RADIOENGINEERING, VOL. 30, NO. 4, DECEMBER 2021

695

Generalized Regression Neural Network Based Channel
Identification and Compensation Using Scattered Pilot
He HE 1 , Shun KOJIMA 1 , Takaki OMURA 1 , Kazuki MARUTA 2 , Chang-Jun AHN 1
1 Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan
2 Academy for Super Smart Society, Tokyo Institute of Technology, Tokyo 152-8552, Japan

kakukaku@chiba-u.jp
Submitted September 15, 2020 / Accepted July 17, 2021

Abstract.
In the high-speed mobile environment, channel state information (CSI) estimated at the beginning of thepacket is quite different at the last part because the actual
channel state changes with time. To overcome this problem,
a neural network (NN) based channel compensation method
was previously developed. Due to inaccurate channel estimation of decision feedback channel estimation (DFCE), thepilot-aided CSI of the first symbol and DFCE-aided CSIs in
the intermediate data part will cause inexact channel statetransition even though the application of NN. Accordingly,
the channel compensation performance is still degraded, especially in the last part of the packet. This paper proposesa new version of GRNN based channel identification andcompensation method by introducing scattered pilot. It can
improve the tracking capability of GRNN thanks to densely
arranged pilot in the time-domain while it cannot reduce thetransmission efficiency. Simulation results show that the proposed method is more effective than the conventional ones interms of RMSE and BER performance, even in the fast fading
environment.

Keywords
OFDM, fast fading, channel estimation, generalized regression neural network, DFCE, scattered pilot

1. Introduction
With the rapid development of communication technology and the spread of a large number of mobile communication terminals, security and certainty of wireless communication services have attracted extensive attention. Theseare essential to achieve a reliable system for fifth generation (5G) mobile communication systems [1]. Packet basedtransmission based on orthogonal frequency division multiple (OFDM) is employed for a large majority of modern
wireless communication systems such as long term evolution(LTE) and Wi-Fi. The quality of channel state information(CSI) directly impacts the performance of the entire system.

DOI: 10.13164/re.2021.0695

Pilot-assisted channel estimation (PCE) [2] is one of the CE
methods and is widely used. Meanwhile, this method cannot
fully compensate for the fluctuation of channel state, i.e. amplitude and phase, caused by temporal fading. Under the fast
fading environment, the channel state changes so rapidly that
the CSI estimated by the PCE especially in the last part of thepacket is largely different from the actual channel state. In
order to trace the channel state transition, several approaches
have been investigated. The periodic pilot-symbol-aided(PSA) channel estimation [3] is one of them. It requiresa large complexity due to the detection methods. Earlier
work in [4], [5] conceived the scattered pilot for the fast fading channel compensation. Scattered pilot has a great effecton fast fading channel. In the scattered pilot, the general
one-dimensional interpolation method is usually performedin the frequency- or time-domains of the scattered pilot to
reduce the amount of computation. However, it is difficult
for the scattered pilot to interpolate in the deep faded channel,
especially in the frequency domain. Moreover, if the coherence bandwidth is narrow relative to the interval of scatteredpilot, the impulse responses will overlap when viewed in
the time domain. To overcome these problems, a multilayer
feedforward neural network (MLFNN) based channel estimation and compensation method was previously proposedin [6], [7]. This method employs MLFNN to compensate thechannel variation through the generalization ability derived
from the nonlinear relationship between input and output, andestimates the entire channel state transition. The MLFNN istrained using partially obtained CSI by the PCE and the dataaided decision feedback channel estimation (DFCE), where
the PCE pilots are inserted at the head of the packet and the
DFCE is applied to the middle part of the packet. The DFCE
directly estimates channel variation at any specific data symbol using the difference between the received symbol and thereplica symbol, which is the multiplication of remodulated
symbol and CSI obtained by the PCE [8], [9]. However,it causes the processing delay due to the huge computation
complexity imposed by the backpropagation (BP) training
for the weight of the neural network [7]. The genetic algorithm [10], [11] and firefly algorithm (FFA) [12] can beapplied to optimize the weight of the NN. Although these

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696

approaches are reasonable to find an optimal solution, we
need to repeat the iterative learning process which causes
an unacceptable latency.
The improved version of this method was developed toreplace MLFNN with a generalized regression neural network (GRNN) for NN part [13]. Due to its outperforming
generalization capability, GRNN based channel estimationand compensation method can improve the transmission performance with less computation load. However, NNs stillcannot estimate the accurate channel state transition due tothe low reliability of desired responses. Especially as one ofthe desired responses, the estimated CSI by DFCE is sometimes incorrect due to decision errors when the channel statetransition has a sharp fluctuation even in the beginning partof the packet.
In order to further improve the reliability of the desired
responses without increasing the number of pilot symbols, wenewly propose the modified version of GRNN based on thechannel estimation method that the structure of pilot symbols is transformed and the CSI interpolated by DFCE in
the frequency-domain is used as the desired responses fortraining. This method not only secures the resolution in thefrequency domain, but also improves the tracking capability
in the time-domain due to the scattered pilot. Since DFCE
only refers to the front and back pilot signals in the time domain, even if one-dimensional interpolation is performed at
the non-pilot position where data symbol is inserted, there isno need to consider the pilot spacing in the frequency domain
and expands the scope of satisfying Nyquist sampling theorem by two times. It can also do better interpolation for deep
fade than the general method [14], [15]. A key contributionof this paper is to increase reliability of the desired responses
in NNs and to estimate the whole channel state transition accurately with maintaining the same transmission efficiency
as well as computation complexity.
The rest of this paper is organized as follows. In Sec. 2,
we overview the system model. Sections 3 and 4 describe
the concept of DFCE and GRNN. Section 5 introduces theconventional GRNN based channel estimation scheme. Sections 6 and 7 present the proposed scheme and its performance through a computer simulation. Finally, Section 8
concludes this paper.

