# Path Loss

Path loss models describe the signal attenuation between a transmit and a receive antenna as a function of the propagation distance and other parameters. Some models include many details of the terrain profile to estimate the signal attenuation, whereas others just consider carrier frequency and distance. Antenna heights are other critical parameters..

## Propagation prediction

 Topographical terrain data is used extensively to predict propagation conditions, to optimally select locations for installing cellular base stations. In an interview, Daniel Davarsilvatham of Bellcore discusses how adequate planning can avoid or reduce costly field tests. Source: Siemens TORNADO D Cellular Planning Tool In a rough coverage estimation, pathloss is computed using a basic propagation model, such as Egli's model, considering neither the topography nor terrain features in great detail. If no interference were present and if omni-directional antennas were used, such coverage plots tend to show circular cell layouts. However, real-life cell layouts substantially differ from the theoretical hexagonal or circular lay-out. Source: Siemens TORNADO D Cellular Planning Tool In practical cell panning, pathloss is computed from the terrain features and antenna data. Received signal powers and interference power levels, determine to coverage of each base station. Mathematical methods have been developed to calculate the signal outage probability, given all these propagation parameters. The link budget is more of a back-of-the-envelope alternative. Source: Siemens TORNADO D Cellular Planning Tool

## Example

In the above path profile, the most appropriate path loss model depends on the receive location:

• At location 1, free space loss is likely to give an accurate estimate of path loss.
• At location 2 and 3, a strong line-of-sight is present, but ground reflections can significantly influence path loss. The plane earth loss model appears appropriate
• At location 4, free space loss needs to be corrected for significant diffraction losses, caused by trees cutting into the direct line of sight.
• Path loss prediction at location 5, 6 and 7 is more difficult than at the other locations. Ground reflection and diffraction mechanisms interact.

# Path-loss law

 Figure: Average path loss versus distance in UHF bands, measured in Northern Germany. (a, green): forestrial terrain (b, orange): open area (grey): Average of (a) and (b) (black): Egli's model Models such as the Egli Path Loss Law can be used for a rough coverage estimation. However, the prediction error standard deviation is on the order of 12 dB. Compare the predicted smooth cell boundaries by the more accurate estimates in the screen displays above. On the right: Results generated by the TORNADO D planning tool by Siemens AG for cellular telephone at 900 MHz. (Qatar, Arabian Peninsula ) Source: Siemens TORNADO D Cellular Planning Tool

## Received signal power and attenuation

Path loss is one of the mechanisms causing attenuation between the transmitter power amplifier and receiver front end. Some other effects are listed below, with an indication of the order of magnitude in a GSM-like system (see also pdf slides on GSM frequency planning).
• Losses in the antenna feeder (0 .. 4 dB)
• Losses in transmit filters, particularly if the antenna radiates signal of multiple transmitters (0 .. 3 dB)
• Antenna directionality gain (0 .. 12 dB)
• Losses in duplex filter
• Fade margins to anticipate for multipath (9 .. 19 dB) and shadow losses (5 dB)
• Penetration losses if the receiver is indoors, typically about 10 dB for 900 MHz signals
These parameters all appear on the link budget.

## Summary

Several path loss models have been proposed in literature, for instance
• Egli's model
• Okumura's model
• Hata's model
• COST 231 - Hata
 SPEC See the Special Purpose Embedded Path Loss Predictor, a spread sheet to forecast path loss.

 Effect of antenna height Effect of frequency Effect of distance Free space none 20 log f 20 log d Theoretical plane earth 6 dB/oct none 40 log d Egli plane earth 6 db/oct 20 log f 40 log d Measured urban 6 dB/oct 20 log f 32 log d