Analysis of peak-to-average power ratio in filter bank multicarrier with offset quadrature amplitude modulation systems using partial transmit sequence with shuffled frog leap optimization technique


ACTA IMEKO 
ISSN: 2221-870X 
March 2022, Volume 11, Number 1, 1 - 5 

 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 1 

Analysis of peak-to-average power ratio in filter bank 
multicarrier with offset quadrature amplitude modulation 
systems using partial transmit sequence with shuffled frog 
leap optimization technique 

Ch. Thejesh Kumar1, Amit Bindaj Karpurapu2, Mayank Mathur3 

1 Department of ECE,Raghu Institute of Technology,Visakhapatnam-531162, Andhra Pradesh, India 
2 Department of ECE,SwarnaBharathi Institute of Science and Technology, Khammam-507002, Telangana, India 
3 University of Technology, Jaipore - 303903, Rajasthan, India 

 

 

Section: RESEARCH PAPER  

Keywords: FBMC-OQAM; PTS; leap frog optimization; PAPR; BER 

Citation: Ch. Thejesh Kumar, Amit Bindaj Karpurapu, Mayank Mathur, Analysis of peak-to-average power ratio in filter bank multicarrier with offset 
quadrature amplitude modulation systems using partial transmit sequence with shuffled frog leap optimization technique, Acta IMEKO, vol. 11, no. 1, 
article 29, March 2022, identifier: IMEKO-ACTA-11 (2022)-01-29 

Section Editor: Md Zia Ur Rahman, Koneru Lakshmaiah Education Foundation, Guntur, India 

Received November 29, 2021; In final form March 5, 2022; Published March 2022 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Corresponding author: Ch. Thejesh Kumar, e-mail: thejeshkumar.ch@gmail.com  

 

1. INTRODUCTION 

The technology of orthogonal frequency division 
multiplexing (OFDM) technology emerged as the suitable 
multicarrier modulation technique for modern wireless 
communications [1]. They are responsible for the effective 
spectral frequency usage while minimizing inter-symbol 
interface. This is usually performed employing the guard interval 
insertion. in the multipath channel. Adding the guard interval, 
however, reduces the efficiency of spectra and power. In order 
to tackle the issue, the filter bank multicarrier with offset 
quadrature amplitude modulation (FBMC-OQAM) based 
technique has been proposed. The technique improves spectral 
efficiency. However, this comes at the cost of computational 

complexity. Further, it has a noticeable impact yielding to 
reduced out-of-band power leakage [2]. 

The FBMC-OQAM is being evaluated as a contender for the 
5G mobile communication standard because to its benefits like 
excellent temporal and frequency localisation. Further, other 
significant features are the minimization of out-of-band emission 
and resistance to phase noise [3]. In the FBMC-OQAM 
approach [4], a prototype filter is used to reduce the 
orthogonality of subcarriers. This is often used to avoid the GI 
insertion. As a result, this can achieve greater spectral efficiency. 
Citing the recent developments in wireless communication, the 
demand for mobile and broad-band service in 5G is ever-
growing. In this line, the FBMC-OQAM approach can be 
considered as the effective to support the OFDM technique [5]. 

ABSTRACT 
Because of its low adjacent channel leakage ratio, the Filter Bank Multicarrier with Offset Quadrature Amplitude Modulation (FBMC-
OQAM) has sparked the attention of many researchers in recent times. However, the problem of high Peak-to-Average Power Ratio 
(PAPR) measurement has a detrimental influence upon the FBMC system's energy measurement efficiency. We study PAPR reduction 
of FBMC-OQAM signals using the Partial Transmit Sequence (PTS) methods in this work. The PTS with shuffled frog leap phase 
optimization method is proposed in this paper to reduce the larger PAPR measurement, which is the major disadvantage of the filter 
bank multicarrier with offset quadrature amplitude modulation system. According to the simulation software findings, the suggested 
approach has a considerably superior PAPR, which may reduce the PAPR by about 2 dB at complementary cumulative distribution 
function 10-3 when compared to the traditional PTS method, and it has a much lower computational complexity than the previous ways. 
The experimental parameters are measured, and results are evaluated using MATLAB tool. 

