# Measurement and Modeling of Narrowband Channels for Ultrasonic Underwater Communications
## 1 Introduction  
Underwater sensor nodes and networks allow a new way to gather data in real time from the submarine environment for applications like pollution monitoring, supervision of undersea equipment of oil and gas companies, search and survey missions, seismic prediction, fish farming maintenance, _etc._ The underwater medium is known to be one of the most challenging communication channels currently in use today. Three technologies have been considered for this purpose over the years: acoustic, optical and electromagnetic. The severe drawbacks of the optical and electromagnetic alternatives (particularly an extremely high attenuation that limits the transmission range) have made acoustic waves the preferred option in most applications [1; 2]. However, the use of acoustic technology is not free of problems. The propagation of an acoustic wave is strongly affected by multiple physical processes whose relative influence is remarkably different from one scenario to another [3]. Basically, the acoustic signal experiences high attenuation and distortion, the latter due to both the multipath propagation and time-variation of the channel. Such time variation has its origin in the movement ofthe underwater environment, and it causes the received signal level to randomly fluctuate with time, which is referred to as fading.  
As will be explained in more detail in the next section, multipath propagation causes frequency selectivity that can be evaluated by estimating the frequency response of the channel or by means of average parameters, like the delay spread or the coherence bandwidth. Regarding the time variation of the channel, it can also be quantified by average parameters, like the coherence time or the Doppler spread, but for a more accurate evaluation of its effect, the fading statistics must be explored [2; 4; 5; 6; 7; 8; 9].  
Most systems designed for underwater acoustic communications (UAC) work in low frequency bands, but currently, there is an increasing concern in going beyond the audio band to take advantage of the smaller wavelength at ultrasonic frequencies. This is of particular interest for sensor networks, because the transmitter and receiver devices can have a more reduced size and weight, and they can operate with a lower energy consumption. The channel has been extensively explored for UAC in the audio band [2; 3; 4; 5; 7; 8; 9; 10], but there are few works devoted to the channel analysis at the ultrasonic band [1; 3; 11]. At these frequencies, communications are more exposed to the effect of fading, and its modeling becomes more important. In this paper, our attention will be centered on the analysis of the channel time variation with the characterization of such fading. We are focusing on telemetry applications that require low digital transmission speeds, and hence, the transmission bandwidth can be considered narrow enough to assume a frequency flat channel (_i.e._, there is no distortion due to frequency selectivity).  
The paper is organized as follows. Section 2 presents a review of the state-of-the-art channel modeling for UAC, including fading models. In Section 3, the measurement procedure and results on actual channels are described. In Section 4, the measurements results are fit to the \(\kappa\)-\(\mu\) shadowed fading model, and in Section 5, the ergodic capacity of the measured channels is analyzed. Finally, some conclusions are summarized in Section 6.