# Channel Estimation Algorithm Based on Parrot Optimizer in 5G Communication Systems
## 2 Channel Estimation Model  
### OFDM Channel Estimation Model  
This section provides a detailed explanation of channel estimation techniques in Orthogonal Frequency Division Multiplexing (OFDM) systems. OFDM systems feature a unique frame structure where the resource grid consists of complex data and pilot symbols, with \(K\) representing the number of subcarriers in the frequency domain and \(L\) representing the number of OFDM symbols in the time domain. At the transmitter, the resource grid is processed through an Inverse Discrete Fourier Transform (IDFT) to generate the baseband signal. During transmission, the baseband signal is affected by multipath channels and superimposed with Additive White Gaussian Noise (AWGN), causing signal distortion and interference. At the receiver, Discrete Fourier Transform (DFT) is typically used to process the received signal and restore the received resource grid. Accurate channel estimation at this stage is crucial for system performance, as it effectively compensates for multipath effects and noise interference, thereby improving the Signal-to-Noise Ratio (SNR) and enhancing data transmission reliability and efficiency.  
Therefore, in the research and application of 5G communication technology, channel estimation techniques hold significant importance. The frequency-selective fading channel environment adopted in 5G systems imposes higher requirements on channel estimation, making the development of efficient and accurate channel estimation methods essential for enhancing the performance of OFDM systems in 5G networks. Existing channel estimation methods include LS and MMSE based techniques, as well as emerging deep learning-based channel estimation methods.  
In an OFDM system, the received signal \(y\) can be expressed as  
\[y=\mathrm{diag}(x)*h+n \tag{1}\]  
where \(\mathrm{diag}(x)\) represents the operation of placing the transmitted signal \(x\) on the diagonal of a matrix, \(h\) is the channel response, and \(n\) is the additive noise. Channel estimation is a critical process that involves estimating the frequency channel response \(h\), which is used for equalizing the received signal \(y\) in the subsequent stage. To estimate the channel, part of the resource grid is used to insert pilot symbols. Figure 1 shows a comb pilot pattern with a 1/4 pilot density. When the channel changes within an OFDM block, this pattern is used for fast fading estimation. First, the channel response values at pilot positions are estimated, denoted as \(h_{p}\). Then, different algorithms are employed to obtain the entire channel response matrix \(h\) from \(h_{p}\). To maintain a reasonable ratio of pilot symbols to the total number of symbols and to improve the accuracy of channel estimation, the number and positions of pilot symbols should be carefully determined based on the deployment scenario.  
This pattern is employed for fast fading estimation when the channel varies within an OFDM block. Pilot symbols are inserted at regular intervals, occupying one fourth of the total subcarriers. These pilots are crucial for accurately estimating the channel response values at the pilot positions, denoted as \(h_{p}\). Subsequently, various algorithms can utilize these estimated values to reconstruct the entire channel response matrix \(h\), ensuring effective equalization of the received signal.