Empirical models are those models which are proposed after many years of trial and error method of research. The final formula is formed which satisfies the tabulated results obtained after the experimentations. This is called as curve fitting technique. This has the advantage of implicitly taking into account all propagation factors, both known and unknown, through actual field measurements. However, the validity of an empirical model at transmission frequencies or environments other than those used to derive the model can only be established by additional measured data in the new environment at the required transmission frequency. Over time, some classical propagation models have emerged, which are now used to predict large-scale coverage for mobile communication systems design. Some of the path loss models are as follows:

1. Log-distance path loss model
2. Log normal shadowing model
3. Longley-Rice model
4. Okumura model
5. Hata model

The Log-distance path loss model and Log-normal shadowing model are described in the following sections:

1. Log-Distance Path Loss Model

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 TR separation is expressed as a function of distance by using a path loss exponent, n. which is as given under:

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

Or

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

where n is the path loss exponent which indicates the rate at which the path loss increases with distance, $d_0$ is a 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 oss values for a given value of d. 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, 1 km reference distances are commonly used , whereas in microcellular systems, much smaller distances (such as 100 m or 1 m) 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. The reference path loss is calculated using the free space path loss formula or through field measurements at distance $d_0$. Following Table lists typical path loss exponents obtained in various mobile radio environments.

2. Log normal shadowing model

Log-distance path loss model does not consider the fact that the surrounding environmental clutter may be vastly different at two different locations having the same T-R separation. This leads to measured signals which are vastly different than the average value predicted by previous model. Measurements have shown that at any value of d, the path loss PL(d) at a particular location is random and distributed log-normally (normal in dB) about the mean distance dependent value . That is,

$P L(d)[d B]=\overline{P L}(d)+X_{\sigma}=\overline{P L}\left(d_{0}\right)+10 n \log \left(\frac{d}{d_{0}}\right)+X_{\sigma}$

and

$P_{r}(d)[d B m]=P_{t}[d B m]-P L(d)|d B|$

where $X_{\sigma}$, is a zero-mean Gaussian distributed random variable (in dB) with standard deviation $\sigma$ (also in dB).

The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation, but have different levels of clutter on the propagation path. This phenomenon is referred to as log-normal shadowing. Simply put, log-normal shadowing implies that measured signal levels at a specific T-R separation have a Gaussian (normal) distribution . The standard deviation of the Gaussian distribution that describes the shadowing also has units in dB.

The close-in reference distance $d_0$, the path loss exponent n, and the standard deviation a, statistically describe the path loss model for an arbitrary location having a specific T-R separation, and this model may be used in computer simulation to provide received power levels for random locations in communication system design and analysis.