Index exceeds the number of array elements. Index must not exceed 512.

Hi! I have a problem while generating a OFDM signal in 512 points. The program works fine using OFDM in 1024 points, but when I change the parameters I get this error and I can't figure out where is the problem.

The error is: Index exceeds the number of array elements. Index must not exceed 512.

Error in Rx (line 18)

x_demod = QAM_demodulation(x_time_domain(1:modulation_length),M);

Error in main (line 45)

[x_Rx, x_before_demodulation] = Rx(M, L, y_Tx1, y_Tx2, x_QAM_modulated, h1, h2, fft_size);

Code is the following:

main.m:

close all;
%% SIMO (Single Input Multiple Output) 
% Paramters
%-------------------------------
% For M = 64 ---> N_bits = 3504 
% For M = 16 ---> N_bits = 2336 
%-------------------------------
N_bits = 2336; 
M = 16;
fft_size = 1024;
frames_num = 25;
ofdm_synbols_per_frame = 25;
channel_type = "Multipath";

Eb_No = -20:3:20;
Eb = 2*(M-1)/(3*log2(M)); 
No_vect = Eb./(10.^(Eb_No/10));
Pe_vect = zeros(1,length(Eb_No));

for i = 1:length(Eb_No)
  Pe_avg_frames_per_frame = 0;
  
  for k = 1:frames_num
    
    if channel_type == "Multipath"
        L = 50;
        h1 = (1/sqrt(2*L))*(randn(1,L)+1i*randn(1,L));
        h2 = (1/sqrt(2*L))*(randn(1,L)+1i*randn(1,L));
    elseif channel_type == "AWGN"
        L = 1;
        h1 = 1;
        h2 = 1;
    end
    
    count_err_per_ofdm_symbol = 0;
    count_err_per_frame = 0;
    for j = 1:ofdm_synbols_per_frame
        % Generate seq
        x = randi([0 1],1,N_bits);
        
        % Tx (Channel encoding, QAM modulation, OFDM)
        [y_Tx1, y_Tx2, x_QAM_modulated] = Tx(x, M, N_bits, L, No_vect(i), h1, h2, fft_size);
        
        % Rx (OFDM, QAM demodulation, Channel decoding)
        [x_Rx, x_before_demodulation] = Rx(M, L, y_Tx1, y_Tx2, x_QAM_modulated, h1, h2, fft_size);
        
        % Calc BER
        count_err_per_ofdm_symbol = biterr(x,x_Rx);

        % Average BER per run
        count_err_per_frame = count_err_per_frame + count_err_per_ofdm_symbol;
        
    end
    
    Pe_avg_frames_per_frame = Pe_avg_frames_per_frame + count_err_per_frame/(N_bits*ofdm_synbols_per_frame);
  end

  Pe_vect(i) = Pe_avg_frames_per_frame;

end

figure()
plot(real([y_Tx1, y_Tx2, x_QAM_modulated])); xlabel('Time'); ylabel('Amplitude');
title('OFDM Signal');grid on;

figure()
plot(real([x_Rx, x_before_demodulation])); xlabel('Time'); ylabel('Amplitude');
title('OFDM Signal AFTER');grid on;

%% plot
figure
semilogy(Eb_No,Pe_vect);
title('BER vs Eb/No ' + channel_type + ' for ' + M + ' QAM');

xlabel('Eb/No (dB)');
ylabel('BER (dB)');

numerrs = biterr(x,x_Rx) 

channel_encoding.m:

function x_encoded = channel_encoding(x,N_bits)
%Hamming Coding (Channel Encoding)
x_encoded = zeros(1,N_bits*(7/4)); % Output after encoding
d1 = [1;0;0;0]; % index of first element of 4 bits encoding
d2 = [0;1;0;0];
d3 = [0;0;1;0];
d4 = [0;0;0;1];
p1 = [0;1;1;1]; % First parity of encoding p1 = d2+d3+d4
p2 = [1;0;1;1];
p3 = [1;1;0;1];
G = [p1 p2 p3 d1 d2 d3 d4]; % Generator Matrix of Hamming(4,7) 
k = 1;
for i = 1:4:N_bits
    x_encoded(k:k+6) = mod(x(i:3+i)*G,2);
    k = k+7;
    
end

end

Channeldecoding.m:

function x_decoded = Channeldecoding(x_demod)
p1 = [0;1;1;1]; % First parity of encoding p1 = d2+d3+d4
p2 = [1;0;1;1];
p3 = [1;1;0;1];
H = [eye(3) [p1' ;p2' ;p3']];
k = 1;

err_values = [0 0 0 0 0 0 0; 0 0 0 0 0 0 1;0 0 0 0 0 1 0;0 0 0 0 1 0 0;0 0 0 1 0 0 0;0 0 1 0 0 0 0;0 1 0 0 0 0 0;1 0 0 0 0 0 0];
syndroms = [0; 7; 6; 5; 3; 1; 2; 4];


for i = 1:7:length(x_demod)
    s = mod(x_demod(i:i+6)*H',2);
    s_dec = bin2dec(strjoin(string(s),''));

   index = syndroms==s_dec;

