MATLAB: How to construct a vector of complex numbers whose absolute value is not above 1

Question

I want to add complex noise to my signal but the absolute value of my signal + added complex noise has to be equal to or smaller than 1.

Answer 1

You can generate a vector of complex number where the maximum absolute value is always 1:

 C = rand(1,10) + 1i*rand(1,10);
 C = C/max(abs(X(:)));

If you are not happy that the maximum value is always 1, subtract a random complex number:

 C = C - rand - 1i*rand;