# MUSIC Spectrum

MUSIC 2D spatial spectrum estimator

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

## Description

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.

## Ports

### Input

`Port 1`

— Received signal

*M*-by-*N* complex-valued
matrix

Received 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 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

### Output

`Y`

— MUSIC 2-D spatial spectrum

non-negative real-valued *P*-by-*Q*
matrix

2-D MUSIC spatial spectrum, returned as a non-negative, returned as a real-valued
*P*-by-*Q* matrix. Each entry
represents 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. *P* equals the length
of the vector specified in **Azimuth scan angles
(deg)** and *Q* equals the length of the
vector specified in **Elevation scan angles
(deg)**.

**Data Types: **`double`

`Ang`

— Directions of arrival

non-negative, real-valued 2-by-*L* matrix

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

. Angle units are in
degrees.

#### Dependencies

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

**Data Types: **`double`

## Parameters

**Main Tab**

`Signal propagation speed (m/s)`

— Signal propagation speed

`physconst('LightSpeed')`

(default) | real-valued positive scalar

Signal 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 scalar

System operating frequency, specified as a positive scalar. Units are in Hz.

`Forward-backward averaging`

— Enable forward-backward averaging

off (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 vector

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

`Elevation scan angles (deg)`

— Elevation scan angles

`0`

(default) | real-valued scalar | real-valued row vector

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

`Enable DOA output`

— Output directions of arrival through output port

off (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 integer

Specify 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).

**Sensor Array Tab**

`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 array

Phased 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])`

#### Dependencies

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

.

**Element Parameters**

`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 vector

Specify 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.

#### Dependencies

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 vector

Specify 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.

#### Dependencies

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 zero

off (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.

#### Dependencies

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 values

Specify 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.

#### Dependencies

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

.

`Frequency responses (dB)`

— Antenna and microphone frequency response

`[0,0]`

(default) | real-valued row vector

Frequency 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.

#### Dependencies

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.

#### Dependencies

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 vector

Specify 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.

#### Dependencies

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 vector

Specify 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.

#### Dependencies

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-*P* row vector

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.

#### Dependencies

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-*Q* row vector

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.

#### Dependencies

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

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

.

`Magnitude pattern (dB)`

— Magnitude of combined antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L* array

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.

#### Dependencies

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

.

`Phase pattern (deg)`

— Custom antenna radiation phase pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L* array

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 (**

#### Dependencies

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.

#### Dependencies

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

.

`Polar pattern frequencies (Hz)`

— Polar pattern microphone response frequencies

1e3 (default) | real scalar | real-valued 1-by-*L* row vector

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.

#### Dependencies

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-*P* row vector

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.

#### Dependencies

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

.

`Polar pattern (dB)`

— Custom microphone polar response

`zeros(1,361)`

(default) | real-valued *L*-by-*P* matrix

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.

#### Dependencies

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

.

**Array Parameters**

`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 2

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

#### Dependencies

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 arrays

Spacing 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]`

.

#### Dependencies

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.

#### Dependencies

To enable this parameter, set

**Geometry**to`ULA`

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

`Array size`

— Dimensions of URA array

`[2,2]`

(default) | positive integer | 1-by-2 vector of positive integers

Dimensions 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 the
leftmost array column, and continued 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.

#### Dependencies

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.

#### Dependencies

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. |

#### Dependencies

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

or `UCA`

.

`Radius of UCA (m)`

— UCA array radius

0.5 (default) | positive scalar

Radius of UCA array, specified as a positive scalar.

#### Dependencies

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

.

`Element positions (m)`

— Positions of conformal array elements

`[0;0;0]`

(default) | 3-by-*N*matrix of real values

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.

#### Dependencies

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-*N* matrix

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 tapers

1 (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`

## See Also

### Blocks

### Objects

`phased.MUSICEstimator2D`

|`phased.MUSICEstimator`

|`phased.ConformalArray`

|`phased.UCA`

|`phased.ULA`

|`phased.URA`

### Functions

**Introduced in R2016b**

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