MATLAB code for image transmission using BPSK

Question

Problem: when I enter this code in matlab, i face the following respond :

Requested 65536x65536 (32.0GB) array exceeds
maximum array size preference (5.0GB). This
might cause MATLAB to become unresponsive.

Can anybody please run the code for me and send me the results ?

I need to show the right graphical results of the code

I = imread('lena.jpg'); % Read the image file
I = rgb2gray(I); % Convert the image to grayscale
I = imresize(I, [256 256]); % Resize the image to 256x256 pixels
p = double(I(:)); % Convert the image to a vector of pixel values
% Modulation scheme
b = p > 128; % Convert the pixel values to bits using a threshold value
s = 2*b - 1; % Convert the bits to BPSK symbols
% Carrier frequency
fc = 10000; % Set the carrier frequency to 10 kHz
fs = 100000; % Set the sampling frequency to 100 kHz
t = (65535:length(s)-1)/fs; % Define the time vector
x = s .* cos(2pifc*t); % Multiply the modulated signal by a cosine wave
% Transmit filter
[b1, a1] = butter(4, 12000/(fs/2)); % Design a bandpass Butterworth filter of order 4 and cutoff frequency 12 kHz
xf = filter(b1, a1, x); % Apply the filter to the transmitted signal
% Channel model
sigma = 0.1; % Set the noise variance
n = sigma * randn(size(xf)); % Generate AWGN with zero mean and sigma variance
Omega = 1; % Set the channel scale parameter
h = sqrt(Omega/2) * (randn(size(xf)) + 1i*randn(size(xf))); % Generate Rayleigh fading with Omega scale parameter
y = h .* xf + n; % Multiply the filtered signal by the channel and add the noise
% Receive filter
[b2, a2] = butter(4, 12000/(fs/2)); % Design a bandpass Butterworth filter of order 4 and cutoff frequency 12 kHz
yf = filter(b2, a2, y);
% Demodulation scheme
yr = yf .* cos(2pifc*t); % Multiply the received signal by a cosine wave
[b3, a3] = butter(4, 1000/(fs/2), 'low'); % Design a lowpass Butterworth filter of order 4 and cutoff frequency 1 kHz
yrf = filter(b3, a3, yr); % Apply the filter to the demodulated signal
bhat = yrf > 0; % Convert the demodulated signal to bits using a threshold value
% Output image
phat = 255 * bhat; % Convert the bits to pixel values
phat = reshape(phat, [256 256]); % Reshape the vector to a matrix
Ihat = uint8(phat); % Convert the matrix to a grayscale image
% Graphical results
figure(1) % Create a figure window
subplot(2,2,1) % Create a subplot
imshow(I) % Display the input image
title('Input image') % Add a title
subplot(2,2,2) % Create another subplot
plot(t, abs(x)) % Plot the magnitude of the transmitted signal
xlabel('Time (s)') % Add an x-axis label
ylabel('Amplitude (V)') % Add a y-axis label
title('Transmitted signal') % Add a title
subplot(2,2,3) % Create another subplot
plot(t, abs(y)) % Plot the magnitude of the received signal
xlabel('Time (s)') % Add an x-axis label
ylabel('Amplitude (V)') % Add a y-axis label
title('Received signal') % Add a title
subplot(2,2,4) % Create another subplot
imshow(Ihat) % Display the output image
title('Output image') % Add a title

Answer 1

The demodulation scheme doesn't work.

Here is the result so far, corrected.

Check the line

h = sqrt(Omega/2) * (randn(size(xf)) + randn(size(xf)));

Which has no sense at all with imaginary terms passed through the filtering stages.

enter image description here

I = imread('soe.jpg'); % Read the image file
I = rgb2gray(I); % Convert the image to grayscale
I = imresize(I, [256 256]); % Resize the image to 256x256 pixels
p = double(I(:)); % Convert the image to a vector of pixel values
% Modulation scheme
b = p > 128; % Convert the pixel values to bits using a threshold value
s = 2*b - 1; % Convert the bits to BPSK symbols
% Carrier frequency
fc = 10000; % Set the carrier frequency to 10 kHz
fs = 100000; % Set the sampling frequency to 100 kHz
t = (1:length(s))'/fs; % Define the time vector
x = s.*cos(2*pi*fc*t); % Multiply the modulated signal by a cosine wave
% Transmit filter
[b1, a1] = butter(4, 12000/(fs/2)); % Design a bandpass Butterworth filter of order 4 and cutoff frequency 12 kHz
xf = filter(b1, a1, x); % Apply the filter to the transmitted signal
% Channel model
sigma = 0.1; % Set the noise variance
n = sigma * randn(size(xf)); % Generate AWGN with zero mean and sigma variance
Omega = 1; % Set the channel scale parameter
h = sqrt(Omega/2) * (randn(size(xf)) + randn(size(xf))); % Generate Rayleigh fading with Omega scale parameter
y = h .* xf + n; % Multiply the filtered signal by the channel and add the noise
% Receive filter
[b2, a2] = butter(4, 12000/(fs/2)); % Design a bandpass Butterworth filter of order 4 and cutoff frequency 12 kHz
yf = filter(b2, a2, y);
% Demodulation scheme
yr = yf.*cos(2*pi*fc*t); % Multiply the received signal by a cosine wave
[b3, a3] = butter(4, 1000/(fs/2), 'low'); % Design a lowpass Butterworth filter of order 4 and cutoff frequency 1 kHz
yrf = filter(b3, a3, yr); % Apply the filter to the demodulated signal
bhat = yrf > 0; % Convert the demodulated signal to bits using a threshold value
% Output image
phat = 255 * bhat; % Convert the bits to pixel values
phat = reshape(phat, [256 256]); % Reshape the vector to a matrix
Ihat = uint8(phat); % Convert the matrix to a grayscale image
% Graphical results
figure(1) % Create a figure window
subplot(2,2,1) % Create a subplot
imshow(I) % Display the input image
title('Input image') % Add a title
subplot(2,2,2) % Create another subplot
plot(t, abs(x)) % Plot the magnitude of the transmitted signal
xlabel('Time (s)') % Add an x-axis label
ylabel('Amplitude (V)') % Add a y-axis label
title('Transmitted signal') % Add a title
subplot(2,2,3) % Create another subplot
plot(t, abs(y)) % Plot the magnitude of the received signal
xlabel('Time (s)') % Add an x-axis label
ylabel('Amplitude (V)') % Add a y-axis label
title('Received signal') % Add a title
subplot(2,2,4) % Create another subplot
imshow(Ihat) % Display the output image
title('Output image') % Add a title