# ESPRIT DOA

ESPRIT direction of arrival (DOA) estimator for ULA

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

## Description

The ESPRIT DOA block estimates the direction of arrival of a specified number of narrowband signals incident on a uniform linear array using the ESPRIT algorithm.

## Ports

### Input

`Port_1`

— Input signal

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

Input signal, specified as an
*N*-by-*M* complex-valued matrix.
*N* corresponds to the number of samples.
*M* corresponds to the number data channels.

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`

### Output

`Ang`

— Estimated broadside direction-of-arrival angles

*M*-by-1 real-valued vector

Estimated broadside direction-of-arrival angles, returned as an
*M*-by-1 real-valued vector. Units are in
degrees.

**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

`3e8`

(default) | positive real scalar

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

`Number of signals`

— Number of signals

`1`

(default) | positive integer scalar

Specify the number of signals as a positive integer scalar.

`Spatial smoothing`

— Enable spatial smoothing

`0`

(default) | non-negative integer

Specify 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.

`Type of least squares method`

— Type of least squares method

`TLS`

(default) | `LS`

Specify the least squares method used for ESPRIT as one of `TLS`

or `LS`

where `TLS`

refers to total least squares and `LS`

refers to least squares.

`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.

`Row weighting factor`

— Row weighting factor

`1`

(default)

Specify the row weighting factor for signal subspace eigenvectors as a
positive integer scalar. This parameter controls the weights applied to
the selection matrices. In most cases higher value are better. However,
the value can never be greater than *(N-1)/2* where
*N* is the number of elements of the array.

`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.

**Element Parameters**

`Element type`

— Array element types

`Isotropic Antenna`

(default) | `Cardioid Antenna`

| `Cosine Antenna`

| `Custom Antenna`

| `Gaussian Antenna`

| `Sinc Antenna`

| `Omni Microphone`

| `Custom Microphone`

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

`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 antenna or microphone element

`[0,1e20]`

(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`

.

`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`

.

`Null axis direction`

— Null axis direction

`-x`

(default) | `+x`

| `+y`

| `-y`

| `+z`

| `-z`

#### Dependencies

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

.

`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
```

.

`Operating frequency vector (Hz)`

— Operating frequency range of custom antenna or microphone elements

`[0,1e20]`

(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.

`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`

.

`Align element normal with array normal`

— Align element normal with array normal

on (default) | off

#### Dependencies

This parameter is enabled when **Element type** is set to
`Custom Antenna`

.

`Radiation pattern beamwidth (deg)`

— Radiation pattern beamwidth

`[10,10]`

(default)

#### Dependencies

This parameter is enabled when **Element type** is set to `Gaussian 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`

.

**ULA Parameters**

`Number of elements`

— Number of array elements in U

`2`

(default) | positive integer greater than or equal to two

The 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 scalar

Distance 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`

. 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.

`Taper`

— ULA array taper

`1`

(default) | complex-valued vector

Tapers, also known as *element weights*, are applied to sensor
elements in the array. Tapers are used to modify both the amplitude and phase of the
transmitted or received data.

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. 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. A
weight must be applied to each element in the sensor array.

**Example: **[0.5;1;0.5]

**Data Types: **`double`

**Complex Number Support: **Yes

`Expression`

— MATLAB expression used to create an array

Phased Array System Toolbox™ array System object

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

**Example: **`phased.ULA('NumElements',13)`

#### Dependencies

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

.

## Version History

**Introduced in R2014b**

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