Performance Improvement for the Single Carrier in FBMC Systems by PAPR Reduction

International Journal of Computer Networks & Communications (IJCNC) Vol.14, No.5, September 2022
DOI: 10.5121/ijcnc.2022.14502 17
PERFORMANCE IMPROVEMENT FOR THE SINGLE
CARRIER IN FBMC SYSTEMS BY PAPR REDUCTION
Mohammed A. Salem1
, Mohamed A. Aboul-Dahab2
,
Sherine M. Abd El-kader3
and Radwa A. Roshdy1
1Department of Electrical Engineering, Higher Technological Institute,
Tenth of Ramadan city, Egypt
2
Department of Electronics and Communications Engineering, Arab Academy for
Science & Technology and Maritime Transport, Cairo, Egypt
3Department of Computers and Systems, Electronics Research Institute, Giza, Egypt
ABSTRACT
The benefits of Filter Bank Multicarrier (FBMC) make it an attractive waveform instead of orthogonal
frequency division multiplexing (OFDM). However, a high peak-to-average power ratio (PAPR) is a
significant drawback in FBMC. Exploiting a single carrier effect is considered an effective technique to
reduce PAPR in FBMC systems with a small amount of additional complexity. Nevertheless, the PAPR
reduction amount is different from the single carrier effect in the single carrier frequency division multiple
access (SC-FDMA). This is because of the overlapping structure of the in-phase and quadrature (IQ)
between offset quadrature amplitude modulation (OQAM) FBMC symbols. So, we introduce an algorithm,
based on signal distortion techniques, to improve the performance of the single carrier effect techniques in
the PAPR reduction for the FBMC systems. Simulation results depict that the single carrier effect
techniques with the proposed algorithm achieve an extra amount of PAPR reduction compared to the same
techniques without using the proposed algorithm. In addition, the simulation results show that the
proposed algorithm maximizes the PAPR reduction amount without affecting the complexity.
KEYWORDS
Filter bank multicarrier, FBMC, DFT spreading, single carrier effect, generalized DFT, PAPR reduction.
1. INTRODUCTION
Waveform design is considered the main entrance to 5G to increase data rates and the network
capacity to get more services with a higher quality of services [1]-[3]. Orthogonal frequency
division multiplexing (OFDM) has merits that do not exist in the previous waveforms; it has low
complexity implementation as it is using FFT and IFFT, it has higher flexibility in maintaining
adaptive modulation per subcarrier, it is also equalized simply and supports multiple input
multiple outputs (MIMO) [4]-[5].
Although privileged by the previously mentioned merits, OFDM has several limitations that
make it less efficient to achieve 5G requirements. It requires high synchronization accuracy, and
any synchronization error leads to a detriment in the orthogonality and causes interference. It
includes a cyclic prefix (CP) to prevent inter-symbol interference (ISI), which results in limiting
the spectral efficiency. OFDM has round trip time (RTT) which makes it not very efficient in
terms of communication signaling overhead to support M2M applications. In addition, OFDM
has also high out-of-band emission, OOB, due to the large power side lobe [6]. So new
waveforms are needed to replace the OFDM. FBMC is a strong candidate as a waveform-based

