148
M. El Ghzaoui and S. Das
Codage et
t l
S
/
P
ConstellaƟon
I
D
F
T
CP
P
/
S
CNA
Amplificateur
Up Conversion
Canal
Fig. 3 Schematic diagram of the insertion of the cyclic prefix
20% of TB). Some OFDM systems are also taking advantage of the progress in the
field of equalization to overcome them.
So in order to avoid these interferences, the guard interval must not be silent, but
be the copy of the N g last symbols of the OFDM frame, as shown in the diagram
in Fig. 3. We speak in this case of cyclic prefix. The advantage of this copying is
that each signal, coming from a multiple path, will always have an integer number
of sinusoids over the duration T B .
The OFDM signal with cyclic prefix is given by:
x(t) =
N
k=1
c i,k exp
j2π
k
T B
t
, − T g ≤ t ≤ T B
(8)
The prefix is added to the program after the IFFT, then removed at the reception
before the FFT module.
5.2 Analytical Calculation of the Power Spectral Density
The power spectral density (DSP) of a signal x is defined as being the fourier transform
of the autocorrelation function of this signal x, x being supposed to be a stationary
signal at order 2. Thus, if we denote by Γ s (τ ), the autocorrelation function of a
continuous signal x(t) stationary at order 2:
Γ x (τ ) = E
x(t)x
∗
(t − τ )
(9)
We then obtain the DSP of x, noted Φ x ( f ), as:
Φ x ( f ) =
Γ x (τ )e
− j2π f τ dτ
(10)
M. El Ghzaoui and S. Das
Codage et
t l
S
/
P
ConstellaƟon
I
D
F
T
CP
P
/
S
CNA
Amplificateur
Up Conversion
Canal
Fig. 3 Schematic diagram of the insertion of the cyclic prefix
20% of TB). Some OFDM systems are also taking advantage of the progress in the
field of equalization to overcome them.
So in order to avoid these interferences, the guard interval must not be silent, but
be the copy of the N g last symbols of the OFDM frame, as shown in the diagram
in Fig. 3. We speak in this case of cyclic prefix. The advantage of this copying is
that each signal, coming from a multiple path, will always have an integer number
of sinusoids over the duration T B .
The OFDM signal with cyclic prefix is given by:
x(t) =
N
k=1
c i,k exp
j2π
k
T B
t
, − T g ≤ t ≤ T B
(8)
The prefix is added to the program after the IFFT, then removed at the reception
before the FFT module.
5.2 Analytical Calculation of the Power Spectral Density
The power spectral density (DSP) of a signal x is defined as being the fourier transform
of the autocorrelation function of this signal x, x being supposed to be a stationary
signal at order 2. Thus, if we denote by Γ s (τ ), the autocorrelation function of a
continuous signal x(t) stationary at order 2:
Γ x (τ ) = E
x(t)x
∗
(t − τ )
(9)
We then obtain the DSP of x, noted Φ x ( f ), as:
Φ x ( f ) =
Γ x (τ )e
− j2π f τ dτ
(10)