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plotGratingLobeDiagram(H,FREQ)
plotGratingLobeDiagram(H,FREQ,ANGLE)
plotGratingLobeDiagram(H,FREQ,ANGLE,C)
plotGratingLobeDiagram(H,FREQ,ANGLE,C,F0)
hPlot = plotGratingLobeDiagram(___)
plotGratingLobeDiagram(H,FREQ) plots the grating lobe diagram of an array in the u-v coordinate system. The System object™ H specifies the array. The argument FREQ specifies the signal frequency and phase-shifter 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(H,FREQ,ANGLE), in addition, specifies the array steering angle, ANGLE.
plotGratingLobeDiagram(H,FREQ,ANGLE,C), in addition, specifies the propagation speed by C.
plotGratingLobeDiagram(H,FREQ,ANGLE,C,F0), in addition, specifies an array phase-shifter frequency, 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.
hPlot = plotGratingLobeDiagram(___) returns the handle to the plot for any of the input syntax forms.
H |
Antenna or microphone array, specified as a System object. |
FREQ |
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 H.Element. The frequency property is named FrequencyRange or FrequencyVector, depending on the element type. |
ANGLE |
Array steering angle, specified as either a 2-by-1 vector or a scalar. If ANGLE is a vector, it takes the form [azimuth;elevation]. The azimuth angle must lie in the range [-180°,180°]. The elevation angle must lie in the range [-90°,90°]. All angle values are specified in degrees. If the argument ANGLE is a scalar, it specifies only the azimuth angle where the corresponding elevation angle is 0°. Default: [0;0] |
C |
Signal propagation speed, specified as a scalar. Units are meters per second. Default: Speed of light in vacuum |
F0 |
Phase-shifter frequency of the array, specified as a scalar. Frequency units are hertz When this argument is omitted, the phase-shifter frequency is assumed to be the signal frequency, FREQ. Default: FREQ |
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 URA 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 URA, the array pattern depends only on the wavenumber component of the wavefield in the array plane (the y and z directions for the phased.URA System object). The wavenumber components are related to the look-direction of an arriving wavefield by k_{y} = –2π sin az cos el/λ and k_{z} = –2π sin el/λ. The angle az is azimuth angle of the arriving wavefield. The angle el is elevation angle of the arriving wavefield. The look-direction points away from the array to the wavefield source.
The array pattern possesses an infinite number of periodically-spaced peaks that are equal in strength to the mainlobe peak. If you steer the array to the az_{0}, el_{0} azimuth and elevation direction, the array pattern for the URA has its mainlobe peak at the wavenumber value, k_{y0} = –2π sin az_{0} cos el_{0}/λ, k_{z0} = –2π sin el_{0}/λ. The array pattern has strong peaks at k_{ym} = k_{y0} + 2π m/d_{y}, k_{zn} = k_{z0} + 2π n/d_{z}. for integral values of m and n. The quantities d_{y} and d_{z} are the inter-element spacings in the y- and z-directions, respectively. Expressed in terms of direction cosines, the grating lobes occur at u_{m} = u_{0} –mλ/d_{y} and v_{n} = v_{0} –nλ/d_{z}. The mainlobe direction cosines are given by u_{0} = sin az_{0} cos el_{0} and v_{0} = sin el_{0} when expressed in terms of the look-direction.
Grating lobes can be visible or nonvisible, depending upon the value of u_{m}^{2} + v_{n}^{2}. When u_{m}^{2} + v_{n}^{2} ≤ 1, the look direction represent a visible direction. When the value is greater than one, the grating lobe is nonvisible. For each visible grating lobe, you can compute a look direction (az_{m,n},el_{m,n}) from u_{m} = sin az_{m} cos el_{m} and v_{n} = sin el_{n}. The spacing of grating lobes depends upon λ/d. When λ/d is small enough, multiple grating lobe peaks can correspond to physical look-directions.