IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023

1

A Modified Delay and Doppler Profiler based ICI Canceling OFDM
Receiver for Underwater Multi-path Doppler Channel
Catherine Akioya1), Shiho Oshiro2), Hiromasa Yamada3) and Tomohisa Wada4)
1) Graduate School of Engineering and Science University of the Ryukyus, Okinawa, Japan
2) Information Technology Center, University of the Ryukyus, Okinawa, Japan
3) Oki Com-Echoes, Shizuoka, Japan
4) Dept. of Engineering, University of the Ryukyus, Okinawa, Japan
Summary

An Orthogonal Frequency Division Multiplexing (OFDM) based
wireless communication system has drawn wide attention for its
high transmission rate and high spectrum efficiency in not only
radio but also Underwater Acoustic (UWA) applications. Becauseof the narrow sub-carrier spacing of OFDM, orthogonality
between sub-carriers is easily affected by Doppler effect causedby the movement of transmitter or receiver. Previously, Doppler
compensation signal processing algorithm for Desired propagation
path was proposed. However, other Doppler shifts caused bydelayed Undesired signal arriving from different directions cannot
be perfectly compensated. Then Receiver Bit Error Rate (BER) is
degraded by Inter-Carrier-Interference (ICI) caused in the case ofMulti-path Doppler channel. To mitigate the ICI effect, a modified
Delay and Doppler Profiler (mDDP), which estimates not only
attenuation, relative delay and Doppler shift but also samplingclock shift of each multi-path component, is proposed. Based on
the outputs of mDDP, an ICI canceling multi-tap equalizer is also
proposed. Computer simulated performances of one-tap equalizer
with the conventional Time domain linear interpolated Channel
Transfer Function (CTF) estimator, multi-tap equalizer based on
mDDP are compared. According to the simulation results, BER
improvement has been observed. Especially, in the condition of
16QAM modulation, transmitting vessel speed of 6m/s, two-path
multipath channel with direct path and ocean surface reflection
path; more than one order of magnitude BER reduction has been
observed at CNR=30dB.

Keywords:

Underwater Acoustic Communication, OFDM,
Estimation, modified Delay and Doppler Profiler

I.

ChannelIntroduction

Underwater wireless communication is demanded formany applications such as surveillance of areas asharbors, ports and coastlines or monitoring of fishes andexcavation sites such as oil well, trenches and so on to
reduce cable cost or time consuming deploy [1]. In order
to increase data Bandwidth, Orthogonal Frequency
Division Multiplexing (OFDM) based wirelesscommunication system has drawn wide attention for its
high transmission rate and high spectrum efficiency evenin Underwater applications. The moving of equipment
Manuscript received July 5, 2023
Manuscript revised July 20, 2023
https://doi.org/10.22937/IJCSNS.2023.23.7.1

Fig. 1: UWA communication through Multi-path Doppler channel

and/or surface ship causes Doppler shift effect during
underwater wireless communication, so the receiver of
each side is necessary to have the signal processing for
Doppler shift compensation capabilities. Previously,
Doppler compensation signal processing algorithm for
Desired propagation path was proposed [2-4].
Fig.1 shows UWA communication scene with multipath propagation path. Because Desired path L1 anddelayed Undesired path L2 are different direction at
AUV receiver, different Doppler shifted arriving signals
are multiplexed. Even when L1 path Doppler effect iscompensated, the difference between L1 and L2 Doppler
still remain. Then Receiver Bit Error Rate (BER) is
degraded by Inter-Carrier-Interference (ICI) caused by
the difference. In the previous paper [5], Delay andDoppler Profiler (DDP), which estimates attenuation,
relative delay and Doppler shift of each multi-path
component, is used to estimate more accurate Channel
Transfer Function (CTF) [6-8].
In this paper, in order to mitigate the ICI, a modified
Delay and Doppler Profiler (mDDP), which estimates

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IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023

Table 1: UWA OFDM System Parameters

Parameters

Value

Sampling Frequency Fs

102.4kHzBand Width

8 kHz

Passband frequency

16 kHzFFT size

2048

OFDM symbol length T
Guard Interval lengthTg
Sub-carrier spacing

20.0 ms (2048 points)

