The channel matrix in wireless communication is a matrix that describes the impact of the channel on the transmitted signal. The channel matrix can be used to model the effects of the atmospheric or underwater environment on the signal, such as the absorption, reflection or scattering of the signal by surrounding objects.
When addressing multi-antenna communication, the term "channel matrix" is used. Let's assume that only one TX and one RX are in communication and there's no surrounding object. Here, in our case, we can apply the proper threshold condition to a received signal and get the original transmitted signal at the RX side. However, in real-world situations, we see signal path blockage, reflections, etc., (NLOS paths [↗]) more frequently. The obstruction is typically caused by building walls, etc.
Multi-antenna communication was introduced to address this issue. It makes diversity approaches possible, greatly increasing the likelihood of the signal being received.
Let me show an example to describe the channel matrix. Assume that the TX and RX communication antennas each have two antenna elements. T1, T2, and R1, R2 are the corresponding TX and RX MIMO antennas.
The complex channel gain between T1 and R1, T1 and R2, T2 and R1, and T2 and R2 is represented by the channel matrix, H.
In a channel matrix, for example, the elements h11 and h21 each represent the complex channel gain between R1 and T1 antennas, R2 and T1 antennas, and so on.
Example of a 4 X 16 Channel Matrix:
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The sample shown above is a 4 x 16 channel matrix demonstration. In this illustration, there are 16 TX antennas and 4 Rx antennas. We diagonalize the channel matrix to allow communication between T1 and R1, T2 and R2, and so on, in order to enable practical MIMO antenna communication. Interference is any signal that is received at R1 from T2, T3, and so on, etc. By diagonalizing data, it is possible to minimize signal interference between many simultaneous data streams.
What is rank of a channel matrix?
The rank of the channel matrix is evolving into a crucial wireless communication parameter as we move steadily toward MIMO and higher frequency transmission. The number of the stronger independent data streams that can travel between the TX and RX in MIMO communication is indicated by the rank of the channel matrix.
Procedure of finding rank of channel matrix in MATLAB [click here]
Python code to find rank of a matrix [click here]
What is condition number of a channel matrix:
We can determine the strength of a channel matrix's maximum singular value by comparing it to its lowest singular value using the condition number.
MATLAB code to find condition number of a channel matrix. [go]