MATLAB Code for Ergodic Capacity of Rayleigh Fading MIMO Channels

The following MATLAB code example demonstrates how to calculate the ergodic capacity of Rayleigh fading MIMO channels, providing both implementation details and conceptual understanding:

% Initialize system parameters

nT = 2; % Number of transmit antennas

nR = 2; % Number of receive antennas

nChannels = 1000; % Number of channel realizations for statistical analysis

% Generate Rayleigh fading channel realizations

% Complex Gaussian random variables with unit variance per dimension

H = (randn(nR, nT, nChannels) + 1i * randn(nR, nT, nChannels)) / sqrt(2);

% Calculate channel capacity for each realization

C = zeros(nChannels, 1); % Preallocate capacity array

for i = 1:nChannels

% Perform singular value decomposition (SVD) of channel matrix

[~, ~, V] = svd(H(:, :, i));

% Calculate capacity using water-filling principle (equal power allocation)

% Sum of log2(1 + eigenvalue) for parallel subchannels

C(i) = sum(log2(1 + diag(V).^2));

end

% Statistical analysis of capacity results

averageCapacity = mean(C); % Ergodic capacity estimate

maxCapacity = max(C); % Maximum instantaneous capacity

minCapacity = min(C); % Minimum instantaneous capacity

% Display performance metrics

disp(['Average Capacity: ', num2str(averageCapacity)]);

disp(['Maximum Capacity: ', num2str(maxCapacity)]);

disp(['Minimum Capacity: ', num2str(minCapacity)]);

This code implementation helps demonstrate key MIMO concepts including channel matrix decomposition, parallel subchannel capacity calculation, and statistical performance evaluation. The SVD operation diagonalizes the channel matrix to create independent parallel subchannels, while the capacity calculation follows Shannon's formula with eigenvalue-based power allocation.

We hope this code example assists in understanding Rayleigh fading MIMO channel ergodic capacity calculation and implementation techniques. Please feel free to ask if you have any technical questions about the algorithm or code implementation.