# Measurement and Modeling of Narrowband Channels for Ultrasonic Underwater Communications
## Channel Characterization for UAC  
The main factors that adversely affect the propagation of a signal in an UAC channel are:  
* _Attenuation_: In UAC channels the attenuation is, in general terms, much higher than in terrestrial radio frequency (RF) channels and strongly depends on frequency and distance. Empirical formulas to predict the _path loss_, or mean attenuation, are available in the literature [12]. The mechanisms responsible for the path loss are basically signal _absorption_ (part of the signal energy is transferred to the medium) and signal _spreading_ (which depends on the geometry of propagation). Absorption increases rapidly with frequency, while spreading does with distance, yielding a limited range and limited bandwidth channel.
* _Distortion_: This is due to _multipath propagation_ and _fading_. Multipath propagation in shallow UAC is caused by the reflections of the acoustic signal on the seabed, the surface of the sea and any other objects, and the different paths undergo different delays at reception that result in a dispersion in time (it can also be seen as the superposition of constructive and destructive contributions selective in frequency) [3]. A common way to characterize the time dispersion of the channel, or its frequency selectivity, is by evaluating parameters like the _coherence bandwidth_ or the _delay spread_, which is several orders of magnitude higher than those measured in RF channels [13] due to the relatively low speed of sound in water. A typical propagation scenario is shown in Figure 1a, where a main component (line of sight (LOS)) is represented along with various multipath components. This multipath scenario is not static, but varies with time due to several factors, like surface waves (that change the reflection angles of the multipath components), internal waves, the motion of transmitter/receiver, changes in the medium physical conditions, _etc_. The time variation results in a fluctuation of the received signal level, the so-called fading. This fluctuation may also be experienced by the LOS component, a phenomenon referred to as _shadowing_. A simple way to characterize the time variation is directly, through the _coherence time_, or indirectly, through the Doppler spread_, which measures the frequency broadening. This effect can be remarkably intense in UAC due, again, to the relatively low speed of sound in water.  
One step further in the evaluation of the distortion caused by the time variation of the channels is the statistical modeling of the fading. Different models correspond to different assumptions on the ray tracing from transmitter to receiver. Ray tracing can be considered a valid approximation in ultrasonic UAC, since the involved wavelengths are in the range of cm, similar to microwaves in electromagnetic communications. Three main assumptions are taken into consideration for modeling the fading: (1) the existence of a LOS component or not; (2) the deterministic or random behavior of the LOS component and (3) the possibility of the signal traveling through different clusters of multipath waves. In the next section, a review of different fading models is presented.