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MUSIC 2D spatial spectrum estimator

**Library:**Phased Array System Toolbox / Direction of Arrival

The MUSIC Spectrum block uses the MUltiple SIgnal Classification (MUSIC) algorithm to estimate the spatial spectrum of incoming narrowband signals. The block optionally calculates the direction of arrival of a specified number of signals by finding the peaks of the spectrum.

`Port 1`

— Received signalReceived signal, specified as an *M*-by-*N* complex-valued
matrix. The quantity *M* is the length of the signal,
the number of sample values contained in the signal. The quantity *N* is
the number of sensor elements in the array.

The size of the first dimension of this input matrix can vary to simulate a changing signal length, such as a pulse waveform with variable pulse repetition frequency.

**Data Types: **`double`

**Complex Number Support: **Yes

`Y`

— MUSIC 2-D spatial spectrumnon-negative, real-valued column vector

2-D MUSIC spatial spectrum, returned as a non-negative, real-valued *K*-length
column vector representing the magnitude of the estimated MUSIC spatial
spectrum. Each entry corresponds to an angle specified by the **Azimuth
scan angles (deg)** and **Elevation scan angles (deg)** parameters.

**Data Types: **`double`

`Ang`

— Directions of arrivalnon-negative, real-valued column vector

Directions of arrival of the signals, returned as a real-valued
2-by-*L* matrix. *L* is the number
of signals specified by the **Number of signals** parameter.
The direction of arrival angle is defined by the azimuth and elevation
angles of the source with respect to the array local coordinate system.
The first row of the matrix contains the azimuth angles and the second
row contains the elevation angles. Angle units are in degrees.

Select the **Enable DOA output** parameter
to enable this output port.

**Data Types: **`double`

`Signal propagation speed (m/s)`

— Signal propagation speed`physconst('LightSpeed')`

(default) | real-valued positive scalarSignal propagation speed, specified as a real-valued positive
scalar. The default value of the speed of light is the value return
by `physconst('LightSpeed')`

.

`Operating frequency (Hz)`

— System operating frequency`300.0e6`

(default) | positive real scalarSpecify the operating frequency of the system as a positive scalar. Units are in Hz.

`Forward-backward averaging`

— Enable forward-backward averagingoff (default) | on

Select this parameter to use forward-backward averaging to estimate the covariance matrix for sensor arrays with a conjugate symmetric array manifold structure.

`Azimuth scan angles (deg)`

— Azimuth scan angles`[-90:90]`

(default) | real-valued scalar | real-valued row vectorAzimuth scan angles, specified as a real-valued row vector. Angle units are in degrees. The angle values must lie between –180° and 180°, inclusive, and specified in ascending order.

`Elevation scan angles (deg)`

— Elevation scan angles`0`

(default) | real-valued scalar | real-valued row vectorElevation scan angles, specified as a scalar or real-valued row vector. Angle units are in degrees. The angle values must lie between –90° and 90°, inclusive, and specified in ascending order.

`Enable DOA output`

— Output directions of arrival through output portoff (default) | on

Select this parameter to output the signals directions of arrival
(DOA) through the **Ang** output port.

`Number of signals`

— Expected number of arriving signals`1`

(default) | positive integerSpecify the expected number of signals for DOA estimation as a positive scalar integer.

`Simulate using`

— Block simulation method`Interpreted Execution`

(default) | `Code Generation`

Block simulation, specified as `Interpreted Execution`

or ```
Code
Generation
```

. If you want your block to use the MATLAB^{®} interpreter,
choose `Interpreted Execution`

. If you want
your block to run as compiled code, choose `Code Generation`

.
Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and
tuning a model. The block runs the underlying System
object™ in MATLAB.
You can change and execute your model quickly. When you are satisfied
with your results, you can then run the block using ```
Code
Generation
```

. Long simulations run faster than in interpreted
execution. You can run repeated executions without recompiling. However,
if you change any block parameters, then the block automatically recompiles
before execution.

When setting this parameter, you must take into account the
overall model simulation mode. The table shows how the **Simulate
using** parameter interacts with the overall simulation mode.

When the Simulink^{®} model is in `Accelerator`

mode,
the block mode specified using **Simulate using** overrides
the simulation mode.

