Blind Channel Estimation Method Using CNN-Based Resource Grouping

Abstract

This paper proposes a novel blind channel estimation method using convolutional neural network (CNN)-based resource grouping. The traditional K-means-based blind channel estimation scheme suffers limitations in reflecting fine-grained channel variations in both the time and frequency domains. To address these limitations, we propose dynamic resource grouping based on CNN architecture utilizing a two-step learning process that adapts to various channel conditions. The first step of the proposed method identifies the optimal number of subcarriers for each channel condition, providing a foundation for the second step. The second step adjusts the number of orthogonal frequency division multiplexing (OFDM) symbols, a parameter for determining the proposed pattern in the time domain, to adapt to dynamic channel variations. Simulation results demonstrate that the proposed CNN-based blind channel estimation method achieves high channel estimation accuracy across various signal-to-noise ratio (SNR) levels, attaining the highest accuracy of 82.5% at an SNR of 10 dB. Even when classification accuracy is relatively low, the CNN effectively mitigates signal distortion, delivering superior performance compared to conventional methods in terms of mean squared error (MSE) across diverse channel conditions. Notably, the proposed method maintains robust performance under high-mobility scenarios and severe channel variations.

1. Introduction

The 3rd Generation Partnership Project (3GPP) is currently advancing the standardization of Release-19, which corresponds to 5G-Advanced, while also discussing the roadmap for 6G standardization [1]. To realize 5G-Advanced and beyond, including 6G, active research is being conducted to integrate artificial intelligence (AI)-based machine learning (ML) and deep learning (DL) into communication services. AI has been widely applied to various technologies, such as traffic prediction, beamforming and beam management, cell coverage optimization, and channel estimation [2,3,4,5,6].

Several methods have been proposed to improve channel estimation performance, which is a core aspect of wireless communication systems [7,8,9,10]. In [7], a deep neural network (DNN)-based channel prediction framework was introduced to mitigate the degradation of channel estimation accuracy in scenarios with rapidly varying consecutive channel responses. Another approach to enhancing channel estimation performance proposed the sliding bidirectional gated recurrent unit (SBGRU) estimator, which integrates the recurrent neural network (RNN) structure with the sliding window concept [8]. To further enhance channel estimation, a convolutional neural network (CNN)-based method was proposed to tackle performance degradation caused by spreading factor interference in long-range (LoRa) systems [9]. Moreover, for doubly selective channels in high-speed mobile scenarios, channel estimation was enhanced through the compression-and-reconstruction channel estimation network (CRCENet) [10]. Therefore, accurate channel estimation is crucial to ensuring network stability and improving the quality of received signals across various environments.

For channel estimation, the demodulation reference signal (DM-RS), commonly referred to as a pilot signal, has been adopted as a standard technology for channel estimation. DM-RS is allocated to radio resources and transmitted along with uplink and downlink data, enabling it to effectively respond to real-time channel variations. However, due to its inherent characteristic of occupying radio resources, inefficient resource management of DM-RS can lead to resource wastage. Several studies have explored neural network-based approaches to optimize DM-RS resource management efficiently. Beyond optimizing existing DM-RS resources, channel estimation algorithms leveraging the most significant lag (MSL) have been proposed, along with semi-blind channel estimation methods that combine conventional DM-RS with detected symbols [11,12]. Moreover, blind channel estimation methods utilizing the K-means clustering algorithm, a widely used unsupervised learning scheme, have also been introduced [13]. K-means clustering-based channel estimation enhances wireless resource efficiency by relying solely on received signals, eliminating the need for DM-RS consumption. This approach provides an advantage over semi-blind channel estimation methods that require a significant number of DM-RS resources to ensure reliable operation. Therefore, this paper aims to improve the K-means algorithm-based channel estimation method, which is one of the blind channel estimation schemes that do not utilize DM-RS.

K. Jung and H. Wang [13] proposed a K-means-based blind channel estimation method that performs clustering on the received signals without transmitting DM-RS. In this study, the received signals are clustered using the K-means algorithm, and the centroids of the clusters are used to identify the original positions of quadrature phase shift keying (QPSK) symbols of the transmitted signal. By identifying the phases of QPSK symbols significantly altered due to multipath fading back to their original positions, this method achieves channel estimation without pilot signals, effectively canceling noise. However, this method has the limitation of determining the same channel for all received signals processed by the K-means clustering algorithm, making it ineffective in addressing channel variations at the subcarrier and orthogonal frequency division multiplexing (OFDM) symbol levels.

