Signal Processing - September 2017 - 35

pu
mE,
100

(1)

where p u is the percentage of unpredictable chips embedded in
the received code sequence. On the other hand, for option B, it
can be easily demonstrated that the resulting degradation is twice
that resulting from (1). The value of p u is a key parameter in the
SCA approach and has to be designed by trading off between the
level of spoofing robustness and the requirements of backward
compatibility. In fact, existing receivers would not tolerate high
∆C/N 0 values, as in the case of the recent LightSquared/Ligado controversy, where the threshold for harmful interference
has been established at 1 dB [48].
The trend of ∆C/N 0 is also shown in Figure 3, for option A
(dotted blue curve), and option B (solid green curve), varying
p u from 0% (i.e., without SCA) up to 90%. For example, in the
case of option B, the C/N 0 degradation is equal to 1 dB when
11% of unpredictable chips are present.
Such degradation is strictly related to the reduction of the
correlation gain, due to the mismatch between the SCA bursts
and local chips, depending on p u as shown by (1).
The analytical results related to option B have also been
validated by means of simulations (red squares in Figure 3).
In detail, the tracking performance of a nonparticipant E1-B
receiver has been assessed for different p u values by means
of Monte Carlo simulation campaigns, where a modified E1-B
signal with random SCA bursts has been generated and processed with a software receiver. The results show a good agreement between theory and simulations.
On the other hand, for participant users, it can be demonstrated
that the theoretical performance of the authentication block can
be studied with an approach similar to that used for a classical
GNSS acquisition block (e.g., see [49]), with the only difference
that the decision is taken on a single variable (time) instead on a
two-dimensional search space (time and frequency).
The performance can be then assessed in terms of P AUTH
D
AUTH
and P FA
(defined respectively as the detection and false
alarm probabilities of the bursts of chips used for authentication) and evaluated in relation with the authentication technique
parameters (e.g., percentage of unpredictable chips, integration
time, C/N 0 , number of coherent sums, etc.).
Obviously, the performance of the authentication block is
strictly related to the value of p u. Analogously, it has to be
considered that the performance of conventional acquisition
systems can be easily improved in two ways: by increasing the
integration time Tint or by coherently accumulating the correlation results of consecutive code periods, thus introducing
multiple coherent sums N CS .
It is then convenient to define an equivalent integration time
eq
T int as the total time over which the signal samples are used
for the correlation

0
-2
C/N0 Degradation (dB)

∆C/N 0 = 10 $ log 10 ;1 - c

pu
(2)
.
100
As an example, Figure 4 plots the theoretical curves of
P AUTH
versus the total integration time, given by N CS $ Tint,
D
assuming a Tint of 4 ms and C/N 0 in the range [29, 41] dB-Hz.
AUTH
In detail, after fixing P FA
equal to 10 -4, the correlation
AUTH
threshold has been evaluated as a function of P FA
, Tint, and
AUTH
N CS, and used to estimate P D . The two families of curves
in the figure refer to the cases of p u = 1% and 5%.
The performance improvement obtained with an increase
of N CS is paid by a larger number of samples to be processed
at each iteration of the authentication procedure. For this reason, the equivalent integration time has to be set, by trading
eq

T int = N CS $ Tint $

-4
-6
-8
-10
-12
-14
Option A-Analytical ∆C/N0
Option B-Analytical ∆C/N0
Option B-Simulated ∆C/N0

-16
-18
-20
0

10

20

30

40 50
pu (%)

60

70

80

90

FIGURE 3. Nonparticipant users: an assessment of the C/N 0 degradation in
the case of SCA implemented on the Galileo E1 OS signals (Tint = 4 ms).

100

10-1
PDAUTH

SCA burst (option A), or those that include the unknown chips
in the correlation operation, thus increasing the noise component
(option B). In the former case, the degradation expressed in terms
of carrier-to-noise density ratio ^∆C/N 0h can be formulated as

10-2

10-3

10-4

0

50

100 150 200 250 300 350 400
Ncs.Tint (ms)

C/N0 = 41 dB-Hz-pu = 5%
C/N0 = 38 dB-Hz-pu = 5%
C/N0 = 35 dB-Hz-pu = 5%
C/N0 = 32 dB-Hz-pu = 5%
C/N0 = 29 dB-Hz-pu = 5%

C/N0 = 41 dB-Hz-pu = 1%
C/N0 = 38 dB-Hz-pu = 1%
C/N0 = 35 dB-Hz-pu = 1%
C/N0 = 32 dB-Hz-pu = 1%
C/N0 = 29 dB-Hz-pu = 1%

FIGURE 4. Participant users: the theoretical performance of the authentication block by varying p u and N CS. C/N 0 in the range [29, 41] dB-Hz
(Tint = 4 ms).

IEEE SIGNAL PROCESSING MAGAZINE

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September 2017

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35
Table of Contents for the Digital Edition of Signal Processing - September 2017
