Two-Ray Multipath Propagation
A two-ray propagation channel is the next step up in complexity from a
free-space channel and is the simplest case of a multipath propagation environment. The
free-space channel models a straight-line line-of-sight path from
point 1 to point 2. In a two-ray channel, the medium is specified as a homogeneous,
isotropic medium with a reflecting planar boundary. The boundary is always set at z
= 0. There are at most two rays propagating from point 1 to point 2. The first
ray path propagates along the same line-of-sight path as in the free-space channel (see the
System object™). The line-of-sight path is often called the direct
path. The second ray reflects off the boundary before propagating to point 2.
According to the Law of Reflection , the angle of reflection equals the angle of incidence.
In short-range simulations such as cellular communications systems and automotive radars,
you can assume that the reflecting surface, the ground or ocean surface, is flat.
The figure illustrates two propagation paths. From the source
position, ss, and the receiver
position, sr, you can compute
the arrival angles of both paths, θ′los and θ′rp.
The arrival angles are the elevation and azimuth angles of the arriving
radiation with respect to a local coordinate system. In this case,
the local coordinate system coincides with the global coordinate system.
You can also compute the transmitting angles, θlos and θrp.
In the global coordinates, the angle of reflection at the boundary
is the same as the angles θrp and θ′rp.
The reflection angle is important to know when you use angle-dependent
reflection-loss data. You can determine the reflection angle by using
rangeangle function and
setting the reference axes to the global coordinate system. The total
path length for the line-of-sight path is shown in the figure by Rlos which
is equal to the geometric distance between source and receiver. The
total path length for the reflected path is Rrp=
R1 + R2. The
quantity L is the ground range between source and
You can easily derive exact formulas for path lengths and angles in terms of the ground range and object heights in the global coordinate system.