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www.etasr.com Raza et al.: Performance Analysis of Selective Mapping in Underwater Acoustic Orthogonal Frequency …

Performance Analysis of Selective Mapping in

Underwater Acoustic Orthogonal Frequency Division

Multiplexing Communication System

Waleed Raza

College of Underwater Acoustic
Engineering and Key Laboratory of
Marine Information Acquisition and

Security, Ministry of Industry and

Information Technology, and
Acoustic Science and Technology

Laboratory, Harbin Engineering

University, Harbin China

waleed@hrbeu.edu.cn

Xuefei Ma

College of Underwater Acoustic
Engineering and Key Laboratory of
Marine Information Acquisition and

Security, Ministry of Industry and

Information Technology, and
Acoustic Science and Technology

Laboratory, Harbin Engineering

University, Harbin China

maxuefei@hrbeu.edu.cn

Amir Ali

College of Underwater Acoustic
Engineering, Harbin Engineering

University, Harbin, China

amir@hrbeu.edu.cn

Asif Ali

College of Nuclear Science and
Technology, Harbin Engineering

University, Harbin, China

aliasif@hrbeu.edu.cn

Asif Raza

College of Mechanical and Electrical
Engineering, Harbin Engineering

University, Harbin, China

asif.raza57@yahoo.com

Shahabuddin Shaikh

College of Underwater Acoustic
Engineering, Harbin Engineering

University, Harbin, China

shahabshaikh@hrbeu.edu.cn

Abstract-Under-Water Acoustic (UWA) communication

networks are commonly formed by associating various

independent UWA vehicles and transceivers connected to the

bottom of the sea with battery-operated power modems.

Orthogonal Frequency Division Multiplexing (OFDM) is one of

the most vital innovations for UWA communications, having

improved data rates and the ability to transform fading channels
into flat fading. Moreover, OFDM is more robust on Inter-

Symbol and Inter-Carrier Interferences (ISI and ICI

respectively). However, OFDM technology suffers from a high

Peak to Average Power Ratio (PAPR), resulting in nonlinear

distortions and higher Bit Error Rates (BERs). Saving power of

battery deployed modems is an important necessity for
sustainable underwater communications. This paper studies

PAPR in UWA OFDM communications, employing Selective

Mapping (SLM) as a tool to mitigate PAPR. The proposed SLM

with the oversampling factor method proves to be less complex

and more efficient. Simulation results indicate that SLM is a

promising PAPR reduction method for UWA OFDM

communications reducing BER.

Keywords-underwater acoustic communication; orthogonal

frequency divisional multiplexing; peak to average power ratio;

selective mapping

I. INTRODUCTION

Under-Water Acoustic (UWA) wireless communications
are utilized in military and civil applications. For military
purposes, reliable communication is needed between

submarines and autonomous underwater vehicles on the
battlefield [1], as the overall operations depend on fast and
flexible communications. In civil applications, UWA is
essential in studying the underwater environment, and
investigating further oil and gas explorations [2, 3]. UWA-
based networks are different from terrestrial radio-based
networks due to propagation delays, transmit energy,
bandwidth, and multipath effects that affect the channel
drastically [4-6]. Acoustic signals have a limited propagation
speed around to five orders of magnitude lower than radio
signals. Therefore, the techniques used in radiofrequency
cannot be directly implemented in UWA-based networks. In
UWA wireless communication, OFDM is implemented over
UWA channels keeping in mind channel propagation and the
complexity of the medium, while multipath arrivals and
Doppler shifts make it more challenging [7]. However, OFDM
has several advantages as it improves the flexibility of channel
conditions and data rates, and results in better bandwidth with
high spectral efficiency [8-10]. However, OFDM has several
drawbacks, such as high PAPR and carrier frequency offset.
When the peaks of a signal move towards the nonlinear region
of the Power Amplifier (PA), distortion is created, overall
system's efficiency is reduced, particularly for PA, while the
complexity increases sharply for Analog to Digital (ADC) and
Digital to Analog Converters (DAC) [11, 12].

