The log-distance path loss model is a radio propagation model that predicts the path loss a signal encounters inside a building or densely populated areas over distance.
Log-distance path loss model is formally expressed as:
where
This corresponds to the following non-logarithmic gain model:
where is the average multiplicative gain at the reference distance from the transmitter. This gain depends on factors such as carrier frequency, antenna heights and antenna gain, for example due to directional antennas; and is a stochastic process that reflects flat fading. In case of only slow fading (shadowing), it may have log-normal distribution with parameter dB. In case of only fast fading due to multipath propagation, its amplitude may have Rayleigh distribution or Ricean distribution. This can be convenient, because power is proportional to the square of amplitude. Squaring a Rayleigh-distributed random variable produces an exponentially distributed random variable. In many cases, exponential distributions are computationally convenient and allow direct closed-form calculations in many more situations than a Rayleigh (or even a Gaussian).
Empirical measurements of coefficients and in dB have shown the following values for a number of indoor wave propagation cases.[4]
Building type | Frequency of transmission | [dB] | |
---|---|---|---|
Vacuum, infinite space | 2.0 | 0 | |
Retail store | 914 MHz | 2.2 | 8.7 |
Grocery store | 914 MHz | 1.8 | 5.2 |
Office with hard partition | 1.5 GHz | 3.0 | 7 |
Office with soft partition | 900 MHz | 2.4 | 9.6 |
Office with soft partition | 1.9 GHz | 2.6 | 14.1 |
Textile or chemical | 1.3 GHz | 2.0 | 3.0 |
Textile or chemical | 4 GHz | 2.1 | 7.0, 9.7 |
Office | 60 GHz | 2.2 | 3.92 |
Commercial | 60 GHz | 1.7 | 7.9 |