Soderi, Mucchi, Hämäläinen, Piva, and Iinatti
124
Figure 6.3 shows how the eavesdropper, Eve, is capable of observing Alice’s transmission over an independent discrete‐time Rayleigh channel, that is, a non‐degraded wiretap
channel. The i‐th sample of the signal received by Eve is given by
y i h i x i g i x i n i
E
E
J
J
E
( )= ( ) ( )
( ) ( )
( ),
S
(6.2)
where h E (i) is the wiretap channel’s complex Gaussian fading coefficient between Alice
and Eve, n E (i) is the complex zero‐mean Gaussian noise, and g J (i) is the jamming channel complex Gaussian fading coefficient. It is assumed that all channels are quasi‐static
fading channels, which mean that the channel gain coefficients remain constant during
the transmission of a code word: h M (i) = h M , h E (i) = h E , k J (i) = k J and g J (i) = g J , i
N
=1,..., .
6.2.1 Transmitter
In accordance with the data decomposition method proposed in Section 10.1, Alice
conveys the information by means of two independent paths. The information is sent to
the legitimate user by means of a narrowband signal. On the other hand, Alice also
embeds a SS watermark in the host narrowband signal. The watermark conveys part of
the information to the legitimate user, Bob, through a secondary channel.
In accordance with the framework presented by Cox et al. [6], the transmitter
combines the original modulated signal with an SS watermark, with an embedding rule
defined as
x
x
w
i
i
i
S
S
( )
( )
( ),
(6.3)
where x S (i) is the i‐th sample of the amplitude shift keying (ASK) transmitted signal, μ
is the scaling parameter, and w(i) is SS watermark. Without loss in generality, in the
rest of the chapter we use the direct sequence spread spectrum for watermarking. On
the other hand, the same mechanism developed in WBPLSec can be implemented
throughout orthogonal frequency division multiplexed (OFDM) signals. Corresponding
to iJAM, the utilization of OFDM ensures the jammed samples are indistinguishable
from the clean samples
1
.
The host amplitude shift keying (ASK) modulated signal x S can be expressed as
x i
A T
cos
f i
S
a
hs
hs
( )=
2
(2
),
,
0,
for 0 i T
elsewhere
hs
(6.4)
where A a is the amplitude, T hs is the symbol time, and f hs is the frequency of the
modulated signal. We propose as proof‐of‐concept the utilization of DSSS signal for
watermarking as
w i
g i kT jT c i x i
k
j
N c
b
c
W
j W
k
( )=
(
)( ( )) ( ( )) ,
=
= 0
1
(6.5)
1 OFDM time samples approximate Gaussian distribution and if jamming signal has the same distribution,
the overall distribution after jamming does not modify the distribution of an OFDM signal [27].
124
Figure 6.3 shows how the eavesdropper, Eve, is capable of observing Alice’s transmission over an independent discrete‐time Rayleigh channel, that is, a non‐degraded wiretap
channel. The i‐th sample of the signal received by Eve is given by
y i h i x i g i x i n i
E
E
J
J
E
( )= ( ) ( )
( ) ( )
( ),
S
(6.2)
where h E (i) is the wiretap channel’s complex Gaussian fading coefficient between Alice
and Eve, n E (i) is the complex zero‐mean Gaussian noise, and g J (i) is the jamming channel complex Gaussian fading coefficient. It is assumed that all channels are quasi‐static
fading channels, which mean that the channel gain coefficients remain constant during
the transmission of a code word: h M (i) = h M , h E (i) = h E , k J (i) = k J and g J (i) = g J , i
N
=1,..., .
6.2.1 Transmitter
In accordance with the data decomposition method proposed in Section 10.1, Alice
conveys the information by means of two independent paths. The information is sent to
the legitimate user by means of a narrowband signal. On the other hand, Alice also
embeds a SS watermark in the host narrowband signal. The watermark conveys part of
the information to the legitimate user, Bob, through a secondary channel.
In accordance with the framework presented by Cox et al. [6], the transmitter
combines the original modulated signal with an SS watermark, with an embedding rule
defined as
x
x
w
i
i
i
S
S
( )
( )
( ),
(6.3)
where x S (i) is the i‐th sample of the amplitude shift keying (ASK) transmitted signal, μ
is the scaling parameter, and w(i) is SS watermark. Without loss in generality, in the
rest of the chapter we use the direct sequence spread spectrum for watermarking. On
the other hand, the same mechanism developed in WBPLSec can be implemented
throughout orthogonal frequency division multiplexed (OFDM) signals. Corresponding
to iJAM, the utilization of OFDM ensures the jammed samples are indistinguishable
from the clean samples
1
.
The host amplitude shift keying (ASK) modulated signal x S can be expressed as
x i
A T
cos
f i
S
a
hs
hs
( )=
2
(2
),
,
0,
for 0 i T
elsewhere
hs
(6.4)
where A a is the amplitude, T hs is the symbol time, and f hs is the frequency of the
modulated signal. We propose as proof‐of‐concept the utilization of DSSS signal for
watermarking as
w i
g i kT jT c i x i
k
j
N c
b
c
W
j W
k
( )=
(
)( ( )) ( ( )) ,
=
= 0
1
(6.5)
1 OFDM time samples approximate Gaussian distribution and if jamming signal has the same distribution,
the overall distribution after jamming does not modify the distribution of an OFDM signal [27].