# How to model airborne sound channel

I'm making a soft demodulation/decoding to communicate a microphone and a speaker in short range. I have to calculate the LLR using my constellation and the airborne sound channel probability density function (pdf). I have searched a lot about airborne sound or acoustic channel model, and I just found out some considerations about the attenuation depending on the frequency. My questions are:

2. If I use a pdf estimator of the channel, how can I use the estimation to find the LLR of my received symbols?
3. Can I use another model to aproximate the airborne acoustic channel (it could be related to AWGN), or which book can I read to learn about how to model a communication channel?
• there is indoor and outdoor and the term short range is not very specific. – user28715 Jan 27 '18 at 22:55
• I'm working on indoor environments and short range refers to distances from 0.25m - 2m. – Titan Jan 28 '18 at 20:04
• is there a reason why you don’t use wire? – user28715 Jan 29 '18 at 15:52
• I'm using the wireless scenario to benchmark how soft modulations perform in airborne acoustic channel and then use the results for future communication systems on this kind of environment that i want to implement. – Titan Jan 29 '18 at 20:26

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 $\in \mathbb C \times \mathbb R$).