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MUSIC spatial spectrum estimator for ULA

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

The ULA MUSIC Spectrum block estimates the spatial spectrum of incoming narrowband signals using the MUSIC algorithm. The algorithm computes the MUSIC pseudo-spectrum of a ULA by scanning a region of broadside angles. The block optionally calculates the direction of arrival (DOA) of a specified number of signals by estimating peaks of the spectrum.

`Port 1`

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

The size of the first dimension of the input matrix can vary to simulate a changing signal length. A size change can occur, for example, in the case of a pulse waveform with variable pulse repetition frequency.

**Data Types: **`double`

**Complex Number Support: **Yes

`Y`

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

MUSIC spatial spectrum, returned as a non-negative, real-valued
column vector representing the magnitude of the estimated MUSIC spatial
spectrum. Each entry corresponds to an angle specified by the **Scan
angles (deg) ** parameter.

**Data Types: **`double`

`Ang`

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

Directions of arrival of the signals, returned as a real-valued row vector. The direction of
arrival angle is the broadside angle between the source direction and
the array axis. The length of the vector is the number of signals
specified by the `Number of signals`

parameter. If
the object cannot identify peaks in the spectrum, it will return
`NaN`

. 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 returned by `physconst('LightSpeed')`

.
Units are in meters per second.

**Example: **`3e8`

**Data Types: **`double`

`Operating frequency (Hz)`

— System operating frequency`3.0e8`

(default) | positive real scalarSystem operating frequency, specified 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.

`Spatial smoothing`

— Enable spatial smoothing`0`

(default) | non-negative integerSpecify the amount of averaging used by spatial smoothing to estimate the covariance
matrix as a nonnegative integer. Each increase in smoothing handles one extra coherent
source, but reduces the effective number of elements by one. The maximum value of this
parameter is *N – 2*, where *N* is the number of
sensors in the ULA.

`Scan angles (deg)`

— Search angles for spectrum peaks`-90:90`

(default) | real-valued row vectorSpecify the scan angles in degrees as a real-valued row vector. The angles are array broadside angles and must lie between –90° and 90°, inclusive. You must specify the angles in increasing 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 with generated code than in
interpreted execution. You can run repeated executions without recompiling, but if you
change any block parameters, then the block automatically recompiles before
execution.

This table shows how the **Simulate using** parameter affects the overall
simulation behavior.

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. |

For more information, see Choosing a Simulation Mode (Simulink).

`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 check box to baffle the back response of the element. When back baffled, the responses at all azimuth angles beyond ±90° from broadside are set to zero. The broadside direction is defined as 0° azimuth angle and 0° elevation angle.

To enable this check box, 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 **Exponent of cosine pattern** is a
1-by-2 vector, the first element is the exponent in the azimuth direction and the second
element is the exponent in the elevation direction. When you set this parameter to a
scalar, both the azimuth direction and elevation direction cosine patterns 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`

.

`Input Pattern Coordinate System`

— Coordinate system of custom antenna pattern`az-el`

(default) | `phi-theta`

Coordinate system of custom antenna pattern, specified `az-el`

or `phi-theta`

. When you specify `az-el`

, use the **Azimuth angles (deg)** and **Elevations angles (deg)** parameters to specify the coordinates of the pattern points. When you specify `phi-theta`

, use the **Phi angles (deg)** and **Theta angles (deg)** parameters to specify the coordinates of the pattern points.

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

.

`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 the **Element type** parameter to
`Custom Antenna`

and the **Input Pattern Coordinate
System** parameter to `az-el`

.

`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 the **Element type** parameter to
`Custom Antenna`

and the **Input Pattern Coordinate
System** parameter to `az-el`

.

`Phi Angles (deg)`

— Phi angle coordinates of custom antenna radiation pattern`0:360`

| real-valued 1-by-Phi angles of points at which to specify the antenna radiation pattern, specify as a real-valued 1-by-*P* row vector. *P* must be greater than 2. Angle units are in degrees. Phi angles must lie between 0° and 360° and be in strictly increasing order.

