# Received signal from channel model

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.

• 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. Feb 5 at 14:11
• 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? Feb 5 at 16:11
• I'd suggest spending some time with a good, accessible textbook, like any of Haykin's books on wireless.
– MBaz
Feb 5 at 19:17
• 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. Feb 6 at 22:50