mailto:thejeshkumar.ch@gmail.com


 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 2 

The significant problem persistent in OFDM and FBMC-
OQAM is the peak-to-average power ratio (PAPR) 
enhancement. As a result of this issue, greater non-linear signal 
distortion has developed at the output of a power amplifier, 
resulting in a catastrophic reduction of Bit-Error Rate (BER) 
performance. To address this issue, various PAPR reduction 
techniques for multicarrier modulation systems have been 
developed, including Partial Transmit Sequence (PTS) [6], 
selective mapping [7], and others. Further, the manuscript is 
organized to provide the information on PAPR reduction 
techniques in Section 2. The algorithm is explained in Section 3 
while the demonstration of the application is given in Section 4. 
The simulated results, computations and discussions are 
presented in Section 5. Overall conclusions are given in Section 
6. 

2. PAPR REDUCTION METHODS 

Initially, the concept of PAPR reduction has been considered 
as an essential step in communications especially pointing to 
applications like radar and speech synthesis. Typical Radar 
systems have several limitations in terms of peak power. This is 
very common issue in every communication system. Similarly, 
the speech synthesis application suffers degradation as it is 
severely bounded by peak power. This is due to the reason that 
the larger the signal, land up in the situation where the computing 
machine voice sounds very hard. These features should be 
avoided especially while handling human speech. When a multi-
carrier-based communication system is considered, the primary 
issue to deal with is the inherent PAPR. Hence, the PAPR 
reduction can be considered as the essential part of improving 
the quality of the communication. Several schemes and methods 
are proposed in due course of time to handle the PAPR 
reduction process with ease.  

It is essential to mention that the PAPR should be dealt 
through a non-complex phenomenon. For an OFDM system, 
several PAPR reduction schemes are proposed precisely 
following this rule. To list some of the most successful schemes 
so far, are clipping, Tone Injection and Reservation. Similarly, 
other techniques based on constellations and Transmit 
Sequences are also popular. Along with these techniques like 
Selective Mapping along with block coding are some to mention 
in the popular list. A comparative study of the techniques 
mentioned above essentially gave a deep insight on the potential 
application and strength of each and every method. 

One of the most common PAPR reduction methods is the 
PTS method, which is characterized as a distortion-less 
approach. The minimal PAPR value in the PTS technique is 
obtained by multiplying the data signal cluster of each data 
symbol choosing the available and suitable phase combination. 
While demodulating, the corresponding side information 
provided by the transmitter is essential. Challenging this, a 
solution to this PAPR enhancement issue has been provided in 
specific to the FBMC-OQAM system. This can outperform the 
standard PTS technique in terms of PAPR performance while 
reducing the computational cost of optimizing phase 
combination. The quiet characteristics are that the bigger PAPR 
is minimized using the overlapping-PTS technique [8], [9] and 
the phase combination is optimised utilizing the Shuffled Frog 
Leap (SFL) phase optimization. The receiver, like the PTS 
technique, need transmitters to provide relevant side information 
which is useful for further the data demodulation. 

3. SHUFFLED FROG LEAP OPTIMIZATION  

The SFL algorithm (SFLA) belongs to the class of meta-
heuristic algorithms. It performs a learned heuristic approach for 
searching a solution. Especially, it performs a combinatorial 
optimization employing several heuristic functions. These 
heuristic functions are non-complex mathematical models. The 
evolution of the memes is the factor of inspiration while 
structuring the algorithm. It mimics the way established to 
exchange the information among them. The SFLA is a hybrid of 
deterministic and random methods. As in particle swarm 
optimization, the deterministic method enables the algorithm to 
effectively employ the surface data which is considered to be 
highly responsive. This has often been the potential driving 
source for the heuristic search. The random elements enable the 
search pattern's flexibility and resilience. Like any other 
algorithm, the initial step to choose the population. This refers 
to number of frogs which are randomly generated. This 
consistently includes the whole swamp. The population has been 
classified into multiple parallel communities. These are referred 
as memeplexes. Independent evolution of the individual is 
encouraged to search the space in multiple directions. The frogs 
inside each memeplex are infected by the ideas of other frogs, 
resulting in memetic development. Memetic evolution increases 
the quality of an individual's meme and improves the individual 
frog's performance toward a goal. To keep the infection process 
competitive, frogs with better memes (ideas) must contribute 
more to the creation of new ideas than frogs with weak ideas. 
Using a triangular probability distribution to choose frogs gives 
superior ideas a competitive edge. 

