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Rayleigh vs Rician Fading

 

In Rayleigh fading, the channel coefficients tend to have a Rayleigh distribution, which is characterized by a random phase and magnitude with an exponential distribution. This means the magnitude of the channel coefficient follows an exponential distribution with a mean of 1.

In Rician fading, there is a dominant line-of-sight component in addition to the scattered components. The channel coefficients in Rician fading can indeed tend towards 1, especially when the line-of-sight component is strong. When the line-of-sight component dominates, the Rician fading channel behaves more deterministically, and the channel coefficients may tend towards the value of the line-of-sight component, which could be close to 1.

 

MATLAB Script

clc;
clear all;
close all;

% Define parameters
numSamples = 1000; % Number of samples
K_factor = 5; % K-factor for Rician fading
SNR_dB = 20; % Signal-to-noise ratio (in dB)

% Generate complex Gaussian random variable for Rayleigh fading channel
h_rayleigh = (randn(1, numSamples) + 1i * randn(1, numSamples)) / sqrt(2);

% Generate complex Gaussian random variable for line-of-sight component
h_los = sqrt(K_factor / (K_factor + 1));

% Generate noise
noisePower = 10^(-SNR_dB/10);
noise = sqrt(noisePower/2) * (randn(1, numSamples) + 1i * randn(1, numSamples));

% Combine Rayleigh and line-of-sight components for Rician fading channel
h_rician = h_los + sqrt(1 / (K_factor + 1)) * h_rayleigh;

% Add noise to the channel coefficients for Rayleigh fading channel
h_rayleigh_with_noise = h_rayleigh + noise;

% Add noise to the channel coefficients for Rician fading channel
h_rician_with_noise = h_rician + noise;

% Plot the channel coefficients
figure;
subplot(2,1,1);
plot(real(h_rayleigh_with_noise), imag(h_rayleigh_with_noise), 'b.');
hold on;
plot(real(h_rician_with_noise), imag(h_rician_with_noise), 'r.');
title('Channel Coefficients with Noise');
xlabel('Real');
ylabel('Imaginary');
axis equal;
legend('Rayleigh', 'Rician');
grid on;

subplot(2,1,2);
histogram(abs(h_rayleigh_with_noise), 'Normalization', 'probability', 'EdgeColor', 'b');
hold on;
histogram(abs(h_rician_with_noise), 'Normalization', 'probability', 'EdgeColor', 'r');
title('Magnitude Histogram');
xlabel('Magnitude');
ylabel('Probability');
legend('Rayleigh', 'Rician');
grid on;

 

Output

 

 
 
Fig 1: Rayleigh v/s Rician Fading


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