IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

8

Delay and Doppler Profiler based Channel Transfer Function estimationfor 2x2 MIMO Receivers in 5G system targeting a 500km/h linear motor car
Suguru Kuniyoshi1), Rie Saotome1), Shiho Oshiro2) and Tomohisa Wada3)
1) Magna Design Net Inc., 3-1-15 Maejima, Naha-shi, Okinawa, Japan
2) Information Technology Center, University of the Ryukyus, Okinawa, Japan
3) Dept. of Engineering, University of the Ryukyus, Senbaru 1, Nishihara, Okinawa, Japan
Summary
In Japan, high-speed ground transportation service using linear
motors at speeds of 500 km/h is scheduled to begin in 2027. To
accommodate 5G services in trains, a subcarrier spacing frequencyof 30 kHz will be used instead of the typical 15 kHz subcarrier
spacing to mitigate Doppler effects in such high-speed transport.
Furthermore, to increase the cell size of the 5G mobile system,
multiple base station antennas will transmit identical downlink(DL) signals to form an expanded cell size along the train rails. In
this situation, the forward and backward antenna signals are
Doppler-shifted in opposite directions, respectively, so thereceiver in the train may suffer from estimating the exact Channel
Transfer Function (CTF) for demodulation.
In a previously published paper, we proposed a channel
estimator based on Delay and Doppler Profiler (DDP) in a 5G
SISO (Single Input Single Output) environment and successfully
implemented it in a signal processing simulation system. In thispaper, we extend it to 2x2 MIMO (Multiple Input Multiple Output)
with spatial multiplexing environment and confirm that the delay
and DDP based channel estimator is also effective in 2x2 MIMO
environment. Its simulation performance is compared with that ofa conventional time-domain linear interpolation estimator. The
simulation results show that in a 2x2 MIMO environment, theconventional channel estimator can barely achieve QPSK
modulation at speeds below 100 km/h and has poor CNR
performance versus SISO. The performance degradation of CNR
against DDP SISO is only 6dB to 7dB. And even under severe
channel conditions such as 500km/h and 8-path inverse Doppler
shift environment, the error rate can be reduced by combining theerror with LDPC to reduce the error rate and improve theperformance in 2x2 MIMO. QPSK modulation scheme in 2x2
MIMO can be used under severe channel conditions such as 500
km/h and 8-path inverse Doppler shift environment.

Key words:
5G, 5th Generation Mobile Communication System, MIMO,
Multiple Input Multiple Output, Channel estimation, Delay andDoppler profiler

I.

Introduction

A 500 km/h linear motor high speed terrestrial
transportation service is planned to launch 2027 between
Tokyo and Nagoya in Japan. The maximum speed ofcurrent high speed train Shinkansen is 300 km/h. However,the coming linear motor train’s speed will be 500 km/h byManuscript received September 5, 2023
Manuscript revised September 20, 2023
https://doi.org/10.22937/IJCSNS.2023.23.9.2

Fig. 1: Reception environment of revised Doppler shifted signals by
combining signals originating from two base stations in a single
frequency network with MIMO channels in the high-speed train

using magnetic levitation mechanism. In order to support
5G service in the train, 5G will use some different
configurations. First, increased sub-carrier spacing f0 of 30
kHz is used instead of conventional 15 kHz to mitigate
Doppler frequency shift. This change automaticallyshortens OFDM symbol length by half. Consequently,
channel state change tracking performance will increase.
Second, to increase mobile service cell size, plural Base
Station antennas transmit the identical Downlink (DL)signal to form the expanded cell size along the train rail. In
this situation, forward and backward antenna signals will be
Doppler shifted by reverse directions respectively and thereceiver in the train might suffer to estimate accurate
Channel Transfer Function (CTF) for demodulation. Fig. 1
shows the situation of two DL signals reception in the car.
Approaching TX1 antenna signal is +fd shifted andbackward TX2 signal is -fd shifted. In a MIMO system,
spatial multiplexing is performed using two or moretransmit antennas at the base station. In order to separate thespatially multiplexed signals, two or more antennas of thereceiving equipment are also required. In the previous paper[1], the effectiveness of the channel estimation scheme
using the Delay and Doppler Profiler (DDP) algorithm wasdemonstrated by computer simulations in an environmentIJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023
limited to the SISO (Single Input Single Output)
propagation path. In this paper, we applied the channel
estimation using the DDP algorithm to 2x2 MIMO withspatial multiplexing in order to achieve higher transmission
data rate, and build a simulation model. In section II, first,
targeting 5G Mobile Communication System is briefly
shown. Then the proposed DDP method is explained.
Computer simulation results are shown in section III.
Finally, in section IV, the conclusions will be given.