This paper overcomes the limitations of the methods proposed in [13] by introducing resource grouping patterns for K-means-based blind channel estimation and proposing a two-step learning method using CNN to select optimal patterns. Unlike existing methods, this study focuses on improving the efficiency of radio resource usage by effectively adapting to fine-grained and dynamically changing channel characteristics. The proposed two-step learning structure identifies the optimal number of subcarriers under each channel condition in the first step and refines the number of OFDM symbols based on time-domain variations in the second step. By designing dynamic resource grouping patterns adaptable to various channel conditions, such as signal-to-noise ratio (SNR), UE velocity, and delay spread, this study distinguishes itself from existing K-means algorithm-based approaches. Performance analysis evaluates the channel estimation accuracy of the proposed method and compares it to existing methods in terms of mean squared error (MSE) and resource efficiency. This study provides a foundation for robust and resource-efficient channel estimation in dynamic wireless communication systems.

2. System Model

2.1. NR Frame Structure

In New Radio (NR), transmitted data is allocated to time-frequency resources at the physical layer for transmission. Uplink and downlink data can be assigned to a single or multiple orthogonal frequency division multiplexing (OFDM) symbol(s) in the time domain within a single slot, as well as to a single or multiple RB(s) in the frequency domain. A single slot can consist of 14 OFDM symbols, and a single RB consists of 12 subcarriers [14].

2.2. K-Means-Based Blind Channel Estimation

Channel estimation based on the K-means clustering algorithm is performed on received signals. The generated transmission bits undergo channel coding, QPSK modulation, and OFDM modulation to generate the transmitted signal [14]. The transmitted signal then passes through a wireless fading channel, with noise added to produce the received signal. The noise is modeled as additive white Gaussian noise (AWGN). The receiver performs OFDM demodulation, channel estimation, channel decoding, and QPSK demodulation to estimate the transmitted bits [15]. The channel estimation is carried out using the K-means clustering algorithm. The estimated bits are compared with the original transmitted bits to calculate the bit error rate (BER). The received signal is written as:

$$y_{k,l}=h_{k,l}{x}_{k,l}+n_{k,l},$$

(1)

where $y_{k,l}$ denotes the received signal for the $k$-th OFDM symbol and the $l$-th subcarrier, $h_{k,l}$ represents the wireless fading channel, $x_{k,l}$ denotes the transmitted signal, and $n_{k,l}$ denotes AWGN. The UE receiving $y_{k,l}$ preforms channel estimation based on the K-means clustering algorithm on the OFDM demodulated signal to obtain data information. This channel estimation method appropriately considers the delay spread and the velocity of the UE, classifying the signal into multiple groups. For instance, if the UE is moving at high velocity, the signal should be classified into finer units of OFDM symbols along the time domain. Conversely, if the UE exhibits significant delay spread, classification should occur at finer subcarrier units along the frequency domain. Within each appropriately classified group, the wireless resources are mapped to one of the four QPSK constellation points based on the K-means clustering algorithm, written as:

$$x_{k,l}=c^{{\displaystyle \frac{j\left(2m-1\right)\pi }{4}}}.$$

(2)

within each cluster, four clusters and their respective centroids are derived, as shown in Figure 1.

The data symbols, represented in four distinct colors, are identified as the centroids of each cluster. This process effectively cancels distortions caused by wireless channel effects and noise. However, there is an ambiguity issue, as it is unclear which of the original QPSK constellation points corresponds to the four QPSK symbols. To resolve this, channel estimation is performed based on Equation (3) to determine each centroid as one of the four QPSK symbols:

$${\widehat{h}}_{k,l}={\displaystyle \frac{y_{k,l}}{x_{k,l}}},$$

(3)

where ${\widehat{h}}_{k,l}$ represents the estimated channel, and channel estimation is performed for all four clusters within each group, resulting in a total of 16 estimated channels. The estimated channel for all symbols within the range where the algorithm is applied is considered as the channel estimated by the K-means algorithm. To determine the best ${\widehat{h}}_{k,l}$ among the 16 estimated channels, transmission bit estimation is performed based on:

$${\widehat{x}}_{k,l}={\displaystyle \frac{y_{k,l}}{{\widehat{h}}_{k,l}}},$$

(4)

where ${\widehat{x}}_{k,l}$ represents the estimated transmission signal, used along with the original transmitted signal $x_{k,l}$ to calculate the BER. The channel that achieves the highest BER is ultimately determined as the final estimated channel, ${\tilde{h}}_{k,l}$.

