The channel which is rich in multipath in your case is h(n) = [h1 ... hN] with N channel taps. In the case of rayleigh fading each tap follows a complex gaussian distrbution.
So, if you receive
y(n) = conv(s,h);
Note that h is a different realisation of a complex Gaussian at each transmission block.
Same goes for Rician but the taps follow a Rician distribution.