## 4 Conclusions  
In this article, we present a novel dual-driven learning-based network for massive MIMO detection in UAV AG communications. The proposed network consists of two components: a data-driven network with three fully connected layers that corrects symbol estimation errors to minimize detection errors, and a model-driven OAMP-Net, which performs MIMO detection through iterative processes. The main contribution of this paper is that the proposed dual-driven MIMO detector is a novel combination of a data-driven symbol correction network and the model-driven OAMP-Net. The entire dual-driven network is trained simultaneously to optimize its performance. Our main hypothesis was that the proposed dual-driven MIMO detector will outperform the model-driven OAMP-Net and other traditional MIMO detectors since it has the advantages of both the data-driven network and the model-driven network.  
We analyze the network structure of the dual-driven network and the dual-driven learning-based MIMO symbol detection algorithm in detail. To verify the hypothesis that the proposed dual-driven MIMO detector will outperform OAMP-Net and some other detectors at different noise powers and different channel estimation errors, we carry out extensive test simulations. Through these simulations, we demonstrate that the dual-driven learning detector exhibits significant performance improvements compared to the MMSE, OAMP, and OAMP-Net detectors across a wide range of SNRs (0 dB to 25 dB) and MSEs (\(-40\) dB to \(-26\) dB). When the SNR is \(20\) dB and the MSE is \(-30\) dB, the dual-driven MIMO detector can achieve a BER of \(4\times 10^{-4}\), while the OAMP-Net can only achieve a BER of \(2.48\times 10^{-3}\). Since the only difference between the dual-driven MIMO detector and the OAMP-Net detector is the inserted data-driven symbol correction network, we can verify our hypothesis. In addition, with different layers and different learning rates, the proposed dual-driven detector converges well and maintains stability.  
The proposed dual-driven MIMO detector provides several engineering benefits: enhanced performance, adaptability to various channel conditions, good flexibility and scalability, and near-real-time processing ability.  
This article lays a solid foundation for the advancement of UAV AG communications in the future.  
Conceptualization, H.L. and S.Z.; methodology, H.L.; validation, H.L. and S.Z.; formal analysis, H.Y.; writing--original draft preparation, H.L.; writing--review and editing, Y.H., F.Z. and H.Y. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Please contact the authors for data requests.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} MIMO & Multiple-Input Multiple-Output \\ UAV & Unmanned Aerial Vehicle \\ AG & Air-to-Ground \\
6G & Sixth-Generation Cellular Network \\ mm-wave & millimeter-wave \\ OAMP-Net & Orthogonal Approximate Message Passing Network \\ MMSE & Minimum Mean Square Error \\ OAMP & Orthogonal Approximate Message Passing \\ SNR & Signal-to-Noise Ratio \\ SER & Symbol Error Rate \\ SAGIN & Space-Air-Ground Integrated Network \\
3 GPP & Third-Generation Partnership Project \\ NR & New Radio \\ UE & User Equipment \\ AA & Air-to-Air \\ LMMSE & Linear Minimum Mean Square Error \\ AMP & Approximate Message Passing \\ CG-OAMP-Net & Conjugate Gradient OAMP-Net \\ NN & Neural Network \\ ADC & Analog-to-Digital Converter \\ GS & Ground Station \\ LOS & Line Of Sight \\ NLOS & Non-Line Of Sight \\ Rx & Receiving \\ Tx & Transmitting \\ CSI & Channel State Information \\ QAM & Quadrature Amplitude Modulation \\ PSK & Phase Shift Keying \\ IFFT & Inverse Fast Fourier Transform \\ CP & Cyclic Prefix \\ LE & Linear Estimator \\ NLE & Nonlinear Estimater \\ NMSE & Normalized Mean Square Error \\ BER & Bit Error Rate \\ UPA & Uniform Planar Array \\ Adam & Adaptive Moment estimation \\ \end{tabular}