II. 5G Mobile Communication
MIMO Architecture

System

5th Generation Mobile Communication System [2] is
OFDM communication system standard developed as the
successor to the 4G-LTE (4th Generation Long term
evolution) system with various enhancements. For example,
the sub-carrier spacing was fixed as 15kHz in 4G-LTE but
in 5G variable sub-carrier spacing is supported such as 15 /30 / 60 / 120 / 240 kHz. For the application of the linear
motor train, 30 kHz sub-carrier frequency will be used for
RF Carrier of 3.9 GHz Band. Table I summaries the 5G
system parameters for this application. To support eMBB
(enhanced Mobile Broadband), 100MHz bandwidth isassumed with 3276 sub-carriers. Because of sub-carrier
spacing f0 of 30 kHz, OFDM symbol length T of 33.33us(4096 sampling points) is used.
Fig. 2 shows the 5G frame structure when f0 is 30 kHz.
This structure is a Frequency Range 1 frame structure,commonly referred to as Sub6, which is used when thecenter frequency is below 6 GHz. 1 frame length is 10 ms
and divided into 20 Slots. In one Slot, 14 OFDM symbols
are embedded. Cyclic prefix (CP) length is 288 sampling
points for each 4096 points OFDM symbols except the 1st
CP. The length of the 1st CP is a little expanded such as 352
points. In 5G system, Demodulation Reference Signals(DMRS) are inserted to some Sub-carriers to measure CTF
and the DMRS can be placed with a high degree of freedom
according to the system configuration. This time, DMRS isasserted in S3, S6, S9, S12 OFDM symbols to detect rapidly
time-domain changing CTF [3].
Time-Frequency structure of this 5G system is shownin Fig. 3. Since 12 sub-carriers and 14 OFDM symbols
constitute one Common Resource Block (CRB), the total
3276 sub-carriers correspond to 273 CRBs. The detail of
sub-carrier arrangement in a CRB is also shown in the
figure. For frequency direction (vertically), DMRS for Tx
Antenna 1 are placed every 2 sub-carriers as shown in the
odd number places. Similarly, DMRS for Tx Antenna 2 areplaced every 2 sub-carriers as shown in the even number
places.

Table 1: 5th Generation Mobile Communication System Parameters

Parameters

Value

System Band Width

100 MHz

Sub-carrier Spacing (f0)30 kHzPass Band Frequency

3.9 GHz

OFDM symbol length (T)33.33 us (4096 points)

Number of Common
Resource Blok (CRB)

273

Number of Sub-carriers

3276

Sampling Frequency (Fs)

