2.
Geometrical representation of an attack. I, T, A stand for SSR interrogator, SSR-transponder, and an attacker, respectively. The worst-case
geometry is achieved at T1. The reference angle α is defined at T.
Figure 3.
ϕ ( x) =
The power of the interrogation signal received at the transponder D is the transmit power minus the free-space path loss between
interrogator and transponder
d
d1
takes its maximum at x1. A and I indicated the positions of
the interrogator and attacker as in Figure 1.
2
d2
1 + sin α
.
= φ ( x1 ) =
1 − sin α
d1
T
I
D = EIRP ( I ) + G (T ) − CL( ) − 20log d 2 − 20log f ( ) − 32.45,
φmax = max
with f in megahertz and d in kilometers.
The received power of the unauthorized signal U has a similar
expression:
(2)
The signal continues to be tracked, therefore, as long as
I
A
EIRP( ) − EIRP( ) + 10log φmax < 121
and assuming that the interrogator operates at the maximum specified power of 82.5 dBm. This gives an expression for a successful
disruption:
A
T
T
I
U = EIRP ( ) + G ( ) − CL( ) − 20log d1 − 20log f ( ) − 32.45.
Here, f (I) = 1030 MHz is the carrier frequency of the interrogation
channel. Thus, the ratio of interrogation signal to interference (in
decibels) becomes
A
EIRP( ) > 70.5 + 10log φmax .
Vulnerabilty at the Interrogator
2
d2
D
( A)
(I )
U = EIRP − EIRP + 10log d .
dB
1
(1)
In the last equation, it has been assumed that the transponder's antenna gain G(T) toward both attacker and interrogator is the same.
This is the case for omnidirectional antennas, i.e., G(T) = 0 or for
small dG.
Because the transponder is flying, the S/I is variable and depends on the geometry. However,
2
d
D
A
max = EIRP ( I ) − EIRP ( ) + 10log max 2 .
U
dB
d1
The worst-case geometry is thus achieved when ϕ(x) := (d2/d1)2 is
maximal. This is the case at T1 and x1, as illustrated in Figures 2
In the interrogator-centric analysis, the expressions for D and U,
mentioned previously, need to be modified to accommodate the
received signal frequency and the antenna gains of the interrogator and transponder. The signal received at the interrogator has the
carrier frequency of the transponder f (T) = 1090 MHz, while the
antenna gain is the difference of the transponder gain and the interrogator gain along the particular line of sight: ΔG D( I ) = GD( I ) − GU( I ).
U
D
With this in mind, the expression for becomes
U
d2
D
( A)
(I )
(T )
U = EIRP − EIRP + ΔG D − 20log d
dB
U
G
.
(3)
The distance from the interrogator, at which a transponder will still
receive messages must be such that the received power is 12 dB
above the interfering power, which means that the distance d2 must
satisfy
2
d
and 3, respectively; ϕmax := max 2 can be expressed in terms of
d1
the reference angle a in Figure 2
NOVEMBER 2017
2
2
2
log( d 2 )
IEEE A&E SYSTEMS MAGAZINE
A
I
EIRP (T ) EIRP ΔG D 12
20
U
log( d G ).
(4)
37
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