Enhancing PAPR reduction for FBMC-OQAM systems by joint both tone reservation and companding methods

Indonesian Journal of Electrical Engineering and Computer Science
Vol. 21, No. 2, February 2021, pp. 919~926
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v21.i2.pp919-926  919
Journal homepage: http://ijeecs.iaescore.com
Enhancing PAPR reduction for FBMC-OQAM systems by joint
both tone reservation and companding methods
Salima Senhadji1
, Yassine Mohammed Bendimerad2
, Fathi Tarik Bendimerad3
1,3
LTT Laboratory, Department of Telecommunication, University Abou Baker Belkaid, Algeria
2
Department of Electrical and Electronic Engineering, University of Bechar, Algeria
Article Info ABSTRACT
Article history:
Received Jun 15, 2020
Revised Aug 11, 2020
Accepted Aug 21, 2020
As all multi-carrier designs FBMC-OQAM signal suffers from large peak-to-
average power ratio (PAPR). There are divers PAPR reduction methods to
solve this problem. Tone reservation (TR) scheme is one of the most famous
PAPR reduction techniques in which a peak cancelling signal is added to the
original one in such a way that PAPR will reduce. Companding is another
easy PAPR reduction technique in which compression of large amplitude
samples and expansion of low one. In this paper, we suggest a new PAPR
reduction scheme called TR&Compd, based on combining tone reservation
and Mu-law companding techniques for FBMC-OQAM systems. The
simulation results show that the new proposed scheme (TR&Compd)
presents better results in term of PAPR reduction compared to TR and Mu-
law companding methods taken separately.
Keywords:
FBMC-OQAM
Mu-law companding
PAPR reduction
TR
TR&Compd This is an open access article under the CC BY-SA license.
Corresponding Author:
Salima Senhadji
LTT Laboratory
Department of Telecommunication
Abou Baker Belkaid University
Tlemcen, 1300, Algeria
Email: salima.senhadji@student.univ-tlemcen.dz
1. INTRODUCTION
The multicarrier modulation technique (MCM) is widely used in wireless communication systems
such as LTE, 4G, Wimax and also for the next generation 5G. MCM presents a lot of advantages; the most
interesting is (i) the robustness against multipath propagation and (ii) narrowband interference. Till now,
Orthogonal Frequency Division Multiplex (OFDM) is the most important class of MCM systems. However,
it is a limited version of the new 5G vision due to some drawbacks.
The Filter Bank Multi-Carrier (FBMC) based systems combined with Offset Quadrature Amplitude
Modulation (OQAM) [1-5] are gaining appeal to be the favorite to become the radio waveform in
forthcoming fifth Generation (5G) physical layer [6]. This advanced modulation scheme offers lots of
advantages such as excellent frequency localization [7, 8], low side lobes in its PSD (Power Spectral
Density), robustness to phase noise and frequency offsets making it more suitable than OFDM for 5G [9].
Nevertheless, as all multicarrier designs, FBMC suffers from large Peak-to Average Power Ratio (PAPR)
which leads to saturation of the high power amplifier (HPA) and cause some in band and out of band
distortions which impact the signal quality.
Divers PAPR reduction schemes have been suggested. The most used techniques are: Clipping and
Filtering [10], Coding schemes [11], Nonlinear Companding Transforms [12, 13], tone reservation (TR) [14,
15], Selected Mapping (SLM) [16, 17], and Partial Transmit Sequences (PTS) [18]. In the literature, there

 ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 21, No. 2, February 2021 : 919 - 926
920
have been many works focusing on the PAPR reduction in FBMC-OQAM systems. In [19], a hybrid solution
with conventional SLM and TR was proposed to achieve better PAPR reduction. also in [20], a solution
called TR-PTS hybrid scheme with a multi data block-PTS by taking advantage of the FBMC-OQAM
symbol overlaps was proposed to enhance PAPR reduction. Other works use companding technique only as
in [21], the PAPR of the FBMC system is reduced directly by using A-law and μ-law companding functions
at the expense of a certain BER performance.
In this paper, we propose a new hybrid scheme called TR&Compd for PAPR reduction in FBMC-
OQAM signals which joint tone reservation (TR) and Mu-Law companding methods. For the new
TR&Compd scheme, the first step is to further process the original signals through the TR scheme. Since
some peaks power of the FBMC-OQAM signals usually occur at a few points, we propose to perform Mu-
Law companding function in order to enhance PAPR reduction performance. The simulation results are used
to show the effectiveness of the proposed TR&Compd scheme in reducing the power envelope ﬂuctuations
for FBMC-OQAM signals.
The rest of the paper is organized as follows: Section 2, include a description of FBMC-OQAM
system, the PAPR problem and HPA model, also we present a background about the tone reservation
technique of PAPR reduction, Mu-law companding and the proposed algorithm (TR&Compd). Section 3,
shows the simulation results and analysis. Finally, we end the paper with some conclusions in Section 4.
2. RESEARCH METHODS
2.1. FBMC-OQAM system and PAPR problem
The input of the Filter Bank Multi-Carrier with Offset Quadrature Amplitude Modulation (FBMC-
OQAM system) [22] is generally a complex symbol, which is defined as follows:
(1)
Where , - , - denote the real and imaginary parts of the
complex symbol on the subcarrier respectively. The number of the subcarriers is and the
complex input symbols numbers is. The FBMC-OQAM system transmitter side is shown in Figure 1.
For OQAM, the real and imaginary parts of the complex symbols QAM are staggered in time
domain by , where is the symbol period (equivalent to ). Then, the symbols are passed through a
filter bank of transmission. The transmission FBMC-OQAM symbol can be obtained by adding all
subcarriers, which can be expressed as follow:
( ) ∑ , ( ) ( )- ( )
(2)
Where ( )is the prototype filter impulse response.
Figure 1. The FBMC-OQAM transmitter

Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 
Enhancing PAPR reduction for FBMC-OQAM systems by joint both tone reservation… (Salima Senhadji)
921
In this paper, PHYDYAS [23] filter is considered as the prototype filter. It is characterized by an
overlapping factor noted and the design of this filter is based on the frequency sampling technology. The
impulse response of the PHYDYAS filter is given as [23] in (3) followed by the frequency domain
coefficient of the filter as shown in Table 1.
( ) {√
0 ∑ ( ) . /1
, - (3)
Where:
{
[ ∑ ]
(4)
And
Table 1. The frequency domain coefficient of the PHYDYAS filter
√
√
After filtering, the FBMC-OQAM symbol duration is extended by , which means that
consecutive output symbols overlap with each other in the time domain. After the summation of the
FBMC-OQAM symbols the length is ( ) where ( ) is given as:
( ) ∑ ( ) , . / - (5)
For PAPR analysis, in this paper we consider only the middle area of the FBMC-OQAM signals
from ( ) to ( ) with points that is then divided into intervals equally
with time duration . Thus, the PAPR of each interval is defined by (6) and, we use the complementary
cumulative distribution function (CCDF) presented by (7) to plot it.
( )
( ) (| ( )| )
(| ( )| )
(6)
Where * + denotes the expected value and , -.
( ) ( ) – . – –
/ (7)
A high power amplifier (HPA) is one of the indispensable components in the wireless mobile
communication systems. In this paper, we consider a HPA follows the Rapp model with a smoothness factor
α that control the transition between the linear zone and the saturation one of HPA.The Rapp model [24]
presents only AM/AM conversion. This one can be expressed as:
( ( ))
( )
( (
( )
) )
(8)
( ( )) (9)
Where the smoothness factor is all time
2.2. Tone reservation merhod for FBMC-OQAM PAPR reduction
TR is a linear technique was ﬁrst introduced in [14], but requires an efficient generation of the peak-
canceling signal. The PAPR can be reduced by using the Tone Reservation (TR) technique which exploits a

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small number of unused subcarriers (reserved tones) to generate a peak-canceling signal [15]. In TR scheme
based on iterative clipping filtering algorithm for FBMC-OQAM systems. The total subcarriers (tones) are
partitioned into peak reduction tones (PRTs) and data tones. The positions of the PRTs are known
by the receiver and transmitter. The input complex symbol in frequency domain can be written as:
{ (10)
(11)
Where data block composed of the data vector and the PAPR reduction vector.
* + denotes the set of tones reserved for peak reduction, denotes the set of data subcarriers,
and is the complement set of in * + The data tones in time domain ( )are generated by
point IFFT operation of . The main steps are as:
First step: ( ) is clipped to a threshold as:
( )
̃ {
( ) | ( )|
| ( )|
(12)
Where ( ) | ( )| , is the phase of ( ).
Second step: the original clipping noise ( ) is calculated as:
( ) ( )
̃ – ( ) (13)
{ (14)
Where ( ).
Third step: ( ) is added to ( ) and PAPR of the peak reduced FBMC-OQAM signal can be expressed as:
( ) ( ) | ( ) ( )|
,| ( )| -
(15)
Where ( ) is time domain peak reduction signal.
2.3. Mu-law companding method
Companding is a PAPR reduction technique considered as amplitude limiting scheme, easy to
implement in any numerical system. Different types of nonlinear companding are discussed in literature as A-
law, Mu-law notted also (μ-law) companding. In companding technique, using different functions the higher
amplitudes are compressed and smaller amplitudes are expanded resulting in reduction of PAPR. For the
given input signal , the mathematical formula of the output signal of Mu-law companding and
decompanding techniques are and ̅ respectively given as:
.
| |
/
( )
( ) ( ) (16)
̅ (
| | ( )
) ( ) (17)
Where is the Mu-law parameter of the compander, is input signal, and is the peak amplitude of signal
[25]. is the natural logarithm, and is the signum function. is the received signal at the receiver.
2.4. Proposed joint TR&Compd scheme for FBMC-OQAM PAPR reduction
In this subsection, we present our proposed scheme (TR&Compd) which combines the TR scheme
and the Mu-law companding method to enhance the PAPR reduction in FBMC-OQAM systems. These two
schemes can be complementary, the FBMC-OQAM signal goes through the TR PAPR reduction block in

