Model Log-distance path loss model is formally expressed as: : L=L_\text{Tx}-L_\text{Rx}=L_0+10\gamma\log_{10}\frac{d}{d_0}+X_\text{g} where • {L} is the total
path loss in
decibels (dB). • L_\text{Tx}=10\log_{10}\frac{P_\text{Tx}}{\mathrm{1~mW}} \mathrm{~dBm} is the transmitted power
level, and P_\text{Tx} is the transmitted power. • L_\text{Rx}=10\log_{10}\frac{P_\text{Rx}}{\mathrm{1~mW}} \mathrm{~dBm} is the received power level where {P_\text{Rx}} is the received power. • L_0 is the
path loss in decibels (dB) at the reference distance d_0. This is based on either close-in measurements or calculated based on a free space assumption with the Friis
free-space path loss model. • {d} is the length of the path. • {d_0} is the reference distance, usually 1 km (or 1 mile) for a large cell and 1 m to 10 m for a microcell. (and thus the corresponding power gain F_\text{g}=10^{-X_\text{g}/10} may be modelled as a random variable with
exponential distribution).
Corresponding non-logarithmic model This corresponds to the following non-logarithmic gain model: : \frac{P_\text{Rx}}{P_\text{Tx}}=\frac{c_0 F_\text{g}}{d^{\gamma}} , where c_0={d_0^{\gamma}}10^{-L_0/10} is the average multiplicative gain at the reference distance d_0 from the transmitter. This gain depends on factors such as
carrier frequency, antenna heights and antenna gain, for example due to directional antennas; and F_\text{g}=10^{-X_\text{g}/10} is a
stochastic process that reflects
flat fading. In case of only slow fading (shadowing), it may have
log-normal distribution with parameter \sigma dB. In case of only
fast fading due to
multipath propagation, its amplitude may have
Rayleigh distribution or
Ricean distribution. This can be convenient, because power is proportional to the square of amplitude. Squaring a Rayleigh-distributed random variable produces an
exponentially distributed random variable. In many cases, exponential distributions are computationally convenient and allow direct closed-form calculations in many more situations than a Rayleigh (or even a Gaussian). == Empirical coefficient values for indoor propagation ==