Deciding how many averages are sufficient

Hi,

I am performing the following operations:

All vectors have the same length.

Step 1. Define a vector of constants X
Step 2. Create a vector Z = X + Noise, where Noise is AWGN of N~(, )
Step 3. Compute C

Steps 2-3 must be repeated such that a good average of C is obtained.

As you can see, the value of C will be slightly different each time due to the noise. My question is what theory can I use to determine how many averages of C are enough? (ergo, I can't just take 10 million averages simply because it 'sounds' big enough :o).

I am keen to hear your suggestions.

Thanks.