Adaptive Clipping for a Deterministic Peak-To-Average
Power Ratio
Diallo Mamadou Lamarana and Palicot Jacques
SUPELEC/IETR:, Avenue de la Boulaie-CS 47601-35576 CESSON-SEVIGNE CEDEX, France
{Mamadou-Lamarana.Diallo,Jacques.Palicot}@supelec.fr
Keywords: OFDM, PAPR Mitigation, Clipping and CCDF.
Abstract: Orthogonal Frequency Division Multiplexing (OFDM) is the most commonly used multicarriers modulation
in telecommunication systems due to the efficient use of frequency resources and its robustness to multipath
fading channel. However, as multicarriers modulation in general, OFDM suffers from high Peak-to-Average
Power Ratio (PAPR). Many works exist in literature for PAPR mitigation among which Clipping is one of
the most efficient adding signal techniques in terms of numerical complexity. However, clipping techniques
is a probabilistic technique for PAPR mitigation. In other words, the instantaneous PAPR of each clipped
OFDM symbol depends on its content and then the PAPR at any value of the Complementary Cumulative
Distribution Function (CCDF) increases when its corresponding CCDF values decreases. In this paper, we
propose an adaptive clipping which offers a constant PAPR, so deterministic, at any value of the CCDF and
so this approach outperforms the classical clipping in terms of signal degradation with the same performance
in terms of PAPR reduction. Simulation results validate the interest of this approach.
.
1 INTRODUCTION
Clipping is an efficient technique for PAPR mitiga-
tion which was firstly proposed by X. Li and J. Ci-
mini (Li and Cimini, 1997). The clipping technique
consists to clip the amplitudes of the signal which ex-
ceed a predefined threshold A. In practice, a normal-
ized predefined threshold
is used, where
represents the mean power of the discrete signal
x
n
which we want reduce the PAPR. It can be
remarked that, ρ defines the PAPR below which the
signal is not clipped. Due the strong amplitude
variations of the OFDM symbol in the time domain,
the instantaneous PAPR of each OFDM symbols
highly depends on its content. Therefore, the
instantaneous PAPR after Classical Clipping method
(Li and Cimini, 1997) (CC) with a predefined ρ also
depends on its content. Then, for each positive scalar
value Φ if we denote by PAPR(Φ) the upper bounded
PAPR at the value CCDF(Φ), it can be remarked that
PAPR(Φ) increases when CCDF(Φ) decreases. In this
paper, this upper bounded PAPR(Φ) will be called
simply PAPR at the CCDF value CCDF(Φ).
Many clipping functions are proposed in the
literature in order to avoid some drawbacks inherent
in the classical clipping (CC) such as Out-of-Band
emission, mean power Degradation and bit error rate
(BER) degradation. Generally, clipping is associated
with filtering in order to filter out-of-band emission
(Li and Cimini, 1997). But this filter generates the
peak-regrowth phenomena. In(Kimura et al., 2008)
the authors propose Deep-Clipping to reduce the
peak-regrowth phenomena and Out-of-Band
emission. Mean-Power degradation can be reduced
by using a clipping based on Gaussian function (Guel,
2009). However, all these approaches degrade the
BER and the instantaneous output PAPR of this
techniques also depends on the content of each
OFDM symbol. Note that, BER degradation
drawbacks is solved by means of tone reservation
(TR) clipping (Guel and Palicot, 2009; Wang and
Tellambura, 2008). Nevertheless, this approach
degrades the performances in terms of PAPR
reduction.
In practice, the desired PAPR(Φ) for the Input
Back Off (IBO) definition on the High Power Am-
plifier (HPA) is defines at CCDF(Φ) close to zeros
25
Lamarana D. and Palicot J.
Adaptive Clipping for a Deterministic Peak-To-Average Power Ratio.
