'one vector slides on the other'. This is basically convolution, and since you are finding a mean it is convolution with a vector of ones, of length constant/2. Since the code is not iterative, all the means can be found first.
N = 10000;
constant = 5000;
phi_orig = rand(1,N)+i*rand(1,N);
phi = phi_orig;
for m = 1:length(phi) - (constant)/2
phi(m) = phi(m).*(mean(conj(phi(1+m:(constant)/2+m))));
phi2 = phi_orig;
c2 = constant/2;
A = conv(phi2,ones(1,c2),'valid')/c2;
A(1) = ;
sA = length(A);
phi2(1:sA) = phi2(1:sA).*conj(A);
d = max(abs(phi2-phi))
In your code I used length(phi) rather than size(phi,1) so that phi could be either a row vector or a column vector.