2. Channel ModelIn this paper, we assume time varying multipath fading
channel which is expressed as,ℎ(𝜏, 𝑡) =𝐿−1∑︁ℎ𝑙 (𝑡)𝛿(𝜏 − 𝜏𝑙 )

(1)

𝑙=0

where ℎ𝑙 denotes the complex channel coefficient and 𝛿 is the
Dirac’s delta function. 𝐿 and 𝜏𝑙 indicate the number of discrete paths and the delay time, respectively. The normalizedÍ 𝐿−1path gain is assumed here as 𝑙=0
E|ℎ𝑙2 | = 1, where E| · |indicates the ensemble average operation. The frequency response 𝐻 ( 𝑓 , 𝑡) via Fourier transform of the temporal impulse
response can be obtained as,∫ ∞𝐻 ( 𝑓 , 𝑡) =ℎ(𝜏, 𝑡) exp(−j2𝜋 𝑓 𝜏)d𝜏
(2)
−∞

=

𝐿−1
∑︁

ℎ𝑙 (𝑡) exp(−j2𝜋 𝑓 𝜏𝑙 )

(3)

𝑙=0

where 𝑓 denotes the frequency. In a mobile communication
environment, the frequency response is generally fluctuating.
𝐿 > 1 provides frequency selective fading channel where|𝐻 ( 𝑓 , 𝑡)| fluctuates in the transmission bandwidth [16], [17].

3. Decision Feedback Channel
Estimation (DFCE)
DFCE is one of the channel estimation methods, and it
uses the signals remodulated with DFCE and the reference
CSI obtained by the pilot symbols inserted to the first symbol of the packet. The received signal of the 𝑘-th subcarrier
and the 𝑖-th symbol, 𝑌 (𝑘, 𝑖), is represented and the white
Gaussian noise 𝑁 (𝑘, 𝑖) is added as follows:Y(𝑘, 𝑖) = H(𝑘, 𝑖) · X(𝑘, 𝑖) + N(𝑘, 𝑖).

(4)First, the decision result of the transmitted symbol
D′ (𝑘, 𝑖) is multiplied by the channel H̃(𝑘) estimated fromthe pilot symbol to create a received signal replica Yrep (𝑘, 𝑖).
The channel variations ΔH(𝑘, 𝑖) is obtained by dividing theactual received signal Y(𝑘, 𝑖) by the received signal replica
Yrep (𝑘, 𝑖). Furthermore, this channel variations ΔH(𝑘, 𝑖) is
multiplied by the estimated channel H̃(𝑘, 𝑖) to obtain the adjusted channel Ȟ(𝑘, 𝑖). Finally, in order to reduce the noise
which may result in a slight decrease of demodulation accuracy, the (𝑖 − 1, 𝑖, 𝑖 + 1)th symbols of adjacent adjusted
channel are also added and averaged together. Specifically,
it is expressed by the following equations from (5) to (8).

Yrep (𝑘, 𝑖) = H̃(𝑘)D′ (𝑘),Y(𝑘, 𝑖),ΔH(𝑘, 𝑖) =Yrep (𝑘, 𝑖)Ȟ(𝑘, 𝑖) = ΔH(𝑘, 𝑖) · H̃(𝑘),Í𝑖+1
𝑗=𝑖−1 Ȟ(𝑘, 𝑗)Ĥ(𝑘, 𝑖) =
.
3

(5)
(6)
(7)
(8)

However, decision errors are inevitable in this scheme
resulting in inaccurate CSI estimation, especially under a fast
fading environment where the channel variation from thefront CSI given by PCE to the channel state in the last part ofthe packet is quite huge. Thus, applying DFCE to obtain theestimated CSI cannot improve compensation performance,
especially in the last part of the packet.