122.88 Msps

FFT size

4096

CP length352 or 288 points

Fig. 2: 5G Frame and Slot structure

Fig. 3: Time and Frequency structure of 5G System for 2x2 MIMO

9

10IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

A) Physical layer of 5G communication MIMO system
Fig. 4 shows the block diagram of the Physical Layer(PHY) for 5G 2x2 MIMO (Multiple Input Multiple Output)
system. The upper side is the transmitter and the lower sideis the receiver. The Bit data supplied from the upper MAC(Media Access Control), protocol and application layers are
digitally modulated into QPSK / 16QAM / 64QAM /256QAM at the Antenna mapper, and the modulated
symbols are then split as different streams at each of the twotransmit antennas as shown in Fig. 4. Then the modulated
symbols and DMRS pilot signals for each Tx antennas
configured Slots as shown in Fig. 3. Then Inverse 4096
points Fourier Transform (IFFT) is performed as OFDM
modulation and CP is appended for each Tx antenna. Thissignal is Baseband (BB) signals. Up-conversion is applied
to the BB signal to generate passband signals, which areradiated through a power amplifiers and antennas for eachstream. In this paper, 2x2 MIMO refers to spatial
multiplexing MIMO unless otherwise specified. Thus, 2x2
MIMO has twice the transmission capacity compared to
SISO.
The receiver side basically performs basically thereverse process of the transmitter side. However, since thereceiving signal is distorted through the propagation
channel, CTF, which is a Frequency domain representationof Channel Impulse Response in Time domain, has to be
estimated and the distortion has to be compensated at
Equalizer using the estimated CTF. In addition, signals
transmitted separately at the transmitter end arrive at thereceiver end after being mixed together on the propagation
channel. Therefore, the CTF must be calculated for fourpaths in 2x2 MIMO environment, compared to the amountof CTF calculations required in SISO environment, whichquadruples the amount of calculations required to find theCTF.
Conventional 5G receivers interpolate CTF values
measured at DMRS locations in the frequency and time
domains to obtain CTFs for all subcarrier locations; in a
MIMO environment, channel estimation needs to be moreaccurate than in a SISO environment. To improve CTF
estimation, this paper applies the DDP to 2x2 MIMO withspatial multiplexing environment to study CTF generation
method that is more accurate than conventional CTF
estimation methods.

B)

Fig. 4: Physical layer of 5G communication system for 2x2 MIMO

Fig. 5: Delay and Doppler Profiler based CTF estimator for 2x2 MIMO

Improved Channel Transfer Function estimation
based on Delay and Doppler Profile for 2x2 MIMO

References [4-6] describe detail methods of Delayand Doppler Profile (DDP) based CTF estimation using
pilot signals embedded in OFDM sub-carriers. Fig. 5 is a
block diagram of proposed DDP CTF generation. The upperside of the figure represents the Time-Frequency structureof sub-carriers with time-domain symbol index 𝑘. The DDP

Fig. 6: Basic representation of 2x2 MIMO system

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023
estimates each 𝑁 , multipath component waves to receiving
each antenna. Each analyzed component can becharacterized using three parameters such as Attenuation𝑟 , Propagation Delay time 𝜏 , and normalized Doppler
shift 𝛼 with transmit antenna number 𝑥, receive antenna
number 𝑦 , and wave component index 𝑖 . Here theis complex value including amplitudeAttenuation 𝑟
attenuation and phase rotation and the normalized Doppler
shift is normalized by sub-carrier spacing 𝑓 such as 𝛼𝑓𝑑 /𝑓 . Using the symbol k measured 𝐶𝑇𝐹 𝑘 andsymbol 𝑘 3 measured 𝐶𝑇𝐹 𝑘 3 , the DDP detects
𝑁 sets of those three parameters.
5G baseband transmitting for 2x2 MIMO signals
𝑠 𝑡 and 𝑠 𝑡 can be expressed as Equations (1a) and(1b). As shown in Fig. 4, 𝑠 𝑡 represents the signal fromtransmitting antenna number 1, and 𝑠 𝑡 represents thesignal from transmitting antenna number 2.
𝑠

𝑡

𝑔 𝑡

𝑚𝑇 ∙

𝑑 𝑚, 𝑛 𝑒

⋯ 1𝑎

𝑠

𝑡

𝑔 𝑡

𝑚𝑇 ∙

𝑑 𝑚, 𝑛 𝑒

⋯ 1𝑏

𝑔 𝑡

𝑇

1
𝑓

1
0

𝑇 ≦ 𝑡 1/𝑓
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒𝑇⋯ 2

where, 𝑁 is the number of sub-carriers, 𝑓 is the sub-carrier
spacing, 𝑇 is symbol length as defined in equation (2),𝑑 𝑚, 𝑛 and 𝑑 𝑚, 𝑛 are data symbols of sub-carrier
index n at the 𝑚 OFDM symbol. By assuming thetransmission channel has 𝑁 delay paths, the received
baseband signals can be written as Equations (4a) and (4b).
𝑟