DOI: 10.5220/0005420800250033
In Proceedings of the Third International Conference on Telecommunications and Remote Sensing (ICTRS 2014), pages 25-33
ISBN: 978-989-758-033-8
Copyright
c
2014 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
(10
−4
). In this paper, this value will be denoted by
PAPR
(0)
CC
. So, due to the fact that PAPR(Φ) increases
when CCDF(Φ) decreases, it can be remarked that,
many OFDM symbol are more severely clipped than
necessary or unnecessary clipped with respect to the
desired output PAPR (PAPR
(0)
CC
). That is the reason
why we propose in this paper, an adaptive clipping
(AC) in order to obtain a deterministic output PAPR
i.e a same upper bounded PAPR at any value of the
CCDF. The main goal of this approach is to make
PAPR(Φ) constant at any value of the CCDF and
so minimized the signal degradation with respect to
classical clipping. For this purpose, the normalized
threshold is adapted to the content of each OFDM
symbol in order to get the desired PAPR after clip-
ping. Therefore, in contrast the CC where the instan-
taneous PAPR depends on the content of the OFDM
symbol, in the AC the instantaneous PAPR does not
depends on the content of the OFDM symbol. There-
fore, we qualify this approach as Adaptive Clipping
with a constant output PAPR (PAPR(Φ)).
The paper is organized as follows: In Section
2, we briefly present the clipping technique and the
problem formulation. In Section 3, we will present
the Adaptive Clipping. A comparative study by sim-
ulation with the classical clipping will then be con-
ducted in Section 4. The conclusion will be presented
in Section 5.
2 CLASSICAL CLIPPING
PRINCIPLE AND PROBLEM
FORMULATION
In this paper, the scalars in the time domain and in
the frequency domain will be denoted by lower case
letters and capital letter respectively. The vectors con-
taining the times domain samples and frequency do-
main samples will be represented by lower case letter
in bold and upper case letter in bold respectively.
If z(t) represents a signal in continuous time do-
main its PAPR in continuous time domain and dis-
crete time domain will be denoted by PAPR
z
and
PAPR
[z]
respectively.
2.1 Peak-To-Average Power Ratio
Definition
One OFDM symbol at instant t in time interval nT ≤
t ≤ (n+ 1)T can be expressed as follows:
x
n
(t) =
N−1
∑
k=0
X
n,k
e
2πjkFt
(1)
Where F represents the inter-carrier frequency spac-
ing, T = 1/F is the OFDM symbol duration, X
n,k
is
the n-th QAM symbols conveyed by the sub-carrier
of index k.
The PAPR of this OFDM symbol in continuous
time domain can be expressed as in (Louet and Pali-
cot, 2005) by:
PAPR
x
n
(t)
=
max
t∈[0,T]
|x
n
(t)|
2
E[|x
n
(t)|
2
]
(2)
In practical, discrete OFDM symbol is used to
evaluate the PAPR. In order to get a good approxima-
tion of the true analog PAPR it is necessary to over-
sampled the OFDM signal. Thus, as in (Ochiai and
Imai, 2001) and (Louet and Hussain, 2008), many au-
thors have shown that an oversampling factor of L ≥4
is sufficient to obtain a good approximation of the
analog signal PAPR. In OFDM system, an oversam-
pled signal can be efficiently computed by an IFFT
transformation and can be expressed as follows:
x
n,m
=
NL−1
∑
m=0
X
n,m
e
2jπn
m
NL
, (3)
where X
n
= [X
n,0
,... , X
n,NL−1
] is the L times over-
sampling equivalent QAM vector, generated by zeros
padding X
n
with N(L−1) zeros. Therefore, from this
NL OFDM samples, the discrete time PAPR can be
expressed as in (Louet and Palicot, 2005) by follow-
ing expression:
PAPR
[x
n
]
=
kx
n
k
2
∞
E(kx
n
k
2
2
)
, (4)
where x
n
= [x
n,0
,... , x
n,NL−1
]
T
is the vector contain-
ing the NL samples of the OFDM signal x
n
(t).
2.2 Classical Clipping (CC) Principle
Classical clipping (CC) is a simple adding signal tech-
niques for PAPR mitigation in that the output signal
y
n
= [y
n,0
,... , y
n,NL−1
] after PAPR reduction is given
as follows:
y
n,m
=
x
n,m
if |x
n,m
| > A
Ae
jarg(x
n,m
)
else
(5)
In general, to evaluate the performances of the
PAPR mitigation techniques the CCDF of the PAPR
of signal y
n
is computed or simulated. The CCDF
function is defined as follows:
CCDF
y
n
(Φ) = P
PAPR
[y
n
]
≥ Φ
(6)
This CCDF function for classical OFDM signal is
presented in Figure1.
