Actas JP2011 - Universidad de La Laguna

Actas XXII Jornadas de Paralelismo (JP2011) , La Laguna, Tenerife, 7-9 septiembre 2011transmission) requires only a single call to a Gaussianrandom number generator. Moreover, if the networktopology changes slightly, or if a new node is added, thestatistical model needs to be augmented only by thecorresponding set of nominal transmission losses, eachof which requires a single Bellhop run.Most importantly, the statistical model can easily beused to assess transmit power allocation that willguarantee successful data packet reception with adesired level of performance (e.g. link reliability).Namely, the SPM can easily be used to calculate thetransmission loss values that are not exceeded with agiven probability (i.e cumulative distribution function).For example, a 90% transmission loss is that valuewhich is not exceeded for 90% of time, i.e. in 90% ofchannel realizations. Fig.6 shows the 50%, 75% and90% transmission loss for our system example. Weobserve a good match between the values predicted bythe deterministic model, and those of the statisticalmodel. Note that the X% values of the SPM arecomputed analytically, based only on the knowledge ofthe mean and standard deviation.The availability of X% values is significant fordetermining the transmit power necessary to achieve acertain level of performance. Typically, networkplanning is based on the nominal ray trace, i.e. on the50% transmission loss to which some margin may beadded. If transmit power allocation is based on adifferent value, say 90% transmission loss instead of thenominal 50%, data packets will be more likely to reachtheir destinations. More power will be needed at thesame time, but the overall network performance mayimprove. We say may improve, because a highertransmit power also implies higher levels ofinterference. The resulting performance trade-offs aregenerally hard to address analytically, and are insteadassessed via simulation. A statistical propagation modelthat directly links the transmit power to the X%transmission loss then becomes a meaningful and usefultool for system design.Transmission Loss (dB)706560555045DPM 90%SPM 90%DPM 75%SPM 75%DPM 50%SPM 50%400 500 1000 1500 2000 2500 3000 3500 4000Distance (meters)Fig. 6. Transmission loss value that is not exceeded with a givenprobability (50 %, 70%, 90%) is shown versus distance. The solidand dashed curves show the results obtained from thedeterministic and the statistical propagation models, respectively.V. CONCLUSIONSLarge-scale design of an underwater acoustic networkrequires a judicious allocation of the transmit poweracross different links to ensure a desired level of systemperformance (connectivity, throughput, reliability, etc.).Because of the inherent system complexity, simulationanalyses are normally conducted to assess theperformance of candidate protocols under differentresource allocation policies. These analyses are oftenrestricted to using deterministic propagation models,which, although accurate, do not reflect the randomlytime-varying nature of the channel.While it is possible in principle to examine thenetwork performance for a large set of perturbedpropagation conditions, the computational complexityinvolved in doing so is extremely high. To facilitatenetwork simulation in the presence of channel fading,we investigated a statistical modeling approach. Ourapproach is based on establishing the nominal systemparameters for a desired deployment location (waterdepth, sediment composition, operational frequencyrange) and using ray tracing to compute an ensemble oftransmission losses for typical inter-node distances. Anensemble is generated by considering a set of perturbedsurface conditions, defined by varying wave activity(height, period). The so-obtained ensemble is then usedto determine the statistical parameters of a hypothesizedlog-normal distribution of the transmission loss. For arepresentative example of a small network operating ina 5 km x 5 km area with inter-node distances rangingbetween 500 m and 3.5 km, it was found that the meancan be well approximated by the value obtained usingnominal system parameters, while the variance can bemodeled as distance-independent. Models that are moreelaborated and more accurate than the log-normal onecan also be developed using this approach.This kind of statistical modeling allowscomputationally-efficient inclusion of fading effects intoa network simulator. Namely, to assess the averagesystem performance, network operation has to besimulated over a large set of channel realizations (e.g.varying surface conditions). Whereas repeatedcomputation of the ray trace for different hops that eachof the data packets traverses in a given network may becomputationally prohibitive, statistical modelingrequires only a single call to the Gaussian randomgenerator for each packet transmission. The overallsimulation time is thus considerably reduced, allowing asystem designer to freely experiment with varyingprotocols and resource allocation strategies in anefficient manner. The ultimate goal of such experimentsis to choose the best upper-layer protocol suite and torelate the necessary system resources (power,bandwidth) to the propagation conditions, i.e. to thestatistical parameters of the transmission loss (e.g. X%value), which can in turn be easily generated using theproposed method of statistical modelingJP2011-394