    
   
    err = err_values(index,:);
    %x_hat = bitxor(x_demod(i:i+6),err);
    x_hat = mod(err + x_demod(i:i+6),2);
    x_decoded(k:k+3) = x_hat(4:7);
    
    k = k+4;
end

end

QAM_modulation.m:

function x_QAM_modulated = QAM_modulation(x_encoded, M)
    x_encoded = string(x_encoded);
    M=log2(M);

    greycode = generate_grey_code(M/2);

    if mod(length(x_encoded),M) ~= 0
       x_encoded = [x_encoded zeros(1, M - mod(length(x_encoded),M))];  
    end
    
    x_QAM_modulated = zeros(1,length(x_encoded)/M);

    AMi_vector = zeros(1, length(greycode));
    AMq_vector = zeros(1, length(greycode));

    for m = 1 : length(greycode)
        AMi_vector(m) = 2*m - 1 - length(greycode);
    end

    AMq_vector = AMi_vector;
    AMi_vector;

    
    k=1;
    for i = 1:length(x_QAM_modulated)
        sequence=x_encoded(k:k-1+M);
        sequence_even=sequence(1:length(sequence)/2);
        sequence_odd=sequence((length(sequence)/2)+1:length(sequence));

        sequence_even = strjoin(sequence_even,"");
        sequence_odd = strjoin(sequence_odd,"");

        index_even = find (greycode == sequence_even);
        index_odd = find (greycode == sequence_odd);

        AMi = AMi_vector(index_even);
        AMq = AMq_vector(index_odd);

        x_QAM_modulated(i) = AMi + AMq*j;

        k = k + M;
    end

QAM_demodulation.m

function x_QAM_demodulated = QAM_demodulation(x_QAM_modulated, M)
    M=log2(M);
    
   greycode = generate_grey_code(M/2);

    
    x_QAM_demodulated = strings(1,length(x_QAM_modulated));

    AMi_vector = zeros(1, length(greycode));

    for m = 1 : length(greycode)
        AMi_vector(m) = 2*m - 1 - length(greycode);
    end        
    
    for i = 1:length(x_QAM_demodulated)
        qam_element = x_QAM_modulated(i);
        inphase_value = real(qam_element);
        quadrature_value = imag(qam_element);
        
        % get minmum error
        minimm_vector_even = abs(inphase_value - AMi_vector);
        index_even = find(minimm_vector_even == min(minimm_vector_even));
        if length(index_even) >1
            index_even = index_even(1);
        end
        
        minimm_vector_odd = abs(quadrature_value - AMi_vector);
        index_odd = find(minimm_vector_odd == min(minimm_vector_odd));
        if length(index_odd) > 1
            index_odd = index_odd(1);
        end
        sequence = strjoin(greycode(index_even) + greycode(index_odd));
        x_QAM_demodulated(i) = sequence;

    end
    x_QAM_demodulated = strjoin(x_QAM_demodulated,"");
    x_QAM_demodulated = str2num(strjoin(split(x_QAM_demodulated,""),","));
    
    

Tx.m:

function [y_Tx1 ,y_Tx2, x_QAM_modulated] = Tx(x, M, N_bits, L, No_vect, h1, h2, fft_size)
    % Hamming Coding (Channel Encoding)
    x_encoded = channel_encoding(x,N_bits);

    % Modulation
    x_QAM_modulated = QAM_modulation(x_encoded, M);
    % IFFT 
    x_QAM_modulated = sqrt(fft_size).*x_QAM_modulated;
    x_ifft = ifft(x_QAM_modulated,fft_size);

    %Cyclic prefix
    x_ifft = [x_ifft(length(x_ifft)-L+1+1:length(x_ifft)) x_ifft];

    % channel effect
    noise = sqrt(No_vect/2).*randn(1,(length(x_ifft) + length(h1)-1));
    
    y_Tx1 = conv(x_ifft,h1) + noise;
    noise = sqrt(No_vect/2).*randn(1,(length(x_ifft) + length(h2)-1));
    y_Tx2 = conv(x_ifft,h2) + noise;

