Experiment: Modeling and Simulation of a Multipath Fading Channel

Aim

This experiment uses MATLAB to model and simulate a

Multipath Fading Channel¹.

Theory

Multipath fading happens when a radio signal travels from a transmitter to a receiver via multiple paths, such as reflections from buildings, hills, or other objects²²²². As the signal paths change, their relative strengths and phases also change, which can cause the overall signal at the receiver to fluctuate³³³³.

This phenomenon can cause a variety of problems, including:

• Signal distortion ⁴

• Phase distortion ⁵

• Inter-symbol interference ⁶

Because of these potential issues, it's important to account for multipath fading when designing a radio communications system⁷⁷⁷⁷.

Processing a Fading Channel Signal in MATLAB

To process a signal using a fading channel, you follow these steps⁸:

1. Create a channel System object: This is a MATLAB variable that contains information about the channel, such as the maximum Doppler shift⁹.

2. Adjust properties: Modify the System object's properties as needed to model your specific channel¹⁰.

3. Apply the channel model: Call the System object like a function to generate random path gains and filter the input signal¹¹.

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Program

Matlab

% Rayleigh PDF

% Input section
N = 1000000; % Number of samples to generate
variance = 0.2; % Raleigh feeding envelope with the desired variance
x = randn(1, N);
y = randn(1, N);
r = sqrt(variance * (x.^2 + y.^2));

% Define bin steps and range for histogram plotting
step = 0.1;
range = 0:step:3;

% Get histogram values and approximate it to get the PDF curve
h = hist(r, range);
approxPDF = h / (step * sum(h));

% Simulation of PDF from the X and Y Samples
% Theoretical PDF from the Rayleigh fading equation
theoritical = (range / variance) .* exp(-range.^2 / (2 * variance));

% Plot the simulated and theoretical PDFs
plot(range, approxPDF, 'b', range, theoritical, 'r');
title('simulated and theoritical Rayleigh PDF from variance = 0.5');
legend('simulated PDF', 'Theoritical PDF');
xlabel('r...>');
ylabel('p(r)...>');
grid;

% PDF of phase of the Rayleigh envelope
theta = atan(y./x);
figure(2);
hist(theta); % Plot Histogram of the Phase

% Approximate the histogram of the phase part to a nice PDF curve
[counts, range] = hist(theta, 100);
step = range(2) * range(1);
approxPDF = counts / (step * sum(counts));

% Plot the simulated PDF from x and y samples
bar(range, approxPDF, 'b');
hold on;
plotHandle = plot(range, approxPDF, 'r');
set(plotHandle, 'Linewidth', 3.5);
axis([-2 2 0 max(approxPDF) + 0.2]);
hold off;
title('simulated PDF of phase of Rayleigh Distribution');
xlabel('theta...>');
ylabel('p(theta)...>');
grid;

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Procedure

1. Start the MATLAB program¹².

2. Open a new M-file¹³.

3. Type the program code¹⁴.

4. Save the file in the current directory¹⁵.

5. Compile and run the program¹⁶.

6. View the output in the command window or figure window¹⁷.

7. Stop the program¹⁸.

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Result

The experiment successfully modeled and simulated a Multipath Fading Channel using MATLAB¹⁹.