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

1

A 2x2 MIMO Spatial Multiplexing 5G Signal Reception in a 500 km/h
High-Speed Vehicle using an Augmented Channel Matrix Generated bya Delay and Doppler Profiler
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
SummaryThis paper proposes a method to extend Inter-Carrier
Interference (ICI) canceling Orthogonal Frequency Division
Multiplexing (OFDM) receivers for 5G mobile systems to spatial
multiplexing 2x2 MIMO (Multiple Input Multiple Output)
systems to support high-speed ground transportation services bylinear motor cars traveling at 500 km/h. In Japan, linear-motor
high-speed ground transportation service is scheduled to begin in
2027. To expand the coverage area of base stations, 5G mobile
systems in high-speed moving trains will have multiple basestation antennas transmitting the same downlink (DL) signal,
forming an expanded cell size along the train rails. 5G terminals
in a fast-moving train can cause the forward and backward antenna
signals to be Doppler-shifted in opposite directions, so the receiverin the train may have trouble estimating the exact channel transfer
function (CTF) for demodulation.
A receiver in such high-speed train sees the transmission
channel which is composed of multiple Doppler-shifted
propagation paths. Then, a loss of sub-carrier orthogonality due toDoppler-spread channels causes ICI. The ICI Canceller is realized
by the following three steps. First, using the Demodulation
Reference Symbol (DMRS) pilot signals, it analyzes threeparameters such as attenuation, relative delay, and Doppler-shiftof each multi-path component. Secondly, based on the sets of threeparameters, Channel Transfer Function (CTF) of sender subcarrier number 𝒏 to receiver sub-carrier number 𝒍 is generated. Incase of 𝒏 𝒍, the CTF corresponds to ICI factor. Thirdly, since
ICI factor is obtained, by applying ICI reverse operation by MultiTap Equalizer, ICI canceling can be realized.
ICI canceling performance has been simulated assuming severe
channel condition such as 500 km/h, 8 path reverse Doppler Shiftfor QPSK, 16QAM, 64QAM and 256QAM modulations. In
particular, 2x2MIMO QPSK and 16QAM modulation schemes,
BER (Bit Error Rate) improvement was observed when thenumber of taps in the multi-tap equalizer was set to 31 or moretaps, at a moving speed of 500 km/h and in an 8-pass reverse
doppler shift environment.

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

Manuscript received October 5, 2023
Manuscript revised October 20, 2023
https://doi.org/10.22937/IJCSNS.2023.23.10.1

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 trainI.

Introduction

A high-speed ground transportation service using linear
motors with a speed of 500 km/h is scheduled to begin
between Tokyo and Nagoya in 2027. The current top speedof the Shinkansen is 300 km/h. The maximum speed oflinear motor cars, which will use magnetic levitation, will
be 500 km/h. Even in trains traveling at such high speeds,
there is high demand for access to rich contents, such as
Internet access and watching the movie using mobile
communication systems. High-speed communications are
essential for accessing rich content, and demand for highspeed and stable wireless communications is constantly
increasing regardless of time and location. 5G wirelesscommunication systems can be expected to provide higherspeed, higher-capacity communications than ever before.
However, wireless communications in high-speed moving
trains are subject to a very severe Doppler shift environment.
To support 5G services in trains, 5G will use several
different configurations compared to 4G-LTE (4thGeneration Long term evolution). First, to mitigate theDoppler frequency shift, the subcarrier spacing will be
increased from 15 kHz to 30 kHz. This change

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

automatically shortens the OFDM symbol length by half.
As a result, the performance of tracking changes in channel
conditions is improved. Second, to expand the base station
coverage area for mobile services, the same downlink (DL)signal is transmitted from multiple base station antennas toform an expanded cell size along the train tracks. In such asituation, the forward and backward antenna signals are
Doppler shifted in opposite directions, respectively, and thereceiver in the train may suffer from estimating the exact
channel transfer function (CTF) for demodulation. Fig. 1
shows a situation where two DL signals are received in a
vehicle. Here, 𝑓 represents the carrier frequency.
Approaching TX1 antenna signal is 𝑓 𝑓 shifted andbackward TX2 signal is 𝑓 𝑓 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 reference
paper [1], the effectiveness of the channel estimation
scheme using the Delay and Doppler Profiler (DDP)
algorithm was demonstrated by computer simulations in anenvironment limited to the SISO (Single Input Single
Output) propagation path. In this paper, we applied thechannel estimation using the DDP algorithm to 2x2 MIMO
with spatial multiplexing in order to achieve higher
transmission data rate, and build a simulation model. In
Section II, we first briefly indicate that we are targeting 5G
mobile communication systems. Next, we describe thealgorithm of the DDP-based ICI canceller in the proposed
2x2 MIMO signal reception environment. In Section III, we
present computer simulation results. Finally, Section IV
presents conclusions.

