Hi everyone,

I am trying to derive the error performance of a wireless communications system, and I run into a series of Independent and Identically Distributed (i.i.d.) random variables (RVs) as follows:

Z = X_1 + X_2 + ... + X_N,

where N denotes the number of RVs being summed together. The distribution of each X_1, .., X_N may be Rayleigh, Rice, etc.

Now, I know that the Central Limit Theorem (CLT) can be applied assuming high N, such that the mean of Z becomes:

E[Z] = N*E[X_N],

and the variance of Z becomes:

Var[Z] = N*Var[X_N].

However, in my case, N is not high enough to use CLT. In fact, I am working with N values in the set N = {2, 3, 4, 5, 6, 7, 8, 9, 10}.

So my question is, if I am given the CDF (denoted by F_N(t)) and PDF (denoted by f_N(t)) of each X_1, ..., X_N, how do I evaluate the mean and variance of Z? Do you use some sort of convolution property, or something else?

Any help would be appreciated.

Thank you.