𝑡

𝑟

𝑠

𝑡

𝜏
𝑟

𝑟

𝑡

𝑟

𝑠

𝑡

∆

𝑒

𝜏

𝑠

𝑡

𝜏

𝑒

∆

⋯ 4𝑎

𝑡

𝜏

𝑒

∆

⋯ 4𝑏

∆

𝑒

block of samples is de-modulated by DFT to generate data
symbol 𝑑 𝑘, 𝑙 and l 𝑑 𝑘, 𝑙 as expressed in Equations(6a) and (6b).
𝑑 𝑘, 𝑙𝑡𝑠𝑖𝑁𝑓𝑘𝑇 ⋯ 5where, 𝑟 , 𝜏and ∆𝑓 are attenuation, relative delay
and Doppler-shift of 𝑝 path when the signal from transmit
antenna #𝑥 is received at receive antenna #𝑦, respectively.
After sampling of 𝑟 𝑡 and 𝑟 𝑡 by using Equation (5)with sampling index 𝑖 and OFDM symbol number 𝑘, the𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙

𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙

ℎ

ℎ

ℎ

ℎ

⋯ 6𝑎

𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙ℎ𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙ℎ𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛

𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛𝑤 𝑘, 𝑙𝑤 𝑘, 𝑙𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛

𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛

⋯ 6𝑏where 𝑤 𝑘, 𝑙 and 𝑤 𝑘, 𝑙 are additive noise that
corresponds to the 𝑙 sub-carrier in the 𝑘 OFDM symbol
and ℎ 𝑘, 𝑙, 𝑛 is the channel transfer function fromsymbol 𝑑 𝑘, 𝑛 and 𝑑 𝑘, 𝑛 to the 𝑙 sub-carrier. If 𝑛𝑙, ℎ 𝑘, 𝑙, 𝑛 represents the influence of ICI (Inter Carrier
Interference). ℎ 𝑘, 𝑙, 𝑛 can be expressed as Equations (7),(8a) and (8b).
𝑘, 𝑙, 𝑛ℎ𝑘, 𝑙, 𝑛⋯ 7

𝜋 𝑁 1 𝐴𝑠𝑖𝑛𝑐 𝐴
𝑗
∙𝑒 𝑁
𝐴
𝑠𝑖𝑛𝑐
𝑁

ℎ𝑦𝑥𝑝 𝑘, 𝑙, 𝑛

∙ 𝑟𝑦𝑥𝑝 ∙ 𝑒

2𝜋 𝑛 𝛼𝑦𝑥𝑝 𝜏′𝑦𝑥𝑝
2𝜋𝑘 𝑁 𝐺𝐼 𝛼𝑦𝑥𝑝
𝑗
𝑗
𝑁
𝑁
∙𝑒

𝐴

𝑙

𝑛

⋯ 8𝑎

⋯ 8𝑏

𝛼

where 𝛼∆𝑓 /𝑓 is normalized frequency offset of𝑝 path when the signal from transmit antenna number 𝑥
is received at receive antenna number 𝑦, respectively.
The parameters of channel transfer function ℎ 𝑘, 𝑙, 𝑛
are estimated so as to minimize the mean square error
shown in Equation (9).
𝐸

𝑟

ℎ

ℎ

ℎ

⋯ 3

11

𝑘

𝐶𝑇𝐹

𝑘, 𝑙

ℎ

𝑘, 𝑙, 𝑙

𝑷

𝐶𝑇𝐹

𝑘

3, 𝑙

ℎ

𝑘

3, 𝑙, 𝑙⋯ 9where Σ 𝑷 means that the summation is performed as longas 𝑙 is DMRS pilot symbol.
In order to simplify the problem, it is supposed thatthe channel model contains one path at the first. In this case,criterion is rewritten as Equation (10).

