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A PAPR Reduction and Data Decoding for SLM
based OFDM Systems Without SI
S. A. Adegbite, Student Member, IEEE, S. G. McMeekin, Member, IEEE, and B. G. Stewart, Member, IEEE
Glasgow Caledonian University, United Kingdom
{saheed.adegbite, scott.mcmeekin, b.stewart}@gcu.ac.uk
Abstract—Selected mapping (SLM) is an effective method
for addressing high peak-to-average power ratio (PAPR) issues
in orthogonal frequency division multiplexing (OFDM) systems.
However, the standard SLM approach introduces additional data
decoding challenges in the form of side information (SI) trans-
mission and estimation. In general, SI transmission reduces data
throughput and SI estimation normally involves computationally
complex procedures, which can increase design costs. To eliminate
the need for both SI transmission and SI estimation, this paper
presents an investigation into the PAPR reduction and BER
performance of a new technique based on a modified SLM
approach. It is shown that the proposed method simplifies data
decoding through SI cancellation without SI transmission. Results
show that the proposed method produces similar PAPR reduction
performance and BER performance as standard SLM based
OFDM system, which presumes perfect SI estimation, within a
frequency non-selective (flat) fading channel.
Keywords—orthogonal frequency division multiplexing
(OFDM); selected mapping (SLM); side information (SI)
estimation; peak-to-average power ratio (PAPR) reduction;
Without SI
I. INTRODUCTION
Orthogonal frequency division multiplexing (OFDM) is the
adopted technology in high speed wireless broadband com-
munication systems including Long Term Evolution (LTE),
Digital Video Broadcast (DVB), Wi-Fi and IEEE 802.16 d/e
standards, because it offers high data transmission, but unfor-
tunately, it suffers from the problem of high peak-to-average
power ratio (PAPR) [1]–[3]. This high PAPR signals often
occur at some time instants when there is coherent summation
of phases of individual OFDM subcarriers, resulting in peak
amplitude signals [4]–[6].
High PAPR levels introduce signal distortion by forcing
non-linear operation of power amplifiers (PA) in OFDM trans-
mitters; this increases the bit-error-rate (BER) and thus de-
grades system performance [7]–[9]. In theory, this PA induced
distortion may be eliminated by designing a PA with a large
linear region [10]. However, this is impractical because PAs
with a large linear region are expensive and often result in poor
PA efficiency [11]. This leads to increased power consumption
and increased heat dissipation, which reduces battery life of
user equipment (UE) terminals. In addition, high PAPR levels
require higher resolution specifications of digital-to-analogue
(D/A) and analogue-to-digital (A/D) devices, which further
increases design costs, and may also put additional constraints
on system design [12].
A comprehensive review of common PAPR reduction tech-
niques is presented in [13]–[15]. Amongst these methods,
selected mapping (SLM) is widely considered the most at-
tractive solution to the problem of large PAPR in OFDM
systems even though it introduces additional challenges in
the form of side information (SI) transmission and estimation
[16]–[20]. SI is a data overhead while its transmission wastes
bandwidth, and may also result in reduced data throughput.
In SLM based pilot-assisted OFDM system, studies in [21]
and [22] have achieved SI estimation without the need for SI
transmission, using pilot-assisted statistical decision criteria.
However, since SLM is occasionally implemented, then to
perform SI estimation, the receiver must know when SLM
is implemented. This requires additional system resources
and also introduces additional implementation challenges. In
general, SI estimation are prone to errors, particularly in the
presence of severe fading channel conditions, and also require
highly computationally complex procedures.
To eliminate these two challenges i.e. SI transmission and
SI estimation, this paper presents a modified SLM approach
that facilitate joint PAPR reduction and data decoding without
the need for both SI transmission and SI estimation, in a
pilot-assisted OFDM system. The proposed method is based
on the principle of Embedded Coded Modulation (ECM); a
cluster based phase modulation and demodulation approach,
first introduced in [23]. Simulations will show that the pro-
posed method produces comparable PAPR reduction and BER
performance as the conventional SLM-OFDM method, which
presumes perfect SI estimation at the receiver.
