Actas JP2011 - Universidad de La Laguna

Actas XXII Jornadas de Paralelismo (JP2011) , La Laguna, Tenerife, 7-9 septiembre 2011Statistical Modeling of Transmission Path Lossin Underwater Acoustic NetworksJesús Llor and Manuel Pérez Malumbres 1Abstract—Propagation conditions in an underwateracoustic channel are known to vary in time, causing thereceived signal strength to deviate from the nominal valuepredicted by a deterministic propagation model. Tofacilitate large-scale system design in such conditions (e.g.power allocation), we develop a statistical propagationmodel in which the transmission loss is treated as a randomvariable. By repetitive computation of acoustic field usingray tracing for a set of varying environmental conditions(surface height, wave activity, small displacements oftransmitter and receiver around nominal locations), anensemble of transmission losses is compiled which is thenused to infer the statistical model parameters. A reasonableagreement is found with log-normal distribution whosemean is taken as the nominal transmission loss, and whosevariance appears to be constant for a certain range ofinter-node distances in a given deployment location. Thestatistical model is deemed useful for higher-level systemplanning, where simulation is needed to assess theperformance of candidate network protocols under variousresource allocation policies, i.e. to determine the transmitpower and bandwidth allocation necessary to achieve adesire.Keywords—Underwater acoustics, Acoustic channelmodel, Wireless sensor networks, Network simulation.TI. INTRODUCTIONHE growing need for ocean observation and remotesensing has recently motivated a surge in researchpublications as well as several experimental efforts (e.g.[1]) in the area of underwater acoustic networks. Crucialto these developments is the understanding ofpropagation conditions that define the time-varying andlocation-sensitive acoustic environment, not only fromthe viewpoint of small-scale, rapid signal fluctuationsthat affect the performance of the physical layertechniques, but also from the viewpoint of large-scale,slow fluctuations of the received signal power thataffect the performance of higher network layers. Thisfact has been gaining recognition in the researchcommunity, leading to an increased awareness about theneed for network simulators that take into account thephysics of acoustic propagation [1]-[4]. As a result, thefirst publicly available acoustic network simulators haveemerged [2], and more are likely to come.One of the challenges in the design of underwateracoustic networks is the allocation of power acrossdifferent network nodes. This task is exacerbated by the1 All authors are with the Dept. of Physics and Computer Engineeringat the Miguel Hernandez University (Spain). E-mails: {jllor,mels}@umh.esspatial and temporal variation of the large-scaletransmission loss, and the lack of statistical models thatcapture these apparently random phenomena.While it is well known from field experiments that thereceived power varies in time around the nominal valuepredicted by a deterministic propagation model, little isknown about the statistical nature of these variations.Literature on this topic is scarce; however, several recentreferences indicate that the received signal strengthobeys a log-normal distribution (e.g. [5][6]). A goodsystem design has to budget for signal strengthvariations in order to ensure a desired level of networkperformance (e.g. connectivity), and the budgeting taskcan be made much easier if the statistics of theunderlying process are known.In this paper, we analyze those random variations inthe large-scale transmission loss that are mainlygoverned by the environmental factors such as surfaceactivity (waves) for a particular network scenario. Webegin by employing a prediction model based on theBellhop ray tracing tool [7]. Such a deterministic modelprovides accurate results for a specific geometry of thesystem, but does not reflect the changes that occur as thegeometry changes slightly due to either surface motionor transmitter/receiver motion. Fig.1 illustrates thissituation for a point-to-point link. It shows an ensembleof transmission losses calculated by the Bellhop modelfor a set of varying surface conditions, each slightlydifferent from the nominal.While it is possible in principle to run a deterministicpropagation model for a large number of differentsurface conditions, the underlying computationaldemands are high. In a large network, it is ineffective,and possibly not even feasible, to run a complexprediction model for each packet transmission. Astatistical prediction model then becomes necessary.The goal of our work is to employ an existingdeterministic prediction model (DPM) such as the raytracer [7] to generate an ensemble of channel responsescorresponding to varying propagation conditions in agiven network. Using the so-obtained values, we thenconduct a statistical analysis to obtain the probabilitydensity function (pdf) of the large-scale transmissionloss. The result is a statistical prediction model (SPM)that is easy to employ for network design and analysis.The rest of this paper is organized as follows. In Sec.IIwe outline a specific system example, and discuss thecomputational demands of deterministic propagationmodeling. In Sec.III, we present the results ofdeterministic modeling and develop an underlyingJP2011-391