Third International Conference on Telecommunications and Remote Sensing
26
2.3 Problem Formulation
Let be the Figure 1 in which the CCDF of the CC
technique and Ideal Clipping for PAPR reduction are
shown. Ideal Clipping is a clipping with a constant
upper bounded output PAPR. In other words, the
Ideal Clipping output PAPR could not be greater than
the desired output PAPR (= PAPR
0
), which is repre-
sented in the figure by the vertical solid line curve and
would like to achieve by AC method.
Figure 1: Scenario of CCDF curves of a classical clipping
and Ideal Clipping
In this figure, PAPR
(0)
CC
represents the PAPR (up-
per bounded PAPR) of the clipped signal by CC y
n
at the value of CCDF equal to 10
−4
and PAPR
0
is the
desired output PAPR of the ideal clipping at any value
of the CCDF. In the AC method, the adapted threshold
is computed for each symbol in function of PAPR
0
.
Figure 1 shows that if the CCDF of the AC ap-
proaches the ideal clipping CCDF then AC will less
degrade the signal than the CC with the same perfor-
mance in terms of PAPR reduction.
In fact, let be AREA1 and AREA2 the domains
represented in Figure 1. These domains illustrate
the percentage of the number of OFDM symbols
which PAPR is included in
h
ρ,PAPR
(0)
CC
i
and exceed
PAPR
(0)
CC
respectively. From Figure 1, it can be re-
marked that when PAPR
0
= PAPR
(0)
CC
:
• AREA2 represents the OFDM symbols which are
both clipped by CC and ideal clipping. Therefore,
with respect to PAPR
(0)
CC
, these OFDM symbols
are clipped more severely than necessary in CC.
• AREA1 represents the OFDM symbols which are
not clipped by ideal clipped but clipped in CC.
These OFDM symbols are clipped unnecessary in
CC with respect to PAPR
(0)
CC
.
Now, let be Ω
ρ
the following probability:
Ω
ρ
= Prob
PAPR
[x
n
]
∈ AREA1
.
(7)
When ρ decreases, PAPR
(0)
CC
decreases and then
Ω
ρ
≃0. Thus, to well characterize the probability that
an OFDM symbol is unnecessary clipped, the follow-
ing probability will be considered:
Θ
ρ
=
Prob
PAPR
[x
n
]
∈ AREA1
1−Prob
PAPR
[x
n
]
∈ AREA2
. (8)
We remark that Θ
ρ
represents the probability that
an OFDM symbol is unnecessarily clipped knowing
that their PAPR /∈ AREA2.
Ω
1
ρ
can be computed as follows:
Ω
ρ
= Prob
PAPR
[x
n
]
∈ AREA1
= CCDF
x
n
(ρ) −CCDF
x
n
(PAPR
(0)
CC
)
(9)
Many works exist in the literature on comput-
ing the CCDF of OFDM signal. In (Van Nee and
de Wild, 1998), the authors give an approximation
of the CCDF from a direct computation. However,
other authors propose an approximation of the CCDF
based on statistical studies (Louet and Hussain, 2008;
Ochiai and Imai, 2001) when the oversampling fac-
tor L ≥4. This approach gives a better approximation
of the CCDF. In this paper we use this Y. Louet for-
mula to compute Ω
ρ
which is given by the following
equation
CCDF
x
n
(Φ) = 1−(1−e
−Φ
)
τ
2
N
µ
, (10)
where τ
2
=
5.12
√
e
µ
e
−0.5704
and µ = 1.07. So, us-
ing (10), Θ
ρ
can be expressed as follows:
Θ
ρ
=
1−e
−PAPR
(0)
CC
τ
2
N
µ
−(1−e
−ρ
)
τ
2
N
µ
1−e
−PAPR
(0)
CC
τ
2
N
µ
(11)
Figures 2 and 3 represent the curves of Ω
ρ
and
Θ
ρ
.
Figure 2: Probability that an OFDM symbol is unnecessar-
ily clipped knowing that their PAPR /∈ AREA2.
From these figures, we remark that:
Adaptive Clipping for A Deterministic Peak-To-Average Power Ratio
27
Figure 3: Probability that an OFDM symbol is unnecessar-
ily clipped.
• If 0 ≤ ρ ≤5dB.
Each OFDM symbol is clipped more severely than
necessary with high probability and the probability
to clip the symbol unnecessary is very low. Indeed,
when 0 ≤ ρ ≤ 5dB, Θ
ρ
≃ 1 and Ω
ρ
≃ 0 and then
Prob
PAPR
[x
n
]
∈ AREA2
≃ 1.