Number of sub-carrier

161

Scattered pilot

81 every 2 OFDM
symbols

Continuous pilot

13

Carrier modulation

QPSK/16QAM/64QAM

5.0 ms (512 points)
50 Hz

not only attenuation, relative delay and Doppler shift but
also sampling clock shift of each multi-path component,
is proposed. Based on the outputs of mDDP, an ICI
canceling multi-tap equalizer is also proposed. In section
II, first, UWA OFDM Communication System is shown.
Then proposed mDDP method is explained. Computer
simulation results are shown in section III. Finally, in
section IV, conclusions will be given.

II. mDDP based ICI Canceling UWA OFDM
Communication system
UWA OFDM Communication system is basicallyextension of the system proposed in paper [3]. Detailsystem parameters are listed in Table I. The sub-carrier
spacing of OFDM is 50Hz, then effective OFDM symbol
duration is 20ms with 2048 points IFFT/FFT as
modulation/demodulation. To estimate Channel Transfer
Function (CTF), two kinds of pilot signals are inserted inTime-Frequency sub-carriers’ arrangement as shown in
Fig. 2. The blue circles for CTF estimation are scatteredpilots which is inserted every 2 row and every 2 columns.
The other yellow circles are continuous pilots for
tracking phase-change in time domain.
A)

Fig. 2: Time-Frequency structure of OFDM signal

than 16kHz of Passband frequency narrowband
approximation cannot be assumed. Then to compensate
Doppler effect, the length of received Baseband signal
needs to be shrunk to expanded. 1st dashed line block
named Resampled and De-rotated is the functions for
detecting shrink-expansion factors 𝛽𝛽1 for coarse and 𝛽𝛽2
for fine and signal resample and de-rotate. Detail
explanation can be found in [3]. 2nd dashed line block
named Phase shift compensation is the function for timedomain phase change detect and its compensation.
Fig.4 shows two cases of OFDM signal after 1st dashedline Shrink and Expansion processing. In Fig.4(a) of
Single-path case, the 1st row shows 3 OFDM symbols
with no movement and the 2nd row shows the case ofreceived signal that appears to be stretched by moving
reception. 3 descriptions in the rectangle box
corresponds to the function of 1st dashed line block. Afterthe 1st processing, the received OFDM signal is shrunk
to the same length of no move case. In Fig.4(b) case ofTime-domain pre-processing of Receiver

The upper side of Fig. 3 (before 3rd FFT) is the timedomain pre-processing block of the Receiver. Since
8kHz of OFDM signal bandwidth is not enough, smaller

Fig. 3: Receiver Block Diagram with ICI Canceling Equalizer

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023

(a) Single-path case(b) Case of Multi-path with different Doppler ShiftFig. 4: OFDM signal after the Shrink and Expansion processing

multi-path with different Doppler Shift, Delayed path #2
is added to Fig.4(a). Since expansion factor of path #2 isdifferent from that of path #1 by cos 𝜃𝜃, Delayed path #2
OFDM symbols shown in the bottom row does not matchwith that of no move case. Then the Delayed path #2
disrupts orthogonality between OFDM sub-carriers andInter-Carrier-Interference (ICI) between data subcarriers are introduced.
B)

ICI canceling by modified Delay and Doppler
Profiler

References [6-8] describes detail function of Delay andDoppler Profile (DDP) using pilot signals embedded in
OFDM sub-carriers. DDP estimates attenuation, relative
delay and Doppler shift of each multi-path component.