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

12
𝐸

𝐸

𝑘
𝐶𝑇𝐹

𝑘, 𝑙

𝑓 𝛼

𝑟

𝑘
𝐶𝑇𝐹

2, 𝑘, 𝑙

𝐶𝑇𝐹

2, 𝑘

3, 𝑙

𝑓 𝛼

𝑟

∙𝑒

𝑷

𝐶𝑇𝐹

𝑘

3, 𝑙

𝑓 𝛼

𝑟

∙𝑒

here, 𝑓 𝛼

∙𝑒

⋯ 10

is written as Equation (11).
𝑠𝑖𝑛𝑐 𝛼
𝛼
𝑁

𝑓 𝛼

∙𝑒

𝑠𝑖𝑛𝑐

∙𝑒

⋯ 11

One of the necessary conditions to minimize 𝐸
𝑘 with(relative delay time in sampling points)
regard to 𝑟 , 𝜏
is that its partial derivative of 𝑟 has zero value.
and 𝛼With this condition, 𝑟 can be shown as Equations (12a)and (12b).
𝑆∗ _

𝑟

𝑆∗ _

𝑒

2∙𝑓 𝛼

𝑟

∙𝑒

𝑆

𝑌
𝑌

𝑒

𝐶𝑇𝐹 ∗ 𝑘, 𝑙 𝑒

_

⋯ 12𝑏

By calculate more as shown in references [4-6], 𝛼as Equation (13).
calculated from 𝜏
_

∙𝑒

⋯ 14

𝐻
𝐻

𝑛
𝑛

𝑋
𝑋

𝐻
𝐻

⋯ 15

The equation for channel equalization using the channel
estimation results of the received signal is shown inEquation (16).

𝑷ℑ 𝑆∗ _ ∙ 𝑆
1𝑎𝑟𝑐𝑡𝑎𝑛2𝜋3 𝑁 𝐺𝐼ℜ 𝑆∗ _ ∙ 𝑆𝑁∙𝑒𝑘 contains the influence of other paths, theSince 𝐸
second 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, 𝑁 sets of those threeparameters can be obtained as shown in Fig. 5, and Fig. 6.
The CTF needs to be calculated for the number of
combinations of the number of transmit and receive
antennas. Therefore, in the case of 2x2 MIMO, the numberof CTF calculations is required for four paths 𝐻 , 𝐻 , 𝐻
and 𝐻 as shown in Fig. 6. This can be expressed in thetheoretical equation as shown in Equation (15) below.

⋯ 12𝑎

here,

𝛼

𝑓 𝛼

𝑷

𝑋
𝑋

is

⋯ 13

_

Consequently, once 𝜏
is determined, 𝑟 and 𝛼areeasily obtained from Equations (12a) and (13), respectively.
is changed by 1/ 2𝑁𝑓
In this proposed method, 𝜏(twice of sampling frequency) and rough estimation is firstobtained. And this rough estimation is modified to more
precise value using Newton method as described inreferences [4-6].
According to the computation above, ℎ𝑘, 𝑙, 𝑛can be obtained using Equations (8a) and (8b). Then,measured 𝐶𝑇𝐹 𝑘, 𝑙 and 𝐶𝑇𝐹 𝑘 3, 𝑙 are updated to
𝐶𝑇𝐹 2, 𝑘, 𝑙 and 𝐶𝑇𝐹 2, 𝑘 3, 𝑙 by subtractingℎ
𝑘, 𝑙, 𝑛 and ℎ𝑘 3, 𝑙, 𝑛 respectively. By
removing the influence of the first estimated path from the𝑘 , the following criterion 𝐸
𝑘 cancost function 𝐸
be obtained such as Equation (14).