During evolution, frogs do change their memes. This is 
usually taking in to account the corresponding best available 
information. This information can be usually obtained from the 
memeplex. However, in many cases it can be fetched from the 
whole population basing on the quality. This change refers to the 
jump and the corresponding magnitude is its step size. This yields 
the new meme relative to the updated position of the frog. Every 
frog is reintroduced to the community once it has improved its 
status. The knowledge acquired from a position shift is instantly 
available for improvement. This rapid access to fresh 
information distinguishes this technique from genetic algorithm. 
Usually in the later, the whole population is affected. However, 
in the SFLA, the scenario is different. Every frog in the 
population is considered to be the potential solution. This 
depicts the concepts of idea dissemination. The potential part of 
the algorithm refers to the comparative study as drawn by the 
team of innovators suitably developing the concept. This can also 
be visualised as the engineer who continuously works towards 
bettering the designs. 

3.1. SFLA steps 

Step1. Initialization. Selection of 𝑚 and 𝑛. Here 𝑚 refers to 
number of memeplexes [9]. Similarly, 𝑛 denotes number of frogs 
available every memeplex. The value of 𝐹 is computed as overall 
swamp size 𝐹 = 𝑚 × 𝑛. 

Step2. Generate a virtual population. 
Step3. Sort basing on ranks of the frogs. The sorting should 

follow the process to keep the best on top. 
Step4. Partition of frogs into memeplexes. Partition array X 

into 𝑚 memeplexes 𝑌1, 𝑌2, … . , 𝑌m , each containing 𝑛 frogs, 
such that 



 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 3 

𝑌𝑘 = 𝑈(j)k, f(𝑗)𝒌|U(𝑗)𝒌 = 𝑈(𝑘 + 𝑚(𝑗 − 1)), f(𝑗)𝒌

= f(𝑘 + 𝑚(𝑗 − 1)), 𝑗 = 1, … , 𝑛;  𝑘 = 1, … , 𝑚 . 
(1) 

For instance, if 𝑚 = 3, the corresponding rank 1 goes to 
memeplex-1. Similarly, the rank-2 is assigned to memeplex-2. 
Subsequently the rank 3 awarded to meplex-3 while the 4th rank 
designated to memeplex-1. The process goes on. 

Step5. This step refers to memetic evolution. This takes place 

inside every memeplex. Yield every memeplex 𝑌𝑘 , 𝑘 = 1, … , 𝑚. 
This is in accordance with the SFLA. 

Step6. All the memes are shuffled.  

Following the finite iterative process, 𝑌1, … , 𝑌m should be 

replacing into 𝑋. This is with respect to 𝑋 = {𝑌𝑘 , 𝑘 = 1, … , 𝑚}. 
Further, the step also includes sorting 𝑋 in the decreasing order 
basing on the respective performance index. This finally updates 

the position of the best frog to 𝑃X. 
Step7. Check whether convergence is achieved. Termination 

should be called in once the conference is witnessed. If not go to 
Step#3 once again. The termination criterion can be the 
computational time, number of iterations or the convergence. 
The convergence refers to ‘best memetic pattern’ without 
change. Basing on this the computation of the function 
evaluation takes place. 

