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New Error Function Companding Technique to
Minimize PAPR in LTE Uplink Communications
K. Shri Ramtej, S. Anuradha
Department of Electronics and Communication Engineering
National Institute of Technology, Warangal, Telangana, India
Email: shriramtej@gmail.com, anuradha@nitw.ac.in
Abstract—Single Carrier Frequency Division Multiple Access
(SC-FDMA) has been implemented successfully for uplink
communications in 3rd Generation Partnership Project Long
Term Evolution. SC-FDMA has low peak to average power ratio
(PAPR) in contrast to OFDMA due to lower signal envelope
fluctuations in SC-FDMA signal. But still, there is a need to
minimize PAPR in SC-FDMA systems. Although there are many
methods to minimize PAPR in SC-FDMA systems they are highly
complex or need side information to be transmitted. This paper
proposes a new companding technique based on error function to
minimize PAPR of conventional single carrier FDMA system in
LTE uplink communications. Additionally, the proposed method
improves the BER performance of single carrier FDMA system
along with PAPR reduction. Simulation results demonstrate
that proposed method provides better PAPR reduction when
compared to μlaw companding.
Keywords—Companding; Error function; LTE; PAPR
reduction; SC-FDMA.
I. INTRODUCTION
3rd Generation Partnership Project (3GPP) implemented
Single Carrier Frequency Division Multiple Access
(SC-FDMA) as an alternative to Orthogonal Frequency
Division Multiple Access (OFDMA) in Long Term Evolution
(LTE) for uplink communications [1]. The lower signal
envelope fluctuations in SC-FDMA signal results in low
PAPR in contrast to that of OFDMA. But still, there is a
need for PAPR reduction in SC-FDMA systems [2]. When
PAPR is high, the power amplifier should be operated in
linear region. Due to this, efficiency of power amplifier [3] is
reduced.
In literature, several methods have been studied to minimize
PAPR in SC-FDMA systems. Some of them include pulse
shaping techniques [4], selected mapping technique (SLM) [5],
partial transmit sequence (PTS) [6] and pre-coding techniques
[7,8]. But these techniques are highly complex, or they
need excess bandwidth for transmission of side information.
For simplicity nonlinear companding techniques has been
used in OFDMA to reduce PAPR and provide better BER
performance. They also have low implementation complexity,
does not require any bandwidth expansion. By companding the
original signals using strict monotone increasing function at
the transmitter side, they can be easily recovered at the receiver
side through the corresponding inverse operation. Several
companding methods have been proposed to minimize PAPR
in OFDMA systems. These methods can also be implemented
in SC-FDMA systems for PAPR reduction.
In [9], μlaw companding has been used to minimize PAPR
in SC-FDMA systems. When using μlaw companding, the
companding coefficient affects the performance of PAPR and
BER. As companding coefficient increases PAPR performance
is improved, but BER performance is degraded. The author
selected optimum value for companding coefficient as μ=4.
When μ= 4, PAPR is improved by about 3.25 dB at CCDF=
10−4for Localized SC-FDMA. In [10,11], power function
and raised cosine-like companding schemes have been used
to minimize PAPR. But in [12] author concluded that power
function companding technique has better PAPR reduction
performance when compared to raised-cosine like companding
technique. We can see that there is not much improvement in
PAPR by using these methods. The improvement is less than
3.5 dB. In [13], a nonlinear companding transform has been
proposed to minimize PAPR, but the BER performance has
been degraded. These are the only companding methods that
have been considered in the literature to minimize PAPR in
single carrier FDMA systems.
This paper proposes a new companding technique based
on error function to minimize PAPR in single carrier FDMA
systems. The proposed method also improves the BER
performance of the conventional SC-FDMA system. Also, this
method is very simple and does not need any side information
to be transmitted.
The rest of this paper is organized as follows. SC-FDMA
system model is introduced in Section II. Proposed system
model with New Error Function (NERF) Companding is
described in Section III. PAPR and BER performance results
of proposed system along with conventional SC-FDMA
system are discussed in Section IV. Few conclusions are drawn
in Section V.
