Six-rays model
The six-rays model is applied in an urban or indoor environment where a radio signal transmitted will encounter some objects that produce reflected, refracted or scattered copies of the transmitted signal.
These are called multipath signal components; they are attenuated, delayed and shifted from the original signal (LOS) due to a finite number of reflectors with known location and dielectric properties, LOS and multipath signal are summed at the receiver.
This model approaches the propagation of electromagnetic waves by representing wavefront as simple particles.
Thus reflection, refraction and scattering effects are approximated using simple geometric equation instead Maxwell's wave equations.
[1] The simplest model is two-rays which predicts signal variation resulting from a ground reflection interfering with the loss path.
This model is applicable in isolated areas with some reflectors, such as rural roads or hallway.
The above two-rays approach can easily be extended to add as many rays as required.
We may add rays bouncing off each side of a street in an urban corridor, leading to a six-rays model.
, determining that for the following two rays that are reflected once in the wall, the point in which they collide is equal to said height
Being located in the center of the street the distance between the antennas
, the buildings and the width of the streets are equal in both sides so that
that separates the two antennas, is equal to the first direct ray
applies the theorem of Pythagoras, in the right triangle that forms between the reflection of
the Pythagorean theorem is reapplied, knowing that one of the hinges is double the distances between the transmitter and the building due to the reflection of
is obtained through a geometric analysis of the top view for the model and it applies the Pythagorean Theorem triangles, taking into account the distance between the wall and the antennas
For likeness of triangles in the top view for model is determined the equation
, it means smaller than the transmitter and higher than the receiver and this high is where the two rays impact in the point, then rebound to the receiver.
The ray reflected leaves two reflections, one that it has the same high of the wall and the other the receiver, and the ray of the line of sight maintains the same direction between the
[3] For the mathematical model of six-ray propagation for antennas of different heights located at any point in the street,
that separates the two antennas, the first ray is formed by applying The Pythagorean theorem from the difference of heights of the antennas with respect to the line of sight:
For deducing the third ray it is calculated the angle between the direct distance
By similarity of triangles it can deduce the distance where the ray hits the wall until the perpendicular of the receiver called a achieved:
By similarity of the triangles can be deduced the equation of the fourth ray:
Consider a transmitted signal in the free space a receptor located a distance d of the transmitter.
One may add rays bouncing off each side of a street in an urban corridor, leading to a six-rays model, with rays
each one having a direct and a ground bouncing ray.
[4] An important assumption must be made to simplify the model:
is small compared to the symbol length of the useful information, that is
For the rays rebound outside the earth and on each side of the street, this assumption is fairly safe, but in general will have remembered that these assumptions mean the dispersion of delays (diffusion of the values
Free-space path loss of six rays model is defined as:
