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. 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.

Design the array for a 10-kHz signal by setting Signal Frequencies (Hz) to 10000.

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).

In the Plots section of the Analyzer tab, select Array Geometry button to draw the array. Clicking on the Array Geometry center panel in the display causes the Array Geometry tab to appear. In this tab, 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 2-D 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 line.

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 Angle section of the toolstrip, changing the Steering Angles (deg) values to [30;0] steers the main lobe to 30° in azimuth and 0° elevation. The next figure shows two main lobes, one at 30° as expected, and another at 150°. Two main lobes appear because of the cylindrical symmetry of the array.

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. The next figure shows how the Taylor window reduces all side lobes to –30 dB—but at the expense of broadening the main lobe.

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 100e+6 and the row and column Element Spacing to 0.5 wavelength.

Select the Parameters tab and set the Number of Elements to [6,6]. Set the Element Spacing to 0.5 wavelengths. 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.

From the Row and Column pull-down menu, choose Row and Column. Set Row Taper and Column Taper to a Taylor window using default taper parameters.

The shape of the array is shown in this figure.

Next, display a 3-D array pattern by selecting 3D Array 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 loses 1/2 dB to yield 16.59 dB.

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]. Steer the array to [20;0].

Design the array for a 300-MHz signal by setting Signal Frequencies to 300e+6 and the row and column Element Spacing to 0.7 wavelength.

By setting the row and column Element Spacing to 0.7 wavelengths, you create a spatially under sampled array.

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. Change Steering Angles (deg) in the Analyzer tab to [35;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 Array pull down menu. 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), and (0,0.5,0.866). All elements have the same normal direction [0,20], pointing to 0° azimuth and 20° elevation. Select Array Geometry from the Plots tab.

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 and display the 3D pattern.

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

2. 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);