minimum variance distortionless response

anyone can help me why my code for mvdr error ?, the step of mvdr alghorithm:

s1 : compute the estimated covariance matrix Rxx of the incident signal vector x(n)

Rxx= E(x(n) . x(n)^H) =1/N. x(n). x(n)^H

signal modeled S = [s1, s2, ....., sm]^T

noise modeled No =[no1, no2, ..... uoL]^T

steering vector modeled A=[a(theta 1), a(theta 2),....,a(theta m)

a(theta m)= formula in the figure

the value of am is the angle at which the mic will be placed changing every experiment, one experiment will be placed at an angle (0,20,40,60,80,90,100,120,140,160,180,200, 220,240,260,270,300,320,340,360).

bm value obtained 10.2 degrees

s2 : Calculate the inverse matrix of the covariance matrix Rxx (Rxx-1)

s3: generate steering vector a(theta) as Equation for an angle theta.

s4 : Calculate the signal spectrum P(mvdr) for each value of theta from 0 to 360 degrees with the equation

Pmvdr (theta) 1/ a^H(theta) . Rxx^-1 . a(theta)

s5 : Determine the direction of arrival of the signal arrival direction obtained when the value of Pmvdr(theta) is maximal (or locally maximal if there are multiple sources).

s6: calculate the SNR value from the results to determine whether the SNR is high or low with the formula SNR = 10 .log 10 (S/N)

s7= calculate the MSE result from the results to find out whether the MSE is close to 0 or not MSE formula = ∑upper limit N and lower limit t=1 . (At-Ft)^2 /n

if what is processed by mvdr is in the form of sound samples obtained from 4 mic arrays

with the position of mic 1 at 0 degrees, mic 2 at 90 degrees, mic 3 at 270 degrees and mic 4 at 180 the sound will be in the form of 4 wav files to be processed, with lambda 0.5, Fs = 44100. from the step above, the correct MVDR matlab code will be made.

the incoming signal in the form of S will experience a phase difference so as to form a steering vector A and get additional noise with E{S.N^H}=10 in general the data model can be presented as follows x= AS+No

clear; clc; close all;

% Parameters

N = 4; % Number of microphone elements

d = 0.5; % Distance between microphone elements (in lambda)

theta = [90]; % Actual DoA angle (in degrees)

angles = 70:1:110; % Range of angles to estimate

Fs = 44100; % Sampling frequency

% Read .wav files from 4 microphones (ensure file paths are correct)

wavFiles = {'D:\MVDR\90\mic1.wav', 'D:\MVDR\90\mic2.wav', ...

'D:\MVDR\90\mic3.wav', 'D:\MVDR\90\mic4.wav'};

wavData = cell(1, N);

% Read sound data from each microphone

for i = 1:N

[data, Fs] = audioread(wavFiles{i});

wavData{i} = data;

end

% Determine the minimum signal length for alignment

signal_length = min(cellfun(@length, wavData));

for i = 1:N

wavData{i} = wavData{i}(1:signal_length); % Truncate to minimum length

end

% Combine data from all microphones

X_signal = zeros(N, signal_length);

for i = 1:N

X_signal(i, :) = wavData{i}.';

end

% Estimate the power of the original signal

signal_power = sum(abs(X_signal(:)).^2) / numel(X_signal);

% Set random seed for noise consistency

rng(42); % Set random generator seed

% Add noise to the signal

noise_level = 0.01; % Noise level relative to the signal

X_noise = noise_level * (randn(size(X_signal)) + 1j * randn(size(X_signal)));

X = X_signal + X_noise; % Received signal

% Calculate the actual SNR

noise_actual_power = sum(abs(X_noise(:)).^2) / numel(X_noise);

SNR_actual_dB = 10 * log10(signal_power / noise_actual_power);

% Calculate MSE

MSE = sum(abs(X(:) - X_signal(:)).^2) / numel(X_signal);

% Display SNR and MSE

disp(['Actual SNR: ', num2str(SNR_actual_dB), ' dB']);

disp(['MSE: ', num2str(MSE)]);

% Estimate the covariance matrix

R_xx = (1 / N) * (X * X'); % Covariance matrix of the input

% Compute the MVDR spectrum

P_mvdr = zeros(1, length(angles)); % Initialize MVDR spectrum

for i = 1:length(angles)

theta_angle = angles(i); % Angle being tested

% Steering vector a(theta) for angle theta

a_theta = exp(1j * 2 * pi * d * (0:N-1).' * sin(deg2rad(theta_angle)));

% Compute MVDR response

P_mvdr(i) = 1 / (a_theta' * (R_xx \ a_theta));

end

% Convert to dB

P_mvdr_dB = 10 * log10(abs(P_mvdr) / max(abs(P_mvdr)));

% Plot the sound signals from each microphone

figure;

for i = 1:N

subplot(N+1, 1, i);

t_wav = (1:signal_length) / Fs;

plot(t_wav, real(wavData{i}));

xlabel('Time (s)');

ylabel(['Mic ', num2str(i)]);

title(['Original Sound Signal - Microphone ', num2str(i)]);

grid on;

end

% Plot MVDR spectrum for estimated angles

subplot(N+1, 1, N+1);

plot(angles, P_mvdr_dB, 'LineWidth', 2);

xlabel('Angle (\theta) [degrees]');

ylabel('MVDR Spectrum (dB)');

title('Direction of Arrival Estimation Using MVDR');

grid on;

% Find the angle with the maximum power

[~, idx_max] = max(P_mvdr_dB);

theta_estimated = angles(idx_max);

disp(['Detected strongest source angle: ', num2str(theta_estimated), ' degrees']);

hold on;

plot(theta_estimated, P_mvdr_dB(idx_max), 'ro', 'MarkerFaceColor','r');

legend('MVDR Spectrum', ['Peak at \theta = ', num2str(theta_estimated), '°']);

% Plot with peak marker

figure;

plot(angles, P_mvdr_dB, 'LineWidth', 2);

hold on;

plot([theta_estimated, theta_estimated], ylim, '--r', 'LineWidth', 1.5); % Vertical line at peak detection

plot(theta_estimated, P_mvdr_dB(idx_max), 'ro', 'MarkerFaceColor','r'); % Point marker at peak detection

xlabel('Angle (\theta) [degrees]');

ylabel('MVDR Spectrum (dB)');

title('Direction of Arrival Estimation Using MVDR');

grid on;

legend('MVDR Spectrum', ['Peak at \theta = ', num2str(theta_estimated), '°']);

[salwa]