≅

𝐻
𝐻

𝑌
𝑌

𝐻
𝐻

⋯ 16

Now, if we revise that ICI does not occur, Equations (6a)and (6b) can be rewritten as follows.
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙
𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙

ℎ
ℎ

ℎ
ℎ

𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙
𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙𝑤 𝑘, 𝑙𝑤 𝑘, 𝑙

⋯ 17𝑎
⋯ 17𝑏

Equations (17a) and (17b) can also be rewritten using thematrix as follows.
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙ℎℎ≅𝑘, 𝑙, 𝑙𝑘, 𝑙, 𝑙ℎℎ𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙𝑘, 𝑙, 𝑙𝑘, 𝑙, 𝑙⋯ 18

The equalizer of the 2x2 MIMO receiver can be equatedas follows. Using the DDP algorithm, Attenuation 𝑟 ,Propagation Delay time 𝜏 , and normalized Doppler shift 𝛼
for wave component index 𝑖 of the arrival path of each
receiving antenna are determined and used as CTFs
𝐻 𝑘, 𝑙, 𝑙 , 𝐻 𝑘, 𝑙, 𝑙 , 𝐻 𝑘, 𝑙, 𝑙 and 𝐻 𝑘, 𝑙, 𝑙 . Since
this paper assumes use in 2x2MIMO, the inverse matrix is
calculated by applying the formulas, resulting in thefollowing Equations (19) and (20).
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙
det 𝑯

1
det 𝑯
ℎ

ℎ 𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙, 𝑙𝑘, 𝑙, 𝑙 ℎ𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙, 𝑙𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙ℎ𝑘, 𝑙, 𝑙𝑘, 𝑙, 𝑙 ℎ

⋯ 19
⋯ 20

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

13

Table 2: Simulation Parameters

III. Computer Simulations
Since the actual test environment is not yet available,
computer simulations were used to simulate theenvironment. Fig. 7 shows a computer simulated runninglinear motor train situation. Nearby Base Station (gNB: g
Node B in 5G notation) antennas are located from the train
rail by D (m). In a Single Frequency Network (SFN), thesame DL signal is transmitted from antennas in different
each gNB. The distance between the center of the two Tx
antennas of the gNB and the center of the two Rx antennas
at the receiver is 300 m. The center position of the two Rx
antennas is Xr(t) on the horizontal X axis as shown in Fig.
7. Also, the distance between the Tx antennas is defined as
𝑡𝑑, and the distance between the Rx antennas is defined as𝑟𝑑. The distances between two Tx antennas and the Rx
antenna are 𝐿1 𝑡 , and 𝐿2 𝑡
𝑦 1,2, 𝑥 1,2 asshown in the figure (Fig. 7).
More detail of simulation parameters is listed in Table
2. Assumed Radio passband frequency is 3.9 GHz. In thesimulation, moving train will start receiving 1 frames of DL
signal with Xr(t=0) = -50 m. Path1-4 DL signal comes fromforward antenna with varying length 𝐿1 𝑡 , 𝐿1 𝑡 ,𝐿1 𝑡 , 𝐿1 𝑡 with relative amplitude gain = 1.0. Path58 DL signal comes from backside with 𝐿2 𝑡 , 𝐿2 𝑡 ,𝐿2 𝑡 , 𝐿2 𝑡 distance with relative amplitude gain =0.5. Bit Error Rate (BER) is measured in lower frequency
90 CRBs as shown in Fig. 3. The BER was obtained byadding Additive White Gaussian Noise (AWGN) to thesignal received as a composite wave of the 2gNB-derived
DL signal, varying from -10 dB to 50 dB in 2 dB steps.
Simulated results for QPSK / 16QAM / 64QAM /256QAM BER with Carrier to Noise Ratio (CNR) wereshown in Figs. 8-11. In each figure, (a) corresponds toconventional linearly interpolated CTF estimation and (b)corresponds to proposed DDR based CTF estimation. Figs.
12-15 show BER vs. train moving speed for QPSK with
CNR=22dB, 16QAM with CNR=30dB, 64QAM with
CNR=38dB and 256QAM with CNR=46dB.
Assuming that error correction is possible by theerror correction mechanism if the BER is less than 1.0E-03,
QPSK modulation can be used under severe channel
conditions such as 500 km/h under 8-path inverse Doppler
shift conditions with the channel estimator using the DDP
algorithm based on the proposed method. In the case of
16QAM modulation, the approximate 100 km/h limit isextended to double the speed 200 km/h. 64QAM can only