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4. Generalized Regression Neural
Network (GRNN)
GRNN was proposed by Donald Specht in 1991, which
evaluates the probability density function to solve the nonlinear approximation problem [18]. GRNN has excellent performances in both robust function approximation ability andlearning speed. This is because it can provide convergenceto the optimal regression surface rapidly by using a probability distribution, even though the sparse training samples
included inaccurate responses [19]. Besides, GRNN directly
sets weight value to training samples regarded as the expectedvalue of response, instead of iterative learning to adjust the
optimal value of the weight value [20–22].
As shown in Fig. 1, the GRNN is a parallel four-layer
structure: input layer, pattern layer, summation layer, andoutput layer. The description of calculation flow is given as
follows: the input neurons of input layer receives the input
vector x = [𝑥 1 , 𝑥2 , . . . , 𝑥 𝑛 ]. Then, the input neurons send
these data to the pattern layer, which can realize the nonlinear transformation from the input space to the pattern space.
The output of the 𝑖-th neuron in the pattern layer is expressedas∥x − 𝑐 𝑖 ∥ 2(9)𝜙𝑖 (x) = exp −2𝑟 2
where 𝑟 denotes the radius of the radial basis function (RBF)
and 𝑐 𝑖 is a training input vector(1 ≤ 𝑖 ≤ 𝑝). 𝑝 presents
the number of training sets. 𝑟 determines the generalization
capability of the GRNN by controlling the degree of smoothness. When 𝑟 is large, the ability to approximate dispersed
training samples decreases due to smoother transitions. In
contrast, when 𝑟 becomes very small, the regression curve
will change rapidly, causing a decrease in prediction ability.
The summation layer has two summations, called thesimple summation 𝑆s and the weighted summation 𝑆w , respectively. 𝑆s computes the arithmetic sum of the patternlayer outputs, expressed as
𝑆s =

𝑝
∑︁

𝜙𝑖 (x).

(10)𝑖=1

The 𝑘-th weighted summation 𝑆w computes theweighted sum of the pattern layer outputs, expressed as
𝑆w𝑘 =

𝑝
∑︁

𝑦 𝑖 𝜙𝑖 (x).

In addition, we compare the difference between
MLFNN and GRNN. The MLFNN [7], [10–12] has to renew
parameters iteratively in BP training until any training parameter reaches the target value. From this reason, the iterative
process makes the computational complexity enormous andresults in processing delay. In particular, the simulation results in paper [7] [13] have proved that the BP neural networkneeds to optimize several parameters by iteration to achieve
the optimization of BER characteristics. In order to eliminate
the iterative training process without imparing the generalization capability, we previously proposed the improving NN
approach which employs GRNN for the NN part [13]. Different from the MLFNN back-propagation training that needs
iterative weight update process, the desired response 𝑦 𝑖 of the
training sets in the GRNN can be exploited for the weights
directly like (11). Therefore its learning time can be reduced
significantly.
To support this claim, we measured the calculation timefrom training to predict the channel state by MLFNN and
GRNN in MATLAB. The channel estimation method is introduced in detail in the next section. Computation environment
is Intel Core i5-CPU and 8GB RAM. The running time for
GRNN is 5.912 ms, whereas that for MLFNN is 483.626 ms.
As a result, GRNN can drastically reduce the calculation delay and it could fall within a feasible execution time with the
hardware implementation. Our research focuses on execution time, and the conventional MLFNN cannot be applicablefor the practical use due to its large amount of computation
time. The main objective of this study is to provide a quantitative comparison between the pilot subcarrier interpolation
methods based on GRNN aided channel state tracking.

(11)

𝑖=1

where 𝑦 𝑖 is interconnection weight in the 𝑖-th desired response.
After that, the output of the 𝑘-th output neuron in the
GRNN model is calculated as follows by using (10) and(11) and represented as a weighted average of the desired
responses.
𝑦ˆ 𝑘 = 𝑆w𝑘 /𝑆s .

Fig. 1. Architecture of GRNN.

(12)

5. Conventional GRNN Based
Channel Estimation
Since the reliability of DFCE in the last part of thepacket is low, the conventional GRNN based channel estimation is exploited to improve this problem [13]. This method
only uses the CSIs partially obtained by the pilots inserted at
the first symbol of the packet and that by DFCE in the intermediate data part of the packet, to employ the GRNN for

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channel identification and compensation. The pilot patternof the conventional method is shown in Fig. 2. Because of thenonlinear generalization capabilities, GRNN can be trainedby only a few estimated CSIs to accurately trace the whole
CSI transition. In addition, this approach unnecessitates torepeat the iterative learning process.

Fig. 2. Conventional pilot pattern.

1
2

GRNN

[1,2,…,Nt]

Nf-1
Nf

澽濢濤濩濨

澺濦濙濥濩濙濢濗濭澔濘濝濦濙濗濨濝濣濢濈濝濡濙澔濘濝濦濙濗濨濝濣濢瀖

Figure 3 presents the block diagram of channel estimation based on GRNN when the number of symbols is 𝑁𝑡 andthe number of subcarriers is 𝑁 𝑓 . GRNN can predict an arbitrary function which has the relationship between the input
vector and the desired responses by the training. Here, we
set time-domain symbol indices [1, 2, . . . , 𝑁𝑡 ] as the input
and frequency-domain channel responses Hout are set as the
GRNN output. During the GRNN training as a regressionfunction, indices [1, 𝑠] are set as the training inputs where𝑠 denotes the arbitrary symbol index. The 1st desired response and the 2th one are set as CSIs estimated by PCE forthe 1st symbol and by DFCE for the 𝑠-th symbol, respectively. In addition, the training inputs are the center of each
RBF in the pattern layer. The desired responses are to be
the weight of weighted summation directly in the summation
layer. As a result, it does not need to learn to adjust theweights like MLFNN which must repeat the iterative learning process. Moreover, although the CSI contains real andimaginary parts, the desired responses can be directly set as
the weight of complex value in (11), without being divided
into two parts for the desired responses such as MLFNN.

