% Task 1.1
clc;
clear all;
close all;
EbN0 = linspace(-5,10,16);
%EbN0 = linspace(10^(-0.5),10,16);% from -5 to 10 dB.
Pe = qfunc(sqrt(2 * 10.^(EbN0/10)));
semilogy(EbN0,Pe)
xlabel('$\displaystyle\frac{E_b}{N_0}$ [dB]','interpreter','latex');
ylabel("Pe");
hold on
%% Task 1.2

mu = 0;
Error = zeros(1,16); % Vector where we count number of bit errors
%Pe = zeros(1,16);
for i = 1:16 % We want to loop for each SNR N times
    SNR = 10.^(EbN0(i)/10);
    N0 = 1/SNR;
    sigma = sqrt(N0/2);
    for N = 1:100000
        s = randi([-1 1]); % We transmit 1 or -1.
        while s == 0
            s = randi([-1 1],1);
        end

        noise = normrnd(mu,sigma);
        x = s + noise; % We add noise and receive x.

        if(sign(x) ~= sign(s)) %If true we recieved wrong.
            Error(i) = Error(i) + 1;
        end

    end
    Pe1(i) = Error(i)/100000;
end
semilogy(EbN0,Pe1)
ylim([10^(-4) 1]);
legend("Exact","Experimentally")