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M. El Ghzaoui and S. Das
0
0.2
0.4
0.6
0.8
1
0
10
20
30
40
50
60
70
80
90
100
110
normalized time, t/TB
power magnitude
2
(t)
m
Peak power
Average power
Fig. 7 Instantaneous, average, and peak power of the OFDM (N = 16). PAPR is of about 7.8 dB
6.2 Definition and PAPR Analysis
The PAPR of the OFDM modulation defined by Eq. (5) is given by:
P AP R [s] =
max
0≤t≤T s
|x(t)|
2
P s
(24)
where max
0≤t≤T s
|x(t)|
2 is peak power and Ps is its average power.
Let x[n/J ] be the symbol obtained by oversampling by factor J of the signal x[n].
From (5), x[n/J ] is written as:
x
n
J
=
N −1
k=0
X k e
j2π
k
N J n n = {0, 1, . . . . . . . . . . . . ., J N − 1}
(25)
The PAPR of x[n] can be writing as:
P AP R [s] =
max
0≤n≤N
|x[n]|
2
N −1
n=0 {|x[n]|
2
}
(26)
in the same way the PAPR of x[n/J ] is written: