write a code to do 3d beamforming in the y direction in matlab

To perform 3D beamforming in the y-direction in MATLAB, you can follow these steps:

  1. Define the parameters of the beamforming algorithm, such as the number of sources, number of microphones, and the distance between them.
main.m
numSources = 3;      % number of sources
numMics = 4;         % number of microphones
micSpacing = 0.1;    % distance between microphones (in meters)
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  1. Create a grid in the y-direction representing the space where the sources can be located. Define the range of the grid based on the desired coverage.
main.m
yGrid = -1:0.1:1;   % grid in the y-direction (from -1 to 1 with a step size of 0.1)
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  1. Generate the steering matrix that represents the phase shifts required for beamforming at different angles in the y-direction.
main.m
angleGrid = linspace(-pi/2, pi/2, length(yGrid));   % angles from -pi/2 to pi/2
steeringMatrix = exp(1j*2*pi*micSpacing*sin(angleGrid(:))*(0:numMics-1));
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  1. Generate the received signal at each microphone by simulating the sources and the propagation through free space.
main.m
sourcePositions = zeros(numSources, 3);   % source positions in 3D space
sourcePositions(:, 2) = [0.5, -0.4, 0.8]; % positions along the y-direction

receivedSignal = zeros(length(yGrid), numMics);   % received signal at each microphone

for s = 1:numSources
    distance = sqrt((sourcePositions(s, 1) - micSpacing*(0:numMics-1)).^2 ...
        + (sourcePositions(s, 2)).^2 + (sourcePositions(s, 3)).^2);
    receivedSignal = receivedSignal + exp(1j*2*pi*distance) * randn(1);
end
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  1. Apply the beamforming algorithm to estimate the direction of arrival (DOA) of the sources in the y-direction.
main.m
estimatedDOA = abs(steeringMatrix' * receivedSignal);
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By following these steps, you can implement a 3D beamforming algorithm in MATLAB to estimate the direction of arrival of sources in the y-direction.

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