Subsequently, the channel estimation performance is analyzed through the MSE calculation between ${\tilde{h}}_{k,l}$ and $h_{k,l},$ which is based on:

$$MSE={\displaystyle \frac{1}{n}}\sum _{k=1}^n({\displaystyle \frac{1}{m}}\sum _{l=1}^m{\left|h_{k,l}-{\tilde{h}}_{k,l}\right|}^2),$$

(5)

where $n$ denotes the number of OFDM symbols in the resource grid and $m$ is the number of subcarriers in the resource grid.

3. Proposed Method

3.1. Resource Grouping Pattern

The channel estimation based on the K-means algorithm identifies the centroids of each cluster, effectively counteracting signal distortion. However, this channel estimation method must adequately account for significant channel variability along the time and frequency domains to perform clustering effectively. For instance, if the channel varies rapidly in the time domain due to high Doppler effects, the groups must be densely configured along the time domain. Similarly, if the channel exhibits rapid variation in the frequency domain due to significant delay spread, the groups must be densely configured with single or multiple subcarriers along the frequency domain. Such clustering-based K-means algorithm channel estimation cannot be optimally performed for all UEs. In this paper, to address this limitation, we propose a method that generates resource group patterns within the resource grid for received signals to enable the K-means-based blind channel estimation to operate effectively by identifying the characteristics of the dynamically changing channel. The resource group pattern consists of $t$ consecutive OFDM symbols in the time domain and $f$ consecutive subcarriers in the frequency domain. The number of consecutive OFDM symbols, $t$, can range from {1, 2, …, 14}. If $t$ is not a divisor of 14, which is the total number of OFDM symbols in a single slot, the remaining OFDM symbols that do not satisfy this condition are grouped into the maximum possible number of consecutive OFDM symbols.

In this paper, such groups are defined as remainder groups. Additionally, the number of consecutive subcarriers, $f$, can take any value among the divisors of 120 within 10 RBs. The divisors of 120, $D\left(120\right)$ are expressed in Equation (6) and are listed as {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}, for a total of 16 values:

$$D\left(120\right)=\left\{ 2^a·3^b ·5^c \right|0\le a\le 3, 0\le b\le 1, 0\le c\le 1\}.$$

(6)

In other words, the resource grouping patterns for the received signal can consider 14 cases in the time domain and 16 cases in the frequency domain, resulting in a total of 224 possible patterns. For instance, in a pattern where $t=7$ and $f=60$ within 1 slot in the time domain and 10RBs in the frequency domain, one resource group consists of 7 consecutive OFDM symbols in the time domain and 60 consecutive subcarriers in the frequency domain.

As shown in Figure 2, the clustering pattern consists of a total of four groups, and K-means clustering-based channel estimation is performed for each group within the pattern. In Figure 2, within the resource grid corresponding to one slot in the time domain and 10 RB in the frequency domain, each group is distinguished by different colors, and K-means clustering-based channel estimation is executed for each group. Channel estimation is performed for a single resource group, as shown by the red dashed lines. The estimated channel values are represented as ${\tilde{h}}_1, {\tilde{h}}_2, {\tilde{h}}_3, {\tilde{h}}_4$, and each resource group is estimated to have the same channel.

The generated resource groups must identify QPSK symbols through K-means-based channel estimation, requiring at least four REs within each group. In this paper, this requirement is defined as the minimum RE count condition. Patterns that do not satisfy this condition are excluded. For example, in the pattern where $t=2$ and $f=1$, a single group consists of two consecutive OFDM symbols in the time domain and one subcarrier in the frequency domain, resulting in a total of 840 groups. Since each group in this pattern contains only two REs, channel estimation using the K-means algorithm cannot be performed. Therefore, this pattern is excluded for failing to meet the minimum RE count condition.

