Frequency power vs signal power

Question

I have to analyse a signal which has been modulated with a QPSK using matlab and I can't seem to get things right.

What I have: a complex signal sampled at a known frequency.

What I want: the power ratio of a certain frequency. So if the signal is of the form a*cos(wt)+a*cos(2wt) then I should get 0.5 for w and 0.5 for 2w.

I don't know where is the problem with my code but I get a frequency power higher than the signal power as you can see it in the graph bellow (in blue: signalPower, in red: Fm).

And here is my code:

% Nsym : Number of symbol used for the detection
% Ns : Number ofsamples per symbol
% IQrx : Complex signal to analyse
% Fmod : Modulation frequency

Nt = Nsym*Ns;
signalPower = zeros(1, length(IQrx));
Fp = zeros(1, length(IQrx));
Fm = zeros(1, length(IQrx));
for ii = 1:length(IQrx)
    for jj = 0:Nt-1
        if ii-jj > 0 && ii-jj <= length(IQrx)
            signalPower(ii) = signalPower(ii) + ...
                abs(IQrx(ii-jj))^2;
            Fp(ii) = Fp(ii) + ...
                IQrx(ii-jj) * ...
                exp(1i*2*pi*Fmod*(ii-jj)/obj.Fs);
            Fm(ii) = Fm(ii) + ...
                IQrx(ii-jj) * ...
                exp(-1i*2*pi*Fmod*(ii-jj)/obj.Fs);
        end
    end
    Fp(ii) = abs(Fp(ii))^2;
    Fm(ii) = abs(Fm(ii))^2;
end

Edit: As requested in the comments the formulas that I use are: Consider that i goes in the time window of interest.

signalPower = sum ( signal(i)^2 )

Fp = abs( