## 5 LMS Channel Models  
LMS platforms are gaining a lot of interest in the current generation of wireless systems and are expected to gain even more interest in the next generations due to the feasible services and their ability to serve many users over a large area at a low cost. LMS systems are becoming increasingly important for different types of applications, including navigation, communications, and broadcasting. The satellite channel models are based on statistical formulations that have the task of taking into account different propagation characteristics, as shown in Section 4. The model which is of interest for authors is for a LMS channel in a different land environment, such as urban, suburban, rural road, or highway environments where a LoS signal component is available at the receiver for a time more or less greater than that for multipath components. A complex model must be used to represent the LMS channel [25]. This model tries to characterize the different conditions to which the signal received on the ground can be subjected, unlike other channel models in which the effect of the environment on the received power is incorporated in a single distribution with appropriate statistical parameters that take into account the type of fading to which the signal is subject. In practice, what is used to characterize the channel between a satellite and a terrestrial mobile station is a different model for the various visibility conditions to which the signal (state) can be subjected; subsequently, the individual processes are combined into a single global process based on the transition probabilities of the states. The basic idea is that a random sequence can be generated by different'sources', each of which can be described with a very specific statistical model representing a different'state' of the signal. The link between the various states can be expressed through a Markov chain with as many states as there are different statistical models; therefore, the switching process between the various channel models is described with the Markov chain. The use of a Markov channel model is an approach used for different types of wireless networks [26], such as underwater acoustic channel communications [27; 28], ultra wideband (UWB) networks [29], and vehicle ad hoc networks [30]. The description of the channel is, therefore, extremely important, although very difficult: in fact, communications via satellite to a terrestrial mobile terminal have the drawback of undergoing considerable variations in the received power because the signal, before reaching the terrestrial mobile station, must pass through the various layers of the atmosphere--because it is subject both to fading due to multiple paths, and to absorption (obscuration) due to obstacles (shadowing). Fading occurs when the signal is not only received by a direct path (LoS), but also has reflected components. This means that, for certain periods of the link, the received signal may present a power lower than that foreseen by the theoretical link budget, due to the various components that are added to the receiver in an inconsistent way. On the other hand, shadowing occurs when the propagation path between the satellite and the terrestrial mobile station is obstructed by natural elements (mountains, trees, and so on) or by built structures. A statistical model for the envelope of the signal received in an LMS channel is useful for predicting the performance of a communication system with various modulation schemes. In the following, a classification of satellite channel models on the basis of the number states of a Markov chain is presented in order to provide a comprehensive review of thepossible satellite channel model to be used and to know what represents the adding of a new state in the model. Table 4 gives the main mathematical symbols used in the mathematical formulas provided in the following.