# derive AR model based on the autocorrelation of jakes model

I am trying to derive the channel model based on the autocorrelation of Jakes model. In step 2, i am trying to get rid of $s(n+1)$ by inserting it to $s(n-k)$ in which the limit will change. However i don't think step 2 makes since because the limits should be from $k=-1$ to $M$. However, if that is the case the final results will be different, i.e. we will not reach to step 7. Please take a look and tell me if the derivation is correct if not i would appreciate it if you can correct it.[![page for derivations][3]][3]