Every ~~week~~ month, ATDI compares different propagation models for a given service based on very accurate measurements.

**This week**, FM: Model-Episode 1

Model |
Standard deviation |
Average error |
Correlation factor |
Differences < 6 dB |

ITU-R 525 Deygout 94 Fine integration |
3.42 dB |
0.84 dB |
0.97 |
91.17% |

ITU-R 1546-5 (Broadcast analog) 50% time 50% locations |
7.43 dB |
-5.56 dB |
0.89 |
60.28% |

ITU-R 1812-3 50% time 50% locations |
3.62 dB |
1.57 dB |
0.97 |
88.55% |

Okumura-Hata / original |
5.10 dB |
1.38 dB |
0.94 |
83.46% |

ITM / NTIA – 50% time 50% locations |
6.26 dB |
2.12 dB |
0.92 |
78.75% |

**Next month**, Wimax rel 2 (3 600 MHz)

**Parameters influencing the correlation:**

The configuration of the propagation model: reference (dBd, dBi, dBv), percentage of time and percentage of locations (if applicable), options like Tropo, Climate, Reflections…,

The quality of the cartography used by the planning tool: the resolution of the DTM, and the quality of the clutter file need to be adapted to the technology simulated. Applying the Lee criteria (see below) is for instance a good way to check the sampling resolution to use depending on the frequency of the technology simulated (step = 40 ?),

The quality of the GPS coordinates needs to taken into account: GPS have today an absolute planimetric accuracy of 7.8 meters at a 95% confidence level, and this quality decreases in obstructed environment (decrease of the GDOP)

**The fast fading effect and RF prediction: the LEE criteria**

One of the main aspects to take also into consideration for the correlation with measurement is the fast fading effect. Lee’s goal was to find a valid method of estimating the local average power of a signal in the mobile radio environment. His conclusion, that the proper technique is to average 50 samples taken over a distance of 40 ? (wavelengths), has become a standard technique, widely used within the industry .This basis have

become so widely accepted that it can sometimes used in situations where Lee sampling is not strictly applicable. Even though it may not be optimum in all situations, it does provide a base-line that allows measurements to be compared.

Background to signal level variations: the envelope of a received mobile radio signal is composed of a slow fading signal with a fast fading signal superimposed on it. In many applications it is necessary to measure the local average power of the slow fading signal by smoothing out (or averaging) the fast fading part.

The fading experienced by a moving receiver has two major causes:

• The multi-path phenomenon: the signal transmitted from the base station is usually blocked by these surrounding structures and many reflected waves are generated. Summing ail of the multi-path waves at the mobile unit results in fast variations in the received signal which is called multi-path fading. It is also called short-term fading or fast fading referring to the short time period during which signals change.

• The variation of the average signal power as the mobile moves. This is due to different propagation paths between the base station and the mobile unit moving over different terrain configurations at different times. Since the propagation path is always changing as the mobile moves, the path loss values and hence local average power of the received signal vary. Because it is affected by the location of the mobile moving in real time and it varies slowly, it is called the local mean of the long term fading.

Since the received mobile radio signal contains both short term and long-term fading, to estimate the local mean of long-term fading that predictable using a planning tool, the fast fading effect has to eliminated from the measured signal, otherwise the true average power and the measured average power will not be the same.

Obtaining a Local Average Signal Power (Local Mean): how to measure the local mean of the signal when the signal is received by a moving receiver, Lee addressed two major questions. His approach to both was aimed at reducing the errors in the measurements:

• The first question is how to choose a proper length of signal data for averaging.

• The second question, after determining the length, is how many independent sample points are needed for averaging over that length.

Choosing the Proper Length of a Local Mean: as we know, the length of a local signal has to be chosen properly. If it is chosen too short, the short-term fading is still present after the averaging process. If it is chosen too long, information about the long-term fading which we want to preserve, will be smoothed out. To find the proper length, Lee calculated the variance of the estimated local mean as a function of the length. It is important to note that he assumed that the fast fading followed Rayleigh statistics. The variance of a set of samples is the square of the standard deviation of the samples from their mean and is a measure of the spread of the sample values. Lee presents a graph of the variance in dB against the length.

This graph guides the choice of the length by showing how much variance we can expect when using different lengths. This choice a matter of judgment rather than hard fact. Lee suggested the choice of:

• Length = 20 ?, if we are willing to accept a 1 ?m spread in a range of 1.6 dB

• Length = 40 ? if we are willing to accept a 1 ?m spread in a range of 1.0 dB.

If we try to choose less than 20 wavelengths, the 1 ?m spread increases quickly. If we try to choose the length 2L greater than 40 ?, the 1?m spread decreases very slowly, but, averaging over longer than 40 wavelengths risks smoothing out of long-term fading information. Lee concluded that a length of between 20 wavelengths and 40 wavelengths is the proper length for averaging the signal. It is proper in the sense that a length significantly shorter or longer is likely to result in a reduced accuracy of measurement.

Sampling Average: when using an analogue filter as an averaging process, it is difficult to control the bandwidth and Lee chose to use arithmetic averaging of samples instead of analogue averaging. This led him to address the question of how many samples should be taken across the length. Lee aimed to minimize the number of samples and calculated how many points were needed. The calculation is based upon taking the average of two

variables with different statistical distributions. Lee calculates how many samples must be used for the resulting average to be within +/- 1 dB of the true mean.

The resulting figure of 50 samples does not guarantee that the average is within +/- 1 dB of the true mean, though it gives a 90% confidence that it will be.

Effects of different fading environments: Lee concluded that the measured length of a signal necessary to obtain the local average power is in the range of 20 to 40 wavelengths (?), based on the Rayleigh distribution. The sufficient number of samples for estimating this local average power values is 50, based on a 90 percent confidence interval and less than 1 dB in error in the estimate. The processed average data retain the long-term fading information which is the local average power of the signal and predictable by a planning tool, while the short-term fading can be considered as filtered.

References:

• Estimate of Local Average Power of a Mobile Radio Signal, William c.y. Lee, IEEE Trans.

Veh.Tech. Vol VT-34, No. l, Feb 1985.

• The Mobile Radio Propagation Channel, David Parsons, John Wiley 8: Sons 1992,

• Valid RF Field Measurements using Lee Sampling criteria, Willteck White paper

(http://www.willtek.com/english/service/literature/white_papers)

• TETRA field measurement protocol, Emmanuel Grenier, ATDI, Feb 2004