OFDM has become a significant standard in
communication networks. Its major drawback of high PAPR

Corresponding author: Xuefei Ma

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www.etasr.com Raza et al.: Performance Analysis of Selective Mapping in Underwater Acoustic Orthogonal Frequency …

results in low energy efficiency, hence it is very difficult to
implement an OFDM system in battery-powered modems in a
UWA environment. Utilizing High-Power Amplifiers (HPA)
and linear converters could overcome this drawback, but would
increase cost and complexity. Efficient PAPR reduction
techniques could solve this problem without complex
hardware, keeping in mind the linear range of the power
amplifier before design to avoid the saturation of HPA [12-15].
In- and out-band distortions are created by the saturation
process, which increases BER and band distortion, while it also
causes adjacent channel interference [16-19]. In long-term
applications of UWA communication networks, such as ocean
monitoring, the PA always works in full power mode and the
system becomes vulnerable due to limited powered modems.
Many factors influence the performance of PAPR, including
the subcarrier number, modulation types and order,
constellation type, and pulse shaping. PAPR can be reduced by
many methods having merits and limitations, as there is always
a compromising balance between bandwidth, computational
complexity, average power, etc. Many researchers introduced
such techniques and classified PAPR into several classes. In
terrestrial communication, clipping is the easiest way to
mitigate PAPR [20-23]. Moreover, reconstruction of the lost
clipped signal, iterative clipping, and filtering have been
introduced [24-26]. Peak windowing is an improved clipping
method [27], while a further enhancement was introduced in
[28]. The concept of the envelope scaling method was
suggested in [29]. In probabilistic schemes, SLM and Partial
Transmit Sequence (PTS) were suggested in [30-33]. Tone
Reservation (TR) following as a linear programming problem
and regarded as a Projection Onto Convex Sets (POCS) was
studied in [34-35]. Moreover, several types of companding
techniques have been introduced [36]. An improved
companding technique for UWA OFDM communication was
presented in [37]. The Tone Injection (TI) method had a severe
drawback, as signal power increased due to the injected signal
[38]. The interleaving and active constellation extensions are
also PAPR reduction techniques. This paper proposes the
utilization of Selective Mapping (SLM) with an oversampling
factor in OFDM UWA communications to reduce PAPR and
improve BER with lesser complexity.

II. SYSTEM MODEL AND OFDM MODULATION IN UWA

A. OFDM Modulation

The summation of subcarriers is modulated separately by
using Phase Shift Key (PSK) or Quadrature Amplitude
Modulation (QAM) to form an OFDM signal. They are
transmitted through a transducer as a data stream from the
OFDM modulator. The Inverse Fast Fourier Transform (IFFT)
is applied as:

1 2

,0
( ) ( ) k

N j f t

n k k dn n
X t d t nT e

πφ
∞ −

=−∞ =
 = −
 ∑ ∑ (1)

[ ]2

0 otherwise

,k
j f t

d
te T

πφ

(2)

and:

k
f f

T
= + , ( 0,...., 1)k N= − (3)

where fk shows the kth frequency of subcarriers, f0 is the lowest,
and Td represents the duration of each symbol. The number of
subcarriers is indicated by N when different symbols are
transmitted from the OFDM signal. It can be represented by dn,k
with n intervals of time by using kth subcarrier. The
orthogonality of the subcarrier φk(τ) is described as:

0* 1

0
0

( ) ( ) ( 1) {
dT T k

k l d otherwise
t t dt T kφ φ δ == − =∫ (4)

The demodulator can be represented digitally due to the
orthogonality relationship of the subcarriers, after it undergoes
several processes such as mathematic operations IFFT to FFT
and modulation to demodulation. The OFDM signal can be
implemented as:

( 1)
*

1
( )* ( )

n T

n k k
nT

d x T t dt
T

φ
+

= ∫

(5)

Figure 1 shows the framework of the proposed UWA
OFDM communication system with SLM. Successively,
signals are converted from serial to parallel, mapped in
Quadrature Phase-Shift Keying (QPSK), and IFFT is applied
with the proposed SLM reduction method to select the
minimum PAPR signal. Afterward, the Cyclic Prefix (CP)
amplified by HPA is added, which reduces the ISI. At the
receiver side, the CP is removed from the signal, followed by
the FFT and the process of demodulation. Finally, each QPSK
demodulated symbol is decoded.

Fig. 1. The framework of UWA OFDM communication system.

B. Peak to Average Power Ratio

Peak power is always higher than the average power in an
OFDM signal, as the number of subcarriers is added, resulting
in high PAPR. PAPR is very important in a UWA OFDM
communication system, as it affects power efficiency and PA's
performance. When PAPR is high, the peak signals are shifted
towards the nonlinear region of the PA, decreasing power
efficiency. The PAPR of an OFDM signal is equivalent to
about 12dB. ISI and ICI are due to the nonlinearity among
OFDM signals. PAPR in terms of a discrete-time signal is
given by:

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www.etasr.com Raza et al.: Performance Analysis of Selective Mapping in Underwater Acoustic Orthogonal Frequency …

2
max ( )

2
( )

x n
n

PAPR
E x n
n

=
 
  

(6)

Applying IFFT, discrete time-domain samples are given by:

[ ]
2

1
[ ] , 0 1

N
N

i
x n X i e n N

−

=
= ≤ ≤ −∑ (7)

The value of x[n] is zero when the Gaussian variables are
generated by increasing the value of subcarriers N. We will get
Rayleigh distributed variance when the value of x[n] is
complex Gaussian and the phase of the OFDM signal becomes
uniform. The Rayleigh distribution with a high peak value of
signal exceeds nonzero digit probability. Hence, the PAPR of

the digital signal exceeds the threshold value
2
0

0 2
P

σ
= . The

OFDM signal x[n] is IDFT or IFFT of complex data symbols.
We get this oversampled orthogonal frequency divisional
multiplexing signal with help of QAM or PSK at N subcarriers.

PAPR increases with the subcarrier number N, if N is
assumed as a Gaussian random variable distributed identically

,0 1x n N
n

≤ ≤ − and assume 0 mean and unit power. As we

know
2

( [ ])E x n
n
= is the mean power. Then:

2 2 2
0 1 1

... 1

E x E x E x
N

N N N

−
+ + = (8)

By adding xi coherently the maximum value is given by:

2
1

max ...
0 1

1
x x x

   + + + 
   

(9)

2
[ ]

N
N

N
= (10)

Equation (10) shows that the highest value of PAPR
becomes N with the subcarriers (N).

III. SELECTIVE MAPPING IN UWA OFDM COMMUNICATION

SLM can be considered as the most prominent method in
UWA OFDM communication systems. This process minimizes
PAPR, as it transmits the signal having the least PAPR. The
generated OFDM symbols are termed as candidates. Selective
mapping was introduced in [39]. The signal having the
minimum PAPR is transmitted from a various number of
identical data blocks. The expression for the original data

block , ,...,
0 1 1

T
X X X X

N
 
 −  is extracted by multiplying this

mathematical expression with phase sequence

( ) ( ) ( ) ( )
, ,...,

0 1 1

Tu u u u
P P P P

N
 =  −  where 0,1, 2,3..., 1u U= − is the

phase sequence defined by U. IFFT is applied to each
sequence to get a time-domain signal from the frequency
domain, resulting in different time domains in the OFDM data
blocks. The value of each data block is:

U
( ) ( ) ( ) ( )

...
0 1 1

Tu u u u
X X X X

N
 

+ + + −  and will get a various number of

PAPRs. Finally, the signal with minimum PAPR is selected in
the transmitting transducer from the input data blocks and the
candidates. The block diagram of the SLM with oversampling
factor is shown in Figure 2. X

)
is the OFDM signal candidate

for actual transmission, which defined as:

( )
arg min [ ( )]

u
X PAPR X

u U
= ≤ ≤

)
(11)

Fig. 2. The framework of selective mapping.

Using Nyquist sample rate, the complex envelope of
OFDM signal having N subcarriers is regarded as:

2
1 1

( ) ,0 10

t
j

N Nx t X e t NI iN

π
−∑= ≤ ≤ −=

(12)

The modulated symbols are represented with Xi. Gaussian
variables can be regarded when the value of x(t) is zero,
assuming the subcarrier number N is larger, as proved in the
central theorem. With 0.5 variance in the OFDM signal which
has Rayleigh distribution and the signal x(t) being complex
Gaussian, the signal phase remains unchanged. The nonzero
probability occurs when the signal peaks have Rayleigh
distribution and will surpass any value. Here we have assumed
x(t) average power equal to 1, and for . .i i d random variables
of Rayleigh, it is represented as zn. The probability density
function zn is given as:

( ) 2 , 0,1,2,3..., 1
z

f Z Ze n N
z
n

−
= = −

(13)

The PAPR value is approximated to the maximum value zn.

When the value of
max

Z follows max
max 0,1,2,3..., 1

Z Z
n N n

= = − the

probability of PAPR and the Complementary Cumulative

Distribution Function (CCDF) of
max

Z below threshold can be

given as:

( ) (1 )
z N

P PAPR z e
−

≤ = − (14)

The PAPR value can be determined by the data realization
on OFDM subcarriers and is also dependent on pilot symbols.
To analyze the PAPR in an OFDM signal, the CCDF is
considered as a performance metric when the threshold value is
large. The threshold z is exceeded then to search the probability
of PAPR, assuming the CCDF as:

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( ) 1 (1 )
z N

P PAPR z e
−

> = − − (15)

U phase sequences are created in each data block if the
mapping of each phase sequence is not statistically dependent,
so the CCDF of PAPR in the SLM becomes:

( ) (1 (1 ) )
z N U

P PAPR z e
−

> = − − (16)

where z shows the threshold, N is the number of the
subcarriers, and U represents the phase sequences.

