phased.ESPRITEstimator

ESPRIT direction of arrival (DOA) estimator for ULA

Description

The phased.ESPRITEstimator System object™ estimate the direction of arrival of signals parameters via rotational invariance (ESPRIT) direction of arrival estimate.

To estimate the direction of arrival (DOA):

1. Define and set up your DOA estimator. See Construction.

2. Call step to estimate the DOA according to the properties of phased.ESPRITEstimator. The behavior of step is specific to each object in the toolbox.

Note

Starting in R2016b, instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Construction

H = phased.ESPRITEstimator creates an ESPRIT DOA estimator System object, H. The object estimates the signal's direction-of-arrival (DOA) using the ESPRIT algorithm with a uniform linear array (ULA).

H = phased.ESPRITEstimator(Name,Value) creates object, H, with each specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

Properties

SensorArray	Handle to sensor array Specify the sensor array as a handle. The sensor array must be a phased.ULA object. Default: phased.ULA with default property values
PropagationSpeed	Signal propagation speed Specify the propagation speed of the signal, in meters per second, as a positive scalar. You can specify this property as single or double precision. Default: Speed of light
OperatingFrequency	System operating frequency Specify the operating frequency of the system in hertz as a positive scalar. The default value corresponds to 300 MHz. You can specify this property as single or double precision. Default: 3e8
ForwardBackwardAveraging	Perform forward-backward averaging Set this property to true to use forward-backward averaging to estimate the covariance matrix for sensor arrays with conjugate symmetric array manifold. Default: false
SpatialSmoothing	Spatial smoothing Specify the number of averaging used by spatial smoothing to estimate the covariance matrix as a nonnegative integer. Each additional smoothing handles one extra coherent source, but reduces the effective number of element by 1. The maximum value of this property is M–2, where M is the number of sensors. You can specify this property as single or double precision. Default: 0, indicating no spatial smoothing
NumSignalsSource	Source of number of signals Specify the source of the number of signals as one of 'Auto' or 'Property'. If you set this property to 'Auto', the number of signals is estimated by the method specified by the NumSignalsMethod property. Default: 'Auto'
NumSignalsMethod	Method to estimate number of signals Specify the method to estimate the number of signals as one of 'AIC' or 'MDL'. The 'AIC' uses the Akaike Information Criterion and the 'MDL' uses Minimum Description Length criterion. This property applies when you set the NumSignalsSource property to 'Auto'. Default: 'AIC'
NumSignals	Number of signals Specify the number of signals as a positive integer scalar. This property applies when you set the NumSignalsSource property to 'Property'. The number of signals, Nsig, must be smaller than the number of elements, Nsub, in the subarray derived from the array specified in the SensorArray property. See ESPRIT Subarrays. You can specify this property as single or double precision. Default: 1
Method	Type of least squares method Specify the least squares method used for ESPRIT as one of 'TLS' or 'LS'. 'TLS' refers to total least squares and 'LS'refers to least squares. Default: 'TLS'
RowWeighting	Row weighting factor Specify the row weighting factor for signal subspace eigenvectors as a positive integer scalar. This property controls the weights applied to the selection matrices. In most cases the higher value the better. However, it can never be greater than (Nsub – 1)/2 where Nsub is the number of elements in the subarray derived from the array specified in the SensorArray property. See ESPRIT Subarrays. You can specify this property as single or double precision. Default: 1

Methods

step	Perform DOA estimation

Common to All System Objects
release	Allow System object property value changes

Examples

Estimate DOAs of Two Signals

Estimate the directions-of-arrival (DOA) of two signals received by a standard 10-element ULA with element spacing 1 m. The antenna operating frequency is 150 MHz. The actual direction of the first signal is 10° in azimuth and 20° in elevation. The direction of the second signal is 45° in azimuth and 60° in elevation.

Create the signals.

fs = 8.0e3;
t = (0:1/fs:1).';
x1 = cos(2*pi*t*300);
x2 = cos(2*pi*t*400);
array = phased.ULA('NumElements',10,'ElementSpacing',1);
array.Element.FrequencyRange = [100e6 300e6];
fc = 150e6;

Create the plane waves and add noise.

x = collectPlaneWave(array,[x1 x2],[10 20;45 60]',fc);
noise = 0.1/sqrt(2)*(randn(size(x)) + 1i*randn(size(x)));

Estimate the arrival angles.

estimator = phased.ESPRITEstimator('SensorArray',array,...
    'OperatingFrequency',fc);
doas = estimator(x + noise);
az = broadside2az(sort(doas),[20 60])

az = 1×2

   10.0000   45.0126

Algorithms

ESPRIT Subarrays

The ESPRIT algorithm, as implemented in the phased.ESPRITEstimator System object, reorganizes the ULA elements into two overlapping subarrays. For an original N-element array, the first subarray consist of elements 1,...,N - 1 of the original array. The second subarray consist of elements 2, ... ,N of the original array. There are N_sub = N - 1 elements in each subarray.

Data Precision

This System object supports single and double precision for input data, properties, and arguments. If the input data X is single precision, the output data is single precision. If the input data X is double precision, the output data is double precision. The precision of the output is independent of the precision of the properties and other arguments.

References

[1] Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

This System object supports single and double precision for input data, properties, and arguments. If the input data X is single precision, the output data is single precision. If the input data X is double precision, the output data is double precision. The precision of the output is independent of the precision of the properties and other arguments.

Version History

Introduced in R2011a