# MATLAB code to Generate Raleigh Random Variable

• neeraj.patel1
In summary, the conversation is about generating 100,000 pairs of uniform random variables in Matlab and finding the ratio of each pair. The suggested approach is to use the rand() command and the box muller method. The histogram function is also mentioned for plotting and comparing to the standard Cauchy density. The raylrnd function is mentioned as a possible alternative for generating random variables.
neeraj.patel1
What is the Matlab code for generating 100,000 Raleigh Random Variable with sigma^2=2 using rand command only. Generate histogram and normalize it by dividing 1,00,000 times the bin width

MATLAB code to find ratio of pair of uniform RV

## Homework Statement

Generate 100000 pairs of Uniform RV. Find ratio of each pair of RV.Plot histogram and compare to standard Cauchy density.

## Homework Equations

rand()
box muller
cauchy=1/pi*(1+x^2)
hist()

## The Attempt at a Solution

use box muller to generate rv

The MATLAB code for generating 100,000 Raleigh random variables with sigma^2=2 using the rand command would look something like this:

% Set sigma^2 value
sigma = 2;

% Generate 100,000 random numbers using the rand command
r = sqrt(-2*sigma^2*log(1-rand(1,100000)));

% Plot histogram and normalize it
histogram(r, 'Normalization', 'probability');

% Calculate bin width
bin_width = (max(r)-min(r))/sqrt(length(r));

% Normalize histogram by dividing by 100,000 times the bin width
histogram(r, 'Normalization', 'probability', 'BinWidth', bin_width/100000);

This code first sets the sigma^2 value and then uses the rand command to generate 100,000 random numbers. The Raleigh random variable is calculated using the formula r = sqrt(-2*sigma^2*log(1-rand(1,100000))). Then a histogram is plotted and normalized using the probability option. Finally, the bin width is calculated and the histogram is normalized again by dividing by 100,000 times the bin width to ensure that the histogram is properly normalized. This code can be modified to generate any number of Raleigh random variables with different sigma^2 values.

## 1. What is a Raleigh random variable?

A Raleigh random variable is a continuous probability distribution that is used to model the magnitude of a wave when there is a line-of-sight path between the transmitter and receiver. It is commonly used in wireless communications and radar systems.

## 2. How is a Raleigh random variable generated in MATLAB?

A Raleigh random variable can be generated in MATLAB using the "raylrnd" function, which takes in the scale parameter as input. The scale parameter determines the shape of the distribution and can be adjusted to fit the specific needs of the application.

## 3. What is the difference between a Raleigh random variable and a normal random variable?

A Raleigh random variable is different from a normal random variable in that it has a non-zero minimum value and a longer tail on the right side of the distribution. This makes it a more suitable model for situations where there may be a line-of-sight path between the transmitter and receiver, as it allows for the possibility of large values.

## 4. How can I plot a histogram of a set of Raleigh random variables in MATLAB?

To plot a histogram of Raleigh random variables in MATLAB, you can use the "histogram" function and pass in the array of random variables as the input. You can also specify the number of bins and adjust the appearance of the histogram as needed.

## 5. Can a Raleigh random variable be used for applications other than wireless communications?

Yes, a Raleigh random variable can be used in other applications such as modeling wind speeds, acoustic signals, and earthquake magnitudes. It can also be used in statistical analysis and Monte Carlo simulations.

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