Hout濃濩濨濤濩濨

濈濦濕濝濢濝濢濛澔濧濙濨濧[1,s]Supervised signal:
Desired channel[PCE,DFCE]

Fig. 3. Block diagram of channel estimation based on GRNN.

In the prediction phase, the vector composing of indicesfor the whole symbols [1, 2, . . . , 𝑁𝑡 ] are input to GRNN.
Each output of GRNN (𝑚 = 1, 2, . . . , 𝑁 𝑓 ) corresponds to the𝑚-th subcarrier’s CSI which is the complex value. Therefore,
all of outputs of GRNN can present the whole channel statetransition as follows, ℎout (1, 1)..
Hout = .
 ℎout (𝑁 𝑓 , 1)


···
..
.
···

ℎout (1, 𝑁𝑡 )
..
.




.

ℎout (𝑁 𝑓 , 𝑁𝑡 ) 

(13)

However, under the fast fading environment, the channel statetransition even in the beginning part is rapid so that the CSI estimated by only DFCE may also be inaccurate even if DFCE isconducted in the beginning part of the packet. Furthermore,
GRNN trained by this inaccurate information as the desired
responses cannot correctly compensate for the channel variation especially in the last part of the packet. Therefore, any
method is needed for enhancing the reliability of desired responses and further improving the performance of channel
compensation. Different from the conventional method that
the CSIs in the 𝑠-th symbol are all estimated by DFCE, weintroduce the following proposed method in the pilot patternof Fig. 4.

Fig. 4. Scattered pilot pattern.

6. Proposed System
In order to improve the reliability of the desired responses for the time variation, we incorporate the scatteredpilot into the GRNN based channel identification and compensation. The conventional GRNN based channel estimation used only two spare training sets to estimate the wholetransition of channel state because of the generalization ability of GRNN. Therefore, a modified scheme is proposed forthe training set.

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6.1 Scattered Pilot
In order to have an excellent ability to follow time fluctuations, the scattered pilot shown in Fig. 4 is employed.
Different from the conventional method that the pilots areinserted at the head of the packet, the proposed scatteredpilot is that the pilots are distributed in the front and firsthalf of the packets. In other words, the pilots are inserted
into every other subcarrier in the 1st and the 𝑠-th symbols.
Since the same number of pilots as the conventional method
is used, this scattered pilot pattern can maintain the signaltransmission efficiency. In addition, since half of the pilots
are shifted from the first symbol to the 𝑠-th symbol as thesecond desired response, it can not only ensure the resolution
in the frequency domain, but also raise the stability of thedesired response required for GRNN, which is superior to
track the channel changes over time.

Fig. 5. DFCE in the scattered pilot.
Q
I

CSI

Transmitted signal
Received signal

Q

6.2 DFCE in the Scattered Pilot

I

DFCE implemented in the scattered pilot is different
from the pilots set at the head of packet structure. At the 1stor the 𝑠-th symbols, the 𝑚-th null pilots (𝑚 = 1, . . . , 𝑁 𝑓 /2)
is interpolated by the DFCE which makes the decision fromthe channel H̃P (𝑚) obtained by 𝑚-th pilot signals at the 𝑠-th
symbol or 1st symbol, respectively. Equations (5) and (7) arechanged as follows and the process is shown in Fig. 5.
Yrep (𝑘, 𝑖) = H̃P (𝑚, 𝑜)D′ (𝑘, 𝑖),Ȟ(𝑘, 𝑖) = ΔH(𝑘, 𝑖) · H̃P (𝑚, 𝑜)

(14)
(15)

where 𝑜 = 1 or 𝑜 = 𝑠, 𝑘 = 2𝑚 − 1 or 𝑘 = 2𝑚.

6.3 The Improved Version of GRNN Based
Channel Identification and Compensation
MethodThe proposed scheme then employs GRNN to compensate channel transition using the scattered pilot. In our
proposal, the pilot symbol is inserted to the 1st and the 𝑠-th
symbol as shown in Fig. 5. Thanks to the scattered pilot set
in the beginning part of the packet, we can diminish the influence of decision error by leveraging CSI of the 2nd desired
response corresponding to the 𝑠-th symbol. Due to the higher
reliability of desired symbols, GRNN estimates whole channel state transitions more precisely than the previous scheme.
Figure 6 represents the procedure of the proposed
scheme. These steps are similar to the conventional GRNN
method until GRNN training. After interpolation process, theinterpolated CSIs ĤSP which are set as the desired responses
are shown as
ĤSP (2𝑚 − 1, 1) = H̃P (𝑚, 1),(16)

ĤSP (2𝑚, 1) = Ĥ(2𝑚, 1),(17)

ĤSP (2𝑚, 𝑠) = H̃P (𝑚, 𝑠),(18)

ĤSP (2𝑚 − 1, 𝑠) = Ĥ(2𝑚 − 1, 𝑠).

