Both theoretical and measurement-based propagation models indicate that average received signal power decreases logarithmically with distance, whether in outdoor or indoor radio channels.

Such models have been used extensively in the literature. The average large-scale path loss for an arbitrary T-R separation is expressed as a function of distance by using a path loss exponent,n

$$\overline{P L}(d) \propto\left(\frac{d}{d_{0}}\right)^{n}-----(1)$$

or

$$\overline{P L}(\mathrm{dB})=\overline{P L}\left(d_{0}\right)+10 n \log \left(\frac{d}{d_{0}}\right)-----(2)$$

where n is the path loss exponent which indicates the rate at which the path loss increases with distance, $d_{0}$ is the close-in reference distance which is determined from measurements close to the transmitter, and d is the T-R separation distance.

The bars in both the equations denote the ensemble average of all possible path loss values for a given value of d.

When plotted on a log-log scale, the modelled path loss is a straight line with a slope equal to 10n dB per decade. The value of n depends on the specific propagation environment.

For example, in free space, n is equal to 2 and when obstructions are present, n will have a larger value.

It is important to select a free space reference distance that is appropriate for the propagation environment. In large coverage cellular systems, 1km reference distances are commonly used, whereas in micro cellular systems, much smaller distances are used.

The reference distance should always be in the far field of the antenna so that near-field effects do not alter the reference path loss.

Above table lists typical path loss exponents obtained in various mobile radio environments.