musicdoa

Estimate arrival directions of signals using MUSIC

Syntax

doas = musicdoa(covmat,nsig)

[doas,spec,specang] = musicdoa(covmat,nsig)

[___] = musicdoa(covmat,nsig,___,'ScanAngles',scanangle)

[___] = musicdoa(covmat,nsig,___,'ElementSpacing',dist)

Description

doas = musicdoa(covmat,nsig) uses the MUSIC algorithm to estimate the directions of arrival, doas, of nsig plane waves received on a uniform linear array (ULA). The argument covmat is a positive-definite Hermitian matrix representing the sensor covariance matrix. Detected sources appear as peaks in the spatial spectrum. The argument nsig is the number of arriving signals. Sensor elements are spaced one-half wavelength apart in units of wavelengths. The function forces exact conjugate symmetry of covmat by averaging the covariance matrix with its conjugate transpose.

[doas,spec,specang] = musicdoa(covmat,nsig) also returns the spatial spectrum, spec, and the nsig angles of the spectrum peaks, specang.

[___] = musicdoa(covmat,nsig,___,'ScanAngles',scanangle) specifies the grid of broadside angles to search for spectrum peaks.

[___] = musicdoa(covmat,nsig,___,'ElementSpacing',dist) specifies the spacing between array elements.

Examples

Estimate DOA of Multiple Signals Using MUSIC

Calculate the directions of arrival of 3 uncorrelated signals arriving at an 11-element ULA with half-wavelength spacing. Assume the signals are coming from the broadside angles of 0°, –12°, and 85°. The noise at each element is Gaussian white noise and is uncorrelated between elements. The SNR is 5 dB.

Specify the number of ULA elements and the element spacing (in wavelengths).

nelem = 11;
d = 0.5;
snr = 5.0;
elementPos = (0:nelem-1)*d;

Specify the number of signals and their broadside arrival angles.

nsig = 3;
angles = [0.0 -12.0 85.0];

Create the sensor covariance matrix.

covmat = sensorcov(elementPos,angles,db2pow(-snr));

Estimate the broadside arrival angles.

doas = musicdoa(covmat,nsig)

doas = 1×3

     0    85   -12

The estimated angles match the specified angles.

Display MUSIC Spectrum of Multiple Signals

Calculate the directions of arrival of 3 uncorrelated signals arriving at an 11-element ULA with half-wavelength spacing. Assume the signals are coming from the broadside angles of 0°, –12°, and 85°. The noise at each element is Gaussian white noise and is uncorrelated between elements. The SNR is 2 dB.

Specify the number of ULA elements and the element spacing (in wavelengths).

nelem = 11;
d = 0.5;
snr = 2.0;
elementPos = (0:nelem-1)*d;

Specify the number of signals and their broadside arrival angles.

nsig = 3;
angles = [0.0 -12.0 85.0];

Create the sensor covariance matrix.

covmat = sensorcov(elementPos,angles,db2pow(-snr));

Compute the MUSIC spectrum and estimate the broadside arrival angles.

[doas,spec,specang] = musicdoa(covmat,nsig);

Plot the MUSIC spectrum.

plot(specang,10*log10(spec))
xlabel('Arrival Angle (deg)')
ylabel('Magnitude (dB)')
title('MUSIC Spectrum')
grid

The estimated angles match the specified angles.

Display MUSIC Spectrum Over Specified Direction Span

Calculate the directions of arrival of 4 uncorrelated signals arriving at an 11-element ULA. The element spacing is 0.5 wavelengths. Assume the signals are coming from the broadside angles of –60.2°, –20.7°, 0.5°, and 84.8°. The noise at each element is Gaussian white noise and is uncorrelated between elements. The SNR is 0 dB.

Specify the number of ULA elements and the element spacing (in wavelengths).

nelem = 11;
d = 0.5;
snr = 5.0;
elementPos = (0:nelem-1)*d;

Specify the number of signals and their broadside arrival angles.

nsig = 4;
angles = [-60.2 -20.7 0.5 84.8];

Create the sensor covariance matrix.

covmat = sensorcov(elementPos,angles,db2pow(-snr));

Compute the MUSIC spectrum and estimate the broadside arrival angles in the range from -70° to 90° in 0.1° increments.

[doas,spec,specang] = musicdoa(covmat,nsig,'ScanAngles',[-70:.1:90]);

Plot the MUSIC spectrum.

plot(specang,10*log10(spec))
xlabel('Arrival Angle (deg)')
ylabel('Magnitude (dB)')
title('MUSIC Spectrum')
grid

disp(doas)

   84.8000  -60.2000    0.5000  -20.7000

The estimated angles match the specified angles.

Display MUSIC Spectrum with Specified Element Spacing

Calculate the directions of arrival of 4 uncorrelated signals arriving at an 11-element ULA. The element spacing is 0.4 wavelengths spacing. Assume the signals are coming from the broadside angles of –60°, –20°, 0°, and 85°. The noise at each element is Gaussian white noise and is uncorrelated between elements. The SNR is 0 dB.

Specify the number of ULA elements and the element spacing (in wavelengths).

nelem = 11;
d = 0.4;
snr = 0.0;
elementPos = (0:nelem-1)*d;

Specify the number of signals and their broadside arrival angles.

nsig = 4;
angles = [-60.0 -20.0 0.0 85.0];

Create the sensor covariance matrix.

covmat = sensorcov(elementPos,angles,db2pow(-snr));

Compute the MUSIC spectrum and estimate the broadside arrival angles.

[doas,spec,specang] = musicdoa(covmat,nsig,'ElementSpacing',d);

Plot the MUSIC spectrum.

plot(specang,10*log10(spec))
xlabel('Arrival Angle (deg)')
ylabel('Magnitude (dB)')
title('MUSIC Spectrum')
grid

The estimated angles match the specified angles.

Input Arguments

covmat — Sensor covariance matrix

positive-definite complex-valued M-by-M matrix

Sensor covariance matrix, specified as a complex-valued, positive-definite M-by-M matrix. The quantity M is the number of elements in the ULA array. The function forces Hermiticity property by averaging the matrix and its conjugate transpose.

Data Types: double
Complex Number Support: Yes

nsig — Number of arriving signals

positive integer

Number of arriving signals, specified as a positive integer. The number of signals must be smaller than the number of elements in the ULA array.

Example: 2

Data Types: double

scanangle — Broadside search angles

[-90:90] (default) | real-valued vector

Broadside search angles, specified as a real-valued vector. Angles must lie in the range (–90°,90°) and must be in increasing order.

Example: [-40:0.5:50]

Data Types: double

dist — Distance between array elements

0.5 (default) | real-valued positive scalar

Distance between array elements, specified as a real-valued positive scalar.

Example: 0.45

Data Types: double

Output Arguments

doas — Directions of arrival angles

real-valued vector

Directions of arrival angle, returned as a real-valued 1-by-D vector, where D is the number of arriving signals specified in nsig. Angle units are in degrees. Angle values lie in the range specified by scanangle.

spec — Spatial spectrum

positive real-valued vector

Spatial spectrum, returned as a positive real-valued vector. The dimension of spec equals the dimension of scanangle.

specang — Broadside angles of spectrum peaks

real-valued vector

Broadside angle of spectrum, returned as a real-valued vector. The dimension of specang equals the dimension of scanangle.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

Does not support variable-size inputs.

Version History

Introduced in R2016b