System object: phased.FrostBeamformer
Perform Frost beamforming
Y = step(H,X)
Y = step(H,X,XT)
Y = step(H,X,ANG)
Y = step(H,X,XT,ANG)
[Y,W] = step(___)
Note: H specifies the System object™ on which to run this step method.
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.
Input signal, specified as an M-by-N matrix. M must be larger than the FIR filter length specified in the FilterLength property. N is the number of elements in the sensor array.
Training samples, specified as an M-by-N matrix. M and N are the same as the dimensions of X.
Beamforming directions, specified as a length-2 column vector. The vector has the form [AzimuthAngle; ElevationAngle], in degrees. The azimuth angle must be between –180 and 180 degrees, and the elevation angle must be between –90 and 90 degrees.
Beamformed output. Y is a column vector of length M, where M is the number of rows in X.
Beamforming weights. W is a column vector of length L, where L is the degrees of freedom of the beamformer. For a Frost beamformer, H, L is given by getNumElements(H.SensorArray)*H.FilterLength.
Apply a Frost beamformer to an 11-element array. The incident angle of the signal is –50 degrees in azimuth and 30 degrees in elevation.
% Signal simulation ha = phased.ULA('NumElements',11,'ElementSpacing',0.04); ha.Element.FrequencyRange = [20 20000]; fs = 8e3; t = 0:1/fs:0.3; x = chirp(t,0,1,500); c = 340; % Wave propagation speed (m/s) hc = phased.WidebandCollector('Sensor',ha,... 'PropagationSpeed',c,'SampleRate',fs,... 'ModulatedInput',false); incidentAngle = [-50; 30]; x = step(hc,x.',incidentAngle); noise = 0.2*randn(size(x)); rx = x+noise; % Beamforming hbf = phased.FrostBeamformer('SensorArray',ha,... 'PropagationSpeed',c,'SampleRate',fs,... 'Direction',incidentAngle,'FilterLength',5); y = step(hbf,rx);
phased.FrostBeamformer uses a beamforming algorithm proposed by Frost. It can be considered the time-domain counterpart of the minimum variance distortionless response (MVDR) beamformer. The algorithm does the following:
Steers the array to the beamforming direction.
Applies an FIR filter to the output of each sensor to achieve the distortionless response constraint. The filter is specific to each sensor.
For further details, see .
 Frost, O. "An Algorithm For Linearly Constrained Adaptive Array Processing", Proceedings of the IEEE. Vol. 60, Number 8, August, 1972, pp. 926–935.
 Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002.