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

II. DDP-based ICI Canceller for 2x2 MIMO
in 5G Mobile Communication Systems
The 5th generation mobile communication system [2] isan OFDM communication system standard developed as a
successor to the 4G-LTE system, with various
enhancements. For example, in 4G-LTE, the subcarrier
spacing used in the data channel was fixed at 15 kHz, while
5G supports variable subcarrier spacing of 15/30/60/120. In
the linear motor car application, a subcarrier frequency of
30 kHz is used for the 3.9 GHz RF carrier. Table I
summarizes the 5G system parameters for this application,
assuming 100 MHz bandwidth and 3276 subcarriers to
support eMBB (enhanced mobile broadband). Since thesubcarrier spacing f0 is 30 kHz, an OFDM symbol length Tof 33.33 us (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 toas Sub6, which is used when the center 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

Fig. 3: Time and Frequency structure of 5G System for 2x2 MIMOIJCSNS International Journal of Computer Science and Network Security, VOL.23 No.10, October 2023
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 tosome Sub-carriers to measure CTF and the DMRS can beplaced with a high degree of freedom according to thesystem configuration. This time, DMRS is asserted in S3,
S6, S9, S12 OFDM symbols to detect rapidly time-domainchanging CTF [3].
Time-Frequency structure of this 5G system is shown in
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.

3

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.

A) Physical layer of 5G communication MIMO system
Fig. 4 shows the block diagram of the Physical Layer(PHY) of 5G 2x2 MIMO (Multiple Input Multiple Output)
system. The upper side is the transmitter and the lower sideis the receiver. The Bit data supplied by 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 is basically the reverse process of thetransmitter side. However, since the receiving signal isdistorted through the propagation channel, CTF, which is a
Frequency domain representation of Channel Impulse
Response in Time domain, has to be estimated and the
distortion has to be compensated at Equalizer using theestimated CTF. In addition, signals transmitted separately
at the transmitter end arrive at the receiver end after being
mixed together on the propagation channel. Therefore, theCTF must be calculated for four paths in 2x2 MIMO
environment, compared to the amount of CTF calculations
required in SISO environment, which quadruples theamount of calculations required to find the CTF.

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

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

Fig. 6: Basic representation of 2x2 MIMO system

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

4

B)

ICI Cancellation based on Delay and Doppler
Profiler 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
shows a block diagram of proposed DDP CTF generation.
The upper side of the figure represents the Time-Frequency
structure of sub-carriers with time-domain symbol index 𝑘.
The DDP 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.

𝑟

𝑡

𝑠

𝑟

𝑡

𝑔 𝑡

𝑚𝑇 ∙

𝑑 𝑚, 𝑛 𝑒

𝜏

∆

𝑒
𝑟

𝑠

𝑖
𝑁𝑓

𝑡

𝑡

𝜏

𝑘𝑇

⋯ 5

𝑑 𝑘, 𝑙ℎℎ𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙

𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙

ℎ

𝑡

𝑔 𝑡

𝑔 𝑡

𝑚𝑇 ∙
1
𝑓

1
0

𝑇 ≦ 𝑡 1/𝑓
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑇

⋯ 1𝑏

⋯ 2
⋯ 3

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

∆

𝑒
𝑟

𝑠

𝑡

𝜏

𝑒

∆

⋯ 4𝑏

𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛𝑤 𝑘, 𝑙⋯ 6𝑎𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙ℎ𝑘, 𝑙, 𝑙 𝑑 𝑘, 𝑙ℎ𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛

𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛

𝑘, 𝑙, 𝑛 𝑑 𝑘, 𝑛

⋯ 1𝑎𝑑 𝑚, 𝑛 𝑒𝑇ℎℎ𝑤 𝑘, 𝑙𝑠𝑒where, 𝑟 , 𝜏and ∆𝑓 are attenuation, relative delay
and Doppler-shift of 𝑝 path when the signal from transmit
antenna number 𝑥 is received at receive antenna number 𝑦,respectively. After sampling of 𝑟 𝑡 and 𝑟 𝑡 by using
Equation (5) with sampling index 𝑖 and OFDM symbol
number 𝑘, the block of samples is de-modulated by DFT togenerate data symbol 𝑑 𝑘, 𝑙 and l 𝑑 𝑘, 𝑙 as expressed in
Equations (6a) and (6b).