From (16) and assuming the subcarrier number N of large
and independent samples U by using the Nyquist sampling rate,
without mentioning band limited and oversampling factor we
get (17). A sampled signal doesn't need to have the highest
point up to the original signal. At the same time, for getting real
values of PAPR, the signal must be oversampled by an
oversampling factor L. Authors in [34] first indicated the
acceptable four oversampling. Then peak power distribution
becomes very difficult to derive, hence the approximation of
PAPR with N subcarriers and oversampling distribution with
oversampling factors a and N. It was proven that a=2.8 is the
better value to reach a decent PAPR by taking subcarrier
number larger than 64.

.
( ) ( ) (1 )

N z N
P PAPR z F z e

α−
≤ = = −

(17)

If the PAPR value surpasses the threshold z, the
oversampling is defined as:

.
( ) (1 (1 ) )

z N U
P PAPR z e

α−
> = − −

(18)

This equation was employed to check the performance of
the UWA OFDM communication system, by adding an
oversampling factor a.

IV. RESULTS AND DISCUSSION

The results and numerical analysis of the proposed system
were considered with a different number of subcarriers and
phase sequences. The UWA channel was established based on
the Bellhop ray-tracing model. Simulations were carried out to
further evaluate the performance of the SLM scheme for PAPR
reduction. The simulation parameters are shown in Table I.

TABLE I. UWA OFDM SIMULATION DATA PARAMETERS

S/N Parameters Data

1 Sampling Frequency 100k

2 Bandwidth 6.25k

3 FFT Points 4096

4 OFDM Symbols 23

5 Number of Subcarriers 128,256,512

6 Cyclic Prefix Time 25ms

7 Modulation QPSK

8 PA Saturation level 6

9 Sound Speed 1500m/s

The operating frequency of the transmitted signal was kept
between 12 and 15k. The Bellhop ray tracing channel was
created by giving a sound profile in the ENV file. The
transmitting transducer was fixed at 1.5m depth, while a
hydrophone was fixed at 5m depth at the receiver's side. The

distance between the transmitter and the receiver was 2km, as
shown in Figure 3. The signal was passed through the power
amplifier, transmitted by the transducer, and underwent an
underwater acoustic channel before received by the
hydrophone. Figure 4(a) shows the Eigen ray of the multipath
Bellhop channel. As it can be observed, the underwater
acoustic channel had several multipath delays. The signal was
reflected and refracted at the bottom of the tank/sea and the
surface, while some signals arrived directly at the receiver.
Figure 4(b) shows the sound speed profile measured while
establishing the Bellhop multipath channel.

Fig. 3. Schematic layout of UWA communication with single transducer

and a single hydrophone.

Fig. 4. (a) Multipath channel Eigen ray, (b) sound speed profile in the

water.

Fig. 5. Bellhop channel impulse response.

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Figure 5 shows the channel impulse response of the UWA
channel. The delay between two successive points can be seen
with normalized amplitude. This is due to the nature of the
UWA channel: the signal meets severe multipath and delays
before reaching the destination. Figures 6-8 illustrate the
reduction of PAPR using the SLM scheme. As it can be noted,
increasing phase sequences (U) reduces PAPR, while
increasing the number of subcarriers (N) increases PAPR. The
least PAPR was observed with 128 subcarriers and 16 phase
sequences.

Fig. 6. PAPR of OFDM signal with SLM, N=128, U=1,2,4,8,16.

Fig. 7. PAPR of OFDM signal with SLM, N=256, U=1,2,4,8,16.

Fig. 8. PAPR of OFDM signal with SLM, N=512, U=1,2,4,8,16.

In Figure 9, the BER probability is described using the
Bellhop channel in the QPSK modulation. The proposed
method was compared with the original signal, clipping, and
PTS. As it can be observed, the SLM outperforms the other
PAPR mitigation methods at the range between 20dB and
25dB. Hence, the proposed method can be utilized in a UWA
modem to design a less complex OFDM system. As it can be
noted from Table II, the PAPR reduction is observed at
different numbers of subcarriers and phase sequences. All data
were extracted from Figures 6, 7, and 8 respectively, where the
CCDF of PAPR was equal to

10-4. The best performance of

PAPR was 6.3dB with 128 subcarriers and 16 phase sequences.
The best performance using 256 subcarriers was achieved with
16 phase sequences. Similarly, the optimum performance using
512 subcarriers was achieved with 16 phase sequences. Hence,
increasing the number of phase sequences in the SLM method
reduces PAPR. However, the complexity of the communication
system is slightly increased.