3

However, as explained in Fig.4(b), the Delayed Path #2
causes ICI by its remaining shrink or expansion. Then for
UWA system needs additional shrink or expansion
parameter of each multi-path component.
Consequently, modified DDP is proposed to estimate
not only attenuation, relative delay and Doppler shift but
also sampling clock shift of each multi-path component.
Fig. 5 is a block diagram of proposed mDDP. The upperside of the figure represents the Time-Frequency
structure of sub-carriers with time-domain symbol index
k. The mDDP estimates each Np multipath component
waves to receiver. Each analyzed component can becharacterized using four parameters such as Attenuation
𝑟𝑟𝑝𝑝 , Propagation Delay time 𝜏𝜏𝑝𝑝′ , normalized Doppler shift𝑓𝑓𝑓𝑓𝑝𝑝 and Sampling CLK error 𝛽𝛽𝑝𝑝 for wave component
index 𝑝𝑝 . Here the Attenuation 𝑟𝑟𝑝𝑝 is complex value
including amplitude attenuation and phase rotation and
Doppler shift is normalized by sub-carrier spacing f0
such as 𝛼𝛼𝑝𝑝 = 𝑓𝑓𝑓𝑓𝑝𝑝 /𝑓𝑓0 . Using the symbol k measured
CTF(k) and symbol k-2 measured CTF(k-2), mDDP
detects 𝑁𝑁𝑃𝑃 sets of those four parameters.
UWA OFDM baseband transmitting signal 𝑠𝑠𝐵𝐵 (𝑡𝑡) can be
expressed as (1).
∞𝑠𝑠𝐵𝐵 (𝑡𝑡) = � 𝑔𝑔(𝑡𝑡 − 𝑚𝑚𝑇𝑇𝑠𝑠 )
𝑚𝑚=−∞

𝑁𝑁−1

∙ � 𝑑𝑑(𝑚𝑚, 𝑛𝑛)𝑒𝑒 𝑗𝑗2𝜋𝜋𝜋𝜋𝑓𝑓0(𝑡𝑡−𝑚𝑚𝑇𝑇𝑠𝑠 ) ⋯ (1)𝑛𝑛=0𝑇𝑇𝑠𝑠 =

1+ 𝑇𝑇𝑔𝑔 ⋯ (2)𝑓𝑓0

1 −𝑇𝑇𝑔𝑔 ≦ 𝑡𝑡 < 1/𝑓𝑓0
𝑔𝑔(𝑡𝑡) = �⋯ (3)0𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

where, N is the number of sub-carriers, f0 is the sub-carrier
spacing, 𝑇𝑇𝑠𝑠 is symbol length as defined in (2), 𝑑𝑑(𝑚𝑚, 𝑛𝑛) is
data symbol of sub-carrier index n at the 𝑚𝑚𝑡𝑡ℎ OFDM
symbol. By assuming the transmission channel has 𝑁𝑁𝑃𝑃
delay paths, the received baseband signal can be written as
(4).
𝑁𝑁𝑃𝑃

𝑟𝑟𝐵𝐵 (𝑡𝑡) = � 𝑟𝑟𝑝𝑝 𝑠𝑠𝐵𝐵 �𝑡𝑡 − 𝜏𝜏𝑝𝑝 �𝑒𝑒 𝑗𝑗2𝜋𝜋∆𝑓𝑓𝑝𝑝(𝑡𝑡−𝜏𝜏𝑝𝑝) ⋯ (4)𝑝𝑝=1

where, 𝑟𝑟𝑝𝑝 , 𝜏𝜏𝑝𝑝 and ∆𝑓𝑓𝑝𝑝 are attenuation, relative delay andDoppler-shift of 𝑝𝑝𝑡𝑡ℎ path respectively.
Fig. 5: Modified Delay and Doppler Profiler

𝑡𝑡 =

𝑖𝑖
(1 + 𝛽𝛽) + 𝑘𝑘𝑇𝑇𝑠𝑠 (1 + 𝛽𝛽) ⋯ (5)
𝑁𝑁𝑓𝑓0

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IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023

After sampling of 𝑟𝑟𝐵𝐵 (𝑡𝑡) by using equation (5) withsampling index 𝑖𝑖 and OFDM symbol number 𝑘𝑘, the blockof samples is de-modulated by DFT to generate data symbol𝑑𝑑̂ (𝑘𝑘, 𝑙𝑙) as expressed in (6).
𝑑𝑑̂ (𝑘𝑘, 𝑙𝑙) = ℎ(𝑘𝑘, 𝑙𝑙, 𝑙𝑙)𝑑𝑑(𝑘𝑘. 𝑙𝑙)
𝑁𝑁−1+ � ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛)𝑑𝑑(𝑘𝑘. 𝑛𝑛) + 𝑤𝑤(𝑘𝑘, 𝑙𝑙) ⋯ (6)
𝑛𝑛=0
𝑛𝑛≠𝑙𝑙

