rangeangle
Range and angle calculation
Syntax
Description
The function rangeangle determines the propagation path length and path
direction of a signal from a source point or set of source points to a reference point.
The function supports two propagation models – the free space model
and the two-ray model. The free space model is
a single line-of-sight path from a source point to a reference point. The
two-ray multipath model generates two paths. The first path
follows the free-space path. The second path is a reflected path off a boundary plane at
z = 0. Path directions are defined with respect to either the
global coordinate system at the reference point or a local coordinate system at the
reference point. Distances and angles at the reference point do not depend upon which
direction the signal is travelling along the path.
[
returns the propagation path length, rng,ang]
= rangeangle(pos)rng, and direction angles,
ang, of a signal path from a source point or set of source
points, pos, to the origin of the global coordinate system. The
direction angles are the azimuth and elevation with respect to the global coordinate
axes at the origin. Signals follow a line-of-sight path from the source point to the
origin. The line-of-sight path corresponds to the geometric straight line between
the points.
[
also specifies a reference point or set of reference points,
rng,ang]
= rangeangle(pos,refpos)refpos. rng now contains the
propagation path length from the source points to the reference points. The
direction angles are the azimuth and elevation with respect to the global coordinate
axes at the reference points. You can specify multiple points and multiple reference
points.
[,
also specifies a propagation model. When rng,ang]
= rangeangle(___,model)model is set to
'freespace', the signal propagates along a line-of-sight path
from source point to reception point. When model is set to
'two-ray', the signal propagates along two paths from source
point to reception point. The first path is the line-of-sight path. The second path
is the reflecting path. In this case, the function returns the distances and angles
for two paths for each source point and corresponding reference point.
Input Arguments
|
Source point position, specified as a real-valued 3-by-1 vector or a real-valued
3-by-N matrix. A matrix represents multiple source
points. The columns contain the Cartesian coordinates of
N points in the form
When Position units are meters. |
|
Reference point position, specified as a real-valued 3-by-1 vector or a
real-valued 3-by-N matrix. A matrix represents multiple
reference points. The columns contain the Cartesian coordinates of
N points ins the form
When Position units are meters. Default: |
|
Local coordinate system axes, specified as a real-valued 3-by-3 matrix or a
3-by-3-by-N array. For an array, each page
corresponds to a local coordinate axes at each reference point. The columns
in Default: |
|
Propagation model, specified as Default: |
Output Arguments
|
Propagation range, returned as a real-valued 1-by-N vector or real-valued 1-by-2N vector. When When |
|
Azimuth and elevation angles, returned as a 2-by-N matrix or
2-by-2N matrix. Each column represents a direction
angle in the form When When Angle units are in degrees. |
Examples
Range and Angle Computation
Compute the range and angle of a target located at (1000,2000,50) meters from the origin.
TargetLoc = [1000;2000;50]; [tgtrng,tgtang] = rangeangle(TargetLoc)
tgtrng = 2.2366e+03
tgtang = 2×1
63.4349
1.2810
Range and Angle With Respect to Local Origin
Compute the range and angle of a target located at (1000,2000,50) meters with respect to a local origin at (100,100,10) meters.
TargetLoc = [1000;2000;50]; Origin = [100;100;10]; [tgtrng,tgtang] = rangeangle(TargetLoc,Origin)
tgtrng = 2.1028e+03
tgtang = 2×1
64.6538
1.0900
Range and Angle With Respect to Local Coordinates
Compute the range and angle of a target located at (1000,2000,50) meters but with respect to a local coordinate system origin at (100,100,10) meters. Choose a local coordinate reference frame that is rotated about the z-axis by 45° from the global coordinate axes.
targetpos = [1000;2000;50]; origin = [100;100;10]; refaxes = [1/sqrt(2) -1/sqrt(2) 0; 1/sqrt(2) 1/sqrt(2) 0; 0 0 1]; [tgtrng,tgtang] = rangeangle(targetpos,origin,refaxes)
tgtrng = 2.1028e+03
tgtang = 2×1
19.6538
1.0900
Two-Ray Range and Angle
Compute the two-ray propagation distances and arrival angles of rays from a source located at (1000,1000,500) meters from the origin. The receiver is located at (100,100,200) meters from the origin.
sourceLoc = [1000;1000;500];
receiverLoc = [100;100;200];
[sourcerngs,sourceangs] = rangeangle(sourceLoc,receiverLoc,'two-ray')sourcerngs = 1×2
103 ×
1.3077 1.4526
sourceangs = 2×2
45.0000 45.0000
13.2627 -28.8096
Find the range and angle of the same target with the same origin but with respect to a local coordinate axes. The local coordinate axes are rotated around the z-axis by 45 degrees from the global coordinate axes.
refaxes = rotz(45);
[sourcerngs,sourceangs] = rangeangle(sourceLoc,receiverLoc,refaxes,'two-ray')sourcerngs = 1×2
103 ×
1.3077 1.4526
sourceangs = 2×2
0 0
13.2627 -28.8096
Range and Angle With Respect to Two Origins
Compute the ranges and angles of two targets located at (1000,200,500) and (2500,80,-100) meters with respect to two local origins at (100,300,-40) and (500,-60,10) meters. Specify two different sets of local axes.
targetPos = [1000,2500;200,80;500,-100]; origins = [100,500;300,-60;-40,10]; ax(:,:,1) = rotx(40)*rotz(10); ax(:,:,2) = roty(5)*rotx(10); [tgtrng,tgtang] = rangeangle(targetPos,origins,ax)
tgtrng = 1×2
103 ×
1.0543 2.0079
tgtang = 2×2
6.7285 4.2597
26.9567 1.1254
More About
Angles in Local and Global Coordinate Systems
The rangeangle function returns the path distance and path angles in
either the global or local coordinate systems. Every
antenna or microphone element and array has a gain pattern that is expressed in
local angular coordinates of azimuth and elevation. As the element or array
moves or rotates, the gain pattern is carried with it. To determine the strength
of a signal’, you must know the angle that the signal path makes with respect to
the local angular coordinates of the element or array. By default, the
rangeangle function determines the angle a signal path
makes with respect to global coordinates. If you add the
refaxes argument, you can compute the angles with respect
to local coordinates. As an illustration, this figure shows a 5-by-5 uniform
rectangular array (URA) rotated from the global coordinates (xyz)
using refaxes. The x' axis of the local
coordinate system (x'y'z') is aligned with the main axis of the
array and moves as the array moves. The path length is independent of orientation.
The global coordinate system defines the azimuth and elevations angles
(Φ,θ) and the local coordinate system defines the azimuth and
elevations angles (Φ',θ').
Local and Global Coordinate Axes
Two-Ray Propagation Model
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
phased.FreeSpace
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 phased.TwoRayChannel and phased.WidebandTwoRayChannel System objects model propagation time delay, phase
shift, Doppler shift, and loss effects for both paths. For the reflected path, loss effects
include reflection loss at the boundary.
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
the 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
receiver.
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.
Extended Capabilities
See Also
azel2phitheta | azel2uv | global2localcoord | local2globalcoord