MVDR Spectrum

A spatial spectrum analyzer with minimal variation without distortion (MVDR).

blockType: MVDRSpectrum

Path in the library:

/Phased Array Systems/Direction of Arrival/MVDR Spectrum

Description

Block MVDR Spectrum (Minimum Variance Distortion-Free Response) evaluates the two–dimensional spatial spectrum of incoming narrowband signals by scanning a range of azimuth and elevation angles using a conventional MVDR beamformer. The block additionally calculates the direction of arrival (DOA) of a given number of signals, finding the peaks of the spectrum. This evaluation mechanism is also called the Capon evaluation mechanism.

Ports

Entrance

Port 1 — received pass signal:q[ ] The complex matrix

The input signal is set as a matrix, the columns of which correspond to the channels. The rows correspond to the selections.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool

Support for complex numbers: Yes

Output

Y is the two—dimensional spatial spectrum of
The real matrix

The spatial spectrum returned as a real matrix representing the value of the estimated two-dimensional spatial spectrum. The dimension of the row Y is equal to the number of angles specified in the Elevation scan angles (deg) parameter, and the dimension of the column Y is equal to the number of angles specified in the Azimuth scan angles (deg) parameter.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool

Support for complex numbers: Yes

Ang — directions of arrival of pass signals:q[ ] non-negative real matrix 2 on L

The arrival directions of the signals returned as a 2-by-L real matrix. L is the number of signals specified by the Number of signals parameter. The angle of the arrival direction is determined by the angles of the azimuth and elevation of the source relative to the local coordinate system of the array. The first row of the matrix contains the azimuth angles, and the second row contains the elevation angles. If the block cannot detect peaks in the spectrum, it will return `NaN'. The units of measurement of angles are degrees.

Dependencies

To use this port, check the box for the Enable DOA output option.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool

Parameters

Main

Signal propagation speed — signal propagation speed, m/s
3e8 (default) | positive scalar

The propagation velocity of the signal in the form of a real positive scalar. The default value for the speed of light is `3e8 m/s'.

The units of measurement are meters per second.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64

Operating frequency (Hz) — operating frequency of the pass sy\$
\$ 3e8 (default) | positive scalar

The operating frequency of the system, set as a positive scalar. The units of measurement are hertz.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool

Number of bits in phase shifters — number of phase shift quantization bits
0 (default) | non-negative integer

The number of bits used to quantize the phase shift component of the beamformer or the weights of the control vector. Specify the number of bits as a non-negative integer. A value of zero means that quantization is not performed.

Forward-backward averaging — enable forward-backward averaging
disabled (by default) | enabled

Select this option to use forward-backward averaging to estimate the covariance matrix for arrays of antenna elements with a conjugate-symmetric array structure.

Azimuth scan angles (deg) — azimuth scan angles
-180:180 (default) | real vector

The scanning angles in the azimuthal direction, set as a real vector. Azimuth angles should be in the range of −180° to 180° inclusive. The angles should be indicated in ascending order. The units of measurement are degrees.

Elevation scan angles (deg) — scan angles in the direction of elevation
-90:90 (default) | real vector

The scanning angles in the elevation direction, set as a real vector. The angles should be in the range of −90° up to and including 90°. The angles should be indicated in ascending order. The units of measurement are degrees.

Enable DOA output — output arrival directions via the pass output port:q[ ] disabled (by default) | enabled

Select this option to display the arrival directions of incoming signals (DOA) via the Ang output port.

Number of signals — expected number of incoming pass signals:q[ ] 1 (default) | positive integer

Specify the expected number of signals to estimate the arrival directions of incoming signals (DOA) as a positive integer scalar number.

Dependencies

To use this option, select the Enable DOA output checkbox.

Sensor Array

Specify sensor array as — method for specifying the pass array:q[ ] Array (no subarrays) (default)

The method for setting the array specified as `Array (no subarrays)'.

`Array (no subarrays)'— the block parameters are used to specify the array.

Element

The type of antenna array element.

Available values:

Isotropic Antenna
Cardioid Antenna
Cosine Antenna
Custom Antenna
Gaussian Antenna
Sinc Antenna
Omni Microphone
Custom Microphone

Operating frequency range (Hz) — operating frequency range of the pass antenna array element:q[ ] [0,1e20] (default) | a real vector is a 1 by 2 row

The range of operating frequencies of the antenna array element in the form of a vector row 1 by 2 in the form of [LowerBound,UpperBound]. The element has no response outside this frequency range. The units of frequency measurement are Hz.

Dependencies

To use this parameter, set the Element type parameter to Isotropic Antenna, Cosine Antenna, or 'Omni Microphone'.