where 𝑤𝑤(𝑘𝑘, 𝑙𝑙) is additive noise that corresponds to the 𝑙𝑙 𝑡𝑡ℎsub-carrier in the 𝑘𝑘 𝑡𝑡ℎ OFDM symbol and ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) is thetransfer function from symbol 𝑑𝑑(𝑘𝑘, 𝑛𝑛) to the 𝑙𝑙 𝑡𝑡ℎ sub-carrier.
If 𝑛𝑛 ≠ 𝑙𝑙, ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) represents the influence of ICI. ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛)
can be expressed as (7), (8a) and (8b).

where 𝑓𝑓(𝛼𝛼1 , 𝛽𝛽1 , 𝑙𝑙) is written as (11)𝑓𝑓(𝛼𝛼1 , 𝛽𝛽1 , 𝑙𝑙) =∙ 𝑒𝑒 𝑗𝑗

𝑟𝑟1 =′
2𝜋𝜋�𝑛𝑛+𝛼𝛼𝑝𝑝 �𝜏𝜏𝑝𝑝
2𝜋𝜋𝜋𝜋(𝑁𝑁+𝐺𝐺𝐺𝐺)�𝛼𝛼𝑝𝑝 +𝑛𝑛𝛽𝛽𝑝𝑝 �𝑁𝑁𝑁𝑁∙ 𝑒𝑒 𝑗𝑗⋯ (8𝑎𝑎)∙ 𝑒𝑒
𝐴𝐴 = 𝑛𝑛 − 𝑙𝑙 + 𝑛𝑛𝛽𝛽𝑝𝑝 + 𝛼𝛼𝑝𝑝 (1 + 𝛽𝛽𝑝𝑝 )≅ 𝑛𝑛 − 𝑙𝑙 + 𝑛𝑛𝛽𝛽𝑝𝑝 + 𝛼𝛼𝑝𝑝 ⋯ (8𝑏𝑏)where 𝛼𝛼𝑝𝑝 = ∆𝑓𝑓𝑝𝑝 /𝑓𝑓0 is normalized frequency offset of 𝑝𝑝𝑡𝑡ℎpath.
The parameters of channel transfer function ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) are
estimated so as to minimize the mean square error shown in
(9).

𝑙𝑙=𝑷𝑷

2
2

𝑥𝑥(𝑘𝑘 − 2, 𝑙𝑙)+�− ℎ(𝑘𝑘 − 2, 𝑙𝑙, 𝑙𝑙)� � ⋯ (9)𝑑𝑑(𝑘𝑘 − 2, 𝑙𝑙)

where Σ𝑙𝑙=𝑷𝑷 means that the summation is performed as longas 𝑙𝑙 is scattered pilot symbol.
In order to simplify the problem, it is supposed that thechannel model contains one path at the first. In this case,criterion is rewritten as (10).
𝐸𝐸1 (𝑘𝑘)

