Main Content

pattern

Beam pattern NR rectangular panel array

Since R2023b

collapse all in page

    Syntax

    pattern(array,FREQ)
    pattern(array,FREQ,AZ)
    pattern(array,FREQ,AZ,EL)
    pattern(___,Name,Value)
    [PAT,AZ_ANG,EL_ANG] = pattern(___)

    Description

    pattern(array,FREQ) plots the 3-D array directivity pattern (in dBi) for the array specified in array. The operating frequency is specified in FREQ. You can use this function to display the patterns of arrays that support polarization.

    example

    pattern(array,FREQ,AZ) plots the array directivity pattern at the specified azimuth angle.

    pattern(array,FREQ,AZ,EL) plots the array directivity pattern at specified azimuth and elevation angles.

    pattern(___,Name,Value) plots the array pattern with additional options specified by one or more Name,Value pair arguments.

    [PAT,AZ_ANG,EL_ANG] = pattern(___) returns the array pattern in PAT. The AZ_ANG output contains the coordinate values corresponding to the rows of PAT. The EL_ANG output contains the coordinate values corresponding to the columns of PAT. If the 'CoordinateSystem' parameter is set to 'uv', then AZ_ANG contains the U coordinates of the pattern and EL_ANG contains the V coordinates of the pattern. Otherwise, they are in angular units in degrees. UV units are dimensionless.

    Examples

    collapse all

    Open Live Script

    Construct a 5G antenna array where the grid is 2-by-2 and each panel is a 4-by-4 array. Each antenna element consists of two short-dipole antennas with different dipole axis directions. The antenna elements are spaced 1/2 wavelength apart and the panels are spaced 3 wavelengths apart. Plot the response pattern of the array assuming an operating frequency of 6 GHz.

    c = physconst('LightSpeed');
fc = 6e9;
lambda = c/fc;
antenna1 = phased.ShortDipoleAntennaElement('AxisDirection','Z');
antenna2 = phased.ShortDipoleAntennaElement('AxisDirection','X');
array = phased.NRRectangularPanelArray('ElementSet', ...
        {antenna1, antenna2},'Size',[4, 4, 2, 2],'Spacing', ...
        [0.5*lambda, 0.5*lambda,3*lambda, 3*lambda]);
pattern(array,fc,'ShowArray',true)

    Figure contains 2 axes objects. Hidden axes object 1 contains 7 objects of type scatter, line, text. Hidden axes object 2 with title 3D Directivity Pattern contains 13 objects of type surface, line, text, patch.

    Use the Orientation property of pattern to change the orientation 80∘ along the x-axis, 30∘ along the y-axis and 60∘ along the z-axis.

    pattern(array,fc,'Orientation',[80;30;60],'ShowArray',true)

    Figure contains 2 axes objects. Hidden axes object 1 contains 7 objects of type scatter, line, text. Hidden axes object 2 with title 3D Directivity Pattern contains 13 objects of type surface, line, text, patch.

    Disable the display of local coordinates and the colorbar.

    pattern(array,fc,'ShowLocalCoordinate',false,'ShowColorBar',false)

    Figure contains an axes object. The hidden axes object with title 3D Directivity Pattern contains an object of type surface.

    Input Arguments

    collapse all

    Phased array, specified as a Phased Array System Toolbox System object.

    Frequencies for computing directivity and patterns, specified as a positive scalar or 1-by-L real-valued row vector. Frequency units are in hertz.

    • For an antenna, microphone, or sonar hydrophone or projector element, FREQ must lie within the range of values specified by the FrequencyRange or FrequencyVector property of the element. Otherwise, the element produces no response and the directivity is returned as –Inf. Most elements use the FrequencyRange property except for phased.CustomAntennaElement and phased.CustomMicrophoneElement, which use the FrequencyVector property.

    • For an array of elements, FREQ must lie within the frequency range of the elements that make up the array. Otherwise, the array produces no response and the directivity is returned as –Inf.

    Example: [1e8 2e6]

    Data Types: double

    Azimuth angles for computing directivity and pattern, specified as a 1-by-N real-valued row vector where N is the number of azimuth angles. Angle units are in degrees. Azimuth angles must lie between –180° and 180°.

    The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy plane. When measured from the x-axis toward the y-axis, this angle is positive.

    Example: [-45:2:45]

    Data Types: double

    Elevation angles for computing directivity and pattern, specified as a 1-by-M real-valued row vector where M is the number of desired elevation directions. Angle units are in degrees. The elevation angle must lie between –90° and 90°.

    The elevation angle is the angle between the direction vector and xy-plane. The elevation angle is positive when measured towards the z-axis.

    Example: [-75:1:70]

    Data Types: double

    Name-Value Arguments

    Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

    Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

    Example: CoordinateSystem,'polar',Type,'directivity'

    Plotting coordinate system of the pattern, specified as the comma-separated pair consisting of 'CoordinateSystem' and one of 'polar', 'rectangular', or 'uv'. When 'CoordinateSystem' is set to 'polar' or 'rectangular', the AZ and EL arguments specify the pattern azimuth and elevation, respectively. AZ values must lie between –180° and 180°. EL values must lie between –90° and 90°. If 'CoordinateSystem' is set to 'uv', AZ and EL then specify U and V coordinates, respectively. AZ and EL must lie between -1 and 1.

    Example: 'uv'

    Data Types: char

    Displayed pattern type, specified as the comma-separated pair consisting of 'Type' and one of

    • 'directivity' — directivity pattern measured in dBi.

    • 'efield' — field pattern of the sensor or array. For acoustic sensors, the displayed pattern is for the scalar sound field.

    • 'power' — power pattern of the sensor or array defined as the square of the field pattern.

    • 'powerdb' — power pattern converted to dB.

