Effect of Rayleigh Fading on the Constellation Diagram of Binary ASK

In practical communication systems, direct line-of-sight (LOS) paths are often unavailable, causing the signal to undergo Rayleigh fading. This type of fading occurs due to multipath propagation, where the signal arrives at the receiver through multiple paths with varying delays and phases. While constellation diagrams are typically affected by AWGN (Additive White Gaussian Noise), they are also significantly influenced by multipath fading. Multipath can distort the signal constellation, leading to errors in symbol detection and affecting overall system performance. Techniques like equalization and diversity are commonly used to mitigate the impact of multipath fading in such systems

MATLAB Code for the Effect of Rayleigh Fading on the Constellation Diagram of Binary ASK

% The code is developed by SalimWireless.com
clc; clear; close all;
% Parameters
N = 10000;               % Number of symbols
SNR = 20;               % Signal-to-Noise Ratio in dB (for AWGN)
M = 2;                   % Modulation Order (2 for BPSK)
Fs = 100;                % Sampling frequency (not used directly, but for clarity)
L = 4;                   % Oversampling factor
Rayleigh_factor = 0.5;   % Rayleigh fading factor (scaling of fading)

% Generate random bits for BPSK
% BASK Mapping: 0 -> -1, 1 -> 1
data = randi([0 1], N, 1);
modData = data;    % Map 0 to 0, 1 to 1

% Upsample to simulate higher symbol rate
modData_upsampled = upsample(modData, L);

% Create Rayleigh fading channel (without division)
% Generate random complex Gaussian values for Rayleigh fading (in-phase and quadrature components)
rayleigh_fading = [0.8, 0.6, 0.3];  % No division by sqrt(2)

% Apply Rayleigh fading to the modulated signal
fadedSignal = modData_upsampled .* rayleigh_fading;

% Add AWGN (Noise)
noisySignal = awgn(fadedSignal, SNR, 'measured');

% Plot the constellation diagram
figure;
scatter(real(noisySignal), imag(noisySignal), '.');
title('Received Signal Constellation for BASK (Rayleigh Fading + AWGN)');
xlabel('In-Phase');
ylabel('Quadrature');
axis equal;
grid on;
web('https://www.salimwireless.com/search?q=fading', '-browser');

Output

If you change the number of multipaths to 1, or modify the code in line 20 from
rayleigh_fading = [0.8, 0.6, 0.3];
to
rayleigh_fading = [1];

(Rayleigh fading happens in environments where a direct line-of-sight (LOS) path is absent. For demonstration purposes, we simplify the model by using a channel coefficient $h = [1]$ , which represents a scenario without multipath fading.)

you will get the following output:

You can adjust the SNR value in the code to obtain a more accurate constellation diagram of Binary ASK.

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