• If 5 ≤ ρ ≤6.5dB.
Some signals are more severely clipped than nec-
essary while others are clipped unnecessarily.
Indeed, we remark that when ρ increases, the
percentage of the signals clipped more severely
than necessary i.e Prob
PAPR
[x
n
]
∈ AREA2
=
CCDF
[x
n
]
PAPR
(0)
CC
decreases and at the same time
Ω
ρ
increases (see Figure 3) and then the advantages in
terms of signal degradation (BER degradation, Out-
of-Band emission and Mean Power degradation) of
the AC with respect to the CC will not unchanged.
Thus, we would expect that the AC gives better per-
formances in terms of signal degradation than the CC
when PAPR
0
= PAPR
(0)
CC
and ρ ∈ [0, 6.5db].
• If ρ ≥ 6.5dB.
Θ
ρ
and Ω
ρ
decrease both and then AC will have
the same behavior than the CC.
The main goal of the AC is to minimize the do-
main designed by AREA1 (see Figure 1) by adapt-
ing the normalized threshold clipping to the content of
each OFDM symbol in order to get a constant PAPR
equal to PAPR
0
at any value of the CCDF.
In the following section, the AC is presented and
compared to the CC in terms of PAPR reduction, ad-
jacent channels pollution and data degradation. To
achieve this comparison, two scenarios will be con-
sidered.
• Scenario 1:
This scenario compares the classical clipping at ρ and
AC at PAPR
0
= ρ. Figure 4 illustrates this scenario in
terms of PAPR reduction.
• Scenario 2:
Figure 4: Illustration of Scenario 1 in terms of PAPR reduc-
tion
In this scenario, CC at ρ is compared to AC at
PAPR
0
= PAPR
(0)
CC
. Figure 5 illustrates this scenario
in terms of PAPR reduction.
Figure 5: Illustration of Scenario 2 in terms of PAPR reduc-
tion
As we discussed on Figure 1, we expect that in
scenario 1, AC will give worse performances in terms
of BER degradation, adjacent channels pollution and
mean power degradation than CC, at the opposite
in scenario 2, AC should give better performances.
Note that, in Figure 4 and 5, the solid line curve are
drawn and represent the ideal clipping CCDF which
we would like to obtain by AC.
3 ADAPTIVE CLIPPING
Let be x
n
an OFDM signal which we would like to
reduce its PAPR by classical clipping at threshold
ρ = 20Log
10
A
√
P
x
n
. Note that in CC ρ represents
the ideal PAPR which we would like to obtain after
clipping. But, due to the Mean Power degradation
PAPR
[y
n
]
≥ ρ for any y
n
and then PAPR
(0)
CC
≥ ρ.
Indeed, for each OFDM symbol x
n
the instanta-
Third International Conference on Telecommunications and Remote Sensing
28
neous PAPR of y
n
is given as follows:
PAPR
[y
n
]
=
max
m=0,...,NL−1
|x
n,m
|
2
P
y
n
=
A
2
P
y
n
Since, A =
10
ρ
20
p
P
x
n
the instantaneous PAPR
of y
n
can be rewritten as follows:
PAPR
[y
n
]
=
10
ρ
20
2
P
x
n
P
y
n
=
10
ρ
10
P
x
n
P
y
n
(12)
Thus, since CC degrades the mean power of the
clipped signal then
P
x
n
P
y
n
≥ 1. So the instantaneous
PAPR of y
n
satisfies the following inequality for each
OFDM symbol:
PAPR
[y
n
]
≥ 10
ρ
10
(= ρ in dB), (13)
therefore PAPR
[y
n
]
≥ ρ for any y
n
i.e PAPR
(0)
CC
≥ ρ.
Furthermore, if we denote by PAPR
[y
n
]
(Φ) the out-
put PAPR at any value of the CCDF, then when
CCDF
y
n
(Φ) increases PAPR
[y
n
]
(Φ) decreases, so,
some OFDM symbols are more severely clipped than
necessary or unnecessary clipped with respect to
PAPR
(0)
CC
(see Figure 1).
The main goal of the AC method, is to mini-
mize the percentage of the OFDM symbols which
are more severely clipped than necessary or unneces-
sary clipped with respect to the suitable output PAPR.
