# Feature Extraction in 5G Wireless Systems: A Quantum Cat Swarm and Wavelet-Based Approach
## 4 Results and Discussion
However, QCSO offers better overall balance (0.9) and faster convergence, which compensates for this gap in practical deployments. Quantum cat swarm optimization (QCSO) combines quantum computing principles with the behavioral modeling of cat swarm optimization (CSO), resulting in enhanced performance across several key metrics in feature extraction tasks for 5G wireless systems. Unlike classical binary or real-valued encodings used in GA or PSO, QCSO represents candidate solutions using quantum bits (qubits), formulated as follows:  
\[\psi=\alpha|0\rangle+\beta|1\rangle\quad\text{with}\quad|\alpha|^{2}+|\beta|^{2}=1\]  
This superposition enables simultaneous exploration of multiple states, improving the search capability in high-dimensional feature spaces. QCSO dynamically tunes the exploration-exploitation ratio through quantum rotation gates and adaptive seeking mode behavior. With a balance coefficient of 0.9 (see Table 3), QCSO maintains a better balance compared to PSO (0.5), GA (0.6) and DE (0.75), leading to an effective global and local search. QCSO demonstrates the fastest convergence (450 iterations) and the lowest execution time (2.8 s), indicating efficient navigation through the solution space. This is due to its probabilistic position update mechanism, which avoids the redundant computations typically present in traditional methods. QCSO achieves an avoidance of 83.2% of local minima, higher than GA (65.3%) and PSO (72.1%). This is attributed to the quantum behavior that allows tunneling through local optima barriers, something not possible in conventional metaheuristics. With a feature selection accuracy of 95.3% and a robustness rate of 96.8%, QCSO significantly outperforms other techniques. This is essential to maintain performance under variable 5G channel conditions. QCSO achieves the highest signal reconstruction  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Parameter** & **GA** & **PSO** & **GWO** & **HHO** & **DE** & **QCSO** \\ \hline Convergence Speed (Iterations) & 1500 & 800 & 600 & 700 & 1200 & **450 (Fastest)** \\ \hline Exploration vs. Exploitation Balance & 0.6 (Moderate) & 0.5 (Exploitation-based) & 0.7 (Balanced) & 0.8 (Exploration-based) & 0.75 (Exploration-based) & **0.9 (Best balance)** \\ \hline Feature Selection Accuracy (Vk) & 85.2\% & 88.6\% & 90.4\% & 91.2\% & 87.5\% & **95.3\%** \\ \hline Computational Complexity (Execution Time in sec) & 5.2 s & 3.8 s & **2.9\%** & 3.2 s & 4.7 s & **2.9\%** \\ \hline Robustness Statesquality (24.1 dB SNR) and maintains energy efficiency at 0.88 J per operation, showcasing its suitability for power-sensitive 5G environments. Figure 4 shows the labeled spectrogram for four different classes of 5G signals, distinguishing between different frequency regions. The spectrum is segmented into three distinct zones: new radio (NR), long-term evolution (LTE), and noise. The LTE and NR bands are centrally positioned, surrounded by noise regions. The color scale indicates the intensity of the signal, helping to visualize the signal distribution across the frequency-time domain. The DWT decomposition of the three levels is shown in Figure 5. This figure illustrates the three-level decomposition of 5G LTE signals, where subfigures correspond to different levels of decomposition. The decomposition process enables us to analyze signal variations and extract meaningful frequency components, which are crucial for spectrum detection and classification tasks. Figure 4: Labeled 5G spectrogram with different levels. Figure 5: The 5G LTE signals after three-level decomposition. (**a–d**) correspond to different decomposition levels. The training accuracy graph in Figure 6 demonstrates the benefits of various neural network architectures, such as ResNet18, ResNet50, ImageNet, GoogleNet, AlexNet, ConvNet, and the proposed wavelet network, in different numbers of iterations. The proposed wavelet network consistently surpassed the other architectures in terms of training accuracy.