Under the Analyzer tab, in the Array section of the toolstrip, select ULA. In the Element section of the toolstrip, select Hydrophone.

Select the Parameters tab and set the Number of Elements to 10. Set the Element Spacing to 0.5 wavelengths.

Design the array for a 10 KHz signal by setting Signal Frequencies (Hz) to 10000. Then click the Apply button. You can change many menu items and apply the changes at any time. The parameters that appear in this tab depend on your choice of array and element.

When you choose a sonar element, the app automatically sets the signal propagation speed in water to 1500. You can set the signal propagation speed to any value by setting the Propagation Speed (m/s).

Select the Array Geometry tab and use the check boxes to display element normals (Show Normals), element indices (Show Index), and element tapers (Show Tapers).

In the rightmost Array Characteristics panel, you can view the array directivity, half-power beam width (HPBW), first-null beam-width (FNBW), and side lobe level (SLL).

To display a directivity plot, go to the Plots section of the Analyzer tab. Select Azimuth Pattern from the 2D Pattern menu. The azimuth directivity pattern is now displayed in the center panel of the app. Select the Azimuth Pattern tab, and set the Coordinate to Rectangular.

You can see the main lobe of the array directivity function (also called the main beam) at 0° and another main lobe at ±180°. Two main lobes appear because of the cylindrical symmetry of the ULA array.

A beam scanner works by successively pointing the array main lobe in different directions. In the Steering tab, set Azimuth Angles (deg) to 30 and Elevation Angles (deg) to 0. This steers the main lobe to 30° in azimuth and 0° elevation.

One disadvantage of a ULA is its large side lobes. An examination of the array directivity shows two side lobes close to each main lobe, each down by about only 13 dB. A strong side lobe inhibits the ability of the array to detect a weaker signal in the presence of a larger nearby signal. By using array tapering, you can reduce the side lobes.

Use the Taper option to specify the array taper as a Taylor window with Sidelobe Attenuation set to 30 dB and nbar set to 4. Click the Apply button.

Under the Analyzer tab, in the Array section of the toolstrip, select ULA. Create a ULA with default parameters (with the number of elements set to 4 and the element spacing set to 0.5 meters).

From Subarray on the Analyzer tab of the toolstrip select Partition the array. Design the array for a 1 GHz signal by setting Signal Frequencies (Hz) to 1e9. Then click the Apply button. You can change many menu items and apply the changes at any time. The parameters that appear in this tab depend on your choice of array and element.

Select 2D Pattern in the Analyzer tab and choose the Azimuth pattern to visualize the 2-D azimuth pattern in polar coordinates.

Under the Analyzer tab, in the Array section of the toolstrip, select URA. In the Element section of the toolstrip, select Isotropic.

Design the array for a 100 MHz signal by setting Signal Frequencies to 100e6 and the row and column Element Spacing to [0.5 0.5] wavelength.

Select the Parameters tab and set the Size to [6,6].

From the Taper drop-down, choose Row and Column. Set Row Taper and Column Taper to a Taylor window using default taper parameters. Click the Apply button to apply the changes. You can change many menu items and apply the changes at any time. The parameters that appear in this tab depend on your choice of array and element.

The shape of the array is shown in this figure.

Next, display a 3-D array pattern by selecting 3D Pattern in the Plots section of the Analyzer tab.

A significant performance measure for any array is directivity. You can use the app to examine the effects of tapering on array directivity. Without tapering, the array directivity for this URA is 17.16 dB. With tapering, the array directivity is reduced to 16.03 dBi.

Under the Analyzer tab, in the Array section of the toolstrip, select URA. In the Element section of the toolstrip, select Isotropic. Set the Size to [4,4]. In the Steering tab, set Azimuth Angles (deg) to 20 and Elevation Angles (deg) to 0.

Design the array for a 300 MHz signal by setting Signal Frequencies to 3e8 and the row and column Element Spacing to [0.7,0.7] wavelength. By setting the row and column Element Spacing to [0.7,0.7] wavelengths, you create a spatially under-sampled, array. Then click the Apply button.

Select Grating Lobe Diagram from the Plots section to plot the grating lobes.

This figure shows the grating lobe diagram produced when you beamform the array towards the angle [20,0]. The main lobe is designated by the small black-filled circle. The multiple grating lobes are designated by the small unfilled black circles. The larger black circle is called the physical region, for which u²+ v² ≤ 1. The main lobe always lies in the physical region. The grating lobes can sometimes lie outside the physical region. Any grating lobe in the physical region leads to an ambiguity in the direction of the incoming wave. The green region shows where the main lobe can be pointed without any grating lobes appearing in the physical region. If the main lobe is set to point outside the green region, a grating lobe can move into the physical region.

The next figure shows what happens when the pointing direction lies outside the green region. In the Steering tab, set Azimuth Angles (deg) to 35 and Elevation Angles (deg) to 0. In this case, one grating lobe moves into the physical region.

You can specify an array which has an arbitrary placement of sensors. Select Arbitrary in the Arraydrop-down. Select Isotropic from the Element menu. Enter the elements positions in the Element Position field. The positions of the three elements are (0,0,0), (0,1,0), (0,0.5,0.866). All elements have the same normal direction, pointing to 0° azimuth and 20° elevation and to set the normal in the Element Normal (deg) type [0 0 0;20 20 20] and click the Apply button. Select Array Geometry from the Plots section.

To show the 3-D array directivity, select 3D Pattern from the Plots tab.

At the MATLAB command line, create an element position array, pos, an element normal array, nrm, and a taper value array, tpr.

pos = [0 0 0; 0 1.0 0.5000; 0 0 0.866];
nrm = [0 0 0; 20 20 20];
tpr = [1 1 1];

Enter these variables in the appropriate sensorArrayAnalyzer fields, click Apply button. To show the 3-D array directivity, click 3D Pattern from the Plots tab.

Use the same parameters as in the Uniform Rectangular Array (URA) example and click the Apply button. In the Element section of the toolstrip, select Custom in the Antenna section.

For a custom antenna element, specify the magnitude and phase patterns. Because patterns usually require large matrices, it is better to use the command line to specify the magnitude and phase patterns. The magnitude pattern specified here has directionality along the ±x-axes and is a function of azimuth and elevation. The phase pattern is all zeros. Alternatively, you can specify a pattern in terms of phi and theta angles by setting the Pattern Coordinate System parameter to phi-theta.

azpat = cosd([0:360]).^2 + 1;
elpat = cosd([-90:90]') + 1;
mag = elpat*azpat;
magdb = 10*log10(mag);

To show the 3-D array directivity, select 3D Pattern from the Plots tab.