Other adaptive clipping methods exist in the litera-
ture (Kim et al., 2003; Byuong Moo Lee, 2013). In
(Kim et al., 2003), the authors proposed to adapt the
normalized threshold ρ in function of the mapping
constellation of the OFDM signal for a better com-
promise between PAPR reduction and BER degrada-
tion. In (Byuong Moo Lee, 2013), the authors pro-
posed an iterative clipping and filtering scheme (Arm-
strong, 2002) in which the computation of the am-
plitude threshold A from the predefined normalized
threshold, is processed at each iteration. This ap-
proach improves the performances on PAPR reduc-
tion but degrades more the signal. However, to the
best of our knowledge this is the first work dealing
with the threshold adaptation at each OFDM symbol
in order to minimize the percentage of the OFDM
symbols which are more severely clipped than nec-
essary or unnecessary clipped with respect to the suit-
able output PAPR.
Let be PAPR
0
the constant desired output PAPR
given by an ideal clipping at any value of the CCDF,
so in AC approach, ρ is unknown and it is determined
by the following equation for each OFDM symbol:
PAPR
0
=
10
ρ
10
P
x
n
P
y
n
. (14)
From equation 14, we remark that in AC ρ de-
pends on the content of each OFDM symbol.
3.1 Theoretical Analysis
From equation (14), we can easily deduce the follow-
ing equation.
10
ρ
10
= PAPR
0
P
y
n
P
x
n
So, if we replace this expression in equation (12)
the instantaneous PAPR of the clipped signal by AC
is expressed as follows:
PAPR
[y
n
]
=
PAPR
0
P
y
n
P
x
n
P
x
n
P
y
n
= PAPR
0
, (15)
therefore we can conclude that AC gives a con-
stant output PAPR (upper bounded PAPR) i.e
PAPR
[y
n
]
(Φ) = PAPR
0
at any value of the CCDF.
3.2 Adapted ρ Computation
The computation of the adapted normalized threshold
from equation 14 is a complex problem since P
y
n
de-
pends on the unknown ρ. Thus, we propose in this
paper an exhaustive search to approximate the solu-
tion of the equation (14).
The following algorithm describes this approach.
Algorithm 1 Normalized threshold computation in
AC
Require: x
n
,ε,PAPR
0
Ensure: y
n
ρ
0
← PAPR
0
Compute A such as ρ
0
=
A
√
P
x
n
y
n
← f (x
n
,A)
while |PAPR
[y
n
]
−PAPR
0
| > ε do
ρ
0
← ρ
0
−ε
Compute A such as ρ
0
=
A
√
P
x
n
y
n
← f (y
n
,A)
end while
Adaptive Clipping for A Deterministic Peak-To-Average Power Ratio
29
4 SIMULATION RESULTS
The simulations are performed for a 64 sub-carriers
OFDM system with 16-QAM modulation on each
carrier. For a good approximation of the true analog
PAPR the signal is oversampled at a factor L = 4.
Figure 6 shows the performance in terms of PAPR
reduction for two different case thresholds ρ = 3.5dB
and ρ = 5dB.
4.1 Scenario 1: Comparison Between
AC and CC with PAPR
0
= ρ
Figure 6: Comparison between CC and AC in terms of
PAPR reduction for different thresholds ρ = 3.5dB and
ρ = 5dB
The simulation results show that AC outperforms
CC when PAPR
0
= ρ. We can remark also that AC
converges to the ideal clipping and gives a determin-
istic PAPR equal to PAPR
0
+ ε at any value of the
CCDF. This results confirm our theoretical analysis
equation (15)
4.1.1 Comparison in Terms of BER Degradation
In this subsection, BER degradation are evaluated in
the context of scenario 1.
The Figures 7 and 8 show the performances of AC
compared to classical clipping.
The simulation results (Figure 7,8) confirm that
the CC less degrades the In-Band data than the AC.
Indeed, in order to get a PAPR equal to ρ (normalized
threshold of the CC) the OFDM symbol with high
PAPR are clipped by an adapted threshold smaller
than ρ.
4.1.2 Comparison in Terms of Mean Power
Degradation and Out-of-Band Emission
In this section, the performances in terms of mean
power degradation and adjacent channels pollution
Figure 7: Comparison of CC and AC in terms of BER
degradation for ρ = 3.5 dB.
Figure 8: Comparison of CC and AC in terms of BER
degradation for ρ = 5 dB.
which are achieved.
The Figure 9 compares AC and CC in terms of
mean power variations.