2𝜋𝜋(𝑙𝑙+𝛼𝛼1 )𝜏𝜏1′𝑁𝑁�= � ��𝐶𝐶𝐶𝐶𝐶𝐶(𝑘𝑘, 𝑙𝑙) − 𝑓𝑓(𝛼𝛼1 , 𝛽𝛽1 , 𝑙𝑙)𝑟𝑟1 ∙ 𝑒𝑒 −𝑗𝑗

2

𝑙𝑙=𝑷𝑷

+ �𝐶𝐶𝐶𝐶𝐶𝐶(𝑘𝑘 − 2, 𝑙𝑙)− 𝑓𝑓(𝛼𝛼1 , 𝛽𝛽1 , 𝑙𝑙)𝑟𝑟1 ∙ 𝑒𝑒 −𝑗𝑗

2 ∙ 𝑒𝑒−𝑗𝑗

2𝜋𝜋2(𝑁𝑁+𝐺𝐺𝐺𝐺)𝛼𝛼1∗
𝑁𝑁
𝑆𝑆𝑘𝑘−22𝜋𝜋𝛼𝛼1 𝜏𝜏1′
𝑁𝑁
∑𝑙𝑙=𝑷𝑷|𝑓𝑓(𝛼𝛼1 , 𝛽𝛽1 , 𝑙𝑙)|2

𝑙𝑙=𝑷𝑷

𝑝𝑝=1

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝐴𝐴) 𝑗𝑗𝜋𝜋(𝑁𝑁−1)𝐴𝐴𝑁𝑁∙ 𝑒𝑒∙ 𝑟𝑟𝑝𝑝ℎ𝑝𝑝 (𝑘𝑘, 𝑙𝑙, 𝑛𝑛) =𝐴𝐴
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � �𝑁𝑁𝑥𝑥(𝑘𝑘, 𝑙𝑙)− ℎ(𝑘𝑘, 𝑙𝑙, 𝑙𝑙)�𝑑𝑑(𝑘𝑘, 𝑙𝑙)

𝑆𝑆𝑘𝑘∗ +∙ 𝑒𝑒 𝑗𝑗⋯ (12𝑎𝑎)2𝜋𝜋𝜋𝜋𝜏𝜏1′

𝑆𝑆𝑘𝑘 = � 𝐶𝐶𝐶𝐶𝐶𝐶 ∗ (𝑘𝑘, 𝑙𝑙)𝑓𝑓(𝛼𝛼1 , 𝛽𝛽1 , 𝑙𝑙) 𝑒𝑒 −𝑗𝑗 𝑁𝑁ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) = � ℎ𝑝𝑝 (𝑘𝑘, 𝑙𝑙, 𝑛𝑛) ⋯ (7)𝐸𝐸(𝑘𝑘) = � ��

2𝜋𝜋𝜋𝜋(𝑁𝑁+𝐺𝐺𝐺𝐺)(𝛼𝛼1 +𝑛𝑛𝛽𝛽1 )𝑁𝑁⋯ (11)

One of the necessary conditions to minimize 𝐸𝐸1 (𝑘𝑘) withregard to 𝑟𝑟1 , 𝜏𝜏1′ (relative delay time in sampling points) and
𝛼𝛼1 is that its partial derivative of 𝑟𝑟1 has zero value. With thiscondition, 𝑟𝑟1 can be shown as (12a) and (12b).

𝑁𝑁𝑃𝑃

−𝑗𝑗

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑙𝑙𝛽𝛽1 + 𝛼𝛼1 ) 𝑗𝑗𝜋𝜋(𝑁𝑁−1)(𝑙𝑙𝛽𝛽1+𝛼𝛼1)𝑁𝑁∙ 𝑒𝑒𝑙𝑙𝛽𝛽 + 𝛼𝛼1
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � 1�𝑁𝑁22𝜋𝜋�𝑙𝑙+𝛼𝛼𝑝𝑝 �𝜏𝜏1′−2𝜋𝜋2(𝑁𝑁+𝐺𝐺𝐺𝐺)(𝛼𝛼1 +𝑙𝑙𝛽𝛽1 )𝑁𝑁𝑁𝑁∙ 𝑒𝑒 𝑗𝑗� � ⋯ (10)∙ 𝑒𝑒 𝑗𝑗

2𝜋𝜋(𝑘𝑘)(𝑁𝑁+𝐺𝐺𝐺𝐺)𝑙𝑙𝛽𝛽1
𝑁𝑁⋯ (12𝑏𝑏)

By calculate more as shown in reference [6-8], 𝛼𝛼1 iscalculated from 𝜏𝜏1′ as (13).
𝛼𝛼1=1ℑ(𝑆𝑆𝑘𝑘∗ ∙ 𝑆𝑆𝑘𝑘−2 )𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �� ⋯ (13)2𝜋𝜋2(𝑁𝑁 + 𝐺𝐺𝐺𝐺)(1 + 𝛽𝛽1 )ℜ(𝑆𝑆𝑘𝑘∗ ∙ 𝑆𝑆𝑘𝑘−2 )𝑁𝑁