ℎ
𝑠

𝑡

∆

⋯ 4𝑎

⋯ 6𝑏

where 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).
ℎ𝑘, 𝑙, 𝑛ℎ𝑦𝑥𝑝 𝑘, 𝑙, 𝑛ℎ𝑘, 𝑙, 𝑛⋯ 7

𝜋 𝑁 1 𝐴𝑠𝑖𝑛𝑐 𝐴
𝑗
∙𝑒 𝑁
𝐴
𝑠𝑖𝑛𝑐
𝑁

∙ 𝑟𝑦𝑥𝑝 ∙ 𝑒

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

𝐴

𝑙

𝑛

𝛼

⋯ 8𝑎

⋯ 8𝑏

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.

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

𝑘

𝑘, 𝑙

𝐶𝑇𝐹

ℎ

𝑘, 𝑙, 𝑙

𝑷

𝐶𝑇𝐹

𝑘

3, 𝑙

ℎ

𝑘

⋯ 9

3, 𝑙, 𝑙where 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).
𝐸

𝑘
𝐶𝑇𝐹

𝑘, 𝑙

𝐶𝑇𝐹

𝑘

3, 𝑙

𝑓 𝛼

𝑟

∙𝑒

𝑓 𝛼

𝑟

∙𝑒

5

According to the computation above, ℎ𝑘, 𝑙, 𝑛 canbe obtained using Equations (8a) and (8b). Then, measured
and 𝐶𝑇𝐹 𝑘 3, 𝑙
are updated to
𝐶𝑇𝐹 𝑘, 𝑙
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).
𝐸

𝑘
𝐶𝑇𝐹

2, 𝑘, 𝑙

𝐶𝑇𝐹

2, 𝑘

3, 𝑙

𝑓 𝛼

𝑟

𝑓 𝛼

𝑟

∙𝑒

𝑷

∙𝑒

∙𝑒

⋯ 14

𝑷

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

⋯ 12𝑎

𝑒

here,
𝑆

𝐶𝑇𝐹 ∗ 𝑘, 𝑙 𝑒

_

⋯ 12𝑏

𝑷

By calculate more as shown in reference [4-6], 𝛼as Equation (13).
calculated from 𝜏𝛼ℑ 𝑆∗ _ ∙ 𝑆
1𝑎𝑟𝑐𝑡𝑎𝑛2𝜋3 𝑁 𝐺𝐼ℜ 𝑆∗ _ ∙ 𝑆
𝑁

_

is

⋯ 13

_

Consequently, once 𝜏
is determined, 𝑟 and 𝛼
are easily obtained from Equations (12a) and (13),is changed byrespectively. In this proposed method, 𝜏
1/ 2𝑁𝑓 (twice of sampling frequency) and roughestimation is first obtained. And this rough estimation ismodified to more precise value using Newton method as
described in references [4-6].

Since 𝐸𝑘 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, 𝑁 sets of those threeparameters can be obtained as shown in Fig. 5, and Fig. 6.
After all, complete channel transfer function ℎ 𝑘, 𝑙, 𝑛
can be generated. Since most energy of ICI is concentrated
in the neighborhood of sub-carrier index, the ICI terms
which do not significantly affect 𝑑 𝑘, 𝑙 and 𝑑 𝑘, 𝑙 in(6a) and (6b) can be neglected and it is assumed as (15).
ℎ𝑘, 𝑙, 𝑛0𝑤ℎ𝑒𝑛 |𝑙𝑛|

𝑁𝑢𝑚𝐶𝑂𝐿2

1⋯ 15

where, 𝑁𝑢𝑚𝐶𝑂𝐿 is the number of neighborhood subcarrier taken into account against 𝑙 sub-carrier. By
considering the reverse operation of the ICI effect byℎ 𝑘, 𝑙, 𝑛 , Multi Tap ICI Canceling Equalizer has been
implemented as shown in Fig. 4. as a Fixed Impulse
Response Filter.
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 (16) below.
𝑌
𝑌

𝐻
𝐻

𝑛
𝑛

𝑋
𝑋

𝐻
𝐻

⋯ 16

The equation for channel equalization using the channel
estimation results of the received signal is shown inEquation (17).
𝑋
𝑋

