# Channel Estimation Algorithm Based on Parrot Optimizer in 5G Communication Systems
## 3 Numerical Simulations
### BER Comparison Analysis  
BER is a crucial metric for evaluating the performance of communication systems. It is calculated using the following formula:  
\[\text{BER}=\frac{\text{Number of erroneous bits}}{\text{Total number of transmitted bits}} \tag{43}\]  
The number of erroneous bits indicates the number of bits incorrectly decoded at the receiver, while the total number of received bits refers to the total number of bits received during transmission. BER reflects the probability of bit errors occurring during transmission, directly impacting the reliability and performance of the communication system.  
In 5G systems, the accuracy of channel estimation significantly affects BER. Firstly, BER directly reflects the quality of channel estimation. By analyzing BER, the performance of different channel estimation algorithms under various channel conditions can be evaluated, thereby optimizing the algorithm to improve the overall system performance. Secondly, BER provides a theoretical basis for optimizing channel estimation algorithms.  
When designing and optimizing channel estimation algorithms, minimizing BER is often the target. Through simulations and practical testing, analyzing the BER performance of different algorithms under various channel conditions allows for the selection of the optimal algorithm. Thirdly, BER can guide the adjustment of system parameters. Byanalyzing BER, the optimal parameter configuration can be found to enhance the overall system performance.  
Figure 3 shows the BER performance of LS, PO, and MMSE channel estimation algorithms under different SNR. Under high SNR conditions, the BER of the PO algorithm is close to that of the MMSE algorithm, while under low SNR conditions, the PO algorithm outperforms the LS algorithm. This makes the PO algorithm an ideal choice for practical applications, capable of maintaining high estimation accuracy while reducing computational complexity and improving system efficiency.  
At approximately 0 Db SNR, the BER of the LS algorithm is 0.4380, the PO algorithm is 0.4433, and the MMSE algorithm is 0.4290. Under low SNR conditions, the BER of all three algorithms is relatively high with little difference, but the MMSE algorithm performs slightly better. As the SNR increases to approximately 5 Db, the BER of the LS algorithm is 0.3969, the PO algorithm is 0.3931, and the MMSE algorithm is 0.3825. At SNRs of approximately 10 Db, 20 Db, and 30 Db, both the PO and MMSE algorithms outperform the LS algorithm.  
Overall, while the LS algorithm is simple to implement, it has a large error under low SNR conditions, resulting in the highest BER. As the SNR increases, the BER gradually decreases, but it still lags behind the PO and MMSE algorithms at higher SNRs. The PO algorithm consistently demonstrates high channel estimation accuracy across all SNR conditions, especially under medium to high SNR conditions where its BER is close to that of the MMSE algorithm. The MMSE algorithm shows the best channel estimation performance under all SNR conditions but relies on precise prior channel statistical information. The PO algorithm strikes a balance between performance and computational complexity, making it highly valuable for practical 5G communication systems. By optimizing channel estimation algorithms, the accuracy of channel estimation and overall system performance can be significantly improved, providing support for efficient and reliable wireless communication.