Modeling for Geo-Routing in Multi-Hop Wireless Networks - Application and Multidisciplinary Aspects of Wireless Sensor Networks - page 144

Path Loss between Rx and Tx

160

LOS
NLOS
weighted

140

120

100

80

60

40

Height of Tx = 1.5 & Rx = 1.5m

20

0 0.5 1 1.5 2 2.5 3

Distance between Rx and Tx in logscale

Fig. 7.2 The weighted average path-loss model that combines LOS and NLOS propagation using
a smooth transition model as proposed in [ 4 ]

We fix the transmitter power to P =- 27 dBW and the receiver sensitivity to

tx

- 131dBW and its noise floor to N =- 112 dBW , such that

ppr = 0.5

occurs at

d = . These receiver and transmitter characteristics correspond approximately
to an IRIS mote specification.
When

65 m

σ , the packet reception probability at each value of d becomes itself
a stochastic variable with a given spread of values around those depicted in Fig. 7.1 .
The

0

dB

σ model simply extends the UDG by introducing concentric probability
of packet reception contours as shown in Fig. 7.1b , but the

0

dB

model cannot σ > 0

dB

account for the fact that the spatial random field, () x σ , possesses a characteristic

spatial correlation length, 50 d in a meaningful way, since cumulative outage
probabilities will always result in a circularly symmetric model.

7.4 Spatially Correlated Shadow Fading

Modeling the spatially correlated nature of shadow fading can be achieved through
a variety of models of varying sophistication [ 6 and references therein]. We choose
a conceptually simple-to-understand method that is not particularly computationally