# Measurement and Modeling of Narrowband Channels for Ultrasonic Underwater Communications
## Channel Characterization for UAC
### UAC Fading Models Review  
There is no general agreement about the best suited distribution model for the statistical characterization of this kind of channel. Several statistical fading models have been proposed in the literature. Although the main attribute of a model is its ability to fit experimental data, other features must be taken into account, for instance the easiness for mathematical manipulation and the existence of an underlying physical mechanism that justifies the model. Here are the main distribution models addressed for underwater acoustic channels, most of them also employed in terrestrial RF scenarios [13; 14; 15]:  
* _Rayleigh distribution_: This corresponds to a situation where a high number of multipath fluctuating components arrive at the receiver and there is no direct path, _i.e._, no LOS component [1; 7; 10].  
Figure 1: Channel modeling diagrams: (**a**) example of underwater acoustic communications system; (**b**) classification of fading models.  
* _Rice distribution_: This is a generalization of the Rayleigh distribution used when a LOS component with non-fluctuating level is added to the weaker multipath fluctuating components of the previous scenario [6; 7; 8; 9].
* _Nakagami-m distribution_: This is another generalization of the Rayleigh distribution, but considering the case where \(m\) clusters of multipath waves propagate in a non-homogeneous environment and arrive at the receiver with no main components within each cluster (strictly speaking, only for a cluster without reflections, the main component represents a LOS path; for the remaining clusters, with some reflections, the main component corresponds to the ray tracing for the reflected path). The envelope of each cluster signal is hence considered Rayleigh distributed. Nakagami-\(m\) with \(m=1\) is Rayleigh [16].
* \(\kappa\)-\(\mu\) _distribution_: This consists of a generalization of the Nakagami-\(m\) distribution where a non-fluctuating main component is considered within each cluster [17]. Actually, the \(\kappa\)-\(\mu\) distribution is a generalization of the three previous distributions. Nakagami-\(m\) is approached if the level of the LOS components tends to zero. Rice is obtained if the number of clusters is set to one, and Rayleigh is obtained if both particularizations are simultaneously assumed.
* _K distribution_: This is a mixture of Gamma and Rayleigh distributions. The underlying mechanism for signal fluctuation that leads to this distribution is not clear (a question may arise about if some of the models can be regarded (entirely or partially) as merely fitting functions) [18].
* _Rice shadowed distribution_: This represents a generalization of the Rice distribution where the main component is assumed to be a random Nakagami-\(m\) variable [19]. It models the case where the LOS component experiences shadowing.
* \(\kappa\)-\(\mu\) _shadowed distribution_: This is a generalization of the \(\kappa\)-\(\mu\) distribution where the main components are considered Nakagami-\(m\) random variables. This distribution includes Rayleigh, Rice, Rice shadowed, Nakagami-\(m\) and \(\kappa\)-\(\mu\) as particular cases. A better behavior of the \(\kappa\)-\(\mu\) shadowed model over the rest has been addressed in [20] for UAC.  
A summary of these models is shown in Figure 1b (where the \(K\) distribution is intentionally not included).