This paper is organised as follows. Section II gives an
overview of a typical SLM based pilot-assisted OFDM system
model. Section III describes the proposed modified SLM-
OFDM method. Section IV presents results and discussions
on the comparison of PAPR reduction performance between
standard SLM-OFDM and the proposed method for various
cluster sizes. It also presents BER performance between the
two considered methods, when transmission is over a flat
fading channel condition. Finally, conclusions based on the
outcomes of the paper are presented in section V.
II. STAN D A RD SLM BASED PILOT-ASSISTED OFDM
SYSTEM
This section outlines a standard SLM implementation and
associated data decoding procedure for an SLM based pilot-
aided OFDM system and introduces the concepts of clustered
OFDM notations.
A. Transmitter Side
Consider an OFDM sequence Xconsisting of Nvsubcar-
riers. Let kfor 0≤k≤Nv−1represent a subcarrier index
978-1-4799-8088-8/15/$31.00 ©2015 IEEE
Figure 1: Cluster – data-pilot positions
that corresponds to a subcarrier symbol X[k], where
X=X[0] X[1] ... X[k]... X[Nv−1].(1)
Assuming a pilot-assisted OFDM, this OFDM sequence X
may consists of Nddata and Nppilot components such that
Nv=Nd+Np. For an equi-spaced pilots with Las the pilot
spacing, and by letting cand lrespectively represent arbitrary
indices for 0≤c≤Np−1and 0≤l≤L−1, each subcarrier
X[k]is represented through (e.g. [21])
X[k]=X[cL +l],for0≤l≤L−1
=Xp[c],l=lp=0
Xd[cL +l],otherwise,l=ld,(2)
where the terms Xp[c]and Xd[cL +l]respectively represent
the pilot and data components. Also, for a given value of
c, both lpand ldrepresent indices for pilot and the data
respectively. For 0≤n≤N−1where Nrepresents the
length of a time-domain OFDM signal x[n], expressed by
x[n]=
Nv−1
k=0
X[k]exp(j2πnk/N ).(3)
The PAPR of x[n]may be defined by the ratio
PAPR{x[n]}=max{|x[n]|2}
E{|x[n]|2},(4)
where E{·} denotes the expectation function. Alternatively,
X[k]may also be represented using a clustered notation (see
Fig. 1) as follows:
X[k]=Xc[l]=Ac[l]exp(jθc[l])
=Xc[lp]=Xp[c]
Xc[ld]=Xd[cL +l],
where Ac[l]and θc[l]respectively represent the amplitude and
the phase component of Xc[l]. Fig. 2 shows a block diagram
representation of an SLM based pilot-assisted OFDM (SLM-
OFDM) system. Let Bu
c[l]=Bu[k]represent a set of SLM
phase rotation sequences for u=1,2, ... U where Uis the
number of SLM sequence vectors. SLM creates Ualternative
OFDM signals from which one of the modified signals with
the lowest PAPR value is selected for transmission [16].
Figure 2: SLM in Pilot-assisted OFDM
B. Receiver Side
Consider an OFDM transmission over a multipath fading
channel with frequency response H[k]. Then, after the imple-
mentation of SLM, the received OFDM sequence
¯
Y[k]may
be expressed through
¯
Y[k]=H[k]X[k]B¯u[k]+V[k],(5)
where V[k]represent a complex-valued additive white
Gaussian noise (AWGN) component. Similar to X[k],the
expression in (5) can also be represented in clustered form as
¯
Yc[l]=Hc[l]Xc[l]B¯u
c[l]+Vc[l],(6)
where
¯
Yc[l],Hc[l],B¯u
c[l]and Vc[l]respectively represents
the clustered representations of
¯
Y[k],H[k],B¯u[k]and V[k].