Baffle the back of the element — accounting for radiation through the rear beam of the radiation pattern into the rear hemisphere of the Isotropic Antenna element or

Omni Microphone' 
 `disabled (by default)

| enabled

Set this flag to exclude radiation into the rear hemisphere. The response from the rear hemisphere at all azimuth angles outside the ±90° range from the wide side is set to zero. The wide-angle direction is defined as the azimuth angle of 0° and the elevation angle of 0°.

Dependencies

To use this parameter, set the Element type parameter to Isotropic Antenna or `Omni Microphone'.

Null axis direction — the direction of the axis along the zero radiation.
-x (default) | +x | +y | -y | +z | -z

The direction of the axis is along the zero radiation.

Dependencies

To use this parameter, set the Element type parameter to Cardioid Antenna.

Exponent of cosine pattern — exponent exponent when defining the shape of a cosine radiation pattern
[1.5, 1.5] (default) | non-negative scalar | a real matrix of non-negative values of 1 by 2

The exponent of the exponent of the cosine model in the form of a non-negative scalar or a 1 by 2 real matrix of non-negative values. If the Exponent of cosine pattern is a 1 by 2 vector, then the first element is the exponent in the direction of the azimuth, and the second is in the direction of the angle of the place. With a scalar value of this parameter, the cosines in the azimuthal and elevation directions are raised to one power.

Dependencies

To use this parameter, set the Element type parameter to `Cosine Antenna'.

Operating frequency vector (Hz) — array of operating frequencies of the antenna array element
[0,1e20] (default) | real vector is a string

The array of operating frequencies of the antenna array element in the form of a vector row 1 on increasing actual values. The element has no response beyond the frequency range specified by the minimum and maximum elements of this vector. The units of frequency measurement are Hz.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna or `Custom Microphone'. To set the responses at these frequencies, use the Frequency responses (dB) parameter.

Frequency responses (dB) — frequency responses of the antenna array element
[0,0] (default)| real vector string

The frequency response of the user elements of the antenna arrays is determined by the parameter Operating frequency vector (Hz). The dimensions of the Frequency responses (dB) vector must match the dimensions of the vector specified by the Operating frequency vector (Hz) parameter.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna or `Custom Microphone'.

Input Pattern Coordinate System — selection of the coordinate system of the radiation pattern of the user antenna
az-el (default) | phi-theta

The choice of the coordinate system of the radiation pattern of the user antenna is indicated by az-el or phi-theta'. When selecting `az-el, the Azimuth angles (deg) and Elevations angles (deg) parameters are used to set the coordinates of the directional pattern points. When specifying the phi-theta parameter, the Phi angle (deg) and Theta angles (deg) parameters are used to set the coordinates of the part points.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna.

Azimuth angles (deg) — azimuth angles of the antenna radiation pattern
[-180:180] (default) | real vector is a string

The values of the azimuth angles, which will be used to calculate the antenna pattern in the form of a vector row 1 on . it must be more than 2. The azimuth angles should be in the range of −180° up to 180° inclusive and arranged in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to az-el.

Elevation angles (deg) — values of the angles of the antenna pattern position
[-90:90] (default) | real vector is a string

The values of the angles of the location at which it is necessary to calculate the radiation pattern in the form of a vector 1 on . it must be more than 2. The units of measurement of angles are degrees. Elevation angles should be in the range of −90° to 90° inclusive and arranged in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to az-el.

Phi Angles (deg) — values of the Phi angles of the antenna radiation pattern
[0:360] (default) | real vector is row 1 on P

The angular coordinates of the Phi points where the antenna radiation pattern is set. They are defined as a real vector-row 1 on . it must be more than 2. The units of measurement of angles are degrees. The values of the Phi angles should be in the range from 0° to 360° and arranged in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to phi-theta.

Theta Angles (deg) — values of the angles of the Theta radiation pattern of the antenna
[0:180] (default) | real vector-row 1 on Q

The angular coordinates of the Theta points where the antenna radiation pattern is set. They are defined as a real vector-row 1 on . it must be more than 2. The units of measurement of angles are degrees. The values of the Theta angles must range from 0° to 180° and be arranged in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to phi-theta.

Magnitude pattern (dB) — the magnitude of the antenna radiation pattern
zeros(181.361) (default) | real matrix Q on P | real array Q on P on L

The value of the antenna pattern, set as a matrix on or an array on on .

If the Input Pattern Coordinate System parameter is set to `az-el', then is equal to the length of the vector defined by the Elevation angles (deg) parameter, in turn, — the length of the vector defined by the Azimuth angles (deg) parameter.
If the Input Pattern Coordinate System parameter is set to `phi-theta', then is equal to the length of the vector defined by the parameter Theta Angles (deg), in turn, — the length of the vector defined by the Phi Angles (deg) parameter.

Value is equal to the value of the Operating frequency vector (Hz) parameter.