≅

𝐻
𝐻

𝐻
𝐻

𝑌
𝑌

⋯ 17

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

6

Assuming the number of TAPs ( 𝑁𝑢𝑚𝐶𝑂𝐿 ) for themulti-tap ICI cancel equalizer is 3taps, Equations (6a) and(6b) can be rewritten as follows.
𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙
𝑤 𝑘, 𝑙 1
𝑤 𝑘, 𝑙⋯ 18𝑎𝑤 𝑘, 𝑙 1ℎ𝑘, 𝑙 1, 𝑙 1ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1

𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙, 𝑙ℎ 𝑘, 𝑙 1, 𝑙 1 ℎ 𝑘, 𝑙 1, 𝑙
𝑤 𝑘, 𝑙 1
𝑤 𝑘, 𝑙⋯ 18𝑏
𝑤 𝑘, 𝑙 1ℎ𝑘, 𝑙 1, 𝑙 1
𝑘, 𝑙, 𝑙 1
ℎ 𝑘, 𝑙 1, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1ℎ 𝑘, 𝑙, 𝑙 1ℎ 𝑘, 𝑙 1, 𝑙 1ℎ𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙 1

𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙 1
𝑑 𝑘, 𝑙𝑑 𝑘, 𝑙 1

Equations (18a) and (18b) can also be rewritten using
the matrix as follows.
𝑑 𝑘, 𝑙 1⎡
𝑑 𝑘, 𝑙⎢⎢ 𝑑 𝑘, 𝑙 1⎢ 𝑑 𝑘, 𝑙 1⎢
𝑑 𝑘, 𝑙⎢⎣ 𝑑 𝑘, 𝑙 1

⎤
⎥
⎥
⎥
⎥
⎥
⎦

𝑑 𝑘, 𝑙 1⎡
𝑑 𝑘, 𝑙⎢⎢ 𝑑 𝑘, 𝑙 1⎢ 𝑑 𝑘, 𝑙 1⎢
𝑑 𝑘, 𝑙⎢⎣ 𝑑 𝑘, 𝑙 1

𝑯𝟏𝟏
𝑯𝟐𝟏

𝑯𝟏𝟐
𝑯𝟐𝟐

ℎ

𝑘, 𝑙 1, 𝑙
𝑘, 𝑙, 𝑙𝑘, 𝑙 1, 𝑙⎤⎥⎥⎥ ⋯ 19𝑎
⎥
⎥
⎦

here,
𝑯𝒚𝒙

ℎ
ℎ
ℎ

𝑘, 𝑙 1, 𝑙 1
𝑘, 𝑙, 𝑙 1
𝑘, 𝑙 1, 𝑙 1

ℎ
ℎ

ℎ
ℎ
ℎ

𝑘, 𝑙 1, 𝑙 1
𝑘, 𝑙, 𝑙 1
𝑘, 𝑙 1, 𝑙 1⋯ 19𝑏

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 ,𝐻 , 𝐻 and 𝐻 . Since this paper assumes use in
2x2MIMO, the inverse matrix is calculated by applying theformulas, resulting in the following Equation (20).
𝑑 𝑘, 𝑙 1⎡
𝑑 𝑘, 𝑙⎢⎢ 𝑑 𝑘, 𝑙 1⎢ 𝑑 𝑘, 𝑙 1⎢
𝑑 𝑘, 𝑙⎢⎣ 𝑑 𝑘, 𝑙 1

⎤
⎥
⎥
⎥
⎥
⎥
⎦

𝑯𝟏𝟏
𝑯𝟐𝟏

𝑯𝟏𝟐
𝑯𝟐𝟐

𝑑 𝑘, 𝑙 1⎡
𝑑 𝑘, 𝑙⎢⎢ 𝑑 𝑘, 𝑙 1⎢ 𝑑 𝑘, 𝑙 1⎢
𝑑 𝑘, 𝑙⎢⎣ 𝑑 𝑘, 𝑙 1⎤⎥⎥⎥ ⋯ 20⎥⎥⎦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.
The conventional method shall obtain the channel
estimates in the frequency and time directions for each slot
by performing the following two steps. As the first step, a
half-band FIR (Finite Impulse Response) filter is passed

Fig. 7: Simulation model of train moving situation for 2x2 MIMO environmentIJCSNS International Journal of Computer Science and Network Security, VOL.23 No.10, October 2023

