# Enhancing Beamforming Efficiency Utilizing Taguchi Optimization and Neural Network Acceleration
## 4 Neural Networks for Synthesis and Optimization of Antenna Arrays
### Taguchi-Neural Network Architectures
Backpropagation is often chosen for its simplicity, effectiveness, and versatility, making it a preferred choice for machine learning and neural network training. Figure 8: Taguchi-neural network architecture. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Abbreviation** & **Algorithm** & **Performance** \\ \hline LM & Levenberg-Marquardt & High convergence rate \\ BFG & BFGS Quasi-Newton & Fast convergence \\ RP & Resilient Backpropagation & Robust to noise \\ BR & Bayesian Regularization & Effective for small data \\ SCG & Scaled Conjugate Gradient & Memory efficient \\ CGB & Conjugate Gradient with Powell/Beale Restarts & Balanced performance \\ CGF & Fletcher-Powell Conjugate Gradient & Stable convergence \\ CGP & Polak-Ribiere Conjugate Gradient & Good for sparse data \\ OSS & One-Step Secant & Fast convergence \\
**GDX** & **Variable Learning Rate Backpropagation** & **Adaptive learning rate** \\ GD & Basic Gradient Descent & Simple, easy to implement \\ GDM & Gradient Descent with Momentum & Accelerated convergence \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance comparison of training algorithms for neural networks [69]. Figure 11: Taguchi- neural network training; \(R=0.99933\). Figure 10: Taguchi- neural network Mean Squared Error (MSE). Figure 9: Taguchi-neural network training (epoch 290, performance goal met). With a fifteen-neuron input layer and a ten-neuron output layer in a Self-Organizing Map (SOM), each neuron in the output layer represents a cluster or grouping of similar data from the input layer. The SOM (see Figure 12) reduces the dimensionality of the input space into a ten-dimensional output space, preserving spatial relationships between similar data points. Each output neuron acts as a centroid or representative of a cluster of similar data, grouping input data points that are closest in terms of distance. This interpolation of data into the output space allows for information aggregation and helps mitigate over-fitting issues. Having only ten neurons in the output layer facilitates visualization and interpretation of the resulting map, allowing for an understanding of how different clusters are organized spatially. In summary, this configuration provides a compact representation of input data, easing visualization, interpretation, and data analysis while preserving the relationships between similar data points. The SOM neighbor weight distances and sample hits (see Figure 13) are crucial metrics for comprehending Self-Organizing Maps (SOMs). The neighbor weight distances measure the similarity or dissimilarity between adjacent neurons' weights. Smaller distances indicate a smooth transition in representing input space, suggesting similar responses to similar input patterns among neighboring neurons. Conversely, larger distances imply a more abrupt transitions, indicating differing responses to similar inputs. The sample hits metric tracks how often each neuron is selected as the best-matching unit (BMU) for input samples during training. Neurons with higher hits represent densely populated regions of the input space, while lower-hit neurons represent sparser regions. Analyzing the neighbor weight distances helps evaluate the map's ability to capture the underlying structure of input data (see Figure 14), while the sample hits reveal the distribution and density of the data, aiding in identifying clusters or patterns. Together, these metrics provide insight into how the SOM organizes and represents input data, facilitating interpretation and understanding of its performance. One possible concrete application of the Taguchi method with smart antennas and neural networks could be the design of an adaptive wireless communication system. By using the Taguchi method to optimize antenna parameters in combination with neural networks for decision-making and dynamic adaptation, a system could be created that optimizes its performance in real time based on changing communication channel conditions.