# DNN Beamforming for LEO Satellite Communication at Sub-THz Bands
## 2 DNN Beamforming  
The LEO satellite moves at very high velocity in its orbit and hence the angle of arrival at the ground station receiver is constantly changing. The transmitted signals from the satellite that arrive at the ground station based phased array elements have different delays at the array output and thus has to be combined in such a way that there is a constructive interference at the beamformer output. Each antenna element is thus provided a phase shifter that delays the signal accordingly to get a constructive interference. However, the performance of phase shifter would degrade as the frequency of arriving signal changes and thus the spacing between antenna elements would change in terms of wavelength. This will lead to the problem of beam squinting [30] that would cause significant degradation in the performance of massive array receiver for a wideband system. Moreover, massive antenna array design will also require very large number of phase shifters for phased array receiver thus raising the cost of implementation much higher. To avoid these problems due to phase shifters, true-time delay can be employed at each of the array elements but it will be a costly implementation due to massive number of antenna elements used for beamforming. The true-time delay provides exact time delay needed at the output of each antenna elements for providing a constructive interference at the output. Therefore, we propose to perform the signal processing of the received signal at each antenna elements by a DNN beamforming algorithm. Recently deep learning and machine learning algorithm has helped improved the system performance in many scenarios and diverse range of applications [31; 32; 33]. Such an algorithm, that is mainly data-driven once trained, can be deployed in real-time applications for the prediction, optimization and management of scarce communication resources. It has been successfully implemented to improve the performance of signal processing algorithms [34; 35], design of intelligent communication systems [36], optimization of satellite resources and its allocation [37]. The data-driven DNN algorithms have also been applied in obtaining hybrid beamforming to solve spectral efficiency maximization problems [38], optimization of downlink beamforming [39], and the support of highly mobile systems [40]. In our proposed algorithm, the DNN is trained such that it minimizes the error in the predicted output voltage by tracking the output voltage of a TTD beamformer as the AoA at the receiver changes due to movement of LEO satellite. In Figure 1, we show the schematic of phase shift beamforming and the DNN beamforming for the phased array antenna receiver based at the ground station for a given AoA \(\theta_{0}\). For a uniform linear array of isotropic radiators receiver, the signal voltage at the array output will be expressed as [41]  
\[V_{out}=\sum_{n=1}^{N}V_{n}e^{-j\frac{2\pi d}{\lambda}(n-1)\cos\theta_{0}} \tag{1}\]  
Figure 1: Schematic of Phase shift and DNN Beamforming. where \(d\) is the spacing between the array elements, \(\lambda\) is the wavelength, \(N\) is the number of array elements, \(\theta_{0}\) is the angle of arrival of signal at the antenna elements measured from local zenith, and \(V_{n}\) is the signal amplitude at \(n\)th element. Assuming the plane wave at the receiver with uniform illumination of the array elements, we can express the signal amplitude at the array elements as  
\[V_{n}=\sqrt{\frac{\eta_{T}\eta_{R}P_{T}G_{T}}{L_{FS}(\theta_{0})L_{A}(\theta_{0 })}} \tag{2}\]  
where \(\eta_{T}\) and \(\eta_{R}\) are the efficiencies of transmitting and receiving antennas respectively, \(P_{T}\) is the transmitted power, \(G_{T}\) is the gain of transmitting antenna, \(L_{FS}(\theta_{0})\) is the free-space path loss, and \(L_{A}(\theta_{0})\) is the absorption loss in the atmosphere for a given AoA at the ground station. The losses are dependent on the AoA of the signal at the receiver as the slant path length changes due to movement of LEO satellite.