Fig. 9. BER vs signal to noise ratio for QPSK modulation in the Bellhop

channel.

TABLE II. REDUCTION OF PAPR USING SLM AT VARIOUS PHASE
SEQUENCES AND NUMBERS OF SUBCARRIERS

Number of phase

sequences (U)

Number of

subcarriers (N)
PAPR at 10-4

128

11.2dB

2 9.4dB

4 8dB

8 7.1dB

16 6.3dB

256

11.7dB

2 10.1dB

4 8.8dB

8 8.1dB

16 7.5dB

512

12.2dB

2 10.6dB

4 9.6dB

8 8.9dB

16 8.4B

V. CONCLUSION AND FUTURE WORK

OFDM is considered as an important modulation technique
in UWA communication systems, as it can convert frequency

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fading channels to flat fading channels. It also has robustness
over ISI and ICI, but it is very difficult to implement due to the
severe environment of UWA channels. This paper focused on
the study of the PAPR of a UWA OFDM communication,
utilizing the SLM method to design a novel energy-efficient
system. Simulation results showed that the SLM is the most
promising technique to reduce PAPR. We also showed that
increasing the phase sequences in SLM resulted in significant
gains of the OFDM system in terms of PAPR and BER
reduction. A future study could examine the improvements in
the power efficiency of a UWA OFDM communication system
by detecting different monomial phase sequences in
probabilistic techniques. Moreover, the authors plan to
continue this research by introducing some innovative, less
complex, and intelligent methods for the reduction of PAPR in
UWA communication networks.

ACKNOWLEDGMENT

This work was supported by Key Technology Research of
Underwater Long-Time Signal Collector (No. MB70569),
Heilongjiang Natural Science Foundation Joint Guidance
Project (No. JJ2019LH0977), Equipment Pre-Study Ship
Heavy Industry Joint Fund (No. 6141B042865)), Key
Laboratory of the Ministry of Education of Xiamen University
(No. UAC201804), Key Research & Development and
Transformation Plan of Science and Technology Program for
Tibet Autonomous Region (No. XZ201901-GB-16), and
Special Fund for Local Universities Supported by the Central
Finance of Tibet University in 2018.

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AUTHOR PROFILES

Waleed Raza received a B.E. degree in Electronic Engineering from the
Department of Electronic Engineering, Dawood University of Engineering

and Technology, Karachi, Pakistan, in 2017. He is currently pursuing an M.S.
degree in underwater acoustic communication engineering in the College of

Underwater Acoustic Engineering, Harbin Engineering University, China. His
research areas of interest include underwater acoustic OFDM communication,

machine learning, and digital signal processing.

Xuefei Ma received a B.S. degree in electronic information engineering from
the Harbin Engineering University, China, in 2003, an M.S. degree in

information and communication engineering from the Harbin Engineering
University, China, in 2006, and a Ph.D. degree in signal and information

processing engineering from the School of College of Underwater Acoustic
Engineering, Harbin Engineering University, China, in 2011, where he is

currently an Associate Professor. His research interests include underwater

acoustic communication and underwater acoustic signal processing.

Amir Ali received a B.E in Electronic Engineering from Mehran University

of Engineering and Technology Jamshoro, Pakistan in 2016. He was a Junior
Expert Engineer in National Engineering Services Pakistan from 2016 to

2018. Currently, he is pursuing an M.S. in Underwater Acoustic Engineering,
from Harbin Engineering University, China. His research interests are wireless

communication, underwater image processing, 5G, and IoT.

Asif Ali received a B.S degree in Physics from Shah Abdul Latif University,

Khairpur, Pakistan in 2017. Currently, he is getting an M.S. degree in nuclear
engineering from Harbin Engineering University, China. His current research

interests include system engineering, nuclear physics, and nuclear power plant

safety.

Asif Raza received a B.E in Mechanical Engineering from the Quaid-e-Awam

University of Engineering, Science, and Technology Nawabshah, Pakistan in
2015. Currently, he is getting an M.S. degree in mechanical engineering from

Harbin Engineering University, China. His current research interests include
thermodynamic engineering, tensegrity compression, and expansion with

interdependent dynamics.

Shahabuddin Shaikh received a B.E in Mechanical Engineering from Quaid-
e-Awam University of Engineering, Science and Technology Nawabshah,

Pakistan in 2002. He acquired an M.S. in underwater acoustic engineering
from Harbin Engineering University, China in 2014. Since 2006 he belongs to

NESCOM in Pakistan, and works as a General Manager (Technical).
Presently, he is pursuing a Ph.D. in Underwater Acoustic Engineering from

Harbin Engineering University, China. His research interests are underwater

sound propagation and marine sediments.