The Statistical Correlation between Clipping Noise
and
P
APR
in
OFDM Systems
Shenglan
Su
*,
Shuang Zhao, Kaiyuan Xue, Hongwen Yang
School
of
Telecommunications Engineering
Beijing University
of
Posts and Telecommunications
Tel: +86-010-62281786
*E-mail: sushenglan@gmail.com
Keywords: OFDM, PAPR, clipping noise, cross-correlation
Abstract
In recent years, the PAPR (Peak-to-Average Power Rate)
of
OFDM system has been intensively investigated and the
published works mainly focus on how to reduce PAPR since
high PAPR will leads to clipping
of
the signal when passed
through a nonlinear amplifier. In this paper we investigate the
statistical correlation between PAPR and the clipping noise.
An interesting result is that the power
of
clipping noise is not
always highly correlated with PAPR, especially when the
signal is heavily or slightly clipped. Moreover, for the fixed
transmit power and clipping threshold (i.e. the same amplifier
with the same backoff), the average power
of
clipping noise is
independent
of
the number
of
subcarriers in OFDM and the
noise power is more stable, thus the OFDM systems with
larger number
of
subcarrier even have better performance.
Whereas we know that larger subcarrier number will always
make the PAPR worse.
1 Introduction
Orthogonal frequency division multiplexing (OFDM) is
chosen to be the key technology in future wireless
communications for its high spectral efficiency, robustness to
frequency selective fading [1] [2]. However, since the OFDM
signal consists
of
a number
of
independently modulated
subcarriers, it produces severer peak-to-average power ratio
(PAPR) than single-carrier signals. The large PAPR
of
the
signal causes clipping when the signal is passed through the
non-linear amplifier. Such clipping produces clipping noise
that will result in performance degradation. In addition,
clipping will also cause spectral re-growth in out-of-band
which may cause interference to other systems. So in the recent
decade, numerous solutions and improved algorithms have
already been proposed to reduce PAPR [3]-[6].
The direct reason that larger PAPR will cause the error rate
performance loss is the clipping noise generated
by
clipping
when the signal is passed through a non-linear amplifier.
Therefore, some published works suggest using clipping noise
rather than PAPR as the metric when error rate performance
degradation is concerned [7-9]. In this paper, we investigate
the relation between the PAPR and the clipping noise power
by theoretical analysis and computer simulations. Our result
seems somewhat surprising: the power
of
clipping noise is not
always highly correlated with PAPR, especially when the
signal is heavily or slightly clipped. Moreover, for the fixed
transmit power and clipping threshold (i.e. the same amplifier
with the same backoff), the average power
of
clipping noise is
independent
of
the number
of
subcarriers in OFDM systems
and the noise power becomes more stable as the number
of
subcarrier increasing, thus the 0 FDM systems with larger
number
of
subcarrier even have better performance, though
we know that larger subcarrier number always produces
higher PAPR. This observation is in fact easy to understand:
The PAPR only depends on the largest one sample in a
OFDM symbol whereas the clipping noise may be contributed
by many clipped samples; The largest peak will naturally
becomes larger when the number
of
subcarriers increases,
while the chance that other samples be clipped will become
less,
if
the average transmit power and the clipping threshold
is unchanged.
The rest part
of
paper is organized as follows. Section 2
describes the system model. In Section III we analyze the
properties
of
clipping noise under the assumption that the input
symbols are Gaussian. To validate the analytical results
of
section 3, section 4 shows the simulation results with practical
data symbols (such as QPSK, QAM, etc), with or without
channel coding. And finally, the concluding remarks are given
in section 5.
2 System model
The transmitter
of
an OFDM system can be modeled as Fig.l
where X
k
E n with
0::::;
k
::::;
N - 1 are the input data
symbols at k-th subcarrier where
n is the signal constellation,
N is the number
of
subcarriers
of
the OFDM system. To
simplifier the analysis, we assume that
{X
k
}
are independent
and identically distributed
(ij.d.)
complex Gaussian random
variables with unit variance, i.e. E[lX
k
I
2
]
= 1 and the real
and imaginary part
of
X
k
are also i.i.d.
__
X_
k
--.I~I
IFFT H Clipping
~
Fig.
1.
System model
The Inverse Fast Fourier Transform (IFFT) transforms the
frequency domain data symbols
{X
k
}
to the time domain
sequence
{xnlO
::::;
n
::::;
N -
1}.
The model does not include
the oversampling for the sake
of
analytical traceability. For
precise evaluation
of
the peak value, time domain signal
should be oversampled otherwize some peak may be missed in
the statistics [12]. Fortunately, the PAPR value elauated with
oversampling generally have small difference to that without