18
technique for 5G as an alternative to OFDM [7]-[9]. FBMC has various advantageous
characteristics that make it a promising 5G waveform candidate. It does not include CP, and this
increases bandwidth efficiency [10]. It also has more flexibility to manage the bandwidth of each
sub-carrier and the degree of overlap because of using non-orthogonal carriers and it is more
flexible to exploit cognitive radio white spaces [11]. In addition, FBMC has the lowest OOB
compared to other 5G waveform candidates like universal filter multicarrier (UFMC),
generalized frequency division multiplexing (GFDM), and filtered OFDM (F-OFDM). Moreover,
FBMC also is more immune to frequency misalignment and synchronization errors [12]. Despite
the previously mentioned merits of FBMC, it suffers from elevated levels of Peak to Average
Power Ratio (PAPR) as it is a multicarrier modulation technique. High PAPR leads to a signal
clipping at the receiver because of the high-power amplifier (HPA) nonlinearity region [13].
Consequently, effective suppression of the OOB emission of FBMC remains under consideration.
Signal distortion techniques such as clipping and filtering, companding, and peak cancellation
were used to reduce PAPR in multicarrier communication systems like OFDM, and FBMC by
distorting the output of the synthesis filter bank before it passes through the HPA. However,
using such techniques degrade the bit error rate (BER) performance of the system and this
requires side information to be transmitted (SI). On the other hand, these SI result in exceeding
the required bandwidth required for the transmission.
The Single carrier effect is considered a promising technique to reduce PAPR effectively in 4G
uplink transmission, this technique is called single carrier frequency division multiple access
(SC-FDMA). But using a single carrier effect technique in FBMC is not as good as in SC-
FDMA. This is because of the staggering between in-phase and quadrature (IQ) channels
utilizing various pulse-shaped structures for offset quadrature amplitude modulation (OQAM)
[14]-[16].
1.1. Motivation and Contributions
The use of DFT spreading, DFT spreading with ITSM and GDFT, in FBMC systems causes a
quite notable reduction of PAPR amount. The way to maximize the PAPR reduction amount is
attained by increasing computational complexity and using SI. The alternative method to avoid
using SI and at the same time reduce the BER degradation is to minimize the signal distortion
amount is low as possible. So, we propose an algorithm based on signal distortion techniques for
keeping the computational complexity unchanged while improving the Performance of the PAPR
reduction in FBMC for the single carrier effect techniques without any need for SI overhead.
The main contributions in this paper are summarized as follows:
• The algorithm to improve the performance of the single carrier effect as a PAPR
improvement technique for the FBMC is proposed without any complexity and SI
overhead.
• The proposed technique is applied to other algorithms of the FBMC single carrier effect
which are available in the literature [19]-[21].
• The PAPR performance of the single carrier effect techniques with the proposed
algorithm is investigated at different numbers of subcarriers. From the simulation results,
the proposed algorithm enables the other techniques of the single carrier effect to reduce
PAPR more than SC-FDMA.
The rest of the paper is organized as follows: Section 2 introduces a literature review about the
FBMC DFT spreading techniques for PAPR reduction. Section 3 reviews the structure of the
FBMC system and other FBMC single carrier techniques that are available in the literature. In
section 4 the proposed algorithm, to improve the single carrier affect performance is introduced.

19
In section 5 the simulation results are introduced. In section 6 the computational complexity of
the single carrier techniques utilizing the proposed algorithm are compared to other conventional
single-carrier techniques. Section 7 concludes the paper.
2. LITERATURE REVIEW
The discrete Fourier transform (DFT) spreading technique is one of the single carrier effect
techniques and it is the technique that is used in SC-FDMA. In [17]-[19] the DFT spreading
technique being used in FBMC for PAPR improvement but the amount of reduction of PAPR is
far away from the PAPR improvement amount that is attained by SC-FDMA. This is due to in
[17]-[19] the DFT spreading is applied directly to the FBMC system without taking the
staggering between in-phase and quadrature (IQ) channels into consideration. In [20] the DFT
spreading technique had been used in the case of Identically-time shifted modulation (ITSM).
This condition is based on the phase shift pattern of the in-phase and quadrature channels.
Although the DFT spreading with the ITSM condition makes use of the single carrier effect, the
amount of PAPR reduction is not so significant. So, the authors in [20] proposed an ITSM
algorithm to increase the PAPR reduction amount by producing four waveforms with different
PAPR, and the one with minimum PAPR was chosen to be sent. But, using the ITSM algorithm
caused more computational complexity and side information (SI). In [21], GDFT had been
proposed in FBMC as a single carrier effect technique instead of DFT as the latter resulted in a
marginal PAPR reduction. Although using GDFT spreading improves the PAPR reduction
performance more than that of various single carrier techniques, the PAPR reduction amount is
not still as good as SC-FDMA. So, the authors in [21] introduced an improvement algorithm to
allow the GDFT spreading to enhance PAPR as efficiently as SC-FDMA. However, the
computational complexity is increased but still better than the ITSM algorithm. In [22], a DFT is
used as a precoding method in FBMC to modify the format of data transmission in a way such
that the PAPR is reduced. In [23], The combination of pruned DFT with spread techniques
removes IFFT effects and the PAPR can be reduced. In [24], the PAPR is reduced by using a
hybrid system of STM and DFT single carrier technique at the expense of adding complexity
overhead.
3. FBMC SINGLE CARRIER TECHNIQUES
Assume M subcarriers and N symbols; as shown in figure 1, the nth complex input symbol at mth
subcarrier xm,n is represented by in-phase and quadrature components indicated by dm,n and um,n
respectively as shown below:
n
m
n
m
n
m ju
d
x ,
,
, 
 (1)
The IQ input components dm,n is then multiplied by the phase shift patterns ρm,n and σm,n at each
mth
subcarrier of the upper and lower IFFT, respectively.
Although there are different patterns for the IQ phase shifts in literature [25]-[26], all these
patterns must attain the next state:








odd
n
j
or
j
even
m
or
n
m
)
(
)
1
(
1
,









odd
n
or
even
m
j
or
j
n
m
)
1
(
1
)
(
,

(2)