II. SC-FDMA SYSTEM MODEL
Conventional SC-FDMA system model is shown in Fig. 1.
Firstly, the data is encoded and modulated by using QPSK
or QAM techniques. Then the modulated data is grouped into
blocks of Nsymbols, xnand passed through N-point DFT to
give the resulting signal Xk.
Xk=
N−1
n=0
xne−j2πnk/N ,k =0,1, ...., N −1(1)
978-1-5090-5356-8/17/$31.00 c
2017 IEEE
2017 Twenty-third National Conference on Communications (NCC)
Fig. 1. Conventional Single Carrier FDMA System.
These Nsymbols are then mapped to Msubcarriers
(N<M, M=QN). For subcarrier mapping in SC-FDMA
systems we have two techniques namely, Distributed FDMA
(DFDMA) and Localized FDMA (LFDMA). Interleaved
FDMA (IFDMA) is one realization of DFDMA. In LFDMA,
each terminal transmits its symbols over adjacent subcarriers
whereas in IFDMA the entire signal band is used to spread
the subcarriers equidistantly. If localized subcarrier mapping
is used then Xlis given by
Xl=Xk(l),(0 ≤l≤N−1)
0,(N≤l≤M−1) (2)
where 0≤l≤M−1. If interleaved subcarrier mapping is
used then Xlis given by
Xl=Xk(l/Q),l =Qk(0 ≤k≤N−1)
0, otherwise (3)
After subcarrier mapping, Xlis passed through M-point
IDFT and the resulting time domain complex signal xmis
given by
xm=1
M
M−1
l=0
Xlej2πlm/M ,m =0,1, ...., M −1(4)
Then cyclic prefix is added to it and transmitted through the
channel. The corresponding inverse operations will be carried
at the receiver side to extract the data. The PAPR of xmis
Fig. 2. Single Carrier FDMA System with Companding.
given by
PAPR(xm)=max|x2
m|
E|x2
m|(5)
III. PROPOSED SYSTEM MODEL
SC-FDMA system model with companding technique is
shown in Fig. 2. Here the data xmis passed through
compander before adding CP to it. At the receiver side, the
inverse operations will be carried out and the data rmis
passed through decompander before applying M-point DFT.
Companding and Decompanding are the additional blocks that
have been added to the conventional system. The PAPR of xm
is given by
PAPR(xm)= max|x2
m|
E|x2
m|(6)
A. New Error Function (NERF) Companding
Basically, companding is a process of enlarging the small
amplitudes signals while compressing the large amplitude
signals. The proposed companding method is inspired from
nonlinear companding transform that has been used in OFDM
system [14]. The NERF companding is given by
xm=2σerf( |xm|
√2σ) sgn(xm)(7)
where xmis the signal before companding process, xmis the
companded signal, σis the standard deviation of xm, erf(.)
is the error function and sgn(.) is the signum function. The
NERF decompanding function at the receiver side is given by
2017 Twenty-third National Conference on Communications (NCC)
rm=√2σerf−1(|rm|
2σ)sgn(rm)(8)
where rmis the received signal after removing CP, rmis
the decompanded signal. The transformation profiles of NERF
companding and decompanding are shown in Fig. 3 and 4
respectively.
The amplitude of SC-FDMA signal does not have Gaussian
distribution and it is difficult to derive the exact form of
the distribution analytically [15]. So we stick to numerical
results using Monte Carlo simulations to compare the
PAPR performance of NERF companding with conventional
SC-FDMA system.
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Fig. 3. Profile of NERF Companding
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Fig. 4. Profile of NERF Decompanding
IV. RESULTS AND DISCUSSION
Here, the performance of the proposed single carrier FDMA
system with NERF companding is compared with conventional
TABLE I
SIMULATION PARAMETERS
Parameter Description
Simulation method Monte Carlo
Subcarriers spacing 9.765625 kHz
System bandwidth 5 MHz
Channel coding 1/2 rate Convolutional code
Modulation type QPSK
N 128
M 512
Subcarrier mapping Localized and Interleaved
CP length 20 samples
Channel model AWGN, Vehicular-A outdoor
Channel estimation Perfect
Equalization MMSE
single carrier FDMA system in terms of PAPR and BER. Table
I lists the simulation parameters [16].
