# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 2 System Model
### Channel Modeling and Simulation  
In this work, we assume that instantaneous SNR, denoted by \(\gamma(t)\), is defined as the following [30]:  
\[\gamma(t)=\frac{P_{T}}{\sigma^{2}d^{\beta}}|h(t)|^{2}, \tag{4}\]  
where \(h(t)\) denotes the time-varying complex channel gain, \(P_{T}\) denotes transmitted power, \(\sigma^{2}\) denotes the variance of the additive Gaussian noise, \(d\) is the distance between transmitter and receiver, and \(\beta\) is the corresponding path-loss factor. Various channel models were developed to describe the propagation conditions in a narrowband land mobile satellite channel. Typically, it is assumed that the fluctuations are the result of weak scattered components (multipath fading) and random variations in the power of multipath components (shadowing). It is typically assumed that the channel gain between the RAN access point and the end-user is composed of two time-varying components [31; 32; 33]:  
\[h(t)=a(t)e^{i\alpha(t)}+z(t)e^{i\alpha_{0}}. \tag{5}\]  
The first term in the above expression corresponds to the scattering component, and the second term corresponds to the line-of-sight (LOS) component. In particular, \(a(t)\) represents the amplitude of the scattering component, \(\alpha(t)\) is the random phase, \(z(t)\) is the amplitude of the LOS component, and \(\alpha_{0}\) denotes the corresponding phase. In [PERSON]'s model, the amplitude of the LOS component is modeled by using the random variable with log-normal distribution [31]. Although this model corresponds to the measurement results available in the literature, the corresponding mathematical analysis is usually too complex. The shadowed Rice model [32; 33] is a simpler but accurate channel model for narrowband land mobile satellite channels. In this model, it is assumed that \(a(t)\) is Rayleigh distributed, \(\alpha(t)\) is uniformly distributed, \(z(t)\) is Nakagami-\(m\) distributed, and \(\alpha_{0}\) is a deterministic value. The corresponding probability density function of the instantaneous power gain in the satellite-terrestrial channel, denoted by \(\lambda(t)=\left|h(t)\right|^{2}\), was derived in the paper [32] and given in the following form:  
\[f_{\Lambda}(\lambda)=\left(\frac{2b_{0}m}{2b_{0}m+\Omega}\right)^{m}\frac{1}{2 b_{0}}e^{-\frac{\lambda}{2b_{0}}}{}_{1}F_{1}\left(m;1;\frac{\Omega\lambda}{2b_{0} (2b_{0}m+\Omega)}\right),\,\lambda\geq 0, \tag{6}\]  
where \({}_{1}F_{1}0\) is the confluent hypergeometric function, \(m\) represents the parameter of Nakagami-\(m\) distribution, \(2b_{0}\) is the average power of the scattering component (the first term in Equation (5)), and \(\Omega\) denotes the average power of the LOS component (the second term in Equation (5)). Three degrees of freedom in this channel model, i.e., parameters \(m\), \(b_{0}\) and \(\Omega\), can be used to accurately describe different propagation conditions in the satellite-terrestrial channel. An accurate simulator of shadowed Rice fading that generates the corresponding fading samples with arbitrary temporal properties was proposed in [34]. A slightly improved version of this simulator, described in [35], is used in this paper. In real-world scenarios, observing channels with various characteristics in a systematic way can be difficult as these characteristics are not necessarily predictable or stable. It is, however, necessary to have a sufficient amount of data for all possible scenarios when developing algorithms that improve telecommunication performance, which can easily be achieved through the usage of simulations. To obtain the most benefit from the availability of the data through simulations, channels with varied characteristics are considered in this paper. Namely, the three characteristics that are varied for the different channels observed in this paper are as follows:  
* **The expected SNR value of the channels;**
* **The level of Doppler frequency shift;**
* **The level of shadowing.