MATLAB Code for Rank and Condition Number of a Channel Matrix

To assess the signal strengths of various multipaths between TX and RX and enable communication, the rank and condition numbers of a channel matrix are highly helpful characteristics. Signal multipath propagation is a typical occurrence in wireless communication. Phases shift and the signal weakens during this process. We are discussing signal phases in this context. When numerous multipaths arrive at the receiver, the resulting signal may be additive or destructive because of phase alterations. A channel matrix is referred to as a sparse matrix if it only has a few stronger elements and the majority of the other elements are zero.

Finding rank and condition number for sparse matrices is important for numerous reasons. That topic has already been covered in another article [click here]. We will just talk about the corresponding MATLAB codes here.

MATLAB Code for Rank and Condition Number of a Channel Matrix

%Author: Salim Wireless For study materials on wireless %communication, go to www.salimwireless.com. %or, if you want to learn MATLAB coding clc; clear; close all; %H=load('H.mat'); % load the genrated data file containing the channel %matrix informations / elements H=[0 0 1; 0 1 0; 0 2 0]; % The code below returns the H matrix's singular values. singular_values = svd(H); % Calculate the condition number of the channel matrix H cnH = max(singular_values)/min(singular_values); % Convert the condition number from linear scale to dB scale cnH_dB = 10*log10(cnH); % Calculate the rank of the matrix H rankH = rank(H,max(singular_values)/1e3);

 In the above code, it processes the rank and condition number for the channel matrix,

H = [0 0 1; 0 1 0; 0 2 0];

Output

Rank of the Channel Matrix = 2

Therefore, only two simultaneous data streams can be operational at once between this 3X3 MIMO systems. For the sake of a short illustration, we also assumed the channel matrix element values.

Before running this code, it is always preferable to generate the channel matrix, which is usually a complex matrix. Then load the "H.mat" file or channel matrix file as shown in the code above.