Figure 9: Comparison of CC and AC in terms of mean
power degradation
Figure 9 shows that the Mean Power degrada-
tion created by AC is more severe than the CC one.
These simulation results are consistent with our ex-
pectations.
Third International Conference on Telecommunications and Remote Sensing
30
The Figures 10 and 11 represent the DSP of
OFDM signal before and after PAPR reduction by AC
and CC.
Figure 10: Comparison of DSP of the AC and CC methods
for ρ = 3.5dB.
Figure 11: Comparison of DSP of the AC and CC methods
for ρ = 5dB.
As in terms of mean power variations, the Out-
Of-Band Emission (Figure 10,11) created by the AC
will be more polluting than those due to the classi-
cal clipping. In addition, we remark that, when ρ in-
creases the Out-of-Band emission due to the AC is
the same as in classical clipping (Figure 11). Never-
theless, when ρ increases PAPR
(0)
CC
−ρ decreases and
therefore AC and classical clipping give same perfor-
mances in terms of PAPR reduction.
In conclusion, these simulation results (Figure 7,8,
9, 10,11) are consistent with our theoretical analysis.
Indeed, from equation (14), we can show that for each
OFDM symbol, the corresponding adapted threshold
is smaller than ρ. This remark can be directly de-
duced from the algorithm used for the adapted thresh-
old computation.
4.2 Scenario 2: Comparison Between
AC and CC with PAPR
0
= PAPR
(0)
CC
In this section, comparison between AC and CC at
same performance in terms of PAPR reduction i.e:
PAPR
0
= PAPR
(0)
CC
is achieved.
Figure 12 shows the performances in terms of
PAPR reduction for two different case thresholds ρ =
3.5dB and ρ = 5dB.
Figure 12: Comparison of CC and AC in terms of PAPR
reduction for different thresholds ρ = 3.5dB and ρ = 5dB.
The simulation results confirm that when
PAPR
0
= PAPR
(0)
CC
AC gives a same performances
in terms of PAPR reduction than classical clipping.
As in the previous scenario (Section 4), We remark
that the AC converges to the ideal clipping and
gives a deterministic PAPR equal to PAPR
0
+ ε at
any CCDF(Φ). This results confirm our theoretical
analysis equation (15).
In the following subsection, AC and CC will be
compared in terms of signal degradation.
4.2.1 Performance in Terms of BER
Degradation
In this subsection, the AC are compared to clipping in
terms of BER degradation.
The Figures 13 and 14 compare the BER degrada-
tion due to AC and CC after PAPR reduction.
As in the theoretical analysis section, the simula-
tion results (Figure 14 and 13) show that AC out-
performs CC in terms of BER degradation. This re-
sults confirm the theoretical analysis (see Figure 2,3)
in that we have shown that many OFDM symbols are
clipped more severely than necessary (ρ = 3, . .. , 5dB)
or unnecessarily (5 dB ≤ ρ ≤ 6.5 dB) with respect to
PAPR
(0)
CC
.
Adaptive Clipping for A Deterministic Peak-To-Average Power Ratio
31
Figure 13: Comparison of CC and AC in terms of BER
degradation for ρ = 3.5 dB.
Figure 14: Comparison of CC and AC in terms of BER
degradation for ρ = 5 dB.
4.2.2 Performance in Terms of Mean Power
Degradation and Out-of-Band Emission
As in subsection 4.1.2, the performances in terms of
mean power degradation and adjacent channels pol-
lution which is caused by the OOB components, are
studied.
The Figure 15 shows the mean power variation of
the signal due to the CC and AC method.
The simulation results (see Figure 15) show that
AC less degrades the Mean Power of the clipped sig-
nal than the CC for the same output PAPR at the
CCDF value less or equal to 10
−4
. For example, for
an output PAPR equal to 4.5dB, ∆E = −0.4dB in CC
method and ∆E = −0.2dB in AC approach.
The Figures 16 and 17 represent the DSP of
OFDM signal before and after PAPR reduction by AC
and CC.
The simulation results (Figure 16,17) show that
the AC less pollutes the adjacent channels than the
CC with the same performances in terms of PAPR re-
duction.
These simulation results in terms of BER degra-
Figure 15: Comparison of CC and AC in terms of mean
power degradation
Figure 16: Comparison of DSP of the AC and CC methods
for ρ = 3.5dB.
