Hello Ahmed M. Alfadhel ,

This can be a typical channel modelling question. As you know, there are many simplified and complicate way for modelling a MIMO channel, which includes at least two examples, depending the systems, channels, band class, your needs and targets, etc. One simple approach is to model each TX-RX channel response as a Gaussian random variable.

In realities or in the industry, because MIMO technology has been intensively studied and adopted in 3GPP, a widely adopted approach is to model MIMO channel according to 3GPP specification for mobile communication channels.

[ Spatial channel model for Multiple Input Multiple Output (MIMO) simulations]

https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=1382

which can also be extended for other systems and channels as well.

Cheers

HI Ahmed M. Alfadhel

Watch this video, it might help you

https://freevideolectures.com/course/4936/nptel-estimation-wireless-communications-mimo-ofdm-cellular-sensor-networks-course-sponsored-aricent/20

There isn't the best way to learn constructing the H matrix that fits all types of channels. There are some common ways to do it. The best way completely depends on the channel type.

One largely adopted approach is to put "pilots" to transmitted signals which are known both to TX and RX. Since RX knows when (and what frequency) TX transmits this pilot, it multiplies it with the same value (or sequence) to find out the correlation. With the help of estimated noise, RX estimates h value for single-channel between TX antenna and RX antenna. Several channel estimation algorithms are available to calculate H, using the pilot and estimated noise. An example is MMSE. In the case of MIMO, this becomes a matrix, say H. Here is a video for MMSE for MIMO DL channels:

https://www.youtube.com/watch?v=SmEvWZPMJko

Hope that helps.

Thanks Shu Wang , Vinod B Durdi , and Yavuz Yaman for your answers they helped me.

Please note the following analogy.

The point is how to put the model of the

channel let us say system equations in

state space representation.

An example to do this for a 2 by 2 system

is in my book

American University Laboratories for Electrical Engineering (part 2)

The elements of the H matrix can i.i.d Gaussian, each with independent real and imaginary parts with means zero, and variance 1/2