# Channel Estimation Algorithm Based on Parrot Optimizer in 5G Communication Systems
## 3 Numerical Simulations  
### Simulation Parameter Settings  
In this section, the goal is to determine the optimal position sought by the parrots. Ideally, the optimal position corresponds to the actual channel. However, at the receiver, the parrots are completely blind to the channel and cannot determine whether their current position is close to the actual propagation path. Therefore, a cost function is defined to guide the population towards the target of minimum BER. Referencing [40], the simulation parameters used in this study are shown in Tables 1-3. The image shows 16 QAM constellation diagrams with different dispersions, with the left diagram being better due to lower dispersion and clearer constellation points. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Dimension & 3 \\ Number of agents & 8 \\ Max number of iterations & 8 \\ Upper bounds & [50, 100, 400] \\ Lower bounds & [0, 20, 0] \\ Initialization distribution & Uniform \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the PO-CE Model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tap** & **Delay (ns)** & **Power (dBm)** & **Fading Distribution** \\ \hline
1 & 0 & \(-7.0\) & Rayleigh \\
2 & 50 & \(-1.0\) & Rayleigh \\
3 & 100 & \(-8.0\) & Rayleigh \\
4 & 150 & \(-2.0\) & Rayleigh \\
5 & 200 & \(-3.0\) & Rayleigh \\
6 & 250 & \(-10.0\) & Rayleigh \\
7 & 300 & \(-9.0\) & Rayleigh \\
8 & 350 & \(-6.0\) & Rayleigh \\
9 & 400 & \(-5.0\) & Rayleigh \\
10 & 450 & \(-11.0\) & Rayleigh \\
11 & 500 & \(-12.0\) & Rayleigh \\
12 & 550 & \(-14.0\) & Rayleigh \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tap Delay Line model of 5G NR TDL-C300 channel (delay Spread = 300 ns). During the movement process, each position of the parrot corresponds to a constellation diagram (which is derived from the channel equalization process). A position is considered better if the constellation diagram at that position exhibits less dispersion (as shown in Figure 2). To determine the variance of the equalized symbols, the signals are clustered into \(K\) clusters, and the distance from the signal to the reference signal \(\sigma^{2}\) is used to represent the dispersion, as follows:  
\[E\{\|X_{\text{est}}-X_{\text{ref}}\|\}= \text{arg min}\sigma^{2} \tag{41}\] \[(SNR,\tau_{\text{rms}},f_{m})\]  
where \(X_{\text{est}}\) and \(X_{\text{ref}}\) are the estimated signal and the reference signal, respectively. Here, \(SNR\in(Lb(1),Ub(1))\), delay spread \(\tau_{\text{rms}}\in(Lb(2),Ub(2))\), Doppler frequency \(f_{m}\in(Lb(3),Ub(3))\), i.e.,  
\[\text{s.t}\,0\leq SNR\leq 50, \tag{42}\] \[20\leq\tau_{\text{rms}}\leq 100,\] \[0\leq f_{m}\leq 400,\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline FFT size & 4096 \\ CP length & 1024 \\ Pilot arrangement & Comb \\ Pilot density & 1/3, 1/6, 1/9, and 1/12 \\ Modulation & QPSK, 16 QAM, 64 QAM, and 256 QAM [41] \\ Subcarrier spacing & 30 kHz \\ Channel model & TDL-C300 \\ Noise model & AWGN \\ SNR range & 0–30 dB (1 dB step and 5 dB step) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters of the OFDM system. Figure 2: 16 QAM constellation diagram with different dispersions (left is better). Figure 2 illustrates the constellation diagrams of a 16 QAM signal under different Signal-to-Noise Ratios (SNR). In (**a**), where the SNR is 15, the constellation points are distinctly concentrated around their ideal positions, indicating minimal noise. This results in higher signal quality and a lower bit error rate (BER). Conversely, in (**b**), with an SNR of 5, the constellation points are more dispersed, with a greater deviation from their ideal positions. This increased dispersion is due to the higher noise level associated with the lower SNR, leading to poorer signal quality and a higher bit error rate. The computational complexity of the PO-based channel estimation algorithm (the PO_CE algorithm is shown in Algorithm 1) is higher than that of the LS and MMSE algorithms.