As we know that Zadoff-Chu matrix is similar to Walsh-Hadamard matrix where every columns in those matrices is orthogonal with the any other column.
For Walsh-Hadmard matrix, the orthogonality is clear and can be demonstrated easily. But regarding the Zadoff-Chu matrix, I don't see that orthogonality is right as shown below:
a = (sqrt(2) + 1j*sqrt(2))/2; W = [a 1 a -1; -1 a 1 a ; a -1 a 1; 1 a -1 a]; %%Zadoff-Chu matrix C1 = W(:,1); %% Take the first column orth_results = ; for j = 1 : size(W,2) results = (abs(sum(W(:,j).*C1)).^2); %Project the first column to every column in matrix W orth_results = [orth_results results]; end
Following the condition of orthogonality between columns,
orth_results should be equals to 0 except in the fist value, but what I get is
orth_results = [8.0000 0 8.0000 0];
What's the problem of that? Is there any issue in the matrix itself ?