%%%Practica 2
Nb=100;
SNR=10;
R=1;
T=1/R;
F=10;
Nm=Nb*F;
fm=F*R;
Tm=1/fm;
%%2.2.Transmisor
%1
b=rand(1,Nb)>0.5;
figure, hold on;
plot(b); %plot(t,b,'o');

%2
t=Tm:Tm:Nb;
%3
%a0=1 y a1=-1 ya que la periodo del pulso mostrado en la teoria es 1
a0=1;
a1=-1;
d_s0_s1=a0-a1;
p_a0=0.5;
p_a1=0.5;
Es_teorica=p_a0*a0^2+p_a1*a1^2;
Ps_teorica=Es_teorica/T;
%4
a=rand(1,Nb);
for i=1:Nb
    if(b(1,i)==0)
        a(1,i)=a0;
    else
        a(1,i)=a1;
    end
end
%5
BPSK=1-2*b;
up_BPSK=zeros(1,Nm);
up_BPSK(1:F:end)=BPSK;
phi_tx = ones(1,F);
s=conv(up_BPSK, phi_tx);
s=s(1:Nm);
figure, hold on;
plot(t,s);
%6
Es=p_a0*a0^2+p_a1*a1^2;
Ps=Es/T;
%%2.3. Canal AWGN
%1
X=(3-4*sqrt(2)):(3+4*sqrt(2));
Y1=(exp(-(X-3).^2/(2*2)))/(sqrt(2*pi)*sqrt(2));
Y2 = normpdf(X,3,sqrt(2));
figure, hold on;
plot(X,Y1);
plot(X,Y2);
%2
SNR_natural=10^(SNR/10);
Pn=Ps_teorica/SNR;
%3
n=0 + sqrt(F*Pn/2)*randn(1,Nm);
%4
r=s+n;
%5
t2=1:Nm;
figure, hold on;
plot(t2,r,'red');
plot(t2,s,'green');
legend('Seņal recibida r(t)', 'Seņal enviada s(t)');
%6
[h,c] = hist(n,20);
h = h/sum(h)/diff(c(1:2));
figure, hold on;
plot(c,h);
X2=(1:20);
f_N = normpdf(X2,0,sqrt(F*Pn/2));
plot(c,f_N);
%7
[h2,c] = hist(r,20);
h2 = h2/sum(h2)/diff(c(1:2));
figure, hold on;
plot(c,h2);
f_R = normpdf(X2,0,sqrt(F*Pn/2)+sqrt(var(s)));
plot(c,f_R);
%%2.4. Receptor y calculo de la probabilidad de error
%1
phi_rx = ones(1,F)/F;
y=conv(s,phi_rx);
%2
%3
%4
%5
%6
%7
%8
%9