# Recurrent Deep Learning for Beam Pattern Synthesis in Optimized Antenna Arrays
## 5 Conclusions  
A methodology based on deep learning using an RNN was introduced and developed for the synthesis of beam patterns for linear arrays. A comparative study among three well-known DNN architectures showed that the LSTM-RNN architecture exhibited better prediction performance in terms of the MAE and MSE. Additionally, the proposed RNN, which was trained and validated on 7623 and 32 previously optimized radiation pattern samples, respectively, demonstrated satisfactory performance in synthesizing corresponding beam patterns with low sidelobe levels and enhanced directivity. The test results of the LSMT-RNN validate that DL is viable for synthesizing ideal radiation patterns (which are characterized by high prediction complexity) and attainable radiation patterns, including geometric and phase coupling effects. In most cases, the outputs closely resembled the input beam patterns, demonstrating the reliability of the approach for beam pattern synthesis within a certain range of input configurations and their potential for application in point-to-point wireless communications, broadcasting, and radar systems, among others. Future research will explore the potential of the RNN-based methodology to complete antenna systems, including beamforming networks. This would involve developing techniques to seamlessly interface the DNN with beamforming hardware, allowing for real-time (or near real-time) adaptation and optimization of beam patterns depending on changing environmental conditions, signal requirements, or system objectives. Further studies will also investigate the feasibility of applying the proposed RNN under various antenna array geometries with different configurations beyond linear arrays. This could involve adapting the model architecture and training process to accommodate different antenna geometries, configurations, and design parameters, as could be the case in two-dimensional synthesis. Finally, although the LSTM-RNN architecture obtained promising results, exploring alternative deep learning architectures and methodologies could provide further insights and improvements in the context of antenna synthesis. This would entail investigating other variants of recurrent neural networks or exploring the use of hybrid architectures.  
Conceptualization, A.A., F.A. and E.S.-N.; methodology, A.A. and F.A.; software, A.A. and F.A.; validation, A.A. and F.A.; formal analysis, A.A. and F.A.; investigation, A.A. and F.A.; resources, E.S.-N., M.C.-J. and A.G.-B.; writing--original draft preparation, A.A., F.A., E.S.-N., U.P.-R. and M.C.-J.; writing--review and editing, A.A., F.A., E.S.-N., M.C.-J. and A.G.-B.; visualization, A.A., F.A. and U.P.-R.; supervision, A.A.; project administration, A.A. and E.S.-N.; funding acquisition, E.S.-N. All authors have read and agreed to the published version of the manuscript.  
The APC was partially funded by Facultad de Ciencias, Universidad Autonoma de San Luis Potosi.  
Data Availability Statement: The data supporting this research article are available upon request to the corresponding author.  
The authors would like to thank the National Council of Humanities, Sciences, and Technologies (CONAHCYT) for the support granted by project No. 872 under \"Investigadoras e Investigadores por Mexico\" program.  
The authors declare no conflicts of interest.