(19)

1

ʀʀʀ

s

ʀʀʀ

ʀʀʀ
ʀʀʀ

ܰ௧

Time

Scattered pilot
DFCE

DFCE

Data symbol
Training input

Fig. 6. The flow of channel estimation based on GRNN.

Then, [1, 𝑠] are defined as the training inputs. Lastly, just likethe conventional scheme, the vector composed of indices for
all data symbols are input to the GRNN. Thanks to improving
the reliability of the desired responses, GRNN outputs Hout
more accurately and we can use this information for channel
compensation.

6.4 Comparison of DFCE and General
Interpolation Method in the Scattered Pilot
Prior to employing GRNN to train, the general onedimensional interpolation in the frequency-domain could
also be used such as linear, spline and other interpolation
approaches [23]. The interpolated CSI is regarded as thedesired response of GRNN. If the CSI of the pilot signals in
the frequency domain is directly used for interpolation, theNyquist sampling theorem must be met as follows [24–26],
𝜏max · △𝐹 · 𝑁𝑖 ≤ 1(20)

where 𝜏max is the maximum multipath delay time, △𝐹 is subcarrier spacing, 𝑁𝑖 is the interval of adjacent pilot in thefrequency-domain. For example, the Nyquist law is to keep
the impulse responses in the time domain without overlapping as shown in Fig. 7(a). On the other hand, the excessive
pilot interval causes overlap of impulse responses, i.e. aliasing, as shown in Fig. 7(b) and it complicates interpolating
CSI for nullified subcarriers.

H. HE, S. KOJIMA, T. OMURA, ET AL., GENERALIZED REGRESSION NEURAL . . .

freq.

Parameters
Transmission scheme
Data modulation
FFT size, Number of carriers
Guard interval
Number of pilot symbols
Number of data symbols
Channel model
Max Doppler frequency
Transmission bandwidth

time

Forward error correction

power
power

power

freq.

time

Ĳmax

Ĳmax

(a) 𝑁𝑖 = 2(b) 𝑁𝑖 = 4

Function of pattern layer

Fig. 7. Time and frequency representations of channel.

For DFCE interpolation in the frequency domain, as
long as each subcarrier has a pilot in the frequency domain,
the range of Nyquist law is the same as the conventional
method of placing the pilot at the beginning of the packet
expressed as follows,𝜏max · △𝐹 ≤ 1.

ValuesOFDM
QPSK
𝑁 𝑓 = 6416
𝑁𝑝 = 1
𝑁𝑡 = 2015 path Rayleigh fading, 1 dB decay
800 Hz20 MHzConvolutional code
(𝑅 = 1/2, 𝐾 = 7)
Gaussian

Tab. 1. Simulation Parameters.

(21)

This is because DFCE refers to the pilot information in thefront and back time directions and no matter what the interval
𝑁𝑖 is. Accordingly, the CSI of the whole subcarriers can becalculated by DFCE. For example, the pilots are distributed
as shown in Fig. 4. When the subcarriers of the frequency
domain without any pilots in the 𝑠-th symbol are interpolated by the general one-dimensional interpolation method
like spline interpolation, the Nyquist theorem must be met as
follows and the spacing of the pilots in the frequency-domain
must be considered as follows,1(22)
𝜏max · △𝐹 ≤2
where the interval in the frequency domain is 𝑁𝑖 = 2. Thisis because only the CSI of the pilot signal of the s-th symbol is used for interpolation in the frequency domain. But
for DFCE, when the CSI of the pilot signal corresponding
to the first symbol is used to implement DFCE, the place
where there is no pilot in the 𝑠-th symbol is interpolated by
the DFCE as formulated in (14), (15) and (19). Accordingly,
the range of satisfying the Nyquist theorem is doubled like
(21). In other words, since the CSI of the pilots in the timedomain is used to interpolate instead of using the CSI of theadjacent pilot in the frequency-domain, only the subcarrier
spacing △𝐹 is considered, and there is no need to consider
the interval of pilots 𝑁𝑖 in the frequency domain.

7. Computer Simulation
7.1 Simulation Parameters
Table 1 summarizes the simulation parameters. The
simulations are performed using MATLAB R2018a, an Intel Core i5 CPU at 3.00 GHz and 8 GB of memory storage. Transmission scheme is OFDM with 64 FFT points.

0
Relative power [dB]

power

700

-5

-10

-15
0

200

400
Delay [nsec]

600

800

Fig. 8. Channel model.

The data stream is encoded by convolution codes (𝑅 =1/2, 𝐾 = 7). 𝑁 𝑝 and 𝑁𝑡 denote the number of pilot and data
symbols, respectively. The transmission bandwidth assumes
20 MHz and the OFDM symbol duration is 4 μs, including
guard interval (GI), referred to the basic Wi-Fi specifications.
The Jakes’ fading model is used to represent time-varying
channel. Suppose 15 multipaths, the average path gain ofeach is attenuated by 1 dB as shown in Fig. 8. Here, multipath time-delay is 50 ns. The maximum Doppler frequency
is 800 Hz, which can indicate a fast fading environment. The
scattered pilot structure assumed in the simulation is shownin Fig. 5. The pilots are set in the odd subcarriers of thefirst symbol and the even subcarriers of the 𝑠-th symbol,
respectively.