Let ˆurepresent an SI estimate, then in the case of perfect
SI estimation i.e. ˆu=¯u. The initial stage of the data decoding
process in an SLM based OFDM receiver normally involves
using the value of ˆufor sequence de-mapping to produce Yc[l]
as follows
Yc[l]=
¯
Yc[l]Bˆu
c[l]∗.(7)
Assuming a true flat (frequency non-selective) fading channel
condition where
Hc[ld]≈Hc[lp]≈Hc.
Then channel equalization may be achieved through a subcar-
rier level (i.e. element by element) division procedure given
as
ˆ
Yc[ld]=Yc[ld]/
ˆ
Hc,(8)
where
ˆ
Hcrepresents the pilot sub-channel estimate obtained
from a subcarrier level division procedure written as
ˆ
Hc=
ˆ
Hc[lp]=Yc[lp]/Xc[lp].(9)
This means even though channel estimation (through interpola-
tion) is not required since the considered channel is frequency
non-selective, SI estimation is however still necessary, to
enable successful data reception in this channel condition.
The final stage of data reception usually produces an
estimated constellation point nearest to
ˆ
Yc[ld]using a form of
Maximum Likelihood (ML) detection defined in [22] through
ˆ
Xc[ld]= min
D[q]∈Q
ˆ
Yc[ld]−D[q]
2,(10)
where
ˆ
Xc[ld]∈Qand Qis a set of Qconstellation points
D[q]for 1≤q≤Q.
III. PROPOSED METHOD
This section introduces the new approach that facilitates
joint PAPR reduction and data decoding in SLM based OFDM
systems, but without the need for SI transmission and SI
estimation.
Modified SLM
Unlike conventional SLM, in the proposed method, a
modified form of phase rotation sequences called SLM by
clustering (SLMC) are defined. For 1≤u≤Uwhere U
represents the number of alternative signal representations, the
proposed phase rotation sequences are defined by
Ju
c[lp]=Ju
c[ld]=Ju
c[l]=Ju
c=exp(jαu
c)(11)
where αu
crepresents the uth phase rotation component for
cluster ci.e. the phase component of Ju
c.LetJ¯u
c=exp(jΘc)
represent the optimum vector that produces the transmitted
signal with the lowest PAPR, in a similar manner as in standard
SLM [16].
Channel Equalization
In this case, the received OFDM sequence
¯
Zc[l]is repre-
sented as
¯
Zc[l]=Hc[l]Xc[l]J¯u
c+Vc[l].(12)
Now assume a flat or very slow fading channel condition where
Hc[l]≈Hc[ld]≈Hc[lp]≈Hc.
Given that the pilots Xc[lp]are usually known at the receiver,
data decoding may be directly achieved through a channel
cancellation procedure. This involves a simple subcarrier level
division, and can be expressed as
ˆ
Zc[ld]=¯
Zc[ld]/
¯
Zc[lp]×Xc[lp]
=HcAc[ld]exp{j(θc[ld]+Θ
c)}
HcXc[lp]exp(jΘc)×Xc[lp]
≈Xc[ld].(13)
This procedure (the division process) cancels out the phase
term Θc, without the need for the receiver to know its value.
In this way, SI cancellation is possible because the modulating
phase component Θcis common to all subcarriers in each
cluster; thus successful data recovery is achieved without SI
estimation at the receiver or separate SI transmission. This
suggests data recovery can be achieved even if Θcis randomly
generated.
6.5 7.5 8.5 9.5 10.5 11.5
0.0001
0.001
0.01
0.1
1
γ (dB)
CCDF(γ)
SLM
Proposed
original OFDM
U = 4
U = 16
Figure 3: CCDF comparisons (L=4)
6.5 7.5 8.5 9.5 10.5 11.5
0.0001
0.001
0.01
0.1
1
γ (dB)
CCDF(γ)
SLM
Proposed
original OFDM
U = 4
U = 16
Figure 4: CCDF comparisons (L=8)
IV. SIMULATION RESULTS
This section presents comparisons of PAPR reduction and
BER performance between the standard SLM based OFDM
and the proposed method. Simulations use QPSK modulated
pilot sequences and the following standard LTE parameters:
OFDM subcarrier spacing of 15 KHz, guard interval of 5.21
μs, sampling frequency of 30.72 MHz and with values of [N
and Nv] set to [2048 and 1200] respectively using randomly
generated 64-QAM complex-valued data symbols and using
as an example, randomly generated phase rotation sequences
chosen from the set [0, 2π) within SLM. Simulations also
consider transmission over a single tap frequency-flat fading
channel.
