How to model airborne sound channel
Well, your channel model might give you an explicit PDF, but:

You need to realize that a channel is not a scalar, ie. your PDF doesn't describe a random variable $\in \mathbb C$ or $\in \mathbb R$, but usually something like an impulse response, that is, something like a function of delay (so, your random variable is $\in \mathbb R \times \mathbb R$ or $\in \mathbb C \times \mathbb R$).

I'm not an acoustics guy myself, but if I've learned one thing it's that at least for indoor acoustics, the "flat channel assumption" (that lets us wireless communication folks model channels as simple complex number) doesn't hold, and that your channel is very frequency-selective. Often, it's time-variant, and sometimes even non-linear.

So, I'm not quite sure what to recommend here:


If you're looking for soft decision in wireless communications, I personally think that Proakis is quite OK. That's one of the standard digital communications textbooks.
That's up to your channel model, and you'll have to specify that.
An AWGN channel is certainly not an adequate approximation of an audio channel.