iaadoa

Estimate direction of signal arrival

Since R2024a

Syntax

ang = iaadoa(X,elempos)

[ang,spec,azimuthspecang,elevationspecang] = iaadoa(X,elempos)

[___] = iaadoa(X,elempos,'NumSignals',nsig)

[___] = iaadoa(X,elempos,'AzimuthScanAngles',azimuthscanang)

[___] = iaadoa(X,elempos,'ElevationScanAngles',elevationscanang)

[___] = iaadoa(X,elempos,...,'NumIterations',niter)

[___] = iaadoa(X,elempos,...,'Tolerance',tol)

Description

ang = iaadoa(X,elempos) returns the estimated direction of arrival, ang, of the signal X at element positions elempos. The function uses the Iterative Adaptive Approach (IAA) algorithm,

[ang,spec,azimuthspecang,elevationspecang] = iaadoa(X,elempos) also returns the spatial power spectrum spec and the corresponding scan angles azimuthspecang along the azimuth direction and elevationspecang along the elevation direction.

[___] = iaadoa(X,elempos,'NumSignals',nsig) also returns the nsig largest peaks of the spatial power spectrum.

[___] = iaadoa(X,elempos,'AzimuthScanAngles',azimuthscanang) searches the azimuth scan angles azimuthscanang and returns the nsig angles corresponding to the highest peaks in the spatial power spectrum the search region.

[___] = iaadoa(X,elempos,'ElevationScanAngles',elevationscanang) searches the elevation scan angles elevationscanang and returns the nsig angles corresponding to the highest peaks in the spatial power spectrum in the search region.

[___] = iaadoa(X,elempos,...,'NumIterations',niter) returns the spatial power spectrum and directions of arrival after a maximum of niter iterations. In cases where any other stopping criteria are not met, the algorithm terminates after the maximum number of iterations.

[___] = iaadoa(X,elempos,...,'Tolerance',tol) returns the spatial power spectrum and directions of arrival, taking into account the specified stop criteria, tol. The 'Tolerance' Name-value pair sets the criteria for stopping, determined by the relative difference between the estimated spectrum of the current iteration and that of the previous iteration.

Examples

Direction of Arrival of Signals at ULA

Calculate the directions of arrival of four uncorrelated signals impinging on a 20-element ULA with half-wavelength spacing. Assume the signals are coming from azimuth 0, -25, 45, and 60 degrees, respectively. The noise is white across all elements and the SNR is 10 dB.

Set up array element positions.

N = 20;
d = 0.5; 
elementPos = (0:N-1)*d;

Set up signal directions.

angles = [0 -25 45 60];
Nsig = 4;

Create single snapshot of received signal.

[x,xcov] = sensorsig(elementPos,1,angles,db2pow(-10));
doas = iaadoa(x,elementPos,'NumSignals',Nsig);
disp(doas)

     0    45   -25    60
     0     0     0     0

Plot IAA Magnitude Spectrum

Calculate the directions of arrival of four uncorrelated signals impinging on a 20-element ULA with half-wavelength spacing. Assume the signals are coming from azimuth 0, -25, 45, and 60 degrees, respectively. The noise is white across all elements and the SNR is 10 dB.

Set up array element positions.

N = 20;
d = 0.5; 
elementPos = (0:N-1)*d;

Set up signal directions.

angles = [0 -25 45 60];
Nsig = 4;

Create single snapshot of received signal.

[x,xcov] = sensorsig(elementPos,1,angles,db2pow(-10));
[doa,spec,specang] = iaadoa(x,elementPos,'NumSignals',Nsig);

Plot spectrum.

plot(specang,10*log10(spec))
xlabel('Broadside Angles (degrees)')
ylabel('Magnitude Spectrum (dB)')
title('IAA Spatial Spectrum')

Plot Power Spectrum of 10-by-10 URA

Calculate the directions of arrival of 2 uncorrelated signals impinging on a 10-by-10 URA with half-wavelength spacing. Assume the signals are coming from azimuth -37, and 17 degrees, and elevation 0, and 20 degrees, respectively. The noise is white across all elements and the SNR is 10 dB.

N = 10; % Elements in array
d = 0.5; % sensor spacing half wavelength
array = phased.URA(N); % generate 2D URA
doa1 = [-37;0];
doa2 = [17;20];
elementPos = getElementPosition(array);
Nsig = 2;

Generate 10 snapshots of received single.

x = sensorsig(elementPos,10,[doa1,doa2],db2pow(-10));

Solve for the directions of arrival.