Consequently, once 𝜏𝜏1′ is determined, 𝑟𝑟1 and 𝛼𝛼1 are easily
obtained from (12a) and (13), respectively. In this proposed
method, 𝜏𝜏1′ is changed by 1/(2𝑁𝑁𝑓𝑓0 ) (twice of sampling
frequency) and rough estimation is first obtained. And thisrough estimation is modified to more precise value using
Newton method as described in references [6-8].
According to the computation above, ℎ1 (𝑘𝑘, 𝑙𝑙, 𝑛𝑛) can beobtained using equations (8a) and (8b). Then, measured
𝐶𝐶𝐶𝐶𝐶𝐶(𝑘𝑘, 𝑙𝑙) and 𝐶𝐶𝐶𝐶𝐶𝐶(𝑘𝑘 − 2, 𝑙𝑙) are updated to 𝐶𝐶𝐶𝐶𝐶𝐶(2, 𝑘𝑘, 𝑙𝑙)
and 𝐶𝐶𝐶𝐶𝐶𝐶(2, 𝑘𝑘 − 2, 𝑙𝑙) by subtracting ℎ1 (𝑘𝑘, 𝑙𝑙, 𝑛𝑛) and ℎ1 (𝑘𝑘 −2, 𝑙𝑙, 𝑛𝑛) respectively. By removing the influence of the firstestimated path from the cost function𝐸𝐸1 (𝑘𝑘), the following
criterion 𝐸𝐸2 (𝑘𝑘) can be obtained such as (14).
𝐸𝐸2 (𝑘𝑘)= � ��𝐶𝐶𝐶𝐶𝐶𝐶(2, 𝑘𝑘, 𝑙𝑙) − 𝑓𝑓(𝛼𝛼2 , 𝛽𝛽2 , 𝑙𝑙)𝑟𝑟2 ∙ 𝑒𝑒𝑙𝑙=𝑷𝑷

+ �𝐶𝐶𝐶𝐶𝐶𝐶(2, 𝑘𝑘 − 2, 𝑙𝑙)− 𝑓𝑓(𝛼𝛼2 , 𝛽𝛽2 , 𝑙𝑙)𝑟𝑟2 ∙ 𝑒𝑒 −𝑗𝑗−𝑗𝑗

2𝜋𝜋(𝑙𝑙+𝛼𝛼1 )𝜏𝜏2′
𝑁𝑁
�

2

2
2𝜋𝜋(𝑙𝑙+𝛼𝛼2 )𝜏𝜏2′−2𝜋𝜋2(𝑁𝑁+𝐺𝐺𝐺𝐺)(𝛼𝛼2 +𝑙𝑙𝛽𝛽2 )𝑁𝑁𝑁𝑁∙ 𝑒𝑒 𝑗𝑗� � ⋯ (14)

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023
Since 𝐸𝐸2 (𝑘𝑘) contains the influence of other paths, thesecond path can be estimated using the same procedure in
the previous section. By repeating this operation by the
number of paths in the channel model, 𝑁𝑁𝑝𝑝 sets of those fourparameters can be obtained as shown in Fig. 5.
After all, complete channel transfer function ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) canbe generated. Since most energy of ICI is concentrated in
the neighborhood of sub-carrier index, the ICI terms which
do not significantly affect 𝑑𝑑̂ (𝑘𝑘, 𝑙𝑙) in (6) can be neglected
and it is assumed as (15).
ℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) = 0 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 |𝑙𝑙 − 𝑛𝑛| >𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 − 1⋯ (15)
2

Transmitting transducer of depth C=2m moves x-axis
direction with speed of v(m/s). Receiving transducer islocated at the depth of B=20m. More detail simulation
parameters are summarized in Table 2.
Fig.6 shows delay time between Direct path L1 andReflection path L2 path and each Doppler velocity,which is effective direction-oriented velocity observed atreceiver, for v=6m/s with 401OFDM symbol simulation.
The delay time is roughly 1.4 to 2.1ms. Direct path
Doppler velocity is slightly larger than it of Reflection
path. Fig.7 shows the changes in time direction of realcomponent of 16QAM constellation and BER. Fig.7(a)where, 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 is the number of neighborhood subcarrier taken into account against 𝑙𝑙 𝑡𝑡ℎ sub-carrier. By
considering the reverse operation of the ICI effect byℎ(𝑘𝑘, 𝑙𝑙, 𝑛𝑛) , Multi-Tap ICI Canceling Equalizer has been
implemented as shown in Fig. 3. as a Fixed Impulse
Response Filter.

