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Grating Lobe Diagram for Microphone URA

Plot the grating lobe diagram for an 11-by-9-element uniform rectangular array having element spacing equal to one-half wavelength.

Assume the operating frequency of the array is 10 kHz. All elements are omnidirectional microphone elements. Steer the array in the direction 20 degrees in azimuth and 30 degrees in elevation. The speed of sound in air is 344.21 m/s at 21 deg C.

cair = 344.21;
f = 10.0e3;
lambda = cair/f;
microphone = phased.OmnidirectionalMicrophoneElement(...
    'FrequencyRange',[20 20000]);
array = phased.URA('Element',microphone,'Size',[11,9],...

Plot the grating lobes. The main lobe of the array is indicated by a filled black circle. The grating lobes in visible and nonvisible regions are indicated by unfilled black circles. The visible region is the region in u-v coordinates for which u2+v21. The visible region is shown as a unit circle centered at the origin. Because the array spacing is less than one-half wavelength, there are no grating lobes in the visible region of space. There are an infinite number of grating lobes in the nonvisible regions, but only those in the range [-3,3] are shown.

The grating-lobe free region, shown in green, is the range of directions of the main lobe for which there are no grating lobes in the visible region. In this case, it coincides with the visible region.

The white areas of the diagram indicate a region where no grating lobes are possible.