Another case is the pattern where $t=1$ and $f=3$, in which a single group consists of one OFDM symbol in the time domain and three subcarriers in the frequency domain, resulting in a total of 560 groups for the entire pattern. Since the REs within each group of this pattern are four or fewer, it is excluded. Additionally, the minimum RE count condition is equally applied to the remainder groups. For example, in the grouping pattern where $t=6$ and $f=1$, a resource group consists of six consecutive OFDM symbols in the time domain and a single subcarrier in the frequency domain. In this case, the 13th and 14th OFDM symbols in the time domain combined with a single subcarrier in the frequency domain form the remainder group, which contains only two REs and, thus, fails to meet the minimum RE count condition. Consequently, this resource grouping pattern is also excluded. Therefore, considering $t$ and $f$, 212 patterns can be configured out of the 224 resource group patterns, excluding those that do not meet the minimum resource count condition.

3.2. Data Set Generation

This paper evaluates channel estimation performance by supporting optimal resource groups for all UEs. To this end, among all configured resource grouping patterns, the pattern that achieves the highest channel estimation performance in arbitrary channel environments is derived based on Equation (5) and utilized as the correct label for the CNN. The channel environment considers factors such as the UE’s velocity and delay spread. For instance, when the UE’s velocity is 30 km/h, the channel environment is relatively stable, making a pattern composed of resource groups with many OFDM symbols effective. Conversely, when the velocity is 150 km/h, a pattern composed of resource groups with a smaller number of OFDM symbols will be more effective.

The delay spread is considered from 50 ns to 300 ns in increments of 50 ns, and velocity is considered from 30 km/h to 150 km/h in increments of 30 km/h, resulting in 30 channel conditions. The SNR is assumed to be perfectly calculated. The parameters used for dataset generation, including these, are summarized in

Table 1. Simulation parameters.

Parameters	Value
Subcarrier spacing	15 [kHz]
Number of RBs	10
Number of OFDM symbols	14
FFT size	2048
Sample rate	61,440,000 [Hz]
Carrier frequency	4 [GHz]
Channel model	tapped-delay line-D
Velocity	30:30:150 [km/h]
Delay spread	50:50:300 [ns]
SNR	−6:2:10 [dB]
Noise	AWGN
$N$	100,000
Iteration	100,000
Batch size	256
Epoch	20
Learning rate	0.002
Dropout period	9
Dropout factor	0.1
Optimizer	Adam

[16].

The K-means algorithm is employed for channel estimation without relying on pilot signals. In this study, an exhaustive search is performed to identify the optimal pattern among the 212 proposed resource grouping patterns for each of the 30 considered channel conditions using the K-means algorithm. The MSE for each pattern is computed using Equation (5), and the pattern with the best performance is selected as the optimal pattern for the corresponding channel condition. The identified optimal patterns are used to generate correct labels for each step of the two-step training process, which is detailed in Section 3.3. Subsequently, a CNN is employed to effectively group the data according to various channel conditions, including delay spread, velocity, and SNR. The CNN is trained to learn the optimal grouping method for each channel condition and outputs the corresponding grouping pattern for each received signal, thereby enabling more accurate channel estimation. K-means algorithm-based channel estimation requires a sufficient number of data samples to achieve accurate channel estimation, and the minimum number of required data samples for channel estimation may vary with the SNR level. When performing K-means algorithm-based channel estimation under low SNR conditions, a relatively larger number of resource grouping patterns from the 212 proposed in this study have proven to be effective. In contrast, at higher SNR levels, patterns with a relatively smaller number of resources are utilized for channel estimation. The proposed 212 patterns can be effective depending not only on the SNR but also on the delay spread, which affects channel variations in the frequency domain, and the velocity, which impacts the time domain.

Therefore, in this study, the optimal pattern obtained through an exhaustive search of the proposed 212 patterns is analyzed to examine the influence of delay spread, velocity, and SNR on channel estimation performance, as illustrated in Figure 3, Figure 4, Figure 5 and Figure 6. The 212 patterns proposed in this paper are grouped by each channel parameter and presented in Figure 3, Figure 4, Figure 5 and Figure 6 to illustrate the distribution of the optimal patterns. Figure 3 shows the distribution of the optimal number of OFDM symbols as $t$, which is the parameter determining the pattern in the time domain under different velocity conditions. The x-axis in each graph, labeled “Number of OFDM symbols per group”, represents the optimal $t$. In Figure 3, as the velocity of the UE increases, channel state variations in the time domain become more frequent and rapid, resulting in smaller values of $t$ appearing more frequently at higher velocities. This indicates that as velocity increases, the number of OFDM symbols per group decreases, necessitating channel estimation at smaller group sizes. Consequently, for relatively low velocities, such as 30 km/h, patterns with larger values of $t$ per group are determined to be optimal. In contrast, at higher velocities, such as 150 km/h, smaller group sizes are more suitable, leading to patterns with fewer OFDM symbols per group being identified as optimal.

