EMF path loss models

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The text on this page is taken from an equivalent page of the IEHIAS-project.

A range of path loss models have been developed for electromagnetic radiation sources, such as radio, TV and mobile phone base stations. The models estimate the reduction in power density (path loss) with distance from the transmission source to receptor, taking account of factors such as obstruction by buildings and effects of surface attenuation and reflection.

Models are based on empirical data for specific environments and transmission conditions (e.g. transmission frequency, transmitter height, distance to receptor and building densities), and care is therefore needed in using the models in other situations. For general applications (e.g. for the exposure assessment), therefore, it is often advisable to use an ensemble of models and take the (weighted) average of the results as the best estimate of the path loss.

Three models are outlined here. Links are also given to tools for EMF modelling:

  • an Excel spreadsheet in which these three models have been programmed (attached as zipped file);
  • the Radioworks software, which enables a range of path loss models to be run for individual sites;
  • the GIS-based Geomorf model, which has been developed specifically for EMF exposure assessment.



Path loss models were designed primarily to facilitate the planning and design of wireless communication systems. They can, however, be used as a basis for estimating ambient power density (and thus to approximate human exposures) as part of epidemiological and health impact studies.


The three models described here have been formulated for specific conditions, as outlined in the table below. Applications outside these conditions needs to be carried out with care, and wherever possible models should be validated for the specific conditions in which they are applied.

Model Frequency range (MHz) Distance range (km) Transmitter height range (m) Receptor height (m) Other comments
COST-231 Hata 1500-2000 1-20 30-200 1-10 Model unreliable where transmitter height < building height
COST-231 Walfisch-Ikegami 800-2000 0.02-5 4-50 1-3 Model unreliable where transmitter height < building height
ECC-33 ~3500 0-100 10-50 <50 Limitations not clearly specified

When using the models for exposure assessment, it also needs to be remembered that the models take no account of losses between the outside and inside of buildings, nor within the indoor environment. Estimated exposures are therefore likely to be substantially above those typically experienced in the home or work place.

Method description


Most path loss models have a broadly similar formulation, and have similar data demands. Key inputs include information on:

  • transmission frequency
  • antenna height
  • receptor height
  • distance from transmitter to receptor

Information is also needed in some cases on the type of terrain (e.g. urban, suburban, rural), and data are needed on the power output of the source antennae to translate the path loss into a measure of received power at the receptor.

For the three models described below, the following data inputs are required:

a = antenna orientation relative to line of street (degrees)

d = distance from base station to receptor (km)

f = transmission frequency (MHz)

hb = height of the building roof above ground (metres)

ht = height of the transmitter above ground level (metres),

hr = receptor height (metres).

sb = average inter-building separation (metres)


Path loss models provide a measure of the loss in power density (PL, in dBm) between the transmitter and receptor.

To estimate power density at the receptor (received power), loss is therefore subtracted from the effective power output of the transmitter (in the same units).



The pattern of electromagnetic radiation in the environment is described in terms of its field strength. The electrical and magnetic fields represent different, though inter-related phenomena, and are thus measured independently, and with different units. Both, however, tend to show marked variations over both space and time, for a number of reasons:

  • A large range of different emission sources exist, including both static transmitters (e.g. TV, radio or mobile phone masts) and mobile transmitters (e.g. in-car and personal phones and other appliances);
  • Usage of the devices that emit electromagnetic radiation varies considerably, often over minutes or hours, causing sharp changes in levels of emission;
  • The pathways taken by the emitted radiation are often complicated, because of the effects of refraction and reflection by buildings and other surfaces, especially in urban environments;
  • The wave structure of the radiation, and disturbance of electromagnetic fields by obstacles, leads to marked variations in the strength of the radiation over short distances, and between different micro-environments.

Modelling electromagnetic fields in the environment as a basis for exposure assessment therefore presents significant challenges. Ideally, methods would be used that can simulate the behaviour of individual rays, and ray-propagation and ray-tracing methods do exist that can provide this capability (Iskander and Yun 2002). Their use is limited, however, because they require large volumes of detailed data about both the source transmitters and the local terrain, and have substantial processing demands.

Path loss models

Given this, much effort has gone into devising and testing simpler statistical models. One of the main approaches has been the development of path loss models. These typically start with a basic, deterministic framework, describing the behaviour of electromagnetic radiation in free-space (i.e. the non-linear reduction of field strength with distance from source), and adapt this to take account of the characteristics of the source (e.g. height and orientation of the transmitter, frequency of the signal), receptor (e.g. height) and intervening terrain (e.g. presence of obstacles, surface roughness).

A number of these models have been developed, using empirical data for different types of transmitter and different environments. Different formulations of the models are often devised for different types of terrain, and for line-of-site (LOS) conditions, where an unostructed view exists along the pathway from antenna to receptor, and non line-of-site (NLOS) conditons, where this view is obstructed. Many of these have been subsequently modified or extended as part of the COST 231 project (Kürner 1999).

Several studies have been done to compare the performance of the different models under different conditions (e.g. Abhayawardhana et al 2005, Burgi et al. 2008), and these suggest that no-one model has general superiority over others. For general application, therefore, it may be appropriate to adopt an 'ensemble' approach - running a number of the models and taking an average of the results.


1. COST-231 Hata model

The COST-231 Hata model is applicable to transmission frequencies from 1500-2000 MHz, for antenna heights of 30-200 metres and for distances of 1-10 km, and includes versions for both suburban/flat rural and urban settings. It has, however, been widely applied outside its design situations, and has generally been shown to provide reasonably good approximations of path loss.

The COST-231 Hata model is defined as:

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for suburban and flat rural environments, or
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for urban environments (and for f>400MHz).

cm is a constant equal to 0 dBm for suburban and 3 dBm for urban environments.

2. COST-231 Walfisch-Ikegami model

In line-of-site conditions the path COST-231 Walfisch-Ikegami model takes the form of a simple free-space attenuation formula:

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In non line-of-site conditions, the COST-231Walfisch-Ikegami model is given as:

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LO represents attenuation in free-space and is defined as:

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LRTS represents diffraction from rooftop to street, and is defined as:

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for LRTS + LMSD > 0, or 0 otherwise.
LORI is a function of the orientation of the antenna relative to the street (a), and is defined as:
-10 + 0.354a for 0o<a<35o,
2.5 + 0.075(a - 35) for 35o<a<55o, and
4 - 0.114(a - 55) for 55o<a<90o

LMSD represents diffraction loss due to multiple screens (obstacles), and is specified as:

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for LRTS + LMSD > 0, or 0 otherwise.
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when ht > hb, or 0 otherwise,
= 54 + 0.8 (ht - hb)2d when ht< hb and d < 0.5 km, or

KA = 54 + 0.8 (ht - hb) when ht< hb and d > 0.5 km, or

= 54 when ht> hb ;
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when ht < hb, or 18 otherwise;
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where k = 0.7 for suburban centers and 1.5 for metropolitan centers.

3. ECC-33 model

Path loss in the ECC-33 model is defined as:

PL = Afs + Abm - Gb - Gr
Afs = 92.4 + 20 log10 (d) + 20 log10 (f)
Abm = 20.41 + 9.83 log10 (d) + 7.894 log10 (f) + 9.56 [log10 (f)]2
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See also

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