Parameters

Value

RF passband frequency

3.9 GHzQPSK / 16QAM /64QAM / 256QAM
0 km/h ~ 500km/h, (100km/h step)
Add to AWGN
-10 dB ~ 50 dB, (2 dB step)
1 Frames(10 ms, 20 slots)
90 CRBs(1080 Sub-carriers)
2x2 MIMO with Spatial
Multiplexing, 8-path
Single Frequency Network

Modulation
RX moving speed
CNR
Number of Frames
Used number of CRBs
ChannelPath Group 1( 𝐿1 𝑡 , 𝐿1 𝑡 ,𝐿1 𝑡 , 𝐿1 𝑡 )Path Group 2( 𝐿2 𝑡 , 𝐿2 𝑡 ,𝐿2 𝑡 , 𝐿2 𝑡 )Tx Antenna Installation Height(𝐷)
Tx Antenna Distance (𝑡𝑑)Rx Antenna Distance (𝑟𝑑)Distance = ~50 meters
Amp gain = 1.0
Distance = ~250 meters
Amp gain = 0.5
𝐷 = 2.0 meters
𝑡𝑑 = 0.5 meters𝑟𝑑 = 0.05 meters

be used in stationary conditions with the conventional
method, while the proposed method can be improved to 100
km/h. In the case of 256QAM modulation, only a slight
improvement has been observed.
Focusing on the contrast with SISO with QPSK
modulation, in 2x2 MIMO environment, conventional
channel estimator can barely achieve QPSK modulation
below 100 km/h, and the performance of CNR against SISO
is poor [1]. DDP based 2x2 MIMO equalizer has aperformance degradation of CNR against DDP SISO is only
6dB to 7dB, and combined with LDPC decoder, the error
rate can be reduced and performance can be improved in
2x2 MIMO even under severe channel conditions such as
500km/h, 8-path inverse Doppler shift environments.
Fig. 16 shows a graph comparing BER vs. CNR under thesame throughput. Since QPSK can transmit a maximum of
2 bits per carrier and 16QAM can transmit a maximum of 4
bits per carrier, the throughput of 16QAM SISO and QPSK2MIMO with spatial multiplexing is equivalent. From Fig.
16 shows that the proposed QPSK 2MIMO transmission has
a lower error rate than the conventional 16QAM SISO
transmission.

Fig. 7: Simulation model of train moving situation for 2x2 MIMO environment

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IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

(a) Conventional CTF Linear Interpolator(a) Conventional CTF Linear Interpolator(b) Delay and Doppler Profiler based CTF(b) Delay and Doppler Profiler based CTF

Fig. 8: BER vs. CNR (dB) for 2x2 MIMO QPSK modulation

Fig. 10: BER vs. CNR (dB) for 2x2 MIMO 64QAM modulation(a) Conventional CTF Linear Interpolator(a) Conventional CTF Linear Interpolator(b) Delay and Doppler Profiler based CTF(b) Delay and Doppler Profiler based CTF

Fig. 9: BER vs. CNR (dB) for 2x2 MIMO 16QAM modulation

Fig. 11: BER vs. CNR (dB) for 2x2 MIMO 256QAM modulation

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

Fig. 12: BER vs. Moving Speed for QPSK

Fig. 13: BER vs. Moving Speed for 16QAM

15

Fig. 15: BER vs. Moving Speed for 256QAM

Fig. 16: BER vs. CNR evaluated in terms of the same modulation bit rate

IV. Conclusion

Fig. 14: BER vs. Moving Speed for 64QAM

We have proposed Delay and Doppler Profiler (DDP)
based channel estimator and successfully implemented it in
a computer simulation of a signal processing simulation
system for a 500 km/h train. In the simulations, we
compared the performance of the proposed DDP algorithmwith that of a conventional channel estimation algorithm
that combines frequency-domain filter interpolation andtime-domain linear interpolation. According to thesimulation results, QPSK modulation can be used under
severe channel conditions such as 500 km/h under 8-pathinverse Doppler shift conditions with the channel estimatorusing the DDP algorithm based on the proposed method.
For 16QAM modulation, roughly 100km/h limitation isextended to double speed of 200km/h. For 64QAM
modulation, the limitation speed is improved from below
100km/h. For 256QAM modulation, only small
improvement has been confirmed.

