azel2uvpat

Convert radiation pattern from azimuth/elevation form to u/v form

Syntax

pat_uv = azel2uvpat(pat_azel,az,el)
pat_uv = azel2uvpat(pat_azel,az,el,u,v)
[pat_uv,u_pat,v_pat] = azel2uvpat(___)

Description

example

pat_uv = azel2uvpat(pat_azel,az,el) expresses the antenna radiation pattern pat_azel in u/v space coordinates instead of azimuth/elevation angle coordinates. pat_azel samples the pattern at azimuth angles in az and elevation angles in el. The pat_uv matrix uses a default grid that covers u values from –1 to 1 and v values from –1 to 1. In this grid, pat_uv is uniformly sampled with a step size of 0.01 for u and v. The function interpolates to estimate the response of the antenna at a given direction. Values in pat_uv are NaN for u and v values outside the unit circle because u and v are undefined outside the unit circle.

example

pat_uv = azel2uvpat(pat_azel,az,el,u,v) uses vectors u and v to specify the grid at which to sample pat_uv. To avoid interpolation errors, u should cover the range [–1, 1] and v should cover the range [–1, 1].

example

[pat_uv,u_pat,v_pat] = azel2uvpat(___) returns vectors containing the u and v coordinates at which pat_uv samples the pattern, using any of the input arguments in the previous syntaxes.

Examples

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Convert a radiation pattern to u-v space, with the u and v coordinates spaced by 0.01.

Define the pattern in terms of azimuth and elevation.

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

Convert the pattern to u-v space.

pat_uv = azel2uvpat(pat_azel,az,el);

Plot the result of converting a radiation pattern to u/v space with the u and v coordinates spaced by 0.01.

The radiation pattern is the cosine of the elevation angle.

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

Convert the pattern to u/v space. Use the u and v coordinates for plotting.

[pat_uv,u,v] = azel2uvpat(pat_azel,az,el);

Plot the result.

H = surf(u,v,mag2db(pat_uv));
H.LineStyle = 'none';
xlabel('u');
ylabel('v');
zlabel('Pattern');

Convert a radiation pattern to u/v form, with the u and v coordinates spaced by 0.05.

The radiation pattern is cosine of the elevation angle.

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

Define the set of u and v coordinates at which to sample the pattern. Then, convert the pattern.

u = -1:0.05:1;
v = -1:0.05:1;
pat_uv = azel2uvpat(pat_azel,az,el,u,v);

Plot the result.

H = surf(u,v,mag2db(pat_uv));
H.LineStyle = 'none';
xlabel('u');
ylabel('v');
zlabel('Pattern');

Input Arguments

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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

Azimuth angles at which pat_azel samples the pattern, specified as a vector of length P. Each azimuth angle is in degrees, between –90 and 90. Such azimuth angles are in the hemisphere for which u and v are defined.

Data Types: double

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

u coordinates at which pat_uv samples the pattern, specified as a vector of length L. Each u coordinate is between –1 and 1.

Data Types: double

v coordinates at which pat_uv samples the pattern, specified as a vector of length M. Each v coordinate is between –1 and 1.

Data Types: double

Output Arguments

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Antenna radiation pattern in u/v form, returned as an M-by-L matrix. pat_uv samples the 3-D magnitude pattern in decibels, in terms of u and v coordinates. L is the length of the u vector, and M is the length of the v vector. Values in pat_uv are NaN for u and v values outside the unit circle because u and v are undefined outside the unit circle.

u coordinates at which pat_uv samples the pattern, returned as a vector of length L.

v coordinates at which pat_uv samples the pattern, returned as a vector of length M.

More About

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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.

U/V Space

The u and v coordinates are the direction cosines of a vector with respect to the y-axis and z-axis, respectively.

The u/v coordinates for the hemisphere x ≥ 0 are derived from the phi and theta angles by:

u=sinθcosϕv=sinθsinϕ

In these expressions, φ and θ are the phi and theta angles, respectively.

In terms of azimuth and elevation, the u and v coordinates are

u=coselsinazv=sinel

The values of u and v satisfy the inequalities

1u11v1u2+v21

Conversely, the phi and theta angles can be written in terms of u and v using

tanϕ=u/vsinθ=u2+v2

The azimuth and elevation angles can also be written in terms of u and v

sinel=vtanaz=u1u2v2

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

sin(el)=sinϕsinθtan(az)=cosϕtanθcosθ=cos(el)cos(az)tanϕ=tan(el)/sin(az)

Extended Capabilities

Introduced in R2012a