IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 38, NO. 4, OCTOBER 2013 701 Statistical Characterization and Computationally Ef ficient Modeling of a Class of Underwater Acoustic Communication Channels Parastoo Qarabaqi, Student Member, IEEE, and Milica Stojanovic, Fellow, IEEE Abstract—Underwater acoustic channel models provide a tool for predicting the performance of communication systems before deployment, and are thus essential for system design. In this paper, we offer a statistical channel model which incorporates physical laws of acoustic propagation (frequency-dependent attenuation, bottom/surface reflections), as well as the effects of inevitable random local displacements. Specifically, we focus on random displacements on two scales: those that involve distances on the order of a few wavelengths, to which we refer as small-scale effects, and those that involve many wavelengths, to which we refer as large-scale effects. Small-scale effects include scattering and motion-induced Doppler shifting, and are responsible for fast variations of the instantaneous channel response, while large-scale effects describe the location uncertainty and changing environmental conditions, and affect the locally averaged received power. We model each propagation path by a large-scale gain and micromultipath components that cumulatively result in a complex Gaussian distortion. Time- and frequency-correlation properties of the path coefficients are assessed analytically, leading to a computationally efficient model for numerical channel simulation. Random motion of the surface and transmitter/receiver displace- ments introduce additional variation whose temporal correlation is described by Bessel-type functions. The total energy, or the gain contained in the channel, averaged over small scale, is modeled as log-normally distributed. The models are validated using real data obtained from four experiments. Specifically, experimental data are used to assess the distribution and the autocorrelation func- tions of the large-scale transmission loss and the short-term path gains. While the former indicates a log-normal distribution with an exponentially decaying autocorrelation, the latter indicates a conditional Ricean distribution with Bessel-type autocorrelation. Index Terms—Channel simulation, Doppler shifting, Doppler spreading, frequency correlation, large-scale fading, scattering, small-scale fading, statistical channel modeling, time correlation, underwater acoustic (UWA) communications. I. INTRODUCTION U NDERWATER ACOUSTIC (UWA) communication systems have to be designed to operate in a variety of conditions that differ from the nominal ones due to the Manuscript received November 19, 2012; revised April 11, 2013; accepted August 08, 2013. Date of publication September 30, 2013; date of current ver- sion October 09, 2013. This work was supported by the U.S. Office of Naval Re- search (ONR) Multidisciplinary University Research Initiative (MURI) under Grant N00014-07-1-0738, by the ONR under Grant N00014-09-1-0700, and by the National Science Foundation (NSF) under Grant CNS-1212999. Associate Editor: J. Potter. The authors are with the Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA (e-mail: qarabaqi@ece.neu. edu; millitsa@ece.neu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JOE.2013.2278787 changes in system geometry and environmental conditions. To allocate the appropriate resources (power, bandwidth) before system deployment, as well as to design appropriate signals and processing algorithms on both the physical link layer and the higher network layers, it is necessary to have a relatively accurate channel model. Beam tracing tools, such as Bellhop [1], use ray theory to provide an accurate deter- ministic picture of a UWA channel for a given geometry and signal frequency, but they do not take into account random channel variation. In recent years, there has been a growing awareness of the need to develop statistical channel models that will lead to computationally efficient tools for numerical simulation. New tools have been developed that address this need to some extent. For example, the Virtual Timeseries EXperiment (VirTEX) code [2] was developed to simulate the effect of channel variation in a manner that is computationally more efficient than repeated application of the Bellhop beam tracing. This algorithm operates by tracing multiple interre- lated beams to assess the cumulative effect on the signal of a given frequency. However, its computational complexity may still be an issue. For example, simulating a channel with a Doppler distortion on the order of 15 Hz requires at least 30 channel realizations per second which amounts to a total of 5400 Bellhop runs for simulating a system with two transmitters and six receiver elements over a period of 15 s. The wave front model [3] offers a deterministic approach which provides approximations to the ray theory to efficiently model the effects of the curvature of the surface waves and the amplitude and arrival time fluctuations that they introduce [4]. Numerous studies have also been conducted to model the UWA channel stochastically, e.g., [5]–[16]. These studies are usually based on the analyses of experimental acoustic data collected in a particular location. Some authors find Ricean fading [5], [7] or Rayleigh fading [6], [8], [13] to provide a good match for their measurements, while others find log-normal distribution [9], [10], the -distribution [11], [12], or a general class of Ricean shadowed distribution [16] to be a better fit. The variety of proposed statistical models is due to experi- ment-specific properties, e.g., the deployment site and the type of signals used for probing, as well as the time intervals during which the channel is observed. Statistical modeling of small-scale phenomena is a subject of ongoing research, which points to different types of fading, and no consensus exists yet on this topic. Modeling of large-scale phenomena has also been addressed only to a very limited ex- tent (see, e.g., [14], which shows some evidence of log-normal fading), while a few attempts have been made at unifying the 0364-9059 © 2013 IEEE