Cryptography Reference
In-Depth Information
The energy E s for transmitting a phase state, that is, a group of log 2 ( M ) binary
data, is equal to:
T
A 2 cos 2 (2 πf 0 t + ϕ 0 + φ j ) dt = A 2 T
2
E s =
if f 0 >> 1 /T
(2.18)
0
Energy E s is always the same whatever the phase state transmitted. The energy
used to transmit a bit is E b = E s / log 2 ( M ) .
For the transmission of a continuous data stream, the modulated signal can
bewrittenintheform:
S ( t )= A i
a i h ( t
iT )cos(2 πf 0 t + ϕ 0 )
i
iT )sin(2 πf 0 t + ϕ 0 )
(2.19)
b i h ( t
where the modulation symbols a i and b i take their values in the following sets:
cos (2 j +1) M
+ θ 0
a i
0
j
( M
1)
b i sin (2 j +1) M
+ θ 0
(2.20)
0
j
( M
1)
The signal S ( t ) can again be written in the form given by (2.11) with:
s e ( t )= A
i
c i h ( t
iT ) ,
i = a i + jb i
(2.21)
Taking into account the fact that the data d i provided by the source of infor-
mation are iid , the modulation symbols c i are independent, with zero mean and
unit variance.
The psd of the signal S ( t ) is again equal to:
γ S ( f )= 1
f 0 )+ 1
4 γ s e ( f
4 γ s e ( f + f 0 )
with this time:
γ s e ( f )= A 2 T sin πfT
πfT
2
(2.22)
the psd looking like that of Figure 2.3.
Quadrature Amplitude Modulation using two quadrature carriers (M-
QAM)
For this modulation, also called Quadrature Amplitude Modulation (M-QAM),
it is two quadrature carriers cos(2 πf 0 t + ϕ 0 ) and
sin(2 πf 0 t + ϕ 0 ) that are
amplitude modulated. The modulator provides signals of the form:
s j ( t )= A j h ( t )cos(2 πf 0 t + ϕ 0 )
A j h ( t )sin(2 πf 0 t + ϕ 0 )
(2.23)
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