923
order to reduce its high envelope ﬂuctuations, but a few peaks of the complex symbol cannot be canceled by
this way only, and will be affected by the non linearity of the power amplifier. For this, we propose to apply
Mu-law companding function to enhance high peaks reduction. This proposed PAPR reduction approach
combines the advantages of linearity from the first step (TR) with the reduced computation complexity of the
second step (Mu-law), providing a better PAPR reduction with good efficiency. The steps of the proposed
TR&Compd scheme are described as below:
Proposed algorithm
1. Sepecify a desired threshold , reserved tones and the maximal
iteration numbers for TR scheme.
2. Generate the time domain signal ( ) of all the data blocks at the
output of the FBMC-OQAM transmitter using (6).
3. Clip the FBMC-OQAM signal at by using (11).
4. Generate a peak cancelling signal by :
 Calculate the clipping noise using (12) ( ).
 Convert it to the frequency domain ( ).
 Remodulate ( ) to get ( ).
5. Calculate the new TR-FBMC-OQAM signal by adding ( ) to ( ) .
6. Applay Mu-law Companding to the TR-FBMC-OQAM signal i.e., ( )
, ( ) ( )- using (15).
7. Calculate the PAPR of the new TR&Compd FBMC-OQAM signal by (7).
3. RESULTS AND DISCUSSION
In this section, to estimate the performance of the proposed scheme TR&Compd for FBMC-OQAM
system PAPR reduction we have done extensive simulations. Mu-law compander is used because
theoretically it gives better BER compared to A-law compander. Table 2 shows the simulation parameters
used in this paper for FBMC-OQAM system, Tone Reservation, Mu-law companding and HPA Rapp model.
From the CCDFs curves (Figure 2 and the numerical values reported in Table 3), we can see that the PAPR
of the unchanged FBMC-OQAM signal is , For a . Moreover, when the CCDF is ,
among three schemes (TR, Compd, TR&Compd), TR&Compd scheme decreases by a gain equal to ,
TR decreases by , while Compd decreases the PAPR by It can be observed that the proposed
TR&Compd performs better than TR and Companding separately in terms of PAPR reduction.
Table 2. The simuation parameters
Parameters Values
Modulation model 4OQAM
Overlapping factor ρ=4
Number of data blocks M=16
Number of subcarriers N=64
Number of PRTs P=8
Number of iteration for TR I=8
Threshold β=2
Mu-ratio μ=1
Smoothness factor α=3
IBO 3-6dB
Figure 2. CCDFs of TR, Compd, TR&Compd schemes and
original FBMC-OQAM signal
Table 3. The CCDF values at 10-3
Algorithms Original TR Companding TR&Compd
CCDF Values 10dB 7.3dB 8.2dB 6.2dB

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We have performed the simulation (see Figure 3. (a)) with different Mu-ratio when the
fixed parameters are , . From Figure 3. (a), we note that the PAPR decreases as the
increasing of Mu-ratio. For example, when and , the PAPR value of the proposed
scheme is . For respectively, at , the PAPR is and . It can be
verified that the suggested scheme have improved the peak reduction (PAPR). Then, different number of
iterations with the fixed parameters , are considered in Figure 3. (b). We
note that the gain of PAPR reduction increases by increasing the iterations number, for the gain of
reduction is . In Figure 3. (c), we show the PAPR threshold of the proposed scheme using different
clipping thresholds with fixed parameters: . is selected as
respectively. It is illustrated that the small threshold ( ) may not contribute in reducing PAPR for the
suggested way. For example, when , the PAPR values of the combined scheme with
are about , respectively. As simulation results show, it can be
verified that the proposed TR&Compd scheme have improved the PAPR reduction in FBMC/OQAM system.
Figure 4. (a) and (b) compare the BER performances of TR scheme, TR &Compd and FBMC-
OQAM signals in the presence of HPA Rapp model for and over
Additive White Gaussian Noise (AWGN) channel. From both ﬁgures, we can notice that the BER
performance of TR&Compd is slightly degraded than TR scheme only. We can deal this degradation by
adding a simple precoding to greatly improve the overall system performance.
(a) (b)
(c)
Figure 3. CCDFs of TR&Compd scheme with different parameters

925
(a) (b)
Figure 4. BER performance of TR, TR&Compd schemes and Original FBMC-OQAM in presence of HPA
Rapp model over AWGN channel for IBO=3dB (a), IBO=6 dB (b)
4. CONCLUSION
In this paper, we proposed a combined scheme TR&Compd based on both Tone Reservation
approach and the Companding (Mu-law) technique. The proposed approach can reduce the PAPR on FBMC-
OQAM signals in a significant way. Based on the present findings, this proposed serial approach outperforms
the separate use of TR and Companding schemes in terms of PAPR gain reduction. Moreover, the serial
combination in terms of BER in the presence of a HPA with amplitude distortion it is noted that the BER
performance slightly degrades with using the joint schemes but we can deal this degradation by using any
sort of precoding.
ACKNOWLEDGEMENTS
This work was supported by the national project with technological development and socio-
economic impact under code N ° 13-2019-DGRSDT / Univ Tlemcen, entitled: contribution to the spectral
and energetic efficiency of 5G communications systems.
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