**Acceleration Modes**

Block Simulation | Simulation Behavior | ||

`Normal` | `Accelerator` | `Rapid Accelerator` | |

`Interpreted Execution` | The block executes using the MATLAB interpreter. | The block executes using the MATLAB interpreter. | Creates a standalone executable from the model. |

`Code Generation` | The block is compiled. | All blocks in the model are compiled. |

**Data Types: **`char`

`Specify sensor array as`

— Method to specify array`Array (no subarrays)`

(default) | `MATLAB expression`

Method to specify array, specified as ```
Array (no
subarrays)
```

or `MATLAB expression`

.

`Array (no subarrays)`

— use the block parameters to specify the array.`MATLAB expression`

— create the array using a MATLAB expression.

`Expression`

— MATLAB expression used to create an arrayPhased Array System Toolbox™ array System object

MATLAB expression used to create an array, specified as a valid Phased Array System Toolbox array System object.

**Example: **`phased.URA('Size',[5,3])`

To enable this parameter, set **Specify sensor array
as** to `MATLAB expression`

.

`Element type`

— Array element types`Isotropic Antenna`

(default) | `Cosine Antenna`

| `Custom Antenna`

| `Omni Microphone`

| `Custom Microphone`

Antenna or microphone type, specified as one of the following:

`Isotropic Antenna`

`Cosine Antenna`

`Custom Antenna`

`Omni Microphone`

`Custom Microphone`

`Operating frequency range (Hz)`

— Operating frequency range of the antenna or microphone element`[0,1.0e20]`

(default) | real-valued 1-by-2 row vectorSpecify the operating frequency range of the antenna or microphone
element as a 1-by-2 row vector in the form `[LowerBound,UpperBound]`

.
The element has no response outside this frequency range. Frequency
units are in Hz.

To enable this parameter, set **Element type** to ```
Isotropic
Antenna
```

, `Cosine Antenna`

, or ```
Omni
Microphone
```

.

`Operating frequency vector (Hz)`

— Operating frequency range of custom antenna or microphone elements`[0,1.0e20]`

(default) | real-valued row vectorSpecify the frequencies at which to set antenna and microphone
frequency responses as a 1-by-*L* row vector of increasing
real values. The antenna or microphone element has no response outside
the frequency range specified by the minimum and maximum elements
of this vector. Frequency units are in Hz.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

or `Custom Microphone`

. Use **Frequency
responses (dB)** to set the responses at these frequencies.

`Baffle the back of the element`

— Set back response of an `Isotropic Antenna`

element or an `Omni Microphone`

element to zerooff (default) | on

Select this checkbox to baffle the back response of the element. When backbaffled, the responses at all azimuth angles beyond ±90° from broadside are set to zero. The broadside direction is 0° azimuth angle and 0° elevation angle.

To enable this checkbox, set **Element type** to ```
Isotropic
Antenna
```

or `Omni Microphone`

.

`Exponent of cosine pattern`

— Exponents of azimuth and elevation cosine patterns`[1.5 1.5]`

(default) | nonnegative scalar | real-valued 1-by-2 matrix of nonnegative valuesSpecify the exponents of the cosine pattern as a nonnegative
scalar or a real-valued 1-by-2 matrix of nonnegative values. When
you set **Exponent of cosine pattern** to a 1-by-2
vector, the first element is the exponent for the azimuth direction
cosine pattern, and the second element is the exponent for the elevation
direction cosine pattern. When you set this parameter to a scalar,
both the azimuth direction cosine pattern and the elevation direction
cosine pattern are raised to the same power.

To enable this parameter, set **Element type** to ```
Cosine
Antenna
```

.

`Frequency responses (dB)`

— Antenna and microphone frequency response`[0,0]`

(default) | real-valued row vectorFrequency response of a custom antenna or custom microphone
for the frequencies defined by the **Operating frequency vector
(Hz)** parameter. The dimensions of **Frequency responses
(dB)** must match the dimensions of the vector specified
by the **Operating frequency vector (Hz)** parameter.

To enable this parameter , set **Element type** to ```
Custom
Antenna
```

or `Custom Microphone`

.

`Azimuth angles (deg)`

— Azimuth angles of antenna radiation pattern `[-180:180]`

(default) | real-valued row vectorSpecify the azimuth angles at which to calculate the antenna
radiation pattern as a 1-by-*P* row vector. *P* must
be greater than 2. Azimuth angles must lie between –180°
and 180°, inclusive, and be in strictly increasing order.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Elevation angles (deg)`

— Elevation angles of antenna radiation pattern`[-90:90]`

(default) | real-valued row vectorSpecify the elevation angles at which to compute the radiation
pattern as a 1-by-*Q* vector. *Q* must
be greater than 2. Angle units are in degrees. Elevation angles must
lie between –90° and 90°, inclusive, and be in strictly
increasing order.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Magnitude pattern (dB)`

— Magnitude of combined antenna radiation pattern`zeros(181,361)`

(default) | real-valued Magnitude of the combined antenna radiation pattern, specified
as a *Q*-by-*P* matrix or a *Q*-by-*P*-by-*L* array.
The quantity *Q* equals the length of the vector
specified by **Elevation angles (deg)**. The quantity
*P* equals length of the vector specified by **Azimuth
angles (deg)**. The quantity *L* equal the
length of the **Operating frequency vector (Hz)**.