4. PAPR REDUCTION USING PTS-SFL 

4.1. PAPR 

PAPR is the ratio of the peak power of a multicarrier signal 
to its average power. As the PAPR value rises, it shows that the 
system requires High-Power Amplifiers (HPAs) to function in 
their saturation area, which is essential since any additional 
increase in signal amplitude forces the HPA to operate in its 
nonlinear region, resulting in signal distortion. The reduction 
methods in OFDM systems are performed separately to each 
symbol, and the PAPR of each symbol is computed 
independently. The overlapping of data blocks is not considered 
for FBMC/OQAM signal which is good sign. To compute the 
PAPR correctly, the overlapping of the symbol blocks must be 
taken into account [10]. The PAPR of pure FBMC/OQAM in 
dB can be expressed as follows: 

𝑃𝐴𝑃𝑅(dB) = 10 log10

max
(𝑚 − 1) ≤ 𝑡 ≤ 𝑚 𝑇

|𝑠(𝑡)m|
2

E[|𝑠(𝑡)|2]
 

(2) 

From above equation (2) the numerator represents the peak 

power in the duration of the input 𝑚thdata block, 𝑇 (𝑚 − 1) ≤
𝑡 ≤ 𝑚 𝑇, and the denominator E[|𝑠(𝑡)|2] represents the average 
power of the FBMC signal. 

4.2. PTPS 

In the conventional PTS method, an input block is divided 

into 𝑉 sub-blocks. Each sub-block is zero-padded to create a 
vector of length 𝑁. Inverse fast Fourier transform is performed 
separately for each sub-block, significantly increasing the 
computation complexity. Adjacent, interleaving, and pseudo-
random are some of the widely used partitioning schemes [11]. 
The adjacent method is used in the proposed method, owing to 
its simplicity and effectiveness. From Figure 1, it can be observed 
that the resulting sequences are optimized by phase rotation 

factors 𝑏 = [𝑏1, 𝑏2, … , 𝑏V], where 𝑏V = ej 2 π 𝑣/𝑊 and 𝑣 =
0, 1, … , 𝑊 − 1 , to create symbol candidates referred to as partial 
transmit sequences. This operation results in a variation of the 

peak values for the signal candidates, and the one with the 
minimum PAPR is chosen for transmission. 

The total number of signal candidates depends on V and W, 
where W is the number of the phase factors allowed for a single 
sub-block. The process of producing the optimum phase factor 
vector that reduces the PAPR is as follows [12]-[17] 

{�̃�1, �̃�2, … �̃�V} = arg
min

[𝑏1, … , 𝑏V]
max

0 ≤ 𝑡 ≤ 𝑇
|∑ 𝑠m

𝑣 𝑏𝑣
𝑉

𝑣=1

|

2

. (3) 

The transmit signal after reducing the PAPR can be expressed as 
follows: 

�̃�m(𝑡) =  ∑ 𝑠m
𝑣 �̃�𝑣

𝑉

𝑣=1

 . (4) 

Direct application of this method to each FBMC symbol 
separately is not effective. 

As the symbols overlap, the parts where the symbols overlap 
will have a peak regrowth, increasing the PAPR again [18]. 

4.3. PTS-SLF 

It is evident that the proposed yielded excellent PAPR 
reduction. This comes with a performance that reported lower 
computational complexity [19]-[22]. The process of SFL in 
optimizing the phase is performed according to the algorithm 
discussed in Section 2. The proposed block diagram is shown in 
Figure 1. 

5. RESULTS AND DISCUSSION  

Following the implementation of the SFLA to the problem of 
PAPR reduction, the simulation-based experiment has been 
carried out and the results are presented in this Section. The 
experimental computations are responsible for the deep insights 
which can be drawn on the concept of PAPR reduction. Clearly, 
the induction of the PTS-SFL and the effect on the PAPR are 
the part of study. The probabilistic approach and the 
computations based on complementary cumulative distribution 
function (CCDF) are performed as a part of the simulation. It is 
evident that the corresponding parameter has a direct impact on 
the PAPR. The results demonstrate various PAPR reduction 
techniques and are compared with proposed model. 

 

Figure 1. The proposed PTS-SFL Technique.  