Figure 4 illustrates the distribution of the optimal number of subcarriers, $f$, which is the parameter that determines the resource grouping pattern in the frequency domain under different delay spread conditions. This is represented on the x-axis of each graph.

In Figure 4, as the delay spread increases, channel variations in the frequency domain occur more rapidly and irregularly, requiring smaller values of $f$ per group for channel estimation in the frequency domain. For a low delay spread, such as 50 ns, forming groups is frequently determined as optimal patterns. In contrast, for a high delay spread, such as 300 ns, the group size becomes smaller to respond more finely to channel variations, and smaller values of $f$ are more widely distributed. This indicates that creating groups with smaller units is more effective under conditions of high delay spread, emphasizing the necessity of finer resource grouping in the frequency domain as the delay spread increases. Figure 3 and Figure 4 demonstrate that resource grouping into smaller units is effective under relatively high levels of velocity and delay spread. However, a substantial proportion of cases were identified where larger units of $t$ and $f$ were optimal, which shows that the $f$ with a value of 120 was the most frequently identified optimal value. Because the channel environments considered in this study include both low and high SNR levels, channel estimation based on the K-means algorithm requires an appropriate amount of data to achieve sufficient channel estimation performance based on the SNR level. This requirement increases as the SNR decreases, requiring more data. To meet this requirement, $f$, which offers more data points, is more effective than $t$ in terms of data quantity. Consequently, when performing K-means-based channel estimation under high SNR conditions, smaller units of $t$ and $f$ are determined while satisfying the relatively small data requirements.

The optimal data requirements for channel estimation under varying SNR levels are shown in Figure 5 and Figure 6. Figure 5 illustrates the optimal number of data counts per group at SNR levels of −6, −4, −2, and 0 dB, while Figure 6 shows the corresponding values at SNR levels of 2, 4, 6, 8, and 10 dB. In low-SNR conditions, relatively large data quantities, such as 960, 1080, 1200, and 1680, were detected to ensure channel estimation performance. In contrast, under high-SNR conditions, smaller data quantities were more broadly distributed. As shown in Figure 3, Figure 4, Figure 5 and Figure 6, the analysis of optimal patterns demonstrates that appropriate resource grouping in the time and frequency domains is essential for K-means-based channel estimation methods, considering channel factors such as UE velocity, delay spread, and SNR. Furthermore, it was confirmed that the amount of data required to ensure the performance of K-means-based channel estimation must also be considered.

The input data for the CNN is generated based on simulations. The two-step CNN training process is conducted using the final optimal patterns derived from exhaustive search, characterized by the frequency domain parameter $f$ and the time domain parameter $t$. Thus, each step involves distinct input data and correct labels. For instance, during training in the frequency domain, the optimal patterns are classified based on the number of subcarriers $f$ within the patterns. The grouped patterns are then defined with $f$ as the correct label. The input data is generated based on the channel conditions associated with the patterns sharing the same correct label. Single or multiple patterns with the defined correct label $f$ have associated channel conditions, such as delay spread, velocity, and SNR. These channel conditions are used to generate a tapped-delay line (TDL)-D channel. The channel generation process is repeated $N$ times, and for each iteration, the channel conditions are randomly selected from the patterns with the same $f$, following a discrete uniform distribution. The transmitted signal $x_{k,l}$ passes through the generated TDL-D channel, and noise is added to produce $y_{k,l}$, as expressed in Equation (1).

The received $N$ signals are processed as input data for the CNN by separating the real and imaginary components and adjusting the size to $1\times 1680\times 2\times N$. The values are normalized between −1 and 1. In this study, $N$ is set to 100,000. The generated dataset of 100,000 samples is divided into training, validation, and test datasets in proportions of 0.8, 0.1, and 0.1, respectively. The training dataset serves as input data for the CNN.

3.3. Optimal Resource Grouping Pattern Selection

To reduce the complexity of selecting the optimal resource grouping pattern and to efficiently extract features, a two-step learning process is performed by dividing the proposed 212 resource grouping patterns into frequency and time domains. In the first step, learning is focused on selecting the optimal parameter $f$, which is used to determine the resource grouping pattern in the frequency domain among the proposed resource grouping patterns. In the second step, the learning is focused on the parameter $t$, which determines the resource grouping pattern in the time domain. After completing the learning process, the trained CNN combines the optimal values of $t$ and $f$ to output the optimal resource grouping pattern within the given channel condition.

In the first step, since the network focuses solely on the frequency domain, learning is performed based exclusively on the number of subcarriers. First, the 212 resource grouping patterns are classified into groups that have the same number of subcarriers, $f$. Then, for the resource grouping patterns that use the same number of subcarriers, the corresponding subcarrier count, $f$, is defined as the new correct label for CNN training. The dataset is normalized to values between −1 and 1 under the channel conditions corresponding to this correct value, with a size of $1\times 1680\times 2\times N$, and the network is constructed accordingly. After completing the first-step of training, the CNN outputs the optimal $f$. In the second step, since the network focuses solely on the time domain, learning focuses exclusively on the number of OFDM symbols in the proposed resource grouping patterns. First, the proposed patterns are grouped according to the same number of OFDM symbols, $t$. Then, for the patterns with the same number of OFDM symbols, the corresponding number, $t$, is defined as the new correct label for the second step of CNN training. For the channel conditions corresponding to this correct label, the dataset is normalized to values between −1 and 1, with a size of $1\times 1680\times 2\times N,$ and the network is constructed accordingly. Upon completing the second stage of training, the CNN outputs the optimal $t$, which is combined with the optimal $f$ from the first stage to determine the optimal resource grouping pattern for the given channel environment.

3.4. Proposed CNN Structure

The proposed CNN architecture in this study is illustrated in Figure 7. As shown in Figure 7, the CNN consists of an input layer and 6 convolutional (Conv) layers. The input layer has dimensions of $1\times 1680\times 2\times N$, where 1680 represents the total number of resources in the resource grid considered in this study, 2 corresponds to the real and imaginary parts of the received signal, and $N$ denotes the total number of data samples. The network includes batch normalization (BN), rectified linear unit (ReLU) activation functions, and max pooling (MaxPool) layers, which are sequentially arranged in the structure.

The filter size for the convolutional layers is set to $1\times 12$, and the number of filters gradually increases as the layers deepen, specifically to 16, 24, 32, 48, 64, and 96 filters. This incremental increase in the number of filters is designed to enable the CNN to extract progressively complex features, aligning with prior studies [17,18,19], which have shown that increasing the number of filters enhances data representation capabilities and learning accuracy in large-scale MIMO and mmWave systems. Furthermore, prior examples in OFDM systems demonstrate the effectiveness of this design in enabling the CNN to learn temporal and frequency-domain features effectively [20,21,22]. The increase in the number of filters in the CNN layer design is a critical criterion, ensuring efficient data processing in bandwidth- and noise-intensive channel environments. This approach maximizes the feature extraction capability, particularly in complex channel conditions [23,24]. The filter size is optimized for effectively learning long time-series data, and previous studies have reported that such designs contribute to improving the SNR [25,26].

Batch normalization and ReLU activation functions are employed as key components to maintain training stability and prevent overfitting. Following each convolutional layer, a MaxPool layer with a size of $1\times 2$ is used to reduce the data dimensions, thereby decreasing the computational load while retaining essential features [27,28]. This multi-layer structure is designed to enable the CNN to efficiently learn spatial and temporal features.

4. Simulation Results

This section provides a detailed analysis of the accuracy of the proposed two-step learning process and the CNN-based channel estimation performance. The $N$ data samples used in the two-step training process were divided into training, validation, and test datasets in proportions of 0.8, 0.1, and 0.1, respectively. The training results are presented in

Table 2. Classification accuracy for the two-step training process.

	SNR [dB]		−6	−4	−2	0	2	4	6	8	10
Learn Method
[step 1] Learning according to the size of f		Accuracy [%]	100	55.9	51.7	57.1	55.02	72.0	70.6	78.2	87.3
[step 2] Learning based on the size of t when f has the same size		$f$	120	60	40	24	20	24	15	12	12
		Accuracy [%]	25	100	100	100	100	70.5	100	100	93.4
		$f$		120	60	30	24	30	20	15	15
		Accuracy [%]		29.8	100	100	100	89.3	84.3	93.3	95.2
		$f$			120	40	30	40	24	20	20
		Accuracy [%]			50.0	78.8	100	73.5	96.5	93.5	95
		$f$				60	40	60	30	24	24
		Accuracy [%]				57.9	89.9	73.5	90.6	93.6	98
		$f$				120	60	120	40	30	30
		Accuracy [%]				57.7	73.8	82.9	86.1	90.6	89.3
		$f$					120		60	40	40
		Accuracy [%]					74.2		85.3	99.4	92.8
		$f$							120	40	40
		Accuracy [%]							100	90.2	90.1
Total accuracy [%]			25	36.3	43.1	45.0	49.3	56.2	64.8	73.6	82.5

. The horizontal axis represents the SNR, and the vertical axis corresponds to the learning accuracy at each step. The accuracy of the first step of learning shows 100% at an SNR of −6 dB, as the optimal pattern consistently selects $f$ = 120. However, as the SNR increases from −4 dB to 2 dB, adjacent $f$ values, such as $f$ = 12, 15 or $f$ = 24, 30 exhibits similar channel estimation performance, resulting in approximately 50% accuracy. When the SNR exceeds 4 dB, the CNN begins to effectively reflect channel states influenced by delay spread and velocity, achieving over 70% accuracy.

The accuracy of the two-step learning represents the classification performance of the optimal $t$ for each $f$ selected at the corresponding SNR. At −6 dB, due to the severely poor channel conditions, as shown in Figure 8 and Figure 9, channel estimation performance in this low SNR range is significantly degraded. Consequently, the classification accuracy of the CNN was also found to be considerably low. At −4 dB, the first-stage learning identified $f$ = 60 and $f$ = 120 as optimal. However, due to the same reasons observed at −6 dB, the two-step learning recorded a low accuracy of 36.3%. Similarly, at −2 dB, the accuracy remained low at 43.1%. From 0 dB onward, as the SNR increased, the accuracy of the two-step learning progressively improved. The total accuracy also increased, reaching 82.5% at 10 dB. This improvement indicates that the CNN was able to more effectively learn the optimal $t$ as the stability of the channel conditions improved at higher SNR.

The proposed two-step learning method demonstrates a complementary structure. The first step of the learning accurately identifies the optimal number of subcarriers per group $f$, providing a solid foundation for the two-step learning to fine-tune $t$. This allows the CNN to adapt effectively to dynamic channel conditions. However, at low SNR values such as −6 dB, the significant degradation of channel conditions leads to imbalanced data distribution and excessive noise, which limit the accuracy of the CNN. These limitations highlight the potential for improvement through noise-resilient learning methods or data augmentation strategies.

In conclusion, the proposed two-step learning process adapts effectively to dynamic channel environments, maintaining consistently high accuracy as the SNR increases. Future research could focus on evaluating CNN performance under a wider range of channel conditions or incorporating reinforcement learning methods to enable real-time adaptation and further improve performance.

Figure 8 illustrates the MSE performance of three patterns according to SNR. The left graph represents the case with a delay spread of 50 ns, while the right graph corresponds to 300 ns. The bold dashed lines represent the optimal patterns obtained from the exhaustive search, as shown in Figure 3 through Figure 6. The solid lines represent the Proposed Pattern obtained using the two-step CNN training introduced in this paper. The thin dashed line representing the Conventional Pattern indicates the channel estimation performance from the most recent study on K-means algorithm-based channel estimation, presented in [13].

In the Conventional Pattern, the K-means algorithm is applied to resources corresponding to one slot in the time domain Iand ten RB in the frequency domain, demonstrating superior performance compared to the traditional least-squares (LS) channel estimation method. Since the method proposed in this paper is designed to address the limitations of [13], its performance is analyzed through a comparison with the Conventional Pattern.

The red, green, and blue curves indicate velocities of 30 km/h, 90 km/h, and 150 km/h, respectively. The optimal pattern exhibited the best performance across all SNR ranges, followed by the proposed pattern and the conventional pattern. The proposed pattern showed slightly inferior performance compared to the optimal pattern, with the performance gap widening in the SNR range of −2 dB to 2 dB. However, beyond 2 dB, the gap gradually decreased, and the proposed pattern achieved performance close to the optimal pattern. In contrast, the conventional pattern exhibited the worst performance across all SNR ranges and tended to converge to a fixed MSE threshold beyond 0 dB. This indicates that the conventional pattern determines the same channel for all received signals processed through clustering, failing to effectively reflect the complexity of the channel environment, which limits performance improvement even in high-SNR conditions. For a delay spread of 50 ns, all patterns demonstrated relatively good MSE performance, and the proposed pattern consistently maintained lower MSE compared to the conventional pattern across all SNR ranges. On the other hand, when the delay spread increased to 300 ns, channel variations became more irregular, causing performance degradation for all patterns. Nonetheless, the proposed pattern continued to outperform the conventional pattern, demonstrating its reliability.

In the velocity analysis, at 30 km/h, the performance gap between the proposed pattern and the optimal pattern was minimal, while the proposed pattern outperformed the conventional pattern by approximately 3 dB. At higher velocities, such as 150 km/h, the performance of the proposed pattern was slightly degraded as a result of increased channel variability but still maintained significantly lower MSE compared to the conventional pattern, demonstrating high reliability even in high-mobility scenarios.

Figure 9 illustrates the MSE performance of three patterns according to SNR. The left graph represents the case where the UE velocity is 30 km/h, and the right graph corresponds to 150 km/h. The red, green, and blue curves represent the delay spread conditions of 100 ns, 200 ns, and 300 ns, respectively. The optimal pattern demonstrated the best performance across all SNR ranges under all conditions, while the proposed pattern showed slightly lower performance but maintained a similar trend. In the low SNR range from −6 dB to −2 dB, the proposed pattern exhibited performance close to the optimal pattern. However, as the SNR increased from −2 dB to 4 dB, the performance gap became more pronounced. Beyond 4 dB, the gap decreased, and the proposed pattern achieved performance close to the optimal pattern. At a velocity of 30 km/h, the performance gap between the proposed pattern and the optimal pattern was relatively small across all SNR ranges. In contrast, at a velocity of 150 km/h, the temporal variability of the channel increased, causing a slight degradation in the performance of the proposed pattern.

Nevertheless, it consistently outperformed the conventional pattern, demonstrating high reliability even in high-mobility scenarios. For a delay spread of 100 ns, all patterns demonstrated stable MSE performance across all SNR ranges, with the proposed pattern maintaining consistently lower MSE compared to the conventional pattern. On the other hand, when the delay spread increased to 300 ns, all patterns experienced performance degradation due to more irregular channel variations. Nonetheless, the proposed pattern still outperformed the conventional pattern, proving its high reliability. The conventional pattern showed a rapid performance degradation as the delay spread increased or the velocity rose, with its performance degradation particularly evident in high-mobility scenarios. Additionally, when the SNR increased beyond 2 dB, the conventional pattern tended to converge to a fixed MSE threshold. This is attributed to the fact that the conventional pattern estimates all received signals processed by the clustering algorithm as the same channel, failing to effectively reflect subtle channel state variations in high-SNR conditions.

5. Conclusions

This paper proposed a novel method to enhance the performance of K-means algorithm-based channel estimation by utilizing a CNN-based two-step learning method. To overcome the limitation of the conventional K-means-based blind channel estimation method, which determines the same channel for all received signals processed through clustering and thus fails to effectively reflect fine-grained channel variations at the subcarrier and OFDM symbol levels, this study designed dynamic clustering grouping patterns and a two-step learning structure adaptable to dynamic channel conditions. The simulation results demonstrated that the proposed method consistently maintained high channel estimation performance under various channel conditions. Compared to the optimal pattern, the proposed scheme showed similar channel estimation performance across all SNR ranges, achieving near-optimal performance in low SNR and progressively improving to closely match the optimal pattern in high SNR. Additionally, the proposed CNN-based learning method outperformed the conventional pattern in all conditions in terms of MSE and maintaining stability, even in high-mobility scenarios with significant channel fluctuations. These results highlighted the proposed scheme’s adaptability to dynamic channel conditions.