7.2 Simulation Results
As the preliminary evaluation, we compare the scattered pilot method of DFCE with the general interpolation
method which performs low-complexity interpolation in thefrequency-domain. Here we use calculation time to compare
the computation complexity as summarized in Tab. 2. The
spline interpolation requires complex computation with allreference values and thus it takes twice as much time to interpolate CSI in the frequency-domain than DFCE. Therefore,
DFCE-aided interpolation is computationally efficient.
MethodSplineDFCE

Calculation time
0.905 ms
0.406 ms

Tab. 2. Computation time comparison

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Root mean square error (RMSE) is then used to compare
the interpolation accuracy with the CSI at the first symbolof the packet. In Fig. 9, the lowest RMSE values are presented when the DFCE method is applied to interpolate the
CSI in the frequency domain. From this result, the DFCE
method has the best performance and can be introduced into
the desired response of GRNN in the proposed method.
Hereafter the optimum parameters for the conventional
and the proposed methods are examined for fair comparison.
Figure 10 presents the bit error rate (BER) versus radius of
RBF 𝑟 for the conventional method and the proposed method
at Eb /N0 = 25 dB and 𝑠 = 10. When the radii of RBF 𝑟 are 4.5
and 5, the conventional and the proposed methods show thebest BER performance, respectively. The above parameters
are used to verify the best parameters. Figure 11 presents the
BER performance comparison with the position of the second scattered pilot at Eb /N0 = 25 dB. Both methods achieve

the best BER performance at 𝑠 = 10. From this result, weapply parameters as 𝑠 = 10 and 𝑟 = 4.5 for the conventional
method, and 𝑠 = 10 and 𝑟 = 5 for the proposed method.
Figure 12 shows the BER performances of the DFCE
only, the conventional GRNN method and the proposed
method. The BER performance of the DFCE significantly
deteriorates because decision errors frequently happen in thelast part of the packet. Although the conventional GRNN
method can obtain more improved BER performance thanthat of the DFCE only, the error floor appears at around
BER = 10−4 . The proposed approach removes the error floor
and achieves the best BER performance below 10−5 . Basedon this result, it was confirmed that the proposed method
could improve the reliability of the desired response derived
from the DFCE-aided interpolation of scattered pilot symbols. Therefore, channel tracking performance with compensation is greatly improved for all data symbols by GRNN, andSplineDFCE

0-4Con.GRNN[no-sp]
Pro.GRNN[sp]

10

BER

RMSE

10

701

-1

-5

10

-6

10

10
0

5

10

15

20

25

30

0

2

Eb/No
Fig. 9. RMSE vs. Eb /N0 for the interpolation methods.

-3

8

10

Fig. 10. BER vs. Radius of RBF 𝑟 (Eb /N0 = 25 dB, 𝑠 = 10).

Con.GRNN[no-sp]
Pro.GRNN[sp]1046radius of RBF r

10

Con.DFCE
Con.DFCE-GRNN
Pro.DFCE-GRNN

0

-1

10
-4

10

-2

BER

BER

10

-5

10

-3

10

-4

10

-5

10
-6

10

-6

0

5

10

15

20

10

0

5

Symbol number s
Fig. 11. BER vs. Symbol index 𝑠 (Eb /N0 = 25 dB).

10

15
Eb/No

Fig. 12. BER vs. Eb /N0 .

20

25

30

702

H. HE, S. KOJIMA, T. OMURA, ET AL., GENERALIZED REGRESSION NEURAL . . .

the proposed system provides the superior channel tracking
capability. From the above, it is shown that the DFCE methodin the scattered pilot is quite effective under high mobility environment and has better performance than the conventional
GRNN method and the general interpolation method.

[7] OMURA, T., KOJIMA S., MARUTA, K., et al. Neural network based channel identification and compensation. IEICE
Communications Express, 2019, vol. 8, no. 10, p. 416–421.
DOI: 10.1587/comex.2019XBL0095

8. Conclusion[9] YOFUNE, M., AHN, C. J., KAMIO, T., et al. Decision direct andlinear prediction based fast fading compensation for TFIOFDM. Far
East Journal of Electronics and Communications, 2009, vol. 3, no. 1,
p. 35–52.

In this paper, we proposed the GRNN based channel
identification and compensation method using the scatteredpilot to improve the reliability of the desired response for
the GRNN. From the simulation results of the general lowcomplexity interpolation method and the proposed method
comparisons, the proposed method is the most effective forinterpolating in the frequency domain of the scattered pilot
with lower computation complexity. Moreover, comparing
the proposed method with the conventional method, the proposed method that changes the distribution of pilots can refine
the performance of the desired response without degrading
the transmission efficiency, thus improving the whole channel
tracking performance of the GRNN. Through the computer
simulation, the proposed method has shown the best BER
performance compared with the DFCE only and the conventional GRNN method even at 800 Hz maximum Doppler
frequency. Accordingly, we can conclude that the proposed
method greatly enhances the effect of channel compensation,even in the high mobility environment.