 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 4 

The signals are optimized independently inconsideration of 
the overlapping signals, the complexity of the algorithm can be 
reduced using fewer combinations of phase factors. Herein, we 
explore the effects of different combinations of phase factors on 
the performance of the proposed technique. Figure 2 shows the 
CCDF curves for the proposed technique without clipping and 
with four sub-blocks. From Figure 2 it is shown that PAPR is 
around 8.1db using SFL optimization technique. Further, 8 sub-
blocks are considered and PAPR results are evaluated and is 
shown in Figure 3. 

By considering 𝑉 = 8, the threshold PAPR obtained using 
PTS is 7.5 dB, using segment-based optimization the PAPR 
value is around 7.4 dB and using Ant colony optimization 
technique is around 7.1 dB. The PAPR value obtained using SFL 
optimization is 6.5 dB which is almost 38 % reduction of PAPR 
compared to original FBMC model. 

From Figure 4, it is shown that for different 𝑉 values our 
proposed SFLA performance is better comparing to other 

existing techniques. The performance of BER is shown in Figure 
5. 

At SNR of 10 dB, the BER is very low for proposed method 
compared to clipping signal and original FBMC and also other 
two techniques i.e., Satin Bowerbird Optimization (SBO) and  
Ant Colony Optimization (ACO). The bit error rate values at 
SNR of 10 S dB are tabulated and are shown in Table 1. 

6. CONCLUSIONS 

In this paper, the technique of overlapping-PTS has been 
formulated and demonstrate. The technique has been 
successfully simulated and applied to the problem of PAPR 
reduction in the considered system. The proposed technique 
featured with reduced computational complexity. It is also 
reported that the phase optimization can be achieved in the 
perceived technique using the artificial bee colony phase 
optimization. The analysis of the simulated reports yielded an 
excellent insight which is sufficient to consider that the technique 
can achieve dominating PAPR performance. This can 
subsequently suppress the PAPR by 2 dB at least. The 
corresponding suppression reported as per the experimentation 
seems to be having an average of 38 %. This significant part is 
that the PAPR performance does not degrades the BER.  

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Figure 2. Comparison of PAPR for different techniques.  

 

Figure 3. Comparison of PAPR with respect to threshold values. 

 

Figure 4. Comparison of PAPR for V = 4 and V = 8 using different methods.  

 

Figure 5. Comparison of BER with respect to SNR. 

Table 1. BER obtained using different techniques for SNR of 10 dB (S - surge 
of information). 

Technique BER 

Clipping at S = 90 10-2* 

Clipping at S = 30 10-2.8 

Clipping at S = 15 10-3 

FBMC original 10-3.4 

SBO 10-3.45 

ACO 10-3.6 

Proposed SFLA 10-3.8 

https://doi.org/10.1109/TVT.2008.2004555


 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 5 

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https://doi.org/10.1109/MSP.2014.2337391
https://doi.org/10.1109/EW.2010.5483518
https://doi.org/10.1109/ISCCSP.2014.6877912
https://doi.org/10.1109/ACCESS.2019.2894527
https://doi.org/10.1109/JPHOT.2019.2894986
https://doi.org/10.1109/WOCC.2016.7506550
https://doi.org/10.1080/03052150500384759
https://doi.org/10.3390/electronics10060642
https://doi.org/10.1109/ACCESS.2019.2894527
https://doi.org/10.1109/ACCESS.2016.2605008
https://doi.org/10.1109/TBC.2005.856727
https://doi.org/10.1109/PIMRC.2007.4393989
https://doi.org/10.1109/TWC.2010.062310.100191
https://doi.org/10.1109/TBC.2010.2079691
https://doi.org/10.1109/GLOCOM.2000.891239
https://doi.org/10.1109/VETECF.2003.1285976
https://doi.org/10.1109/PIMRC.2003.1264266
https://doi.org/10.1016/j.measurement.2021.109267
http://dx.doi.org/10.21014/acta_imeko.v10i3.1020
http://dx.doi.org/10.21014/acta_imeko.v9i2.802