You forgot to attach the .mat files so we can't do much. The first row of the val matrix stored in the mat file is extracted and put into a variable you cryptically call "d". We don't know what that first row means and so we can't "explain" it. All we can tell is that the first row of val from A is stored in a row vector "d" and then you're transposing it and putting it into column vector d_T, and you're then getting the third row of the val matrix from a different mat file and calling that noise, and also transposing that row vector into a column vector called "noisy_sig_T".
Can't you ask the people who created the mat file? If you don't even know what it means, then why do you want to do anything with it? Where did you get that script, or did you write it?