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

and the **Input Pattern Coordinate System** parameter to `phi-theta`

.

`Theta Angles (deg)`

— Theta angle coordinates of custom antenna radiation pattern`0:180`

| real-valued 1-by-Theta angles of points at which to specify the antenna radiation pattern, specify as a real-valued 1-by-*Q* row vector. *Q* must be greater than 2. Angle units are in degrees. Theta angles must lie between 0° and 360° and be in strictly increasing order.

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

and the **Input Pattern Coordinate System** parameter to `phi-theta`

.

`Radiation pattern (dB)`

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

| complex-valued matrix | complex-valued MATLAB arrayMagnitude of the combined polarized antenna radiation pattern,
specified as a *Q*-by-*P* matrix
or a *Q*-by-*P*-by-*L* array.
The value of *Q* must equal the value of *Q* specified
by **Elevation angles (deg)**. The value of *P* must
equal the value of *P* specified by **Azimuth
angles (deg)**. The value of *L* must equal
the value of *L* specified by **Operating
frequency vector (Hz)**.

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.

When the

**Input Pattern Coordinate System**parameter is set to`az-el`

,*Q*equals the length of the vector specified by the**Elevation angles (deg)**parameter and*P*equals the length of the vector specified by the**Azimuth angles (deg)**parameter.When the

**Input Pattern Coordinate System**parameter is set to`phi-theta`

,*Q*equals the length of the vector specified by the**Theta Angles (deg)**parameter and*P*equals the length of the vector specified by the**Phi Angles (deg)**parameter.

The quantity *L* equals 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.

When the

**Input Pattern Coordinate System**parameter is set to`az-el`

,*Q*equals the length of the vector specified by the**Elevation angles (deg)**parameter and*P*equals the length of the vector specified by the**Azimuth angles (deg)**parameter.When the

**Input Pattern Coordinate System**parameter is set to`phi-theta`

,*Q*equals the length of the vector specified by the**Theta Angles (deg)**parameter and*P*equals the length of the vector specified by the**Phi Angles (deg)**parameter.

The quantity *L* equals 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 (**

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

.

`MatchArrayNormal`

— Rotate antenna element to array normal`on`

(default) | `off`

Select this check box to rotate the antenna element pattern to align with the array normal. When not selected, the element pattern is not rotated.

When the antenna is used in an antenna array and the **Input Pattern Coordinate System** parameter is `az-el`

, selecting this check box rotates the pattern so that the *x*-axis of the element coordinate system points along the array normal. Not selecting uses the element pattern without the rotation.

When the antenna is used in an antenna array and **Input Pattern Coordinate System** is set to `phi-theta`

, selecting this check box rotates the pattern so that the *z*-axis of the element coordinate system points along the array normal.

Use the parameter in conjunction with the **Array normal** parameter of the `URA`

and `UCA`

arrays.

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

.

`Polar pattern frequencies (Hz)`

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

Polar pattern microphone response frequencies, specified as a real scalar, or a
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** 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)**. 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. The polar pattern is symmetric around the
central axis. You can construct the microphone response pattern in 3-D space from the
polar pattern.

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

.

`Number of elements`

— Number of array elements in U`2`

(default) | positive integer greater than or equal to twoThe number of array elements for ULA arrays, specified as an integer greater than or equal to two.

**Example: **`11`

**Data Types: **`double`

`Element spacing`

— Distance between ULA elements`0.5`

(default) | positive scalarDistance between adjacent ULA elements, specified as a positive scalar. Units are in meters.

**Example: **`1.5`

`Array axis`

— Linear axis direction of ULA`y`

(default) | `x`

| `z`

Linear axis direction of ULA, specified as `y`

, `x`

,
or `z`

. Then, all ULA array elements are
uniformly spaced along this axis in the local array coordinate system.

`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 side lobes
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`

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