If this parameter is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the**Operating frequency vector (Hz)**parameter.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the**Operating frequency vector (Hz)**parameter.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Phase pattern (deg)`

— Custom antenna radiation phase pattern`zeros(181,361)`

(default) | real-valued Phase of the combined antenna radiation pattern, specified as
a *Q*-by-*P* matrix or a *Q*-by-*P*-by-*L* array.
The quantity *Q* equals the length of the vector
specified by **Elevation angles (deg)**. The quantity
*P* equals length of the vector specified by **Azimuth
angles (deg)**. The quantity *L* equal the
length of the **Operating frequency vector (Hz)**.

If this parameter is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the**Operating frequency vector (Hz)**parameter.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the**Operating frequency vector (Hz)**parameter.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Polar pattern frequencies (Hz)`

— Custom microphone response frequencies1e3 (default) | real scalar | real-valued 1-by-

Response frequencies of the custom microphone of the polar pattern,
specified as a real scalar or real-valued 1-by-*L* vector.
The response frequencies lie within the frequency range specified
by the **Operating frequency vector (Hz)** vector.

To enable this parameter, set **Element type** is
set to `Custom Microphone`

.

`Polar pattern angles (deg)`

— Polar pattern response angles`[-180:180]`

(default) | real-valued -by-Specify the polar pattern response angles, as a 1-by-*P* vector.
The angles are measured from the central pickup axis of the microphone
and must be between –180° and 180°, inclusive.

To enable this parameter, set **Element type** to ```
Custom
Microphone
```

.

`Polar pattern (dB)`

— Custom microphone polar response`zeros(1,361)`

(default) | real-valued Specify the magnitude of the custom microphone element polar
patterns as an *L*-by-*P* matrix. *L* is
the number of frequencies specified in **Polar pattern frequencies
(Hz)**. *P* is the number of angles specified
in **Polar pattern angles (deg)**. Each row of the
matrix represents the magnitude of the polar pattern measured at the
corresponding frequency specified in **Polar pattern frequencies
(Hz)** and all angles specified in **Polar pattern
angles (deg)**. Assume that the pattern is measured in the
azimuth plane. In the azimuth plane, the elevation angle is 0°
and the central pickup axis is 0° degrees azimuth and 0°
degrees elevation. Assume also that the polar pattern is symmetric
around the central axis. You can construct the microphone’s
response pattern in 3-D space from the polar pattern.

To enable this parameter, set **Element type** to ```
Custom
Microphone
```

.

`Geometry`

— Array geometry`ULA`

(default) | `URA`

| `UCA`

| `Conformal Array`

Array geometry, specified as one of

`ULA`

— Uniform linear array`URA`

— Uniform rectangular array`UCA`

— Uniform circular array`Conformal Array`

— arbitrary element positions

`Number of elements`

— Number of array elements`2`

for ULA arrays and `5`

for
UCA arrays (default) | integer greater than or equal to 2The number of array elements for ULA or UCA arrays, specified as an integer greater than or equal to 2.

To enable this parameter, set **Geometry** to `ULA`

or `UCA`

.

`Element spacing (m)`

— Spacing between array elements`0.5`

for ULA arrays and `[0.5,0.5]`

for
URA arrays (default) | positive scalar for ULA or URA arrays | 2-element vector of positive values for URA arraysSpacing between adjacent array elements:

ULA — specify the spacing between two adjacent elements in the array as a positive scalar.

URA — specify the spacing as a positive scalar or a 1-by-2 vector of positive values. If

**Element spacing (m)**is a scalar, the row and column spacings are equal. If**Element spacing (m)**is a vector, the vector has the form`[SpacingBetweenArrayRows,SpacingBetweenArrayColumns]`

.

To enable this parameter, set **Geometry** to `ULA`

or `URA`

.

`Array axis`

— Linear axis direction of ULA`y`

(default) | `x`

| `z`

Linear axis direction of ULA, specified as `y`

, `x`

,
or `z`

. All ULA array elements are uniformly
spaced along this axis in the local array coordinate system.

