step

System object: phased.MUSICEstimator
Namespace: phased

Estimate direction of arrival using MUSIC

Syntax

spectrum = step(estimator,X)
[spectrum,doa] = step(estimator,X)


Description

Note

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.

spectrum = step(estimator,X) returns the MUSIC spectrum for a signal specified by X.

[spectrum,doa] = step(estimator,X) also returns the signal broadside directions of arrival, doa. To use this syntax, set the DOAOutputPort property to true.

Note

The object performs an initialization the first time the object is executed. This initialization locks nontunable properties and input specifications, such as dimensions, complexity, and data type of the input data. If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first call the release method to unlock the object.

Input Arguments

estimator — MUSIC estimator

phased.MUSICEstimator System object

MUSIC estimator, specified as a phased.MUSICEstimator System object.

Example: phased.MUSICEstimator

X — Received signal

M-by-N complex-valued matrix

Received 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.

Example: [[0;1;2;3;4;3;2;1;0],[1;2;3;4;3;2;1;0;0]]

Data Types: double
Complex Number Support: Yes

Output Arguments

spectrum — MUSIC spatial spectrum

nonnegative, real-valued K-length column vector

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 ScanAngles property.

doa — Directions of arrival

real-valued L-length row vector

Directions of arrival of the signals, returned as a real-valued L-length row vector. The direction of arrival angle is the angle between the source direction and the array axis or broadside angle. Angle units are in degrees. L is the number of signals specified by the NumSignals property or computed using the method specified by the NumSignalsMethod property.

Dependencies

To enable this output argument, set the DOAOutputPort property to true.

Examples

Plot MUSIC Spectrum of Two Signals Arriving at ULA

Estimate the DOAs of two signals received by a standard 10-element ULA having an element spacing of 1 meter. Then plot the MUSIC spectrum.

Create the ULA array. The antenna operating frequency is 150 MHz.

fc = 150.0e6;
array = phased.ULA('NumElements',10,'ElementSpacing',1.0);

Create the arriving signals at the ULA. The true direction of arrival of the first signal is 10° in azimuth and 20° in elevation. The direction of the second signal is 60° in azimuth and -5° in elevation.

fs = 8000.0;
t = (0:1/fs:1).';
sig1 = cos(2*pi*t*300.0);
sig2 = cos(2*pi*t*400.0);
sig = collectPlaneWave(array,[sig1 sig2],[10 20; 60 -5]',fc);
noise = 0.1*(randn(size(sig)) + 1i*randn(size(sig)));

Estimate the DOAs.

estimator = phased.MUSICEstimator('SensorArray',array,...
    'OperatingFrequency',fc,...
    'DOAOutputPort',true,'NumSignalsSource','Property',...
    'NumSignals',2);
[y,doas] = estimator(sig + noise);
doas = broadside2az(sort(doas),[20 -5])

doas = 1×2

    9.5829   60.3813

Plot the MUSIC spectrum.

plotSpectrum(estimator,'NormalizeResponse',true)

Compute DOA of Two Nearby Signals Using MUSIC

First, estimate the DOAs of two signals received by a standard 10-element ULA having an element spacing of one-half wavelength.Then, plot the spatial spectrum.

The antenna operating frequency is 150 MHz. The arrival directions of the two signals are separated by 2°. The direction of the first signal is 30° azimuth and 0° elevation. The direction of the second signal is 32° azimuth and 0° elevation. Estimate the number of signals using the Minimum Description Length (MDL) criterion.

Create the signals arriving at the ULA.

fs = 8000;
t = (0:1/fs:1).';
f1 = 300.0;
f2 = 600.0;
sig1 = cos(2*pi*t*f1);
sig2 = cos(2*pi*t*f2);
fc = 150.0e6;
c = physconst('LightSpeed');
lam = c/fc;
array = phased.ULA('NumElements',10,'ElementSpacing',0.5*lam);
sig = collectPlaneWave(array,[sig1 sig2],[30 0; 32 0]',fc);
noise = 0.1*(randn(size(sig)) + 1i*randn(size(sig)));

Estimate the DOAs.

estimator = phased.MUSICEstimator('SensorArray',array,...
    'OperatingFrequency',fc,'DOAOutputPort',true,...
    'NumSignalsSource','Auto','NumSignalsMethod','MDL');
[y,doas] = estimator(sig + noise);
doas = broadside2az(sort(doas),[0 0])

doas = 1×2

   30.0000   32.0000

Plot the MUSIC spectrum.

plotSpectrum(estimator,'NormalizeResponse',true)

Version History

Introduced in R2016b