Rx.m:

    function [x_Rx, x_time_domain] = Rx(M, L, y_Tx1, y_Tx2, x_QAM_modulated, h1, h2,fft_size)
    % Check which channel has bigger energy (smaller effect on signal)
    % To equalize (remove channel effect) its recived signal 
    % And remove cyclic prefix
    if norm(h1) > norm(h2)
        y1 = y_Tx1(L:fft_size+L-1);
        y1 = y1./sqrt(fft_size);
        x_time_domain = fft(y1)./fft([h1 zeros(1,length(y1)-length(h1))]);
    else
        y2 = y_Tx2(L:fft_size+L-1);
        y2 = y2./sqrt(fft_size);
        x_time_domain = fft(y2)./fft([h2 zeros(1,length(y2)-length(h2))]);
    end


    % Demodulation
    modulation_length = length(x_QAM_modulated);
    x_demod = QAM_demodulation(x_time_domain(1:modulation_length),M);

    % Channel Decoding
    x_Rx = Channeldecoding(x_demod);
    

syndrom_table.m:

function err = syndrom_table(s)
s_dec = bin2dec(strjoin(string(s),''));
err_values = [0 0 0 0 0 0 0; 0 0 0 0 0 0 1;0 0 0 0 0 1 0;0 0 0 0 1 0 0;0 0 0 1 0 0 0;0 0 1 0 0 0 0;0 1 0 0 0 0 0;1 0 0 0 0 0 0];
syndroms = [0; 7; 6; 5; 3; 1; 2; 4];
i = find(syndroms==s_dec);
err = err_values(i,:);
end

generate_grey_code.m:

function grey_code = generate_grey_code(n)
    arr = strings(1,2);
    
    arr(1) = '0';
    arr(2) = '1';
    
    i=2;
    j=0;
    
   
    while(i < 2^n)
        start = i-1;
        step = -1;
        N= length(arr);
        start+step*(0:N-1);
        for j = start+step*(0:N-1)
            arr = [arr arr(j+1)];
        end    
        
        for j = linspace(1,i,i)
            arr(j) = "0" + arr(j);
        end
        
        for j = linspace(i,(2*i)-1,i)
            arr(j+1) = "1" + arr(j+1);
        end
        
        i = bitshift(i,1);
    end      
  
    grey_code = arr;
 

Answer 1

[Sulaymon Eshkabilov]

It is easier to check the syntaxes if these function files are put into one M-file and executed as whole one file (in my opinion). If you do so, everything works ok. I have made a few syntax changes by closing functions.

close all;
%% SIMO (Single Input Multiple Output) 
% Paramters
%-------------------------------
% For M = 64 ---> N_bits = 3504 
% For M = 16 ---> N_bits = 2336 
%-------------------------------
N_bits = 2336; 
M = 16;
fft_size = 1024;
frames_num = 25;
ofdm_synbols_per_frame = 25;
channel_type = "Multipath";

Eb_No = -20:3:20;
Eb = 2*(M-1)/(3*log2(M)); 
No_vect = Eb./(10.^(Eb_No/10));
Pe_vect = zeros(1,length(Eb_No));

for i = 1:length(Eb_No)
  Pe_avg_frames_per_frame = 0;
  
  for k = 1:frames_num
    
    if channel_type == "Multipath"
        L = 50;
        h1 = (1/sqrt(2*L))*(randn(1,L)+1i*randn(1,L));
        h2 = (1/sqrt(2*L))*(randn(1,L)+1i*randn(1,L));
    elseif channel_type == "AWGN"
        L = 1;
        h1 = 1;
        h2 = 1;
    end
    
    count_err_per_ofdm_symbol = 0;
    count_err_per_frame = 0;
    for j = 1:ofdm_synbols_per_frame
        % Generate seq
        x = randi([0 1],1,N_bits);
        
        % Tx (Channel encoding, QAM modulation, OFDM)
        [y_Tx1, y_Tx2, x_QAM_modulated] = Tx(x, M, N_bits, L, No_vect(i), h1, h2, fft_size);
        
        % Rx (OFDM, QAM demodulation, Channel decoding)
        [x_Rx, x_before_demodulation] = Rx(M, L, y_Tx1, y_Tx2, x_QAM_modulated, h1, h2, fft_size);
        
        % Calc BER
        count_err_per_ofdm_symbol = biterr(x,x_Rx);

        % Average BER per run
        count_err_per_frame = count_err_per_frame + count_err_per_ofdm_symbol;
        
    end
    
    Pe_avg_frames_per_frame = Pe_avg_frames_per_frame + count_err_per_frame/(N_bits*ofdm_synbols_per_frame);
  end