If the value of this parameter is a matrix on , then the same scheme is applied for all frequencies specified in the parameter Operating frequency vector (Hz).
If the value is an array on on , each element on The array defines a template for the corresponding frequency specified in the parameter Operating frequency vector (Hz).

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna.

Phase pattern (deg) — phase of the radiation pattern of the user antenna
zeros(181,361) (default) | real matrix Q on P | real array Q on P on L

The phase radiation pattern of the combined antenna, defined as a matrix on or an array on on .

If the Input Pattern Coordinate System parameter is set to `az-el', then is equal to the length of the vector defined by the Elevation angles (deg) parameter, in turn, — the length of the vector defined by the Azimuth angles (deg) parameter.
If the Input Pattern Coordinate System parameter is set to `phi-theta', then is equal to the length of the vector defined by the parameter Theta Angles (deg), in turn, — the length of the vector defined by the Phi Angles (deg) parameter.

Value is equal to the value of the Operating frequency vector (Hz) parameter.

If the value of this parameter is a matrix on , then the same scheme is applied for all frequencies specified in the parameter Operating frequency vector (Hz).
If the value is an array on on , each element on The array defines a template for the corresponding frequency specified in the parameter Operating frequency vector (Hz).

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna.

Align element normal with array normal — align the normal of the antenna array element with respect to the grid normal
enabled (by default) | disabled

If the parameter value is enabled, the radiation pattern of the antenna element is rotated to align with the normal of the array. If it is off, then the drawing of the element does not rotate.

If the antenna is used in an antenna array and the Input Pattern Coordinate System parameter has the value az-el, checking this box rotates the radiation pattern so that the x-axis of the element coordinate system points along the normal of the array. If there is no selection, the element template is used without rotation.

If the antenna is used in an antenna array and the Input Pattern Coordinate System parameter has the value phi-theta, checking this box rotates the radiation pattern so that the z axis of the element coordinate system points along the normal of the array.

Use this parameter together with the Array Normal parameter of the URA and UCA arrays.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna.

Radiation pattern beamwidth (deg) — the beam width of the antenna pattern
[10, 10] (default) | real scalar | a real vector is a 1 by 2 row

The beam width of the antenna pattern in degrees.

Dependencies

To use this parameter, set the Element type parameter to Gaussian Antenna.

Polar pattern frequencies (Hz) — frequency values for the polar pattern of the microphone
1e3 (default) | real scalar | real vector-row 1 on L

The frequency values for the polar radiation pattern are set as a real scalar or a real vector-row 1 on . The frequencies are in the frequency range specified by the parameter Operating frequency vector (Hz).

Dependencies

To use this parameter, set the Element type parameter to Custom Microphone.

Polar pattern angles (deg) — angle values for the polar radiation pattern of the microphone
[-180:180] (default) | real vector is row 1 on P

The angle values for the polar radiation pattern of the microphone are set as a vector . The angles are measured from the central axis of the microphone and should be in the range of −180° to 180° inclusive.

Dependencies

To use this parameter, set the Element type parameter to Custom Microphone.

Polar pattern (dB) — polar directional pattern of the microphone
zeros(1,361) (default) | real vector-row 1 on L

Set the value of the polar radiation pattern of the user microphone element in the form of a real vector-row 1 on , where — the number of frequencies specified in the parameter Polar pattern frequencies (Hz). The string represents the value of the polar radiation pattern measured at the corresponding frequency specified in the Polar pattern frequencies (Hz). The radiation pattern is measured in the azimuthal plane. In the azimuthal plane, the elevation angle is 0°, and the central axis is 0° in azimuth and 0° in elevation. The polar radiation pattern is symmetrical around the central axis. Based on the polar diagram, it is possible to construct a microphone directional pattern in three-dimensional space.

Dependencies

To use this parameter, set the Element type parameter to Custom Microphone.

Array Parameters

Geometry — geometry of the pass array:q[ ] ULA (default) | URA | UCA | Conformal Array

The geometry of the array, set as:

'ULA' is a uniform linear array.
`URA' is a uniform rectangular array.
'UCA' is a uniform circular array.
`Conformal Array' — arbitrary arrangement of elements.

Number of elements — number of elements of the pass array:q[ ] 2 for ULA arrays and 5 for UCA arrays (default) | an integer greater than or equal to 2

The number of array elements for ULA or UCA arrays, set as an integer greater than or equal to 2.

Dependencies

To use this parameter, set the Geometry parameter to ULA or `UCA'.