References[8] SOEJIMA, S., IDA, Y., AHN, C. J., et al. Fast fading compensation
based on weighted channel variance for TFI-OFDM. Journal of Signal Processing, 2013, vol. 17, no. 3, p. 41–49. DOI: 10.2299/jsp.17.41[10] CHENG, C. H., HUANG, Y. H., CHEN, H. C. Channel estimation in
OFDM systems using neural network technology combined with a genetic algorithm. Soft Computing, 2016, vol. 20, no. 10, p. 4139–4148.
DOI: 10.1007/s00500-015-1749-7[11] SARWAR, A., SHAH, S. M., ZAFAR, I. Channel estimation in spacetime block coded MIMO-OFDM system using genetically evolved
artificial neural network. In International Bhurban Conference on
Applied Sciences and Technology (IBCAST). Islamabad (Pakistan),
2020, p. 703–709. DOI: 10.1109/IBCAST47879.2020.9044539[12] SAHU, P., MOHAPATRA, P., PANIGRAHI, S., et al. Neural network
training using FFA and its variants for channel equalization. International Journal of Computer Information Systems and Industrial Management Applications, 2017, vol. 9, p. 257–264. ISSN: 2150-7988[13] OMURA, T., HOEUR, N., MARUTA, K., et al. Improving ANN
based channel identification and compensation using GRNN method
under fast fading environment. In International Conference on Advanced Technologies for Communications (ATC). Hanoi (Vietnam),
2019, p. 28–32. DOI: 10.1109/atc.2019.8924557[14] COLERI, S., ERGEN, M., PURI, A., et al. Channel estimation
techniques based on pilot arrangement in OFDM systems. IEEE
Transactions on Broadcasting, 2002, vol. 48, no. 3, p. 223–229.
DOI: 10.1109/tbc.2002.804034[1] MARTIKAINEN, H., VIERING, I., et al. Mobility and reliability
in LTE-5G dual connectivity scenarios. In IEEE Vehicular Technology Conference (VTC-Fall). Toronto (Canada), 2017, p. 1–7.
DOI: 10.1109/vtcfall.2017.8288056[15] STERBA, J., KOCUR, D. Pilot symbol aided channel estimation forofdm system in frequency selective Rayleigh fading channel. In International Conference Radioelektronika. Bratislava (Slovakia), 2009,
p. 77–80. DOI: 10.1109/radioelek.2009.5158729[2] ALWAKEEL, A. S., MEHANA, A. H. Data-aided channel estimation
for multiple-antenna users in massive MIMO systems. IEEE Transactions on Vehicular Technology, 2019, vol. 68, no. 11, p. 10752–10760.
DOI: 10.1109/tvt.2019.2938344[16] GOLDSMITH, A. Wireless Communications. Cambridge University
Press, 2005. ISBN: 9787115170491[3] FUNADA, R., HARADA, H., KAMIO, Y., et al. A channel estimation method for a highly mobile OFDM wireless access system.
IEICE Transactions on Communications, 2005, vol. E88-B, no. 1,
p. 282–291. DOI: 10.1093/ietcom/e88-b.1.282[4] HAYASHI, H., OKAMOTO, E., IWANAMI, Y. A fast fading channel estimation scheme for OFDM with sparse and scattered pilot
symbols. In International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS). Kanazawa (Japan), 2009,p. 154–157. DOI: 10.1109/ISPACS.2009.5383877[5] OUYANG, R., MATSUMURA, T., MIZUTANI, K., et al. A reliable channel estimation scheme using scattered pilot pattern forIEEE 802.22-based mobile communication system. IEEE Transactions on Cognitive Communications and Networking, 2019, vol. 5,
no. 4, p. 935–948. DOI: 10.1109/tccn.2019.2930594[6] OMURA, T., KOJIMA S., MARUTA, K., et al. Neural network based
channel identification and compensation. In International Symposiumon Communications and Information Technologies (ISCIT). Bangkok(Thailand), 2018, p. 349–354. DOI: 10.1109/iscit.2018.8587981[17] GHASSEMLOOY, Z., POPOOLA, W., RAJBHANDARI, S. Optical Wireless Communications: System and Channel Modelling with
MATLAB. CRC Press, 2017. ISBN: 9781138074804[18] SPECHT, D. F. General regression neural network. IEEE Transactions on Neural Networks, 1991, vol. 2, no. 6, p. 568–576.
DOI: 10.1142/9789812796851-0008[19] AMIRI, M., DAVANDE, H., SADEGHIAN, A. et al Feedback associative memory based on a new hybrid model of generalized regression and self-feedback neural networks. Neural Networks, 2010,
vol. 23, no. 7, p. 892–904. DOI: 10.1016/j.neunet.2010.05.005[20] QI, J., JIANG, G., LI, G., et al. Surface EMG hand gesturerecognition system based on PCA and GRNN. Neural Computing and Applications, 2020, vol. 32, no. 10, p. 6343–6351.
DOI: 10.1007/s00521-019-04142-8[21] GHRITLAHRE, H. K., PRASAD, R. K. Exergetic performance prediction of solar air heater using MLP, GRNN andRBF models of artificial neural network technique. Journalof Environmental Management, 2018, vol. 223, p. 566–575.
DOI: 10.1016/j.jenvman.2018.06.033

