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System object: phased.RootWSFEstimator
Namespace: phased

Perform DOA estimation


ANG = step(H,X)



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 DOAs from X using the DOA estimator H. X is a matrix whose columns correspond to channels. ANG is a row vector of the estimated broadside angles (in degrees). You can specify the argument X as single or double precision.

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.


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.


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First, estimate the DOAs of two signals received by a standard 10-element ULA with element spacing of 1 meter. 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 −5° in elevation.

Create the signals with added noise. Then, create the ULA System object™.

fs = 8000;
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 = 150.0e6;
x = collectPlaneWave(array,[x1 x2],[10 20; 45 60]',fc);
noise = 0.1*(randn(size(x)) + 1i*randn(size(x)));

Construct WSF estimator System object.

estimator = phased.RootWSFEstimator('SensorArray',array, ...
    'OperatingFrequency',fc, ...

Estimate the DOAs.

doas = estimator(x + noise);
doas = broadside2az(sort(doas),[20 -5])
doas =

   10.0002   20.7934