[doas,spec,azimuthSpecAng,elevationSpecAng] = iaadoa(x,elementPos, ...
    "AzimuthScanAngles", -60:60, ...
    "ElevationScanAngles", -60:60, 'NumSignals',Nsig);
imagesc(azimuthSpecAng,elevationSpecAng,spec)
xlabel('Azimuth (degrees)')
ylabel('Elevation (degrees)')
title('IAA Spatial Spectrum')
axis equal
axis tight

Input Arguments

X — Received signal

N_s-by-N complex-valued matrix

Received signal, specified as an N_s-by-N complex-valued matrix representing N_s snapshots of a signal at the N-elements of a sensor array.

Data Types: single | double
Complex Number Support: Yes

elempos — Array sensor element positions

real-valued 1-by-N vector | 2-by-N real-valued matrix | 3-by-N real-valued matrix

Array sensor element positions, specified as a real-valued 1-by-N vector, a real-valued 2-by-N matrix, or a real-valued 3-by-N matrix where N is the number of elements in the sensor array.

• A 1-by-N vector represents the y-coordinates of the elements of a linear array along the yaxis.

• A 2-by-N matrix represents an array lying in the yz-plane. Each column of elempos represents the [y;z] coordinates of an array element.

• A 3-by-N matrix represents an array of arbitrary shape. A each column of elempos represents the [x;y;z] coordinates of an array element.

Units are wavelength.

Data Types: single | double

nsig — Number of largest peaks of spatial power spectrum

1 (default) | positive integer

Number of largest peaks to find of the spatial power spectrum, specified as a positive integer. nsig must be less than the number of array elements N. Use this argument with the 'NumSignals' Name-value pair.

Example: 5

Data Types: single | double

azimuthscanang — Azimuth scan angles

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

Azimuth scan angles, specified as a real-valued row vector. Azimuth scan angles must lie in the range [-180,180]. The nsig peaks of the power spectrum are located at the angles azimuthspecang. Use this argument with the 'AzimuthScanAngles' Name-value pair.

Example: [0:20]

Data Types: single | double

elevationscanang — Elevation scan angles

0 (default) | real-valued row vector

Elevation scan angles, specified as a real-valued row vector. Elevation scan angles must lie in the range [-90,90]. The nsig peaks of the power spectrum are located at the angles elevationspecang. Use this argument with the 'ElevationScanAngles' Name-value pair.

Example: [-40:40]

Data Types: single | double

niter — Maximum number of iterations

15 (default) | positive integer

Maximum number of iterations, specified as a positive integer. Computation stops when number of iterations reaches the maximum number. When other stopping criteria are not met, the algorithm will terminate after niter iterations.

Example: 10

Data Types: single | double

tol — Tolerance

1e-2 (default) | positive scalar in the range (0,1]

Tolerance, specified as a positive scalar in the range (0,1]. Use this argument with the 'Tolerance' Name-value pair to set the criteria for stopping, determined by the relative difference between the estimated spectrum of the current iteration and the previous iteration. Use this argument with the 'Tolerance' Name-value pair.

Example: 1e-3

Data Types: single | double

Output Arguments

ang — Estimated signal direction angles

2-row real-valued matrix

Estimated signal direction angles, returned as a 2-row real-valued matrix where the first row represents the estimated azimuth angles and the second row represents the estimated elevation angle. Units are in degrees.

Data Types: single | double

spec — Spatial power spectrum

real-valued row vector

Spatial power spectrum, returned as a row vector.

Data Types: single | double

azimuthspecang — Azimuth spec angles

real-valued row vector

Azimuth spec angles, returned as a row vector.

Data Types: single | double

elevationspecang — Elevation spec angles

row vector

Elevation spec angles, returned as a row vector.

Data Types: single | double

References

[1] Tarik Yardibi, Jian Li, Petre Stoica, Ming Xue and Arthur B. Baggeroer, "Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares", IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, No. 1, pp. 425-443, Jan. 2010.

[2] Yanqin Xu, Xiaoling Zhang, Shunjun Wei, Jun Shi, Xu Zhan, and Tianwen Zhang, "3D Super-resolution Imaging Method for Distributed Millimeter-wave Automotive Radar Systems". arXiv:2209. 11037, 2022.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2024a