MATLAB, Laplacian Distribution, binary Transmission System Part A Please Transfo

Question

MATLAB, Laplacian Distribution, binary Transmission System

Part A Please

Transformation Method is shown below

4. Simulation of binary transmission systems A binary transmission system sends a "O" bit using a -2 voltage signal and a "l" bit by transmitting a +2. The received signal is corrupted by noise N that has a Laplacian distribution with parameter . Assume that "0" and "1" bits are equiprobable. (a) Write a MATLAB program to generate Laplacian distribution with parameter 2.0.5 respectively. Use the transformation method (refer to Selection 4.9 in textbook) based on t 10000 samples of the unit-interval uniform random variable Plot the resulting Laplacian cdf and pdf in each case (b) Assume the received signal Y is given by Y = X + N. Suppose that the receiver decides a "0" was sent f Y 0. Write a MATLAB program to simulate the transmission of 10,000 bits under the SNR -0dB for this channel and compute the empirical error probability. (c) Derive analytically the expression for the error probability under SNR How does the analysis compare to your simulation from part (b)? 0dB For the above, SNR denotes the Signal-to-Noise Ratio and SNR(dB)-10log10(). You need to express the standard deviation of Laplacian distribution in terms of its parameter o

Explanation / Answer

Program for laplacian PDF:

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clf; %clears previous plot, if any
N=1000; %number of samples
U=rand(N); %generates uniformly distributed random samples
mu=2; %mu parameter
beta=0.5; %beta parameter
X=mu-beta*log(2*beta*U); %generating random variables as per pdf
hold on;
plot(X,U); %plot of pdf
xlabel("X");
ylabel("U");
title("PDF plot")
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Program for Laplacian CDF:

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clf; %clears previous plot, if any
N=1000; %number of samples
U=rand(N); %generates uniformly distributed random samples
mu=2; %mu parameter
beta=0.5; %beta parameter
X = mu - beta*sign(U) .* log(1-2*abs(U)); %generating random variables as per cdf
hold on;
plot(X,U); %plot of cdf
xlabel("X");
ylabel("U");
title("CDF plot");

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