# Radio Propagation Models - MULTIMEDIA

A radio propagation model, also known as the Radio Wave Propagation Model or the Radio Frequency Propagation Model, is an empirical mathematical formulation for the characterization of radio wave propagation as a function of frequency, distance and other conditions. A single model is usually developed to predict the behavior of propagation for all similar links under similar constraints. Created with the goal of formalizing the way radio waves are propagated from one place to another, such models typically predict the path loss along a link or the effective coverage area of a transmitter.

Fading models try to model the amplitude of the superimposed signal at the receiver. The Doppler spread of a signal is defined as the distribution of the signal power over the frequency spectrum (the signal is modulated at a specific frequency bandwidth). When the Doppler spread of the signal is small enough, the signal is coherent — that is, there is only one distinguishable signal at the receiver. This is typically the case for narrowband signals. However, when the signal is wideband, different frequencies of the signal have different fading paths, and a few distinguishable signal paths are observed at the receiver, separated in time. For narrowband signals, the most popular models are Rayleigh fading and Rician fading.

The Rayleigh model assumes an infinite number of signal paths with no line - of - sight (LOS) to the receiver for modeling the probability density function Pr of received signal amplitude r:

where a is the standard deviation of the probability density function. Although the number of signal paths is typically not too large, the Rayleigh model does provide a good approximation when the number of paths is over 5.

A more general model that assumes a LOS is the Rician model. It defines a K - factor as a ratio of the signal power to the scattered power — that is, K is the factor by which the LOS signal is greater than the other paths. The Rician probability density function Pc is

As before, r and α are the signal amplitude and standard deviation respectively, and s is the LOS signal power. Io is a modified Bessel function of the first kind with 0 order.

Rician PDF plot with K - factor = 0, 1, 3, 5, 10, and 20

Note that when s = 0 (K = 0) there is no LOS, and the model thus reduces to a Rayleigh distribution. When K = ∞ the model reflects the additive white Gaussian noise (AWGN) conditions. The above figure shows the Rician probability density function for K-factors of 0, 1, 3, 5, 10, and 20, with standard deviation of σ = 1.0.

For a wideband signal, the fading paths are more empirically driven. One way is to model the amplitude as a summation over all the paths, each having randomized fading. The number of paths can be 7 for a closed - room environment (six walls and LOS) or a larger number for other environments. An alternative technique of modeling the channel fading is by measuring the channel impulse response.

Path Loss

For long - range communication, the signal loss is dominated by attenuation. The free - space attenuation model for LOS transmission is in inverse proportion to the square of distance [d2) and is given by the Friis radiation equation

Sr and St, are the received and transmitted signal power, Gr and Gt are the antenna gain factors, λ is the signal wavelength, and L is the receiver loss. It can be shown, however, that if we assume ground reflection, attenuation increases to be proportional to d4.

Another popular medium - scale (urban city size) model is the Hata model, which is empirically derived based on Okumura path loss data in Tokyo. The basic form of the path loss equation in dB is given by

L = A + B. log10(d) + C

Here, A is a function of the frequency and antenna heights, B is an environment function, and C is a function depending on the earner frequency. Again, d is the distance from the transmitter to the receiver.

Satellite models are attenuated primarily by rain. Hence, meteorological rainfall density maps can be used to communicate with the region. Attenuation is computed according to the amount of rainfall in the area on the given date.