The complementary cumulative distribution function
(CCDF) curves for proposed system and conventional system
without pulse shaping have been presented in Fig. 5. We can
observe that the PAPR of LFDMA with NERF companding
has been improved when compared to that of conventional
LFDMA and μlaw companding. Table II shows the values
of PAPR at CCDF=10−4for LFDMA, LFDMA with μ
law companding and LFDMA with NERF companding. At
CCDF=10−4there is an improvement of about 4.37 dB
for LFDMA. There is no effect of NERF companding on
Interleaved SC-FDMA since no pulse shaping technique
has been used for these simulations. When pulse shaping
technique is not used the PAPR of Interleaved SC-FDMA is
zero.
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Fig. 5. PAPR reduction performance of NERF companding, μlaw
companding and SC-FDMA system without pulse shaping, M=512
The CCDF curves for proposed system and conventional
system with pulse shaping have been presented in Fig. 6. Here
2017 Twenty-third National Conference on Communications (NCC)
TABLE II
PAPR AT CCDF=10−4,WITHOUT PULSE SHAPING
PAPR(dB) at CCDF=10−4
Original μlaw NERF
LFDMA 7.94 4.79 3.57
we used raised cosine (RC) pulse shaping technique with a
roll-off factor, α=0.22 , M=512. In this case, we can observe
that PAPR has been improved for both LFDMA and IFDMA
due to NERF companding. Table III shows the values of PAPR
at CCDF=10−4for both LFDMA and IFDMA without, and
with μlaw and NERF companding. At CCDF=10−4there is
an improvement of about 4.5 dB in LFDMA and about 2.97
dB in IFDMA due to NERF companding which is better than
PAPR reduction provided by μlaw companding.
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Fig. 6. PAPR reduction performance of NERF companding, μlaw
companding and SC-FDMA system with RC pulse shaping, roll-off factor
α=0.22, M=512
TABLE III
PAPR AT CCDF=10−4,WITH RC PULSE SHAPING
PAPR(dB) at CCDF=10−4
Original μlaw NERF
LFDMA 8.11 4.93 3.61
IFDMA 6.30 3.81 3.33
The impact of the number of subcarriers on PAPR
performance of NERF companding is shown in Fig. 7. We can
observe that as M increases PAPR performance is improved.
The Bit Error Rate performance curves for proposed system
and conventional system have been presented in Fig. 8 and
9 for AWGN and Veh-A channels respectively. We can
observe that BER performance is degraded when μlaw
companding is used for IFDMA. But BER performance has
been improved for both LFDMA and IFDMA systems due
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Fig. 7. PAPR performance of NERF companding and SC-FDMA system with
RC pulse shaping, roll-off factor α=0.22 for different numbers of subcarriers
to NERF companding when compared to conventional system
and μlaw companding.
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Fig. 8. BER performance of the proposed system with NERF companding,
μlaw companding and SC-FDMA system over AWGN Channel
V. C ONCLUSION
A simple companding scheme based on error function has
been proposed. The results show that the proposed NERF
companding method provides better PAPR reduction when
compared to other companding methods and conventional
SC-FDMA system. At CCDF=10−4there is an improvement
of about 4.5 dB in LFDMA and about 2.97 dB in IFDMA
due to NERF companding which is better than PAPR
reduction provided by μlaw companding. Also, the proposed
companding method provides better BER performance unlike
other companding methods and conventional SC-FDMA
system. The proposed method is not complex or does not
require any additional side information to be transmitted like
2017 Twenty-third National Conference on Communications (NCC)
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Fig. 9. BER performance of the proposed system with NERF companding,
μlaw companding and SC-FDMA system over Veh-A Channel
PTS and SLM techniques. Hence the proposed companding
method can be used to minimize PAPR of conventional
SC-FDMA system in LTE uplink communications and further
enhance its BER performance.
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