In general, propagation models for both indoor and outdoor radio channels indicate that mean path loss as follow
Lp¯(d)~d/d0nLp¯(d)~d/d0n size 12{ {overline {L rSub { size 8{p} } }} \( d \) "~" left (d/d rSub { size 8{0} } right ) rSup { size 8{n} } } {}(1)
Lp¯(d)dB=Ls(d0)dB+10n.log(d/d0)Lp¯(d)dB=Ls(d0)dB+10n.log(d/d0) size 12{ {overline {L rSub { size 8{p} } }} \( d \) ital "dB"=L rSub { size 8{s} } \( d rSub { size 8{0} } \) ital "dB"+"10"n "." "log" \( d/d rSub { size 8{0} } \) } {} (2)
Where
dd size 12{d} {} is the distance between transmitter and receiver, and the reference distance
d0d0 size 12{d rSub { size 8{0} } } {} corresponds to a point located in the far field of the transmit antenna. Typically,
d0d0 size 12{d rSub { size 8{0} } } {} is taken 1 km for large cells, 100 m for micro cells, and 1 m for indoor channels. Moreover
d0d0 size 12{d rSub { size 8{0} } } {} is evaluated using equation
Ls(d0)=4πd0λ2Ls(d0)=4πd0λ2 size 12{L rSub { size 8{s} } \( d rSub { size 8{0} } \) = left ( { {4πd rSub { size 8{0} } } over {λ} } right ) rSup { size 8{2} } } {}(3)
or by conducting measurement. The value of the path-loss exponent n depends on the frequency, antenna height and propagation environment. In free space, n is equal to 2. In the presence of a very strong guided wave phenomenon (like urban streets),
nn size 12{n} {} can be lower than 2. When obstructions are present,
nn size 12{n} {} is larger.
Measurements have shown that the path loss
LpLp size 12{L rSub { size 8{p} } } {} is a random variable having a log-normal distribution about the mean distant-dependent value
Lp¯(d)Lp¯(d) size 12{ {overline {L rSub { size 8{p} } }} \( d \) } {}
Lp(d)(dB)=Ls(d0)(dB)+10nlog10(d/d0)+Xσ(dB)Lp(d)(dB)=Ls(d0)(dB)+10nlog10(d/d0)+Xσ(dB) size 12{L rSub { size 8{p} } \( d \) \( ital "dB" \) =L rSub { size 8{s} } \( d rSub { size 8{0} } \) \( ital "dB" \) +"10"n"log" rSub { size 8{"10"} } \( d/d rSub { size 8{0} } \) +X rSub { size 8{σ} } \( ital "dB" \) } {}(4)
Where
XσXσ size 12{X rSub { size 8{σ} } } {} denote a zero-mean, Gaussian random variable (in dB) with standard deviation (in dB).
XσXσ size 12{X rSub { size 8{σ} } } {} is site and distance dependent.
As can be seen from the equation, the parameters needed to statistically describe path loss due to large-scale fading, for an arbitrary location with a specific transmitter-receiver separation are (1) the reference distance, (2) the path-loss exponent, and (3) the standard deviation
XσXσ size 12{X rSub { size 8{σ} } } {}.