Figure 17: Comparison of DSP of the AC and CC methods
for ρ = 5dB.
dation, mean power variations and adjacent channels
pollution are consistent with our theoretical analy-
sis of the ideal clipping. Indeed, we have shown
that (Figures 1A, B) when 0 ≤ ρ ≤ 6.5dB and
PAPR
0
= PAPR
(0)
CC
many OFDM symbol are clipped
more severely than necessary or unnecessarily in CC
with respect to PAPR
(0)
CC
.
Third International Conference on Telecommunications and Remote Sensing
32
In conclusion, these simulation results (Figure 13,
14,15,16 and 17) are consistent with our theoretical
analysis.
Indeed, as in section 4.1, we can show from equa-
tion (14) that for each OFDM symbol, the corre-
sponding adapted threshold is greater than ρ when
PAPR
0
= PAPR
(0)
CC
. This remark can be directly de-
duced from the algorithm used for the adapted thresh-
old computation.
5 CONCLUSION AND FUTURE
WORK
In this paper an adaptive clipping is presented and
compared to classical clipping in terms of PAPR re-
duction and signal degradation. This comparison has
been achieved by a theoretical study and validated
by simulation. We have shown that AC approaches
the ideal clipping and then have same performance
in terms of PAPR reduction but outperforms classi-
cal clipping in terms of signal degradation. Further-
more, AC gives a deterministic PAPR which is very
important for IBO definition on high power amplifica-
tion (HPA). However, the computation of the adapted
threshold in AC is complex. A more simple iterative
approach is being studied.
REFERENCES
Armstrong, J. (2002). Peak-to-average power reduction for
OFDM by repeated clipping and frequency domain fil-
tering. Electronics Letters, 38(5):246–247.
Byuong Moo Lee, Y. K. (2013). An adaptive clipping
and filtering technique for PAPR reduction of OFDM
signals. Circuit, Systems and Signal Processing,
32:1335–1349.
Guel, D. (2009). Etude de nouvelles techniques de
r
´
eduction de ”facteur de cr
ˆ
ete” compatibilit
´
e descen-
dante pour les systemes multiporteuses. PhD thesis,
Universit
´
e de Rennes 1.
Guel, D. and Palicot, J. (2009). FFT/IFFT Pair Based
Digital Filtering for the transformation of adding sig-
nal PAPR reduction techniques in Tone Reservation
Techniques. In Wireless and Mobile Communications,
2009. ICWMC ’09. Fifth International Conference on,
pages 200–204.
Kim, H. J., Cho, S. C., Oh, H. S., and Ahn, J. M. (2003).
Adaptive clipping technique for reducing PAPR on
OFDM systems. In Vehicular Technology Conference,
2003. VTC 2003-Fall. 2003 IEEE 58th, volume 3,
pages 1478–1481 Vol.3.
Kimura, S., Nakamura, T., Saito, M., and Okada, M. (2008).
PAR reduction for OFDM signals based on deep clip-
ping. In Communications, Control and Signal Pro-
cessing, 2008. ISCCSP 2008. 3rd International Sym-
posium on, pages 911–916.
Li, X. and Cimini, L. (1997). Effects of clipping and filter-
ing on the performance of OFDM. In Vehicular Tech-
nology Conference, 1997, IEEE 47th, volume 3, pages
1634–1638 vol.3.
Louet, Y. and Hussain, S. (2008). Peak-to-mean envelope
power ratio statistical analysis of continuous OFDM
signal. In Vehicular Technology Conference, 2008.
VTC Spring 2008. IEEE, pages 1681–1685.
Louet, Y. and Palicot, J. (2005). Power ratio definitions
and analysis in signals carrier modulation. In in 13th
European Signal Processing Conference, EUSIPCO,
volume 63, pages 351–368.
Ochiai, H. and Imai, H. (2001). On the distribution of the
peak-to-average power ratio in OFDM signals. Com-
munications, IEEE Transactions on, 49(2):282–289.
Van Nee, R. and de Wild, A. (1998). Reducing the peak-to-
average power ratio of OFDM. In Vehicular Technol-
ogy Conference, 1998. VTC 98. 48th IEEE, volume 3,
pages 2072–2076 vol.3.
Wang, L. and Tellambura, C. (2008). Analysis of clipping
noise and tone-reservation algorithms for peak reduc-
tion in OFDM systems. Vehicular Technology, IEEE
Transactions on, 57(3):1675–1694.
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