  Pe_vect(i) = Pe_avg_frames_per_frame;

end

figure()
plot(real([y_Tx1, y_Tx2, x_QAM_modulated])); xlabel('Time'); ylabel('Amplitude');
title('OFDM Signal');grid on;

figure()
plot(real([x_Rx, x_before_demodulation])); xlabel('Time'); ylabel('Amplitude');
title('OFDM Signal AFTER');grid on;

% plot
figure
semilogy(Eb_No,Pe_vect);
title('BER vs Eb/No ' + channel_type + ' for ' + M + ' QAM');

xlabel('Eb/No (dB)');
ylabel('BER (dB)');

numerrs = biterr(x,x_Rx) 
function x_encoded = channel_encoding(x,N_bits)
%Hamming Coding (Channel Encoding)
x_encoded = zeros(1,N_bits*(7/4)); % Output after encoding
d1 = [1;0;0;0]; % index of first element of 4 bits encoding
d2 = [0;1;0;0];
d3 = [0;0;1;0];
d4 = [0;0;0;1];
p1 = [0;1;1;1]; % First parity of encoding p1 = d2+d3+d4
p2 = [1;0;1;1];
p3 = [1;1;0;1];
G = [p1 p2 p3 d1 d2 d3 d4]; % Generator Matrix of Hamming(4,7) 
k = 1;
for i = 1:4:N_bits
    x_encoded(k:k+6) = mod(x(i:3+i)*G,2);
    k = k+7;
    
end

end
function x_decoded = Channeldecoding(x_demod)
p1 = [0;1;1;1]; % First parity of encoding p1 = d2+d3+d4
p2 = [1;0;1;1];
p3 = [1;1;0;1];
H = [eye(3) [p1' ;p2' ;p3']];
k = 1;

err_values = [0 0 0 0 0 0 0; 0 0 0 0 0 0 1;0 0 0 0 0 1 0;0 0 0 0 1 0 0;0 0 0 1 0 0 0;0 0 1 0 0 0 0;0 1 0 0 0 0 0;1 0 0 0 0 0 0];
syndroms = [0; 7; 6; 5; 3; 1; 2; 4];


for i = 1:7:length(x_demod)
    s = mod(x_demod(i:i+6)*H',2);
    s_dec = bin2dec(strjoin(string(s),''));

   index = syndroms==s_dec;

    
   
    err = err_values(index,:);
    %x_hat = bitxor(x_demod(i:i+6),err);
    x_hat = mod(err + x_demod(i:i+6),2);
    x_decoded(k:k+3) = x_hat(4:7);
    
    k = k+4;
end

end
function x_QAM_modulated = QAM_modulation(x_encoded, M)
    x_encoded = string(x_encoded);
    M=log2(M);

    greycode = generate_grey_code(M/2);

    if mod(length(x_encoded),M) ~= 0
       x_encoded = [x_encoded zeros(1, M - mod(length(x_encoded),M))];  
    end
    
    x_QAM_modulated = zeros(1,length(x_encoded)/M);

    AMi_vector = zeros(1, length(greycode));
    AMq_vector = zeros(1, length(greycode));

    for m = 1 : length(greycode)
        AMi_vector(m) = 2*m - 1 - length(greycode);
    end

    AMq_vector = AMi_vector;
    AMi_vector;

    
    k=1;
    for i = 1:length(x_QAM_modulated)
        sequence=x_encoded(k:k-1+M);
        sequence_even=sequence(1:length(sequence)/2);
        sequence_odd=sequence((length(sequence)/2)+1:length(sequence));

        sequence_even = strjoin(sequence_even,"");
        sequence_odd = strjoin(sequence_odd,"");

        index_even = find (greycode == sequence_even);
        index_odd = find (greycode == sequence_odd);

        AMi = AMi_vector(index_even);
        AMq = AMq_vector(index_odd);

        x_QAM_modulated(i) = AMi + AMq*j;

        k = k + M;
    end
end
function x_QAM_demodulated = QAM_demodulation(x_QAM_modulated, M)
    M=log2(M);
    
   greycode = generate_grey_code(M/2);

    
    x_QAM_demodulated = strings(1,length(x_QAM_modulated));

    AMi_vector = zeros(1, length(greycode));

    for m = 1 : length(greycode)
        AMi_vector(m) = 2*m - 1 - length(greycode);
    end        
    
    for i = 1:length(x_QAM_demodulated)
        qam_element = x_QAM_modulated(i);
        inphase_value = real(qam_element);
        quadrature_value = imag(qam_element);
        
