Gaussian and Laplacian noise of a signal

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James Hayek
James Hayek 2015-7-26
I have no idea how to start this problem...
I am looking to generate a baseband transmission scheme that is made of binary rectangular pulses. The transmitted signal is contaminated by additive noise.
By using mean and variance estimators I am to determine the mean and variance using the generated noise with no signal transmitted.
At that point, I look to subtract the estimated mean from the signal yielding a fairly clean signal.
Using that signal I have to use a "detector" (not sure of what this is referring to) to decide whether a 0 or 1 was transmitted. Then compare the received string and transmitted string to determine the number of errors and the average probability of error.
I was told I needed to learn how to generate a Gaussian random variable. After following some examples I have this: (Please advise me if it does not pertain to a solution of problem I mentioned above)
close all
clc
%%Generation of a signal bpsk modulation
%This takes a set of random numbers and converts them to bits 0's & 1's
%The 2*X-1 will create -1's in place of the 0's from the bit conversion.
signal_i = 2*(rand(1,10^5)>0.5)-1;
signal_q = zeros(1,10^5);
%In communication systems we have two components
%which is why we have singal i and q
scatterplot(signal_i + signal_q);
%%Combining for complex representation
signal = complex(signal_i, signal_q);
p_signal = mean(abs(signal).^2)
e_signal = (abs(signal).^2);
%%Adding some noise of a known variance
for var = 1/50:1/10:0.5
noise = 1/sqrt(2)*(randn(1,10^5)+j*randn(1,10^5))*sqrt(var);
addNoise = signal + noise;
figure(1);
plot(real(addNoise),imag(addNoise),'b*');
drawnow('expose');
end
In the end, I will need to transmit the sequence using two cases with parameters, one Gaussian noise and the other Laplacian.
I was given the sequences of: Equal probabilities: 10001011000111101001 Unequal probabilities: 11001111011011101101
Am I on the right track with the current code vs project requirements? If not, where shall I start?
Thanks in advance.

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