    Example: 'powerdb'

    Data Types: char

    Array orientation, specified as a 3-by-1 real-valued column vector containing three rotation angles. The three angles define orthogonal rotations with respect to the x-, y-, and z-axes of the local coordinate system. To create the full orientation matrix, the orthogonal rotations are applied in this order:

    1. a rotation around the positive x-axis by the angle θx.

    2. a rotation around the positive y-axis by the angle θy.

    3. a rotation around the positive z-axis by the angle θz.

    Positive angles are defined using the right-handed rule. A positive angle defines a rotation that appears clockwise when looking towards the positive direction of the axis, and negative values when the rotation appears counter-clockwise. The right-hand rule is invoked by pointing the right-hand thumb along an axis. Then the other fingers of the right hand curl in the positive direction,

    Display normalized pattern, specified as the comma-separated pair consisting of 'Normalize' and a Boolean. Set this parameter to true to display a normalized pattern. This parameter does not apply when you set 'Type' to 'directivity'. Directivity patterns are already normalized.

    Data Types: logical

    View the array geometry along with the 3D radiation pattern, specified as false or true.

    Data Types: logical

    Show the local coordinate axes, specified as true or false.

    Data Types: logical

    Show the colorbar, specified as true or false.

    Data Types: logical

    Handle to the axes along which the array geometry is displayed specified as a scalar.

    Plotting style, specified as the comma-separated pair consisting of 'Plotstyle' and either 'overlay' or 'waterfall'. This parameter applies when you specify multiple frequencies in FREQ in 2-D plots. You can draw 2-D plots by setting one of the arguments AZ or EL to a scalar.

    Data Types: char

    Polarization type, specified as the comma-separated pair consisting of 'Polarization' and either 'combined', 'H', or 'V'. If Polarization is 'combined', the horizontal and vertical polarization patterns are combined. If Polarization is 'H', only the horizontal polarization is displayed. If Polarization is 'V', only the vertical polarization is displayed.

    Dependencies

    To enable this property, set the array argument to an array that supports polarization and then set the 'Type' name-value pair to 'efield', 'power', or 'powerdb'.

    Data Types: char | string

    Signal propagation speed, specified as the comma-separated pair consisting of 'PropagationSpeed' and a positive scalar in meters per second.

    Example: 'PropagationSpeed',physconst('LightSpeed')

    Data Types: double

    Array weights, specified as the comma-separated pair consisting of 'Weights' and an N-by-1 complex-valued column vector or N-by-L complex-valued matrix. Array weights are applied to the elements of the array to produce array steering, tapering, or both. The dimension N is the number of elements in the array. The dimension L is the number of frequencies specified by FREQ.

    Weights DimensionFREQ DimensionPurpose
    N-by-1 complex-valued column vectorScalar or 1-by-L row vectorApplies a set of weights for the single frequency or for all L frequencies.
    N-by-L complex-valued matrix1-by-L row vectorApplies each of the L columns of 'Weights' for the corresponding frequency in FREQ.

    Note

    Use complex weights to steer the array response toward different directions. You can create weights using the phased.SteeringVector System object or you can compute your own weights. In general, you apply Hermitian conjugation before using weights in any Phased Array System Toolbox function or System object such as phased.Radiator or phased.Collector. However, for the directivity, pattern, patternAzimuth, and patternElevation methods of any array System object use the steering vector without conjugation.

    Example: 'Weights',ones(N,M)

    Data Types: double
    Complex Number Support: Yes

    Weights applied to each subarray element, specified as a NSE-by-N matrix or a cell array. When a matrix, NSE is the number of elements in each individual subarray and N is the number of subarrays. Each column in ElementWeights specifies the weights for the elements in the corresponding subarray.

    Dependencies

    To enable this parameter, set the SubarraySteering property of the array to 'Custom'.

    Data Types: double | cell
    Complex Number Support: Yes

    Output Arguments

    collapse all

    Array pattern, returned as an N-by-M real-valued matrix. The pattern is a function of azimuth and elevation. The rows of PAT correspond to the azimuth angles in the vector specified by EL_ANG. The columns correspond to the elevation angles in the vector specified by AZ_ANG.

    Azimuth angles for displaying directivity or response pattern, returned as a scalar or 1-by-N real-valued row vector corresponding to the dimension set in AZ. The columns of PAT correspond to the values in AZ_ANG. Units are in degrees.

    Elevation angles for displaying directivity or response, returned as a scalar or 1-by-M real-valued row vector corresponding to the dimension set in EL. The rows of PAT correspond to the values in EL_ANG. Units are in degrees.

    More About

    collapse all

    Directivity

    Directivity describes the directionality of the radiation pattern of a sensor element or array of sensor elements.

    Higher directivity is desired when you want to transmit more radiation in a specific direction. Directivity is the ratio of the transmitted radiant intensity in a specified direction to the radiant intensity transmitted by an isotropic radiator with the same total transmitted power

    D=4πUrad(θ,φ)Ptotal

    where Urad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and Ptotal is the total power transmitted by an isotropic radiator. For a receiving element or array, directivity measures the sensitivity toward radiation arriving from a specific direction. The principle of reciprocity shows that the directivity of an element or array used for reception equals the directivity of the same element or array used for transmission. When converted to decibels, the directivity is denoted as dBi. For information on directivity, read the notes on Element Directivity and Array Directivity.

    Azimuth and Elevation Angles

    Define the azimuth and elevation conventions used in the toolbox.

    The azimuth angle of a vector is the angle between the x-axis and its orthogonal projection onto the xy-plane. The angle is positive when going from the x-axis toward the y-axis. Azimuth angles lie between –180° and 180° degrees, inclusive. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy-plane. Elevation angles lie between –90° and 90° degrees, inclusive.

    Version History

    Introduced in R2023b