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I'm struggling with this because I don't fully understand it.

My goal is to estimate a received signal that is transmitted through a channel that follow a stochastic process. My doubt is, if the PDF and its parameters that describes the behaviour of this channel is known, how can I generate the H matrix to estimate the received signal later. In my case, the channel follows a Log-Normal distribution.

$$ y \left( t \right) = x \left( t \right) * h + n \left( t \right) \tag{1} $$

I hope someone can help me a little.

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  • $\begingroup$ Your question is a bit unclear and broad. I believe you should narrow it down to something more specific because as it is written now it kind of asks to describe the content of at least half a textbook on the topic (or even more than a single textbook). You could describe what is that you don’t understand. How to add the noise, how to perform convolution, how to use the PDF of the channel, etc. $\endgroup$
    – ZaellixA
    Feb 5 at 14:11
  • $\begingroup$ Sure, I'm sorry. I'm not understand how to use the PDF of the channel in order tu calculate the H matrix and calculate the received signal. If I know that the channel follows a certain probability distribution, should I calculate the H matrix with the variance? Also another thing is that, for example, if I calculate the power received with the Friis formula, the geometrical losses are present. But in this case, if I calculate either a '1' or a '0' signal with the information of the channel, I don't have this losses in someway? $\endgroup$
    – ThGeng32
    Feb 5 at 16:11
  • $\begingroup$ I believe you should explain a bit more about what is that you don’t understand, but do it in the question body. This information is crucial for people to be able to help you and does not belong in comments. Furthermore, I think you should add some more information about your approach. The equation you provided does not say much, it applies equally well to both stochastic and deterministic signals/systems. So, what are your signal and noise assumptions, do you have any expectations, do you know anything about the variables, etc.? $\endgroup$
    – ZaellixA
    Feb 5 at 17:23
  • $\begingroup$ I'd suggest spending some time with a good, accessible textbook, like any of Haykin's books on wireless. $\endgroup$
    – MBaz
    Feb 5 at 19:17
  • $\begingroup$ When you say PDF of channel, what do you mean? PDF of channel noise is a Gaussian function as per your definition (AWGN). Channel ISI (h) is independent of this noise PDF. Or may be I am misinterpreting your question. $\endgroup$
    – Srini
    Feb 6 at 22:50

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