What is the PDF of the sum of L, i.i.d, non-central chi-square random variables.
The PDF of the non-central chi-square is:
fX(x)= ((1+k)*exp(-k))/(m) *exo(-(1+k)*x/(m)) * I_0(2*sqrt(k*x*(1+k)/m)).
where m is the average value of x, k is the LOS component.
I took the equation from "Digital communication over fading channel" book.