RADIOENGINEERING, VOL. 30, NO. 4, DECEMBER 2021

[22] NETO, M. C. A., ARAUJO, J. P. L., MOTA, R. J. S., et al. Designand synthesis of an ultra wide band FSS for mm-wave application
via general regression neural network and multiobjective bat algorithm. Journal of Microwaves, Optoelectronics and Electromagnetic
Applications, 2019, vol. 18, no. 4, p. 530–544. DOI: 10.1590/217910742019v18i41729[23] MAKKAR, R., SONI, S., BACHKANIWALA, A. K., et al.
Pilot interpolation based channel estimation for LTE systems.
Procedia Computer Science, 2020, vol. 171, p. 2261–2266.
DOI: 10.1016/j.procs.2020.04.244[24] OZDEMIR, M. K., ARSLAN, H. Channel estimation for wireless
OFDM systems. IEEE Communications Surveys and Tutorials, 2007,
vol. 9, no. 2, p. 18–48. DOI: 10.1109/comst.2007.382406[25] ZERHOUNI, K., ELBAHHAR, F., ELASSALI, R., et al. Performance of universal filtered multicarrier channel estimation
with different pilots arrangements. In IEEE 5G World Forum (5GWF). Santa Clara (CA, USA), 2018, p. 327–332.
DOI: 10.1109/5gwf.2018.8517030[26] BAMBHANIYA, A. B., RATHOD, J. M. Research on various pilot
pattern design for channel estimation in OFDM system. International
Journal of Applied Engineering Research, 2017, vol. 12, no. 24,
p. 14403–14407. DOI: 10.1049/el:20000714

About the Authors . . .
He HE received the B.E. in Electrical and Electronics Engineering from Dalian Maritime University, Dalian, China, in2018 and the M.E. degree in Electrical and Electronics Engineering from Chiba University, Chiba, Japan in 2020. He
is now doing his Ph.D. program in the Chiba University. His
research interests include machine learning and developmentof next generation communication algorithm.
Shun KOJIMA received the B.E. and M.E. degrees in Electrical and Electronics Engineering from Chiba University,
Japan, in 2017 and 2018, respectively, where he is currently pursuing the Ph.D. degree with the Graduate Schoolof Engineering. His research interests include MIMO, cooperative communications, adaptive modulation and coding,neural networks, and channel estimation. He received theBest Paper Award from the 26th International Conference
on Software, Telecommunications and Computer Networks(SoftCOM2018).
Takaki OMURA received the B.E. and M.E. degrees inElectrical and Electronics Engineering from Chiba University, Japan, in 2018 and 2020, respectively.
Kazuki MARUTA received the B.E., M.E., and Ph.D. degrees in Engineering from Kyushu University, Japan, in 2006,

703

2008 and 2016, respectively. From 2008 to 2017, he waswith NTT Access Network Service Systems Laboratories andwas engaged in the research and development of interferencecompensation techniques for future wireless communication
systems. From 2017 to 2020, he was an Assistant Professor in the Graduate School of Engineering, Chiba University.
He is currently a Specially Appointed Associate Professor
in the Academy for Super Smart Society, Tokyo Institute ofTechnology. His research interests include MIMO, adaptivearray signal processing, channel estimation, medium access
control protocols and moving networks. He is a memberof the IEEE and The Institute of Electronics, Information
and Communication Engineers (IEICE). He received the IEICE Young Researcher’s Award in 2012, the IEICE Radio
Communication Systems (RCS) Active Researcher Award in
2014, APMC2014 Prize, the IEICE RCS Outstanding Researcher Award in 2018, and the IEEE ICCE Excellent Paper
Award in 2021. He was a co-recipient of the IEICE Best
Paper Award in 2018, SoftCOM2018 Best Paper Award and
APCC2019 Best Paper Award.
Chang-Jun AHN received the Ph.D. degree from the Department of Information and Computer Science from Keio
University, Japan, in 2003. From 2001 to 2003, he was a Research Associate with the Department of Information andComputer Science, Keio University. From 2003 to 2006,
he was with the Communication Research Laboratory, Independent Administrative Institution (National Institute ofInformation and Communications Technology). In 2006, he
was on assignment with ATR Wave Engineering Laboratories. In 2007, he was a Lecturer with the Faculty of Information Sciences, Hiroshima City University. He is currently
a Professor with the Graduate School of Engineering, Chiba
University. His research interests include OFDM, MIMO,
digital communication, channel coding, signal processing
for telecommunications, and wireless power transfer. He
served as an associate editor of the IEICE Trans. on Fundamentals. From 2005 to 2006, he was an expert committee
member for emergence communication committee, Shikoku
Bureau of Telecommunications, Ministry of Internal Affairs
and Communications (MIC), Japan. Dr. Ahn received the
ICF research grant award for Young Engineer in 2002, the Funai Information Science Award for Young Scientist in 2003,
the Distinguished Service Award from Hiroshima City in2010, IEEE SoftCOM2018 Best Paper Award in 2018, IEEE
APCC2019 Best Paper Award in 2019, IEICE ICETC2020
Best Paper Award in 2020, and Journal of Signal Processing
Best Paper Award in 2021. He is a senior member of IEICE
and IEEE.