The PAPR reduction performance is measured by evalu-
ating the well known complementary cumulative distribution
function (CCDF). The CCDF gives the probability of a calcu-
lated PAPR value PAPR (dB) exceeding a certain threshold
6.5 7.5 8.5 9.5 10.5 11.5
0.0001
0.001
0.01
0.1
1
γ (dB)
CCDF(γ)
SLM
Proposed
original OFDM
U = 4
U = 16
Figure 5: CCDF comparisons (L= 12)
6.5 7.5 8.5 9.5 10.5 11.5
0.0001
0.001
0.01
0.1
1
γ (dB)
CCDF(γ)
SLM
Proposed
original OFDM
U = 4
U = 16
Figure 6: CCDF comparisons (L= 24)
0 3 6 9 12 15 18 21 24 27 30
0.0001
0.001
0.01
0.1
1
SNR (dB)
BER
with perfect SI
Proposed
16QAM
64QAM
Figure 7: BER – standard SLM-OFDM (presumes perfect SI
estimation) vs. proposed method (without SI estimation)
level denoted by γdB; thus defined in [8] as
CCDF{γ}=Prob(PAPR > γ).(14)
With Uset to 4 and 16, Figs. 3 to 6 show comparisons
of CCDF curves between the original OFDM (before PAPR
reduction) and when PAPR reduction is performed using
conventional SLM and the proposed method for Lset to
4, 8, 12 and 24 respectively. Results in Figs. 3 to 6 show
that the proposed method produces nearly identical PAPR
distributions as standard SLM. This is because with a large
value of N, the proposed phase rotation sequences maintains
an intrinsic low correlation comparable to standard SLM. This
agrees with recent study in [24], which has indicated that
phase rotation sequences with low correlation values have good
PAPR reduction capabilities than sequences, which have higher
correlation values.
In addition, with Uset to 4, and Lsetto6,theBER
is evaluated when transmission occurs over a flat (frequency
non-selective) fading channel in order to demonstrate, through
simulation, the data decoding capability of the proposed
method. Fig. 7 shows the comparison of BER between the
proposed method (without SI estimation) and the standard
SLM-OFDM method (with perfect SI estimation). This clearly
shows that even though SI estimation is avoided within the
proposed method, it gives similar performance when compared
to a standard SLM-OFDM system, which presumes perfect SI
estimation. This is expected because in this case the channel
condition is assumed to be flat, and the channel equalization
terms i.e.
ˆ
Zc[ld]in the proposed method (13) and
ˆ
Yc[ld]in
the standard method (which presumed perfect SI) in (8), are
both similar. This shows that even with randomly generated
phase rotation sequences, the proposed method can produce
successful reception of payload data information without the
need for both SI transmission and SI estimation, and without
resulting in BER degradation.
Furthermore, the proposed method may be extended to
enable data decoding in the presence of a frequency selective
fading channel, through some form of channel estimation and
equalization, but without SI estimation and SI transmission.
V. C ONCLUSIONS
This paper has introduced a modified SLM-OFDM ap-
proach, which facilitates joint PAPR reduction and data de-
coding (over a flat fading channel), without the need for SI
estimation or SI transmission, thereby resulting in a significant
reduction in the complexity of OFDM receivers. The proposed
method achieves comparable PAPR reduction performance as
standard phase rotation sequences. In addition, the proposed
method produces similar BER performance when compared to
standard SLM based OFDM system, which presumes perfect
SI. Though, the presented implementation of the proposed
approach assumed a flat fading channel condition, it may be
extended to enable data decoding in the presence of frequency
selective fading channel.
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