Element spacing (m) — the distance between the elements of the pass array:q[ ] 0.5 for ULA arrays and [0.5,0.5] for URA arrays (default) | positive scalar for ULA or URA arrays | two-element vector of positive values for URA arrays

The distance between adjacent array elements:

'ULA` — specify the distance between two adjacent array elements as a positive scalar.
URA' — the distance is set as a positive scalar or a vector of positive values 1 by 2. If Element spacing (m) is a scalar, then the distances between rows and columns are equal. If Element spacing(m) is a vector, then the vector has the form `[SpacingBetweenArrayRows,SpacingBetweenArrayColumns].

Dependencies

To use this parameter, set the Geometry parameter to ULA or `URA'.

Array axis — direction of the ULA pass linear axis:q[ ] y (default) | x | z

The direction of the ULA linear axis, set as y, x or z. All elements of the ULA array are evenly distributed along this axis in the local coordinate system of the array.

Dependencies

To use this parameter, set the Geometry parameter to ULA.
This parameter is also used if the block supports only ULA arrays.

Array size — dimensions of the URA pass array:q[ ] [2,2] (default) | positive integer | vector of positive integers 1 by 2

The dimensions of the URA array, specified as a positive integer or a vector of positive integers 1 by 2.

If Array size is a 1 by 2 vector, then the vector has the form [NumberOfArrayRows,NumberOfArrayColumns].
If Array size is an integer, then the array has the same number of rows and columns.

To do this, the array elements are indexed from top to bottom in the leftmost column, and then move to the next columns from left to right.

Dependencies

To use this parameter, set the Geometry parameter to `URA'.

Element lattice — grid of positions of URA pass elements:q[ ] Rectangular (default) | Triangular

A grid of URA element positions, set as rectangular or triangular.

'Rectangular' — aligns all elements in rows and columns.
Triangular — shifts the elements of an even row of a rectangular grid towards the positive direction of the row axis. The offset is half the distance between the elements according to the size of the row.

Dependencies

To use this parameter, set the Geometry parameter to URA.

Array normal — the direction of the normal of the pass array:q[ ] x for URA arrays or z for UCA arrays (default) | y

The normal direction of the array, specified as x, y, or z.

The elements of flat arrays lie in a plane orthogonal to the selected direction of the array normal. The side view directions of the elements are directed along the direction of the array normal.

The 'x` elements of the array lie in the yz plane. The angular coordinate vectors of all elements are directed along the x-axis.
The 'y` elements of the array lie in the zx plane. The angular coordinate vectors of all elements are directed along the y axis.
The 'z` elements of the array lie in the xy plane. The angular coordinate vectors of all elements are directed along the z axis.

Dependencies

To use this parameter, set the Geometry parameter to URA or `UCA'.

Radius of UCA (m) — radius of the UCA pass array:q[ ] 0.5 (default) | positive scalar

The radius of the UCA array, a positive scalar.

Dependencies

To use this parameter, set the Geometry parameter to UCA.

Element positions (m) — positions of elements of the conformal array
[0;0;0] ( by default) | a 3-by-N real matrix

The positions of the elements of the conformal array, specified as a matrix of real values 3 by N, where N is the number of elements in the conformal array. Each column of this matrix represents a vector of coordinates [x;y;z] of an array element in the local coordinate system of the array. The origin of the local coordinate system is (0,0,0). The units of measurement are meters.

Dependencies

To use this parameter, set the Geometry parameter to `Conformal Array'.

Element normals (deg) — direction of the normal vectors of the elements of the conformal array
[0;0] | ` column vector 2 by 1 | matrix 2 by N

The direction of the normal vectors of the elements of a conformal array, defined as a 2-by-1 column vector or a 2-by-N matrix. N means the number of elements in the array. For the matrix, each column specifies the direction of the normal of the corresponding element in the form of [azimuth;elevation] relative to the local coordinate system. In the local coordinate system, the positive x-axis coincides with the direction of the normal to the conformal array. If the parameter value is a 2-by-1 column vector, then the same pointing direction is used for all elements of the array.

Parameters of Element positions (m) and Element normals (deg) can be used to represent any arrangement in which pairs of elements differ from each other by certain transformations. These transformations can include translation, azimuth rotation, and elevation rotation. However, transformations that require rotation relative to the normal direction cannot be used.

Dependencies

To use this parameter, set the Geometry parameter to `Conformal Array'.

Taper — changing the radiation pattern of the elements of the antenna array
1 (default) | complex scalar | complex vector

The change in the radiation pattern of the antenna array elements is set as a complex scalar or a complex vector 1 by , where — the number of antenna array elements.

The coefficients that change the radiation pattern, also called element weights, multiply the responses of the antenna array elements. The coefficients change both the amplitude and the phase of the response to reduce the side lobes or the direction of the main axis of the response.

If the value of the Taper parameter is a scalar, then the same weight is applied to each element. If Taper is a vector, then a weight from the vector is applied to the corresponding element of the antenna array. The number of scales must correspond to the number of antenna array elements.