## Having troubles implementing Costas loop for 4-PAM

Started by 2 months ago●61 views```
N=10000; M=20; Ts=.0001;
time=Ts*(N*M-1); t=0:Ts:time;
m=pammod(randi([0 3],1,N),4);
mup=zeros(1,N*M); mup(1:M:end)=m;
ps=hamming(M);
s=filter(ps,1,mup);
f0=1000; phoff=-1.0;
c=cos(2*pi*f0*t+phoff);
rsc=s.*c;
rlc=(s+1).*c;
fftrlc=fft(rlc);
[mx,imax]=max(abs(fftrlc(1:end/2)));
ssf=(0:length(t))/(Ts*length(t));
freqL=ssf(imax)
phaseL=angle(fftrlc(imax))
%costasr
r=rsc;
fl=500; ff=[0 .01 .02 1]; fa=[1 1 0 0];
h=remez(fl,ff,fa);
mu=.003;
fc=1000;
theta=zeros(1,length(t)); theta(1)=0;
zs=zeros(1,fl+1); zc=zeros(1,fl+1);
output=zeros(1,length(t));
for k=1:length(t)-1
output(k) = 2*r(k)*cos(2*pi*fc*t(k)+theta(k));
zs=[zs(2:fl+1), 2*r(k)*sin(2*pi*fc*t(k)+theta(k))];
zc=[zc(2:fl+1), output(k)];
lpfs=fliplr(h)*zs'; lpfc=fliplr(h)*zc';
theta(k+1)=theta(k)-mu*lpfs*lpfc;
end
```

So I decided to plot `output`

vs `s`

and this is what I got:

If I understood the theory about Costas loop, if the input is s(t)=m(t)*cos(2*pi*f_0*t+theta_i), if the loop worked fine, at the output I should have 0.5∗m(t)cos(theta_i-theta_o)=0.5∗m(t)cos(theta_e) -> for theta_e ~ 0 -> 0.5∗m(t) but as you can see, there's something else besides m(t). Why is this happening? I tried plotting the FFT of the rsc and the output, and as you can see, there is some info at around 2000 Hz that shouldn't be there, only the baseband should:

Also, I've tried a different way of implementing it http://read.pudn.com/downloads80/doc/project/307210/CarrierRecoveryUsingaSecondOrderCostasLoop.pdf and I keep getting the same result, despite the author getting it to work properly

Thanks in advance!