azel2phithetapat

Convert radiation pattern from azimuth-elevation to phi-theta coordinates

Syntax

pat_phitheta = azel2phithetapat(pat_azel,az,el)

pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta)

[pat_phitheta,phi_pat,theta_pat] = azel2phithetapat(___)

Description

pat_phitheta = azel2phithetapat(pat_azel,az,el) expresses the antenna radiation pattern pat_azel in φ/θ angle coordinates instead of azimuth/elevation angle coordinates. pat_azel samples the pattern at azimuth angles in az and elevation angles in el. The pat_phitheta matrix covers φ values from 0 to 180 degrees and θ values from 0 to 360 degrees. pat_phitheta is uniformly sampled with a step size of 1 for φ and θ. The function interpolates to estimate the response of the antenna at a given direction.

pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta) uses vectors phi and theta to specify the grid at which to sample pat_phitheta. To avoid interpolation errors, phi should cover the range [0, 180], and theta should cover the range [0, 360].

[pat_phitheta,phi_pat,theta_pat] = azel2phithetapat(___)returns vectors containing the φ and θ angles at which pat_phitheta samples the pattern, using any of the input arguments in the previous syntaxes.

Examples

Convert Radiation Pattern to Phi-Theta

Convert a radiation pattern to φ/θ form, with the φ and θ angles spaced 1 degree apart.

Define the pattern in terms of azimuth and elevation.

az = -180:180;
el = -90:90;
pat_azel = mag2db(repmat(cosd(el)',1,numel(az)));

Convert the pattern to φ/θ space.

pat_phitheta = azel2phithetapat(pat_azel,az,el);

Plot Converted Radiation Pattern

Plot the result of converting a radiation pattern to $$\varphi /\theta$$ space with the $$\varphi$$ and $$\theta$$ angles spaced 1 degree apart.

The radiation pattern is the cosine of the elevation.

az = -180:180;
el = -90:90;
pat_azel = repmat(cosd(el)',1,numel(az));

Convert the pattern to $$\varphi /\theta$$ space. Use the returned $$\varphi$$ and $$\theta$$ angles for plotting.

[pat_phitheta,phi,theta] = azel2phithetapat(pat_azel,az,el);

Plot the result.

H = surf(phi,theta,mag2db(pat_phitheta));
H.LineStyle = 'none';
xlabel('phi (degrees)');
ylabel('theta (degrees)');
zlabel('Pattern');

Convert Radiation Pattern For Specific Phi/Theta Values

Convert a radiation pattern to $$\varphi /\theta$$ space with $$\varphi$$ and $$\theta$$ angles spaced 5 degrees apart.

The radiation pattern is the cosine of the elevation.

az = -180:180;
el = -90:90;
pat_azel = repmat(cosd(el)',1,numel(az));

Define the set of $$\varphi$$ and $$\theta$$ angles at which to sample the pattern. Then, convert the pattern.

phi = 0:5:360;
theta = 0:5:180;
pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta);

Plot the result.

H = surf(phi,theta,mag2db(pat_phitheta));
H.LineStyle = 'none';
xlabel('phi (degrees)');
ylabel('theta (degrees)');
zlabel('Pattern');

Input Arguments

pat_azel — Antenna radiation pattern in azimuth/elevation form

Q-by-P matrix

Antenna radiation pattern in azimuth/elevation form, specified as a Q-by-P matrix. pat_azel samples the 3-D magnitude pattern in decibels, in terms of azimuth and elevation angles. P is the length of the az vector, and Q is the length of the el vector.

Data Types: double

az — Azimuth angles

vector of length P

Azimuth angles at which pat_azel samples the pattern, specified as a vector of length P. Each azimuth angle is in degrees, between –180 and 180.

Data Types: double

el — Elevation angles

vector of length Q

Elevation angles at which pat_azel samples the pattern, specified as a vector of length Q. Each elevation angle is in degrees, between –90 and 90.

Data Types: double

phi — Phi angles

[0:360] (default) | vector of length L

Phi angles at which pat_phitheta samples the pattern, specified as a vector of length L. Each φ angle is in degrees, between 0 and 360.

Data Types: double

theta — Theta angles

[0:180] (default) | vector of length M

Theta angles at which pat_phitheta samples the pattern, specified as a vector of length M. Each θ angle is in degrees, between 0 and 180.

Data Types: double

Output Arguments

pat_phitheta — Antenna radiation pattern in phi/theta form

M-by-L matrix

Antenna radiation pattern in phi/theta form, returned as an M-by-L matrix. pat_phitheta samples the 3-D magnitude pattern in decibels, in terms of φ and θ angles. L is the length of the phi_pat vector, and M is the length of the theta vector.

phi_pat — Phi angles

vector of length L

Phi angles at which pat_phitheta samples the pattern, returned as a vector of length L. Angles are expressed in degrees.

theta_pat — Theta angles

vector of length M

Theta angles at which pat_phitheta samples the pattern, returned as a vector of length M. Angles are expressed in degrees.

More About

Azimuth Angle, Elevation Angle

The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. These definitions assume the boresight direction is the positive x-axis.

Note

The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB^® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles.

Phi Angle, Theta Angle

The φ angle is the angle from the positive y-axis toward the positive z-axis, to the vector’s orthogonal projection onto the yz plane. The φ angle is between 0 and 360 degrees. The θ angle is the angle from the x-axis toward the yz plane, to the vector itself. The θ angle is between 0 and 180 degrees.

The figure illustrates φ and θ for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles.

The coordinate transformations between φ/θ and az/el are described by the following equations

$$\begin{array}{l}\sin (\text{el})=\sin \varphi \sin \theta \hfill \\ \tan (\text{az})=\cos \varphi \tan \theta \hfill \\ \hfill \\ \cos \theta =\cos (\text{el})\cos (\text{az})\hfill \\ \tan \varphi =\tan (\text{el})/\sin (\text{az})\hfill \end{array}$$

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.