# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 1 Introduction
### Related Work  
In [20], the authors propose a joint user scheduling and beamforming algorithm for LEO satellites following the DVB-S2X standard [11]. The authors consider the influence of Doppler shift and phase disturbance on the CSI estimation, but no prediction of the CSI is performed. The optimization method is based on hierarchical clustering, the semidefinite programming algorithm and the concave-convex process (CCCP). The focus is placed on the optimization of massive multiple input multiple output (MIMO) communication systems, and the authors report that the observed metric, energy efficiency, is higher for the proposed solution when compared to the traditional decoupling design algorithms. The optimization of scheduling in satellite communications has also been analyzed with different optimization scenarios in [21; 22] without focusing on the influence various factors can have on the CSI. The authors in [21] aimed to maximize the sum rate under the per beam power constraint and minimum SINR requirement of scheduled users, proposing a convex-concave procedure-based algorithm. The study described in [22] rather focuses on the separate analysis of intra-beam and inter-beam scheduling and takes the interference among beams into consideration during the scheduling. The authors in [23] observed the ergodic capacity of satellite-terrestrial links in the presence of co-channel interference and outdated CSI and presented an analytical form of the achievable ergodic capacity. The analysis was carried out on channels with both uncorrelated and correlated fading and the numerical and simulation results validate the analysis proposed by the authors. The estimation of a massive MIMO orthogonal frequency division multiplexing channel for LEO satellite communication is presented in [24]. The authors show that an asymptotic minimum mean square error (MMSE) of the estimation can be minimized under certain array response vector conditions. In addition, the authors proposed a two-stage channel estimation, i.e., per-subcarrier space domain processing, followed by per-user frequency domain processing. The simulation results show that the proposed solution can achieve a performance near the MMSE with a much lower complexity. In terms of CSI prediction, the authors in [25] propose a scheme based on a deep neural network to assist LEO satellite massive MIMO systems. The implemented neural networks contain a convolutional and long short-term memory module, which is used to analyze the relationship of uplink-downlink channels between LEO satellites, the mapping between CSI and beamformers, and directly predicting the future downlink CSI of LEO satellites based on the observed uplink CSI. The implemented architectures could also generate the appropriate beamformers based on the predicted downlink CSI. The implemented systems are validated through numerical methods and show a promising application of neural networks in complex communication systems. A comparison between different machine learning methods and a modified autoregressive integrated moving average (ARIMA) model for CSI prediction is presented in [26]. The authors compare the performance of the proposed improved ARIMA model to neural networks (convolutional and long short-term memory (LSTM)), a Markov chain model and a basic ARIMA algorithm. The simulation shows that the performance of the improved ARIMA model has a significant increase in spectral efficiency compared to the other implemented prediction models. CSI prediction was analyzed through the influence of atmospheric attenuation in [27]. The authors implemented several types of neural networks, including a convolutional neural network, LSTM and a multilayer perceptron. The performed simulations show that the prediction of the interference period and types of atmospheric attenuation using the proposed architecture can be effectively obtained.