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System object: phased.RootMUSICEstimator
Package: phased

Perform DOA estimation


ANG = step(H,X)
ANG = step(H,X,ElAng)


    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.

ANG = step(H,X) estimates the direction of arrivals (DOA's) from a signal X using the DOA estimator H. X is a matrix whose columns correspond to the signal channels. ANG is a row vector of the estimated broadside angles (in degrees).

The size of the first dimension of this input matrix can vary to simulate a changing signal length, such as a pulse waveform with variable pulse repetition frequency.

ANG = step(H,X,ElAng) specifies, in addition, the assumed elevation angles of the signals. This syntax is only applicable when the SensorArray property of the object specifies a uniform circular array (UCA). ElAng is a scalar between -90° and 90° and is applied to all signals. The elevation angles for all signals must be the same as required by the phase mode excitation algorithm.

    Note:   The object performs an initialization the first time the step method 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.


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Estimate the DOA's of two signals received by a standard 10-element uniform linear array (ULA) having an element spacing of 1 meter. The antenna operating frequency is 150 MHz. The actual direction of the first signal is 10 degrees in azimuth and 20 degrees in elevation. The direction of the second signal is 45 degrees in azimuth and 60 degrees in elevation.

fs = 8000;
t = (0:1/fs:1).';
x1 = cos(2*pi*t*300);
x2 = cos(2*pi*t*400);
sULA = phased.ULA('NumElements',10,...
sULA.Element.FrequencyRange = [100e6 300e6];
fc = 150e6;
x = collectPlaneWave(sULA,[x1 x2],[10 20;45 60]',fc);
rng default;
noise = 0.1/sqrt(2)*(randn(size(x))+1i*randn(size(x)));
sDOA = phased.RootMUSICEstimator('SensorArray',sULA,...
doas = step(sDOA,x + noise);
az = broadside2az(sort(doas),[20 60])
az =

   10.0001   45.0107

Using the root-MUSIC algorithm, estimate the azimuth angle of arrival of two signals received by a 15-element UCA having a 1.5 meter radius. The antenna operating frequency is 150 MHz. The actual direction of arrival of the first signal is 10 degrees in azimuth and 4 degrees in elevation. The direction of arrival of the second signal is 45 degrees in azimuth and -2 degrees in elevation. In estimating the directions of arrival, assume the signals arrive from 0 degrees elevation.

Set the frequencies of the signals to 500 and 600 Hz. Set the sample rate to 8 kHz and the operating frequency to 150 MHz. Then, create the baseband signals, the UCA array and the plane wave signals.

fs = 8000;
fc = 150e6;
t = (0:1/fs:1).';
x1 = cos(2*pi*t*500);
x2 = cos(2*pi*t*600);
sUCA = phased.UCA('NumElements',15,...
x = collectPlaneWave(sUCA,[x1 x2],[10 4; 45 -2]',fc);

Add random complex gaussian white noise to the signals.

rs = RandStream('mt19937ar','Seed',0);
noise = 0.1/sqrt(2)*(randn(rs,size(x))+1i*randn(rs,size(x)));

Create the phased.RootMUSICEstimator System object

sDOA = phased.RootMUSICEstimator('SensorArray',sUCA,...

Solve for the azimuth angles for zero degrees elevation.

elang = 0;
doas = step(sDOA, x + noise, elang);
az = sort(doas)
az =

    9.9815   44.9986

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