III. Computer Simulations
In order to verify the proposed mDDP based ICI
canceling, Fig.1 situation is modeled by Matlab.
(a) Conventional interpolator CTF equalizer
Table 2: Simulation Parameters

Parameters

Value

Vessel starting position

A=30m

RX transducer depth

B=20m

TX transducer depth
TX-RX minimum
horizontal distance
Vessel Speed
Desired(L1)
Undesired(L2) Ratio

C=2m
Offset=15m
v= 6, 3 m/s
6dB(b) mDDP with NumCOL=1 (No ICI Cancel)(c) mDDP with NumCOL=11 (ICI Cancel)
Fig. 6: Multi-path delay and Doppler velocities

5

Fig. 7: Constellation (Real) and BER dependence on time

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IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023(a) v=6m/s(a) v=3m/s(b) v=3m/s(b) v=3m/s

Fig. 8: BER vs CNR (dB) for 16QAM modulation

Fig. 9: BER vs CNR (dB) for 64QAM modulation

corresponds to the case of conventional linear
interpolated CTF and one-tap equalizer. mDDP with
NumCOL=1 means that CTF is estimated by mDDP but
ICI cancel is not used as shown in Fig.7(b). Fig.7(c)shows the case of ICI canceling by NumCOL=11 multitap equalizer with mDDP. Obviously, BER is drastically
improved by introducing mDDP and ICI canceling.
Fig.8 shows BER vs CNR(dB) for 16QAM with
v=6m/s and 3m/s. Number of OFDM symbols used in thesimulation are 201 and 401, which means the vessel
moves from x= -30m to 0m. For v=6m/s, ICI cancelingwith 11 tap (NumCOL=11) effectively decrease BERs.
However, larger NumCOL of 21 or 31 is not effective.
For lower speed of v=3m/s, mDDP channel estimation
without ICI cancel shows large BER reduction comparewith conventional. Fig.9 and 10 show the same cases for
64QAM and QPSK modulation. For 64QAM, similareffectiveness of mDDP with ICI cancel is observed. For
QPSK, only mDDP effectiveness is observed because of
relatively low BER situation.

IV. Conclusion
modified Delay and Doppler Profiler (mDDP), which
estimates not only attenuation, relative delay andDoppler shift but also sampling clock shift of each multipath component, is proposed. Based on the outputs of
mDDP, an ICI canceling multi-tap equalizer is also
proposed. Computer simulated performances of one-tap
equalizer with the conventional Time domain linear
interpolated Channel Transfer Function (CTF) estimator,
multi-tap equalizer based on mDDP are compared.

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023(a) v=6m/s(b) v=3m/s
Fig. 10: BER vs CNR (dB) for QPSK modulation

According to the simulation results, BER improvement
has been observed. Especially, in the condition of
16QAM modulation, transmitting vessel speed of 6m/s,
two-path multipath channel with direct path and ocean
surface reflection path; more than one order ofmagnitude BER reduction has been observed at
CNR=30dB.

References[1] J. Heidemann, M. Stojanovic, and M. Zorzi,“Underwater sensor networks: Application,
advances and challenges, ”
PhilosophicalTransactions of the Royal Society A, vol. 370, pp.
158-175, Aug 2012.
[2] Taisaku Suzuki, Tomohisa Wada, Hiromasa
Yamada, Shigeo Nakagawa, “An Underwater
Acoustic OFDM Communication System with