        % get minmum error
        minimm_vector_even = abs(inphase_value - AMi_vector);
        index_even = find(minimm_vector_even == min(minimm_vector_even));
        if length(index_even) >1
            index_even = index_even(1);
        end
        
        minimm_vector_odd = abs(quadrature_value - AMi_vector);
        index_odd = find(minimm_vector_odd == min(minimm_vector_odd));
        if length(index_odd) > 1
            index_odd = index_odd(1);
        end
        sequence = strjoin(greycode(index_even) + greycode(index_odd));
        x_QAM_demodulated(i) = sequence;

    end
    x_QAM_demodulated = strjoin(x_QAM_demodulated,"");
    x_QAM_demodulated = str2num(strjoin(split(x_QAM_demodulated,""),","));
end   
    function [y_Tx1 ,y_Tx2, x_QAM_modulated] = Tx(x, M, N_bits, L, No_vect, h1, h2, fft_size)
    % Hamming Coding (Channel Encoding)
    x_encoded = channel_encoding(x,N_bits);

    % Modulation
    x_QAM_modulated = QAM_modulation(x_encoded, M);
    % IFFT 
    x_QAM_modulated = sqrt(fft_size).*x_QAM_modulated;
    x_ifft = ifft(x_QAM_modulated,fft_size);

    %Cyclic prefix
    x_ifft = [x_ifft(length(x_ifft)-L+1+1:length(x_ifft)) x_ifft];

    % channel effect
    noise = sqrt(No_vect/2).*randn(1,(length(x_ifft) + length(h1)-1));
    
    y_Tx1 = conv(x_ifft,h1) + noise;
    noise = sqrt(No_vect/2).*randn(1,(length(x_ifft) + length(h2)-1));
    y_Tx2 = conv(x_ifft,h2) + noise;
    end
        function [x_Rx, x_time_domain] = Rx(M, L, y_Tx1, y_Tx2, x_QAM_modulated, h1, h2,fft_size)
    % Check which channel has bigger energy (smaller effect on signal)
    % To equalize (remove channel effect) its recived signal 
    % And remove cyclic prefix
    if norm(h1) > norm(h2)
        y1 = y_Tx1(L:fft_size+L-1);
        y1 = y1./sqrt(fft_size);
        x_time_domain = fft(y1)./fft([h1 zeros(1,length(y1)-length(h1))]);
    else
        y2 = y_Tx2(L:fft_size+L-1);
        y2 = y2./sqrt(fft_size);
        x_time_domain = fft(y2)./fft([h2 zeros(1,length(y2)-length(h2))]);
    end


    % Demodulation
    modulation_length = length(x_QAM_modulated);
    x_demod = QAM_demodulation(x_time_domain(1:modulation_length),M);

    % Channel Decoding
    x_Rx = Channeldecoding(x_demod);
        end
        function err = syndrom_table(s)
s_dec = bin2dec(strjoin(string(s),''));
err_values = [0 0 0 0 0 0 0; 0 0 0 0 0 0 1;0 0 0 0 0 1 0;0 0 0 0 1 0 0;0 0 0 1 0 0 0;0 0 1 0 0 0 0;0 1 0 0 0 0 0;1 0 0 0 0 0 0];
syndroms = [0; 7; 6; 5; 3; 1; 2; 4];
i = find(syndroms==s_dec);
err = err_values(i,:);
        end
function grey_code = generate_grey_code(n)
    arr = strings(1,2);
    
    arr(1) = '0';
    arr(2) = '1';
    
    i=2;
    j=0;
    
   
    while(i < 2^n)
        start = i-1;
        step = -1;
        N= length(arr);
        start+step*(0:N-1);
        for j = start+step*(0:N-1)
            arr = [arr arr(j+1)];
        end    
        
        for j = linspace(1,i,i)
            arr(j) = "0" + arr(j);
        end
        
        for j = linspace(i,(2*i)-1,i)
            arr(j+1) = "1" + arr(j+1);
        end
        
        i = bitshift(i,1);
    end      
  
    grey_code = arr;
 
end

[Puscas Daniel]

I know it works with fft_size of 1024 but when I try to change that value to 512 it gives me this error:

Index exceeds the number of array elements. Index must not exceed 512.

Error in untitled>Rx (line 207)

x_demod = QAM_demodulation(x_time_domain(1:modulation_length),M);

Error in untitled (line 43)

[x_Rx, x_before_demodulation] = Rx(M, L, y_Tx1, y_Tx2, x_QAM_modulated, h1, h2, fft_size);