7

Table 2: Simulation Parameters

through the carrier for which channel estimation was
performed for the DMRS symbols, and channel estimationis performed in the frequency domain to obtain channel
estimates for each carrier for one symbol. This process isperformed for four symbols containing DMRS for each slot.
In the second step, linear interpolation is performed
between the two symbols for which the channel estimate of
the frequency location was obtained. By repeating thesecond step for each DMRS symbol, time direction channel
estimation can be performed for symbols that do not contain
DMRS. The advantage of the conventional method is that it
is computationally less expensive than the proposed DDP
algorithm, but its disadvantages are that it requires several
consecutive RB assignments to improve channel estimation
accuracy and that it is difficult to perform filter completionat both ends of the RBs used, so separate processing isnecessary.
The proposed DDP-based ICI cancellation equalizer isbased on the estimation of the attenuation 𝑟 , propagation
delay time 𝜏 , and normalized Doppler shift 𝛼 in thearriving wave for each CTF, one pass at a time, as describedin Section II, subsection B, followed by a Fixed Impulse
Response Filter, followed by equalization with a multi-tap
ICI canceller using a Fixed Impulse Response filter.
The number of taps in the fixed impulse response filter of
the ICI canceller equalizer, 𝑁𝑢𝑚𝐶𝑂𝐿=1, corresponds to thecondition where the number of adjacent subcarriers is notconsidered, but the computational complexity is about 16
times that of the conventional method. 8 patterns from
𝑁𝑢𝑚𝐶𝑂𝐿 1 to 𝑁𝑢𝑚𝐶𝑂𝐿 63 were used in thecomputer simulations; CNR versus BER data acquisition
was performed for these eight patterns while varying the
𝑁𝑢𝑚𝐶𝑂𝐿 factor. We performed computer simulations of
the conventional method and the proposed method for theseeight patterns while varying the 𝑁𝑢𝑚𝐶𝑂𝐿 factor for the
proposed method, and obtained CNR vs. BER data.
Simulated results for QPSK / 16QAM / 64QAM /256QAM BER vs Carrier to Noise Ratio (CNR) withmoving speed 500km/h were shown in Figs. 8-11. In eachfigure, (a) shows the simulation results of the conventional
scheme using the basic DMRS pattern and the proposed
scheme using the basic DMRS pattern and varying
𝑁𝑢𝑚𝐶𝑂𝐿 values in a 3GPP standard-compliant downlink
signal in 5G. On the other hand, in the specifications after
3GPP Release 16, the transmit DMRS pattern can bechanged for each antenna. To confirm the effect ofimproving the characteristics by adding a device to further
improve the cross-correlation characteristics by changing
the DMRS pattern for each transmitting antenna, (b) shows
the simulation results when the DMRS pattern is changed
for each transmitting antenna.
Simulation results show that the proposed DDP-based
ICI canceller scheme outperforms conventional schemes,
even at a moving speed of 500 km/h, regardless of themodulation scheme and whether the DMRS pattern

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)Number of Fixed Impulse
Response Filter Taps of
ICI Canceling Equalizer(𝑁𝑢𝑚𝐶𝑂𝐿)

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
8patterns(1, 3, 5, 7, 15, 31, 45, 63)

between the two transmit antennas is common or
independent, by increasing the 𝑁𝑢𝑚𝐶𝑂𝐿 value to about 31,
This indicates that BER can be significantly improved byincreasing the 𝑁𝑢𝑚𝐶𝑂𝐿 value to about 31. Here,𝑁𝑢𝑚𝐶𝑂𝐿 1 corresponds to a DDP-based channel
equalizer without an ICI canceller, which corresponds to thealgorithm presented in reference [7]. In the conventional
method, there was little BER improvement regardless of the
DMRS pattern.
Fig. 8(a) and Fig. 8(b) show a comparison of QPSK
modulation. Fig. 8(a), which uses the same DMRS pattern
across transmit antennas, requires 𝑁𝑢𝑚𝐶𝑂𝐿 3 or more tobe error-free, while Fig. 8(b), which changes the DMRS
pattern for each transmit antenna, shows that 𝑁𝑢𝑚𝐶𝑂𝐿
1 is sufficient to be error-free. In Fig. 9(a) and Fig. 9(b),which are graphs for 16QAM modulation, if we focus on
the graph for 𝑁𝑢𝑚𝐶𝑂𝐿 31, we can see that changing the
DMRS pattern for each transmit antenna improves the BER
by two orders of magnitude. As the modulation value
increases, the improvement in BER becomes smaller, but
we can see that BER improves from QPSK to 256QAM.
The paper concludes that 𝑁𝑢𝑚𝐶𝑂𝐿 31 is the optimalvalue for the DDP algorithm, which is consistent with theconclusions for DDP-based multi-tap channel equalization
in a SISO environment presented in reference [1].