7

RobustDoppler
Compensation,”
IJICSNSInternational Journal of Computer Science andNetwork Security, VOL.17, No.9, September 2017.
[3] Mohammad Ariful Hoq, Shiho Oshiro andTomohisa Wada, "Two steps Doppler compensation
Algorithm from moving AUV to AUV/Mother Shipfor OFDM-based UWA communication system,"International Journal of Computer Science andNetwork Security, VOL.20 No.12, 272-278.
[4] Shiho Oshiro, Yukiko Muller, Hiromasa Yamada
and Tomohisa Wada, “An UWA OFDM
Communication System with Improved Doppler
compensation and Initial Synchronization,”
MTS/IEEE OCEANS 2022 Hampton Roads
Virginia Beach Convention Center In-Person &Virtual: October 17-20, 2022.
[5] Shiho Oshiro, and Tomohisa Wada, “Channel
Transfer Function estimation based on Delay andDoppler Profile for underwater acoustic OFDM
communication system,“ IJICSNS International
Journal of Computer Science and Network Security,
VOL.23, No.1, January 2023.
[6] Mitsuru Nakamura, Makoto Itami, Kohji Itoh and
Hamid Aghvami, “ICI Cancellation Techniquebased on Estimating Delay and Doppler Profile in
OFDM Reception,” The Institute of Image
Information and Television Engineers, Vol. 56, No.
12, pp.1951-1958 (2002).
[7] Mitsuru Nakamura, Masahiro Fujii, Makoto Itami
and Kohji Itoh, “MMSE ICI Canceller for OFDM
Mobile Reception,” The Institute of Image
Information and Television Engineers, Vol. 58, No.
1, pp.83-90 (2004).
[8] Akito Yamazaki, Mitsuru Nakamura, Masahiro Fujii,
Makoto Itami, Kohji Itoh and Hiroki Ohta, “A Studyon Improving Performance of an OFDM ICI
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Catherine Akioya is from Benin City,
Edo State Nigeria. She received her
BSc Degree in Computer Engineeringfrom Benson Idahosa University,
Benin city, Edo State Nigeria in 2007.
She joined Vovida Communications,
Lagos in 2022, which prompted herinterest in wireless communicationand decided to join prolific Prof Wada laboratory tounderstudy and engage in his research on Underwater
OFDM Acoustic wireless communication system. She iscurrently a Master’s Student at the Graduate School of

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IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.7, July 2023

Engineering and Science at the university of Ryukyus since
2021.
Shiho Oshiro
received the
B.E. and M.E. degrees, from the
University of the Ryukyus, Okinawa,
Japan in 2018 and 2020, respectively.
She received the Dr. Eng. degree from
University of the Ryukyus in 2023.
She has been an assistant professor at
University of the Ryukyus since 2023.
She has experienced short-term study
abroad at Madan Mohan Malaviya University ofTechnology (MMMUT) Gorakhpur and Atal Bihari
Vajpayee-Indian Institute of Information Technology andManagement (ABV-IIITM) Gwalior in India, Institute ofTechnology of Cambodia (ITC) in Cambodia, and National
Taiwan University of Science and Technology (TaiwanTech). Her research interest includes Underwater OFDM
Acoustic communication systems, developed Underwater
Acoustic OFDM wireless communication systems,
Underwater Acoustic Positioning systems targeting for
Underwater Drone controls, Flight Control for Underwater
Drone automatically controls, and Autoencoder for OFDM
communication system.
Tomohisa Wada
was born inJapan on December 2, 1959. Hereceived B.S. degree in electronicengineering from Osaka University,
Osaka, Japan, in 1983, M.S.E.E.
degree from Stanford University,
Stanford CA, in 1992, and Ph.D. inelectronic engineering from Osaka
University. in 1994. He joined the
ULSI Laboratory, Mitsubishi Electric Corp. Japan in 1983
and engaged in the research and develop-ment of VLSI such
as High-speed Static Random-access memories, Cachememories for Intel MPUs in 16 years. Since 2001, he has
been a Professor at the Department of Information
Engineering, the University of the Ryukyus, Okinawa,
Japan. In 2001, He was the founding member of Magna
Design Net, Inc., which is a fab-less LSI design Company
for communication related digital signal processing such as
OFDM. Currently, he is also the chief scientist of Magna
Design Net, Inc. who is engaging in the research anddevelopment of a terrestrial video broadcasting receiver, awireless LAN, WiMAX, 4G-LTE and 5G systems. After
2009, he also started Underwater OFDM Acoustic
communication systems and developed Underwater
Acoustic OFDM wireless communication systems andUnderwater Acoustic Positioning systems targeting for
Underwater Drone controls.