# Blind Channel Estimation Method Using CNN-Based Resource Grouping
## 2 System Model
### 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:  
\[y_{k,l}=h_{k,l}x_{k,l}+n_{k,l}, \tag{1}\]  
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:  
\[x_{k,l}=c\frac{\left(\frac{l(2n-1)\pi}{4}\right)}{4}. \tag{2}\]  
within each cluster, four clusters and their respective centroids are derived, as shown in Figure 1.  
Figure 1: Four classified clusters based on K-means clustering of QPSK signal.  
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:  
\[\hat{h}_{k,l}=\frac{y_{k,l}}{x_{k,l}}, \tag{3}\]  
where \(\hat{h}_{k,l}\) 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 \(\hat{h}_{k,l}\) among the 16 estimated channels, transmission bit estimation is performed based on:  
\[\hat{x}_{k,l}=\frac{y_{k,l}}{\hat{h}_{k,l}}, \tag{4}\]  
where \(\hat{x}_{k,l}\) 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, \(\widetilde{h}_{k,l}\).  
Subsequently, the channel estimation performance is analyzed through the MSE calculation between \(\widetilde{h}_{k,l}\) and \(h_{k,l}\), which is based on:  
\[MSE=\frac{1}{n}\sum_{k=1}^{n}\big{(}\frac{1}{m}\sum_{l=1}^{m}\Big{|}h_{k,l}- \widetilde{h}_{k,l}\Big{|}^{2}\big{)}, \tag{5}\]  
where \(n\) denotes the number of OFDM symbols in the resource grid and \(m\) is the number of subcarriers in the resource grid.