For some reason my simulation line is not following the theory line and I'm not sure how to go about fixing it. Any Tips and help is very appreciated.
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%fsk modulation and demodulation
close all;
%number of bits Noit=1e6;
%Generate 1 and 0s
x=round(rand(1,Noit));
%find indices of zeros
zero_ind=find(x==0);
%generate a waveform
T=0.002;
% symbol duration in sec
f0=5000; %in Hz
f1=4500; %in Hz
t=0:1/(100*f0):T; %time window, the duration between two samples is 1/(100*f0)
%Plot symbol waveform
phi= (pi/3);
tn=[];
sn=[];
for mn=1:5
twin=(mn-1)*T+0:1/(100*f0):mn*T; %time widow for each bit
twin2=(mn-1)*T+0:1/(100*f1):mn*T;
tn=[tn,twin]; %total time for three bits
tn2=[tn,twin2];
sn=[sn, cos(2*pi*f0*twin)]; %total waveform for three bits
sn2=[sn, cos(2*pi*f1*twin2)];
end
figure;
plot(tn2,sn2, 'LineWidth',2); %Plot FSK modulated signal
xlabel('time');
ylabel('FSK modulated signal');
grid on;
s1=(1/(sqrt(sum(cos(2*pi*f1*twin).^2))))*(cos(2*pi*f1*t+phi));
plot(t,s1);
s2=(1/(sqrt(sum(cos(2*pi*f0*twin2).^2))))*(cos(2*pi*f0*t+phi));
figure;
plot(t,s1,'g');
plot(t,s2,'b');
data=rand(1,6);
data=round(data);
Ncos=length(s1);
stream=0;
for i=1:length(data)
if data(i)==0
stream=[stream zeros(1,Ncos)];
else
stream=[stream ones(1,Ncos)];
end
end
stream(1)=[];
figure;
subplot(2,1,1)
stem(stream)
title('DATA BITS')
fsk=0;
for i=1:length(data)
if data(i)==1
fsk=[fsk s2];
else
fsk=[fsk s1];
end
end
fsk(1)=[];
subplot(2,1,2)
plot(1:length(stream),fsk)
title('FSK OUTPUT')
snrdB=-4:2:18; %define SNR in terms of dB
snr=10.^(snrdB/10); %change SNR from dB to linear scale
%Initialize the vector of simulated bit error values
biterrSim=zeros(1, length(snr));
%Loop over SNR
for mn=1:length(snr)
%Initialize the vector of detected bits to zeros
detect_bits=zeros(1, Noit);
%FSK modulation and demodulation for each SNR value
%Loop over FSK data
for kn=1:Noit
if (data)kn==1
%time-window for each FSK data
twin=(kn-1)*T+0:1/(100*f0):kn*T;
%Normalization is necessary since cos(2*pi*f0*twin) is not %normalized
normF=sqrt(sum(cos(2*pi*f0*twin).^2));
sM=x(kn)*(1/normF)*cos(2*pi*f0*twin);
% Generate random Gaussin Noise of zero-mean and variance 1
noise=randn(1,length(twin));
%Received signal after AWGN
%We change the power of the modulated signal while keeping
%the variance of noise to 1.
rM=sqrt(snr(mn))*sM+noise;
rM1=rM.*(cos(2*pi*f0*twin)*1/normF);
rM2=rM.*(sin(2*pi*f0*twin)*(1/normF));
z1=mean(rM1+rM2)
else
if (data)kn==0
twin2=(kn-1)*T+0:1/(100*f1):kn*T;
%Normalization is necessary since cos(2*pi*f0*twin) is not
%normalized
normF1=sqrt(sum(cos(2*pi*f1*twin2).^2));
sM1=x(kn)*(1/normF1)*cos(2*pi*f1*twin2);
% Generate random Gaussin Noise of zero-mean and variance 1
noise=randn(1,length(twin));
%Received signal after AWGN
%We change the power of the modulated signal while keeping
%the variance of noise to 1.
rMx=sqrt(snr(mn))*sM+noise;
rM3=rMx.*(cos(2*pi*f1*twin2)*1/normF1);
rM4=rMx.*(sin(2*pi*f1*twin2)*1/normF1);
z2=mean(rM3+rM4);
if(z1>=z2)
%symbol 1 was transmitted detect_bits(kn)=1;
else
%symbol (0) was transmitted
detect_bits(kn)= 0;
end
end
end
end
%Find bit error
%find(detect_bits~=x) finds the indexes where detected bits are not
% equal to actual transmitted data x
%length(find(detect_bits~=x)) find the number of positions in which
% detected bits are not equal to x
biterrSim(mn)=length(find(detect_bits~=x))/Noit;
end
%Calculate theoretical BER for FSK
% You have to change the Q fundtion of lectures notes to MATLAB's erfc( )
biterr_theo=.5*erfc(sqrt(snr/2));
figure;
semilogy(snrdB, biterrSim);
hold on;
semilogy(snrdB, biterr_theo);
legend('Simulation', 'Theory');
xlabel('SNR');
ylabel('Probability of bit error');
grid on;
element of the data array is 'data(kn)'.
