plotGratingLobeDiagram
System object: phased.ULA
Package: phased
Plot grating lobe diagram of array
Syntax
plotGratingLobeDiagram(H,FREQ)
plotGratingLobeDiagram(H,FREQ,ANGLE)
plotGratingLobeDiagram(H,FREQ,ANGLE,C)
plotGratingLobeDiagram(H,FREQ,ANGLE,C,F0)
hPlot = plotGratingLobeDiagram(___)
Description
plotGratingLobeDiagram(
plots
the grating lobe diagram of an array in the uv coordinate
system. The System object™ H
,FREQ
)H
specifies the
array. The argument FREQ
specifies the signal
frequency and phaseshifter frequency. The array, by default, is
steered to 0° azimuth and 0° elevation.
A grating lobe diagram displays the positions of the peaks of the narrowband array pattern. The array pattern depends only upon the geometry of the array and not upon the types of elements which make up the array. Visible and nonvisible grating lobes are displayed as open circles. Only grating lobe peaks near the location of the mainlobe are shown. The mainlobe itself is displayed as a filled circle.
plotGratingLobeDiagram(
,
in addition, specifies the array steering angle, H
,FREQ
,ANGLE
)ANGLE
.
plotGratingLobeDiagram(
,
in addition, specifies the propagation speed by H
,FREQ
,ANGLE
,C
)C
.
plotGratingLobeDiagram(
,
in addition, specifies an array phaseshifter frequency, H
,FREQ
,ANGLE
,C
,F0
)F0
,
that differs from the signal frequency, FREQ
.
This argument is useful when the signal no longer satisfies the narrowband
assumption and, allows you to estimate the size of beam squint.
returns
the handle to the plot for any of the input syntax forms.hPlot
= plotGratingLobeDiagram(___)
Input Arguments

Antenna or microphone array, specified as a System object. 

Signal frequency, specified as a scalar. Frequency units are
hertz. Values must lie within a range specified by the frequency property
of the array elements contained in 

Array steering angle, specified as either a 2by1 vector or
a scalar. If Default: 

Signal propagation speed, specified as a scalar. Units are meters per second. Default: Speed of light in vacuum 

Phaseshifter frequency of the array, specified as a scalar.
Frequency units are hertz When this argument is omitted, the phaseshifter
frequency is assumed to be the signal frequency, Default: 
Examples
Concepts
Grating Lobes
Spatial undersampling of a wavefield by an array gives rise to visible grating lobes. If you think of the wavenumber, k, as analogous to angular frequency, then you must sample the signal at spatial intervals smaller than π/k_{max} (or λ_{min}/2) in order to remove aliasing. The appearance of visible grating lobes is also known as spatial aliasing. The variable k_{max} is the largest wavenumber value present in the signal.
The directions of maximum spatial response of a ULA are determined
by the peaks of the array’s array pattern (alternatively
called the beam pattern or array
factor). Peaks other than the mainlobe peak are called
grating lobes. For a ULA, the array pattern depends only on the wavenumber
component of the wavefield along the array axis (the ydirection
for the phased.ULA
System object). The wavenumber
component is related to the lookdirection of an arriving wavefield
by k_{y} = –2π sin φ/λ.
The angle φ is the broadside angle—the
angle that the lookdirection makes with a plane perpendicular to
the array. The lookdirection points away from the array to the wavefield
source.
The array pattern possesses an infinite number of periodicallyspaced peaks that are equal in strength to the mainlobe peak. If you steer the array to the φ_{0} direction, the array pattern for a ULA has its mainlobe peak at the wavenumber value of k_{y0} = –2π sin φ_{0}/λ. The array pattern has strong grating lobe peaks at k_{ym} = k_{y0} + 2π m/d, for any integer value m. Expressed in terms of direction cosines, the grating lobes occur at u_{m} = u_{0} + mλ/d, where u_{0} = sin φ_{0}. The direction cosine, u_{0}, is the cosine of the angle that the lookdirection makes with the yaxis and is equal to sin φ_{0} when expressed in terms of the lookdirection.
In order to correspond to a physical lookdirection, u_{m} must satisfy, –1 ≤ u_{m} ≤ 1. You can compute a physical lookdirection angle φ_{m} from sin φ_{m} = u_{m} as long as –1 ≤ u_{m} ≤ 1. The spacing of grating lobes depends upon λ/d. When λ/d is small enough, multiple grating lobe peaks can correspond to physical lookdirections.
The presence or absence of visible grating lobes for the ULA is summarized in this table.
Element Spacing  Grating Lobes 

λ/d ≥ 2  No visible grating lobes for any mainlobe direction. 
1 ≤ λ/d < 2  Visible grating lobes can exist for some range of mainlobe directions. 
λ/d < 1  Visible grating lobes exist for every mainlobe direction. 
References
[1] Van Trees, H.L. Optimum Array Processing. New York: WileyInterscience, 2002.