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

(a) DMRS pattern is the same between transmit antennas(b) DMRS pattern changed for each transmit antenna
Fig. 8: BER vs CNR (dB) for 2x2 MIMO QPSK modulation(a) DMRS pattern is the same between transmit antennas(b) DMRS pattern changed for each transmit antenna
Fig. 9: BER vs CNR (dB) for 2x2 MIMO 16QAM modulation(a) DMRS pattern is the same between transmit antennas(b) DMRS pattern changed for each transmit antenna
Fig. 10: BER vs CNR (dB) for 2x2 MIMO 64QAM modulation(a) DMRS pattern is the same between transmit antennas(b) DMRS pattern changed for each transmit antenna
Fig. 11: BER vs CNR (dB) for 2x2 MIMO 256QAM modulation

IJCSNS International Journal of Computer Science and Network Security, VOL.23 No.10, October 2023
Finally, Figs. 12 and 13 show the simulation results
when the parameters are changed from a travel speed of 0km/h to 500 km/h under the condition of changing the
DMRS pattern for each transmit antenna. In this case, the
𝑁𝑢𝑚𝐶𝑂𝐿 value of 31 was used, which was the performance
limit based on the results of Figs. 8-11. It shows that the
BER is better when the DMRS pattern is changed for every
two transmit antennas at all speeds from 0 km/h to 500 km/h
of movement. Fig. 12(b) shows that the 16QAM modulation
scheme is fully usable in a spatial multiplexing 2x2 MIMO
environment. Fig. 13(b) also shows that the 2x2 MIMO
64QAM modulation scheme in combination with LDPC
and other channel decoding can be used in a 500 km/h
environment. At a moving speed of 500 km/h, BER is
improved by two orders of magnitude.

IV. Conclusion
Delay and Doppler Profiler (DDP) based spatial
multiplexing 2x2 MIMO Channel Estimator is proposed
targeting 500km/h train support and it is successfully
implemented in signal processing simulation system.

(a) DMRS pattern is the same between transmit antennas

Simulated performances are compared with theconventional frequency domain using half bandinterpolation filter and time domain linear interpolated
estimator.
Simulation results show that QPSK modulation in aspace-multiplexed 2x2 MIMO environment can be used
under severe channel conditions such as 500 km/h under 8path inverse Doppler shift conditions with a channel
estimator using the DDP algorithm based on the proposed
method.
In addition, by applying the DMRS pattern change pertransmit antenna added after Release 16 of the 5G standard,
the error rate after channel decoding under 500 km/h
moving speed can be kept low even for 16QAM modulation
and 64QAM modulation in a spatial multiplexing 2x2
MIMO environment. However, the improvement rate for
256QAM modulation is small.
Adaptive modulation such that 16QAM modulation is
the upper limit of the modulation scheme during high-speed
movement and 64QAM modulation is the upper limit
during low-speed movement would reduce theretransmission probability and improve total throughput.

(b) DMRS pattern changed for each transmit antenna

Fig. 12: BER vs Moving Speed for 2x2 MIMO 16QAM (NumCOL=31)(a) DMRS pattern is the same between transmit antennas

9(b) DMRS pattern changed for each transmit antenna

Fig. 13: BER vs Moving Speed for 2x2 MIMO 64QAM (NumCOL=31)

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

References[1] Suguru Kuniyoshi, Rie Saotome, Shiho Oshiro and Tomohisa
Wada, “An ICI Canceling 5G system receiver for 500km/h
linear motor car,” IJCSNS International Journal of Computer
Science and Network Security, VOL.23, No.6, pp.27-34,
June 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).
[7] Suguru Kuniyoshi, Rie Saotome, Shiho Oshiro and Tomohisa
Wada, “Delay and Doppler Profiler based Channel Transfer
Function estimation for 2x2 MIMO Receivers in 5G systemtargeting a 500km/h linear motor car,” IJCSNS International
Journal of Computer Science and Network Security, VOL.23,
No.9, pp.8-16, September 2023.

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, 5G-NR, 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 ofTechnology (MMMUT) Gorakhpur and Atal Bihari VajpayeeIndian Institute of Information Technology and Management(ABV-IIITM) Gwalior in India, Institute of Technology ofCambodia (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, and Autoencoder 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.