To enable this parameter, set **Geometry** to `ULA`

.
This parameter is also enabled when the block supports only ULA arrays.

`Array size`

— Dimensions of URA array`[2,2]`

(default) | positive integer | 1-by-2 vector of positive integersDimensions of a URA array, specified as a positive integer or 1-by-2 vector of positive integers.

If

**Array size**is a 1-by-2 vector, the vector has the form`[NumberOfArrayRows,NumberOfArrayColumns]`

.If

**Array size**is an integer, the array has the same number of elements in each row and column.

For a URA, array elements are indexed from top to bottom
along a column, and continuing to the next columns from left to right.
In this figure, the **Array size** value of `[3,2]`

creates
an array having three rows and two columns.

To enable this parameter, set **Geometry** to `URA`

.

`Element lattice`

— Lattice of URA element positions`Rectangular`

(default) | `Triangular`

Lattice of URA element positions, specified as `Rectangular`

or `Triangular`

.

`Rectangular`

— Aligns all the elements in row and column directions.`Triangular`

— Shifts the even-row elements of a rectangular lattice toward the positive row-axis direction. The displacement is one-half the element spacing along the row dimension.

To enable this parameter, set **Geometry** to `URA`

.

`Array normal`

— Array normal direction`x`

for URA arrays
or `z`

for UCA arrays (default) | `y`

Array normal direction, specified as `x`

, `y`

,
or `z`

.

Elements of planar arrays lie in a plane orthogonal to the selected array normal direction. Element boresight directions point along the array normal direction.

Array Normal Parameter Value | Element Positions and Boresight Directions |
---|---|

`x` | Array elements lie in the yz-plane. All
element boresight vectors point along the x-axis. |

`y` | Array elements lie in the zx-plane. All
element boresight vectors point along the y-axis. |

`z` | Array elements lie in the xy-plane. All
element boresight vectors point along the z-axis. |

To enable this parameter, set **Geometry**to `URA`

or `UCA`

.

`Radius of UCA (m)`

— UCA array radius0.5 (default) | positive scalar

Radius of UCA array, specified as a positive scalar.

To enable this parameter, set **Geometry** to `UCA`

.

`Element positions (m)`

— Positions of conformal array elements`[0;0;0]`

(default) | 3-by-Positions of the elements in a conformal array, specified as
a 3-by-*N* matrix of real values, where *N* is
the number of elements in the conformal array. Each column of this
matrix represents the position `[x;y;z]`

of an array
element in the array local coordinate system. The origin of the local
coordinate system is *(0,0,0)*. Units are in meters.

To enable this parameter set **Geometry** to ```
Conformal
Array
```

.

**Data Types: **`double`

`Element normals (deg)`

— Direction of conformal array element normal vectors`[0;0]`

| 2-by-1 column vector | 2-by-Direction of element normal vectors in a conformal array, specified
as a 2-by-1 column vector or a 2-by-*N* matrix. *N* indicates
the number of elements in the array. If the parameter value is a matrix,
each column specifies the normal direction of the corresponding element
in the form `[azimuth;elevation]`

with respect to
the local coordinate system. The local coordinate system aligns the
positive *x*-axis with the direction normal to the
conformal array. If the parameter value is a 2-by-1 column vector,
the same pointing direction is used for all array elements.

You can use the **Element positions (m)** and **Element
normals (deg)** parameters to represent any arrangement in
which pairs of elements differ by certain transformations. The transformations
can combine translation, azimuth rotation, and elevation rotation.
However, you cannot use transformations that require rotation about
the normal direction.

To enable this parameter, set **Geometry** to ```
Conformal
Array
```

.

**Data Types: **`double`

`Taper`

— Array element tapers1 (default) | complex scalar | complex-valued row vector

Specify element tapering as a complex-valued scalar or a complex-valued
1-by-*N* row vector. In this vector, *N* represents
the number of elements in the array.

Also known as *element weights*, tapers
multiply the array element responses. Tapers modify both amplitude
and phase of the response to reduce sidelobes or steer the main response
axis.

If **Taper** is a scalar, the same weight is
applied to each element. If **Taper** is a vector,
a weight from the vector is applied to the corresponding sensor element.
The number of weights must match the number of elements of the array.

**Data Types: **`double`

`phased.ConformalArray`

|`phased.MUSICEstimator`

|`phased.MUSICEstimator2D`

|`phased.UCA`

|`phased.ULA`

|`phased.URA`

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