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IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.9, September 2023

We have also shown that the proposed method oftransmission with QPSK 2MIMO with spatial multiplexing
has a lower error rate than the conventional method of
16QAM SISO.

References[1] Suguru Kuniyoshi, Shiho Oshiro, Gennan Hayashi, andTomohisa Wada, “Channel Transfer Function estimation
based on Delay and Doppler Profiler for 5G System Receivertargeting 500km/h linear motor car,” IJCSNS International
Journal of Computer Science and Network Security, VOL.23,
No.5, pp.121-127, May 2023.
[2] 3GPP TS38.211 V17.4.0: “3rd Generation Partnership
Project; Technical Specification Group Radio AccessNetwork; NR; Physical channels and modulation” Dec. 2022.
[3] Erik Dahlman, Stefan Parkvall, Johan Sköld (2021). 5G NR
THE NEXT GENERATION WIRELESS ACCESSTECHNOLOGY SECOND EDITION. Academic Press.
[4] Mitsuru Nakamura, Makoto Itami, Kohji Itoh and Hamid
Aghvami, “ICI Cancellation Technique based 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).
[5] 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).
[6] Akito Yamazaki, Mitsuru Nakamura, Masahiro Fujii, Makoto
Itami, Kohji Itoh and Hiroki Ohta, “A Study on Improving
Performance of an OFDM ICI Canceller,” The Institute of
Image Information and Television Engineers, Vol. 58, No. 1,
pp.94-101 (2005).

Suguru Kuniyoshi
received
theB.E. and M.E. degrees, from the Universityof the Ryukyus, Okinawa, Japan in 2004
and 2006, respectively. He joined Magna
Design Net, Inc. in 2006 and has engaged
with digital signal processing design ofmodulator and demodulator part for a
Wireless LAN, WiMAX, 4G-LTE, 5G-NR,
and Underwater Acoustic communication.
Currently he is the Engineering Manager of the Development
Department at Magna Design Net, Inc.
Rie Saotome
received
theB.E. and M.E. degree from Tokyo
University of technology, Tokyo, Japan in1999 and 2001, respectively. She received
Dr. Eng. degree from University of the
Ryukyus in 2016. From 2004 to 2016, she
was a part-time lecturer at Univ. of the
Ryukyus, Okinawa Univ., Meio Univ. andOkinawa Polytechnic College. She joined
Magna Design Net, Inc. in 2016. Her
research interest includes Wireless communications systems, 5GNR, Underwater Acoustic communication, and Rain attenuation.

Shiho Oshiro
received
theB.E. and M.E. degrees, from the Universityof the Ryukyus, Okinawa, Japan in 2018and 2020, respectively. She received theDr. Eng. degree from University of the
Ryukyus in 2023. She has been an assistantprofessor at University of the Ryukyus
since 2023. She has experienced shortterm study abroad at Madan Mohan
Malaviya University of Technology (MMMUT) Gorakhpur andAtal Bihari Vajpayee-Indian Institute of Information Technology
and Management (ABV-IIITM) Gwalior in India, Institute ofTechnology of Cambodia (ITC) in Cambodia, and National
Taiwan University of Science and Technology (Taiwan Tech). 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, andAutoencoder for OFDM communication system.

Tomohisa Wada
received B.S.
degree in electronic engineering 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 ULSILaboratory, Mitsubishi Electric Corp.
Japan in 1983 and engaged in the researchand development of VLSI such as High-speed Static Randomaccess memories, Cache memories for Intel MPUs in 16 years.
Since 2001, he has been a Professor at the Department ofInformation 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 forcommunication 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 and development of a terrestrial
video broadcasting receiver, a wireless 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.