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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:

  1. Wich book can I read, so i can learn more about soft demodulation examples: BPSK, QPSK, QAM, FSK?
  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?
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    $\begingroup$ there is indoor and outdoor and the term short range is not very specific. $\endgroup$ – Stanley Pawlukiewicz Jan 27 '18 at 22:55
  • $\begingroup$ I'm working on indoor environments and short range refers to distances from 0.25m - 2m. $\endgroup$ – Titan Jan 28 '18 at 20:04
  • $\begingroup$ is there a reason why you don’t use wire? $\endgroup$ – Stanley Pawlukiewicz Jan 29 '18 at 15:52
  • $\begingroup$ 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. $\endgroup$ – Titan Jan 29 '18 at 20:26
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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:

  1. 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.
  2. That's up to your channel model, and you'll have to specify that.
  3. An AWGN channel is certainly not an adequate approximation of an audio channel.
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