The ns Manual (formerly ns Notes and Documentation)1 - NM Lab at ...

EnvironmentβOutdoor Free space 2Shadowed urban area 2.7 to 5In building Line-of-sight 1.6 to 1.8Obstructed 4 to 6Table 18.1: Some typical values of path loss exponent βEnvironment σ dB (dB)Outdoor 4 to 12Office, hard partition 7Office, soft partition 9.6Factory, line-of-sight 3 to 6Factory, obstructed 6.8Table 18.2: Some typical values of shadowing deviation σ dBThe shadowing model consists of two parts. The first one is known as path loss model, which also predicts the mean receivedpower at distance d, denoted by P r (d). It uses a close-in distance d 0 as a reference. P r (d) is computed relative to P r (d 0 ) asfollows.P r (d 0 )P r (d) = ( dd 0) β(18.4)β is called the path loss exponent, and is usually empirically determined by field measurement. From Eqn. (18.1) we know thatβ = 2 for free space propagation. Table 18.1 gives some typical values of β. Larger values correspond to more obstructionsand hence faster decrease in average received power as distance becomes larger. P r (d 0 ) can be computed from Eqn. (18.1).The path loss is usually measured in dB. So from Eqn. (18.4) we have[ ]P r (d)P r (d 0 )dB( ) d= −10β logd 0(18.5)The second part of the shadowing model reflects the variation of the received power at certain distance. It is a log-normalrandom variable, that is, it is of Gaussian distribution if measured in dB. The overall shadowing model is represented by[ ] ( )Pr (d)d= −10β log + X dB (18.6)P r (d 0 )dBd 0where X dB is a Gaussian random variable with zero mean and standard deviation σ dB . σ dB is called the shadowing deviation,and is also obtained by measurement. Table 18.2 shows some typical values of σ dB . Eqn. (18.6) is also known as a log-normalshadowing model.The shadowing model extends the ideal circle model to a richer statistic model: nodes can only probabilistically communicatewhen near the edge of the communication range.189