# Channel Estimation Algorithm Based on Parrot Optimizer in 5G Communication Systems
## 3 Numerical Simulations
### Impact of Modulation Schemes  
Figure 5 presents the BER performance of LS, PO, and MMSE channel estimation algorithms under different modulation schemes (QPSK, 16 QAM, 64 QAM, and 256 QAM) with a pilot density of 1/12 and a step size of 5 Db. The general trend shows that as  
Figure 4: MSE performance of LS, MMSE, and PO-CE under 256 QAM constellation diagram and 1/12 pilot density (step size is 1 Db). \(X\)-axis: SNR [Db]. The curves are the results of simulations. the Signal-to-Noise Ratio (SNR) increases, the BER of all three algorithms significantly decreases, but the performance of each algorithm varies notably with different modulation schemes. From Figure 5a-d, it can be observed that as the modulation order increases, the differences in BER among the three algorithms narrow, especially at an SNR of 0 Db, where the errors are most pronounced. Simultaneously, the overall BER value increases with higher modulation orders. Specifically, under low SNR conditions, all three algorithms exhibit high errors, with PO and MMSE slightly outperforming LS. Under medium SNR conditions, PO and MMSE algorithms outperform LS. Under high SNR conditions, MMSE slightly outperforms PO, and PO significantly outperforms LS. The LS algorithm shows large errors under low SNR conditions; as SNR increases, BER gradually decreases, but the performance remains poor under high-order modulation (such as 256 QAM) with high BER. The PO algorithm consistently demonstrates high channel estimation accuracy across all SNR conditions, especially under high-order modulation, where its BER is significantly lower than LS and close to MMSE. The MMSE algorithm exhibits the best performance in terms of BER under all SNR conditions. By analyzing the BER under different modulation schemes and considering the complexity of the PO algorithm, it can be concluded that the PO algorithm strikes a balance between performance and computational complexity. It exhibits high channel estimation accuracy under various modulation schemes and SNR conditions, making it suitable for practical applications. In contrast, the LS algorithm is simple to compute but performs poorly under low SNR and high-order modulation conditions; the MMSE algorithm, while superior in performance, is limited by the need for prior knowledge. The PO algorithm provides an effective channel estimation method for 5G communication systems, balancing performance and complexity. By optimizing channel estimation algorithms, the accuracy and overall performance of 5G communication systems can be significantly improved,  
Figure 5: BER performance of LS, PO, and MMSE channel estimation algorithms under different modulation schemes. \(X\)-axis: SNR [Db]. The curves are the results of simulations. supporting efficient and reliable wireless communication. The data in Figure 5 further validate the superiority of the PO algorithm under different modulation schemes and SNR conditions, especially under high-order modulation and high SNR conditions, where the BER of the PO algorithm is close to that of the MMSE algorithm, indicating its potential for practical applications. Figure 6 presents the MSE performance of the LS, PO, and MMSE channel estimation algorithms under different modulation schemes (QPSK, 16 QAM, 64 QAM, and 256 QAM) with a pilot density of 1/12 and a step size of 5 Db. The general trend shows that as SNR increases, the MSE of all three algorithms significantly decreases. 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.