# Channel Estimation Algorithm Based on Parrot Optimizer in 5G Communication Systems
## 3 Numerical Simulations
### MSE Comparison Analysis  
Mean Squared Error (MSE) is a key metric in channel estimation. The formula for MSE is  
\[\text{MSE}=E\{\|H_{\text{est}}-H_{\text{true}}\|^{2}\} \tag{44}\]  
where \(H_{\text{est}}\) represents the estimated channel response, \(H_{\text{true}}\) is the true channel response, \(\|\cdot\|\) denotes the Euclidean norm, and \(E\{\cdot\}\) denotes the expectation. MSE quantifies the deviation between the estimated value and the true value and is a crucial indicator for evaluating the performance of channel estimation algorithms.  
Figure 3: BER performance of LS, MMSE, and PO-CE under 256 QAM constellation diagram and 1/12 pilot density. \(X\)-axis: SNR [Db]. The curves are the results of simulations.  
In 5G communication systems, the accuracy of channel estimation is critical for system performance. Firstly, MSE directly reflects the accuracy of channel estimation. By analyzing MSE, the performance of different channel estimation algorithms under various channel conditions can be quantified, allowing for the selection of the optimal algorithm to enhance the overall system performance. Secondly, MSE provides a theoretical foundation for optimizing channel estimation algorithms. When designing and optimizing channel estimation algorithms, minimizing MSE is often the goal. Through simulations and practical testing, analyzing the MSE performance of different algorithms under various channel conditions can identify the best algorithm. Thirdly, MSE can guide the adjustment of system parameters. By analyzing MSE, the optimal parameter configuration can be found to enhance the overall system performance. Fourthly, MSE plays a significant role in Channel State Information (CSI) feedback. The magnitude of MSE directly affects the accuracy of CSI, thereby impacting the system's adaptive performance. Optimizing channel estimation algorithms to minimize MSE and improve CSI accuracy subsequently enhances system spectral efficiency and transmission reliability.  
Figure 4 illustrates the MSE performance of LS, PO, and MMSE channel estimation algorithms under different SNR conditions. Overall, as SNR increases, the MSE of all three algorithms significantly decreases, indicating improved channel estimation accuracy under high SNR conditions.  
Specifically, under low SNR conditions (0 to 5 Db), the MSE of the three algorithms varies greatly. The LS algorithm performs the worst under low SNR conditions, with an MSE still above 1 at 5 Db SNR. The LS algorithm does not account for noise effects and is based solely on the least squares criterion, resulting in large errors under low SNR conditions. As SNR increases, the MSE of the LS algorithm rapidly decreases, gradually approaching the MMSE and PO algorithms under high SNR conditions. The MMSE algorithm consistently outperforms the LS algorithm across all SNR conditions, with significant advantages under low SNR conditions. At 0 Db SNR, the MSE of the MMSE algorithm is approximately 0.5, significantly lower than that of the LS algorithm. The PO algorithm performs between the LS and MMSE algorithms under low SNR conditions, with an MSE slightly higher than the MMSE algorithm but lower than the LS algorithm at 0 Db SNR. As SNR increases, the MSE of the PO algorithm rapidly decreases, approaching the MMSE algorithm under high SNR conditions.