20
A prototype real symmetric filter with response gm,n(t) is used for filtering each subcarrier. This
prototype filter is described by overlapping factor K, which is defined by the ratio of the duration
of the filter impulse response to the symbol period T of each multicarrier. prototype filter with the
overlapping factor participates effectively in suppressing symbol interference (ISI). Frequency
spreading by the overlapping factor (K) is essential to implement the FBMC system, but this
resulted in increasing system complexity; so, the polyphase network FFT (PPN-FFT) is used.
Although it does not require frequency spreading this results in some additional processing [27].
A concise and simple explanation of PPN-FFT operation is given in [20]. Finally, the IQ
components are shifted in time by half of the complex data symbol duration for each subcarrier T.
this is done by applying the lower PPN output to the delay block T/2[27].
Figure 1. FBMC structure ⨀ represents the multiplication of element by element [21]
The transmitted signal based on the FBMC implementation that is shown in Fig. 1 is given by:
T
mt
j
M
m
N
n
j
n
m e
e
nT
t
g
x
t
s n
m


2
1
0
1
0
,
,
)
(
)
(   





(3)
where n
m
x , the complex FBMC input nth symbol is expressed in (1) and )
( nT
t
g  is a response of
the prototype filter. Its length (l) is defined by {KN} where N represents the OQAM symbol
numbers each subcarrier. n
m
j
e ,

is the phase shift pattern where 


 mod
)
(
2
, n
m
o
n
m 

 ,
n
m
j
e ,

is denoted by n
m,
 for real input symbols and is denoted by n
m,
 for complex input
symbols.
3.1. FBMC DFT spreading technique
In [17]-[19], the DFT spreading is applied directly to FBMC as the same as in the SC-FDMA
system. This is depicted in figure 2. The input data symbol is applied to a DFT. their outputs are
fed to the FBMC input.

21
Figure 2. FBMC DFT spreading
Figure 3. FBMC structure with ITSM spreading
3.2. ITSM Technique
In [20] single carrier property had been fully exploited by applying a condition of an identically
time-shifted multicarrier (ITSM) to the DFT spreading. The ITSM condition is based on
multiplying the phase shift pattern of the quadrature channel {σm,n} by the term (-1)m
, this is
cleared in figure 3. Consequently, the multicarrier for the IQ channel appears identically time-
shifted. However, the PAPR reduction amount was not so significant due to the overlapping
interval among the OQAM symbols of IQ channels; the resultant reduction amount of the PAPR
ranged from 0.6 dB to 0.8 dB.
3.3. FBMC with GDFT Spreading Technique
In GDFT spreading technique the complex input symbol was separated into in-phase and
quadrature-phase terms before being applied to the GDFT as it is depicted in figure 4. Also, the
phase shaping function was set to zero and mM/2 in the case of the in-phase {dk,n} and quadrature

22
{uk,n} channel symbols, respectively. This indicates that the GDFT spreading technique is with a
linear phase [21].
Figure 4. FBMC structure with GDFT spreading
Figure 5. The improved FBMC single carrier structure
4. THE PROPOSED ALGORITHM
The PAPR of FBMC transmitted signal is defined as follows:
1
-
N
0,1,....,
n
]
)
(
[
s(t)
max
2
2
)
1
(

 


t
s
E
PAPR nT
t
T
n
(4)
where {max |s(t)2
|} and {E[|s(t)|2
]} are the peak power and the average power of the transmitted
signal, respectively and N is the number of transmitted symbols. To reduce the level of PAPR either
reduce the Peak power or increase the average power. Reducing the Peak power was achieved in

23
signal distortion techniques such as clipping and peak signal cancellation techniques. In this
method, the FBMC transmitted signal was clipped to a predefined value and as a result, PAPR is
decreased. Nevertheless, clipping noise is a big problem at the receiver. To compensate for this
noise, the receiver complexity was increased. If this noise wasn’t compensated the signal BER
performance will be degraded [28].
Increasing the average power is an alternative solution to reduce PAPR. This is done by
increasing each FBMC symbol by a predetermined value (A). Although this will help in
increasing the peak power the average power also increased and the final ratio will be decreased.
At the receiver, each symbol will be decreased by a predetermined value added to it at the
transmitter. Thus, there is no chance to exist something like noise clipping and the signal BER
performance will not be affected. The block diagram of the single carrier techniques utilizing the
improved algorithm is shown in figure 5.
The following steps illustrate the proposed algorithm for PAPR reduction as follows:
Step 1: The input data frame to the FBMC system is at first divided into a consecutive number of
symbol blocks equal to W and the number of symbols per each block equals to .

Step 2: The symbol index (n) is limited to the )
( th
 data symbols block such
that 1
0 

 W
n  . So, the FBMC complex transmitted signal in (3) can be defined as where M
is the number of subcarriers and xm,n is the complex FBMC input data:
n
m
j
M
m
W
n
n
m e
nT
t
g
x
t
s .
e
)
(
)
( T
mt
2
j
1
0
1
0
,


  







(5)
Step 3: the amplitude of each FBMC symbol is increased by a predetermined small value A. thus
(5) will be expressed as:
T
mt
j
M
m
W
n
j
n
m e
e
nT
t
g
A
x
t
s n
m


2
1
0
1
0
,
,
)
(
)
(
)
(   







(6)
Step 4: The PAPR of each FBMC symbol is determined as follows:
(7)
Step 5: the PAPR of each block is calculated as the addition of the PAPR of each symbol as
follows:
PAPR
PAPR
1
0
W 





n
(8)
Algorithm 1: the proposed algorithm
Initialization
1
W=16
 =1
A=0.05

24
Process
FOR i=0: 
/
W
FOR ii=1: 
Calculate )
(t
sii
in equation (5)
WHILE (absolute value of )
(t
sii
> 0)
DO
Calculate )
(t
sii
in equation (6)
END
PAPR(ii)=
]
)
(
[
}
)
(
max{
2
2
t
s
average
t
s
ii
ii
END
Calculate the PAPR in equation (8)
END
Calculate the PAPR in equation (9)
Finally, the total PAPR for the transmitted signal is calculated by the addition of the PAPR of
each block as follows:
PAPR
PAPR
1
0
total 



W
n
W
(9)
The proposed algorithm is illustrated in algorithm 1.
5. SIMULATION RESULTS
5.1. PAPR Comparison
In this section, the PAPR performance of the single carrier techniques utilizing the proposed
algorithm versus the conventional single-carrier techniques is discussed. Also, the transmitted
FBMC and SC-OFDMA signals are included to be taken as a reference. Simulation results are
performed through upgrading related m-file using MATLAB package version 2021a. The
parameters on which the simulation is based are listed in Table 1. The simulation parameters are
selected to be the same as the parameters that existed in [20] and [21] so that the obtained
simulation results are fairly compared to other conventional single-carrier techniques in [20] and
[21]. The PAPR performance is assessed by the complementary cumulative distribution function
(CCDF) which is denoted by (PAPR0) [29-30]. The DFT spreading technique after using the
proposed algorithm will be called the improved DFT, improved ITSM and improved GDFT.
Table 1. Simulation Parameters.
Parameter VALUE
FBMC FFT/IFFT size 64, 128
Subcarriers (M) numbers 64,128
Symbols/subcarriers numbers 16
Modulation OQPSK
Type of prototype filter PHYDYAS
filter
Overlap factor 4

25
It is observable from Fig. 6 that with a reference value of the CCDF equals 10-3
, the single carrier
techniques utilizing the proposed algorithm, namely improved DFT, improved ITSM and
improved GDFT, enhances the PAPR amount over the conventional single-carrier techniques
namely DFT, ITSM and GDFT by 3.4 dB, 3 dB and 2.6 dB, respectively. Compared to SC-
OFDMA the single carrier techniques with the proposed algorithm increase the PAPR reduction
amount by 1.2 dB, 1.3 dB and 1.9dB in case of improved DFT, improved ITSM and improved
GDFT, respectively.
More PAPR performance improvements are achieved with the increase of subcarrier numbers as
it is depicted in Fig.7. This is because in general the increasing of subcarrier numbers of results in
increasing the PAPR amount and this is happening in the case of conventional single-carrier
techniques. However, increasing the average power as in the proposed algorithm helps in
reducing the amount of PAPR growth with the increase of subcarrier numbers. Consequently, the
improved DFT, improved ITSM, and improved GDFT enhance the PAPR amount over DFT,
ITSM and GDFT spreading by 3.7 dB, 3.2 dB, and 2.8 dB, respectively.
Figure 6. CCDFs comparison of the PAPR for the improved single carrier techniques for M=64.

26
Figure 7. CCDFs comparison of the PAPR for the improved single carrier techniques for M=128.
5.2. PSD Comparison
The PSD characteristics for the FBMC single carrier techniques with and without using the
improved algorithm are demonstrated in figure 8. Using a 0.2 normalized frequency as a mask,
the DFT spreading and the GDFT technique before using the improved algorithm have lower
OOB by -2 dB and -1 dB respectively compared to the same techniques after using the improved
algorithm as it is shown in figure 8(a) and (c). In case of ITSM technique, the use of the
improved algorithm does not affect the PSD performance as shown in figure 8(b).
6. COMPUTATIONAL COMPLEXITY COMPARISON
In this section, we introduce a computational complexity comparison of the single carrier
techniques which utilize the proposed algorithm versus the conventional single-carrier
techniques. The computational complexity is measured based on the number of additions and the
real multiplication. However, measuring computational complexity based on the number of
additions is not considered as multiplication carries the highest computational load. It is depicted
in from Table 2 that the improved single carrier techniques have the same complexity overhead
as that of the conventional techniques.
This is because the improved techniques are based on a proposed algorithm in which the
amplitude of each FBMC symbol is increased by a predetermined value. Consequently, these
additions do not have an impact on increasing the complexity overhead. With M subcarriers of
power 2, the GDFT computational complexity is measured by 4x(M log2M), where the number
(4) denotes the RMs number for one complex multiplication [31]. The M-point IFFT and DFT
with M subcarriers of power 2 computational complexity are calculated by 4x(M log2M+2M)
[32], and 4x(M/2)log2M respectively [33]. The PPN RMs number is given by 8KM [34].

27
(a)
(b)

28
(c)
Figure 8. PSD characteristics for single carrier techniques with and without using the improved algorithm
(a)DFT Spreading, (b) ITSM technique, and (c) GDFT spreading.
Table 2. Computational complexity comparison for different improved single carrier techniques.
Single
carrier
Technique
Main
calculations
the Real
Multiplication (RM)
formula
Computational
complexity/symbol
period for M=64
Computational
complexity/symbol
period for M=128
Original
FBMC
2 IFFTs and 2
PPNs
IFFT: )
2
log
2
(
x
4 2 M
M
M 
PPN: 8KM
11264 24576
DFT
spreading
1 DFT, 2
IFFTs and
2PPNs
DFT: )
log
2
/
(
x
4 2M
M
IFFT: )
2
log
2
(
x
4 2 M
M
M 
PPN: 8KM
12032 26368
Improved
DFT
1 DFT, 2
IFFTs and
2PPNs
12032 26368
ITSM
1 DFT, 2
IFFTs and
2PPNs
12032 26368
Improved
ITSM
1 DFT, 2
IFFTs and
2PPNs
12032 26368
GDFT
spreading
1 DFT, 1
GDFT,2
IFFTs and 2
PPNs
GDFT: )
log
(
x
4 2M
M
DFT: )
log
2
/
(
x
4 2M
M
IFFT: )
2
log
2
(
x
4 2 M
M
M 
PPN: 8KM
13568 19456
Improved
GDFT
1 DFT, 1
GDFT,2
IFFTs and 2
PPNs
13568 19456

29
7. CONCLUSIONS
In FBMC, a higher PAPR is a major disadvantage. Using a single carrier effect is regarded as a
useful strategy for reducing PAPR in FBMC systems with a minimal amount of complexity
overhead. However, the FBMC PAPR reduction performance differs from the performance of the
SC-FDMA technique. This is due to the overlapping structure of the OQAM FBMC symbols' in-
phase and quadrature. In this paper, we proposed a novel algorithm for improving the PAPR
performance of the single carrier techniques. The proposed algorithm was based on increasing the
average power by increasing each FBMC symbol amplitude by utilizing a predetermined small
value. we present a signal distortion-based algorithm for maintaining computational complexity
while enhancing PAPR reduction performance in FBMC for single carrier effect techniques
without the requirement for SI overhead. The presented technique is used in other FBMC single
carrier effect algorithms. At various numbers of subcarriers, the PAPR performance of single
carrier effect approaches is evaluated using the suggested methodology.
From the simulation results, the use of the proposed algorithm resulted in a major reduction of
PAPR in the single carrier techniques namely, DFT, ITSM, and GDFT. This improvement in
PAPR performance was achieved without any complexity overhead. In future work, other
spreading techniques such as discrete cosine transform (DCT) and Hadamard transform should be
investigated under the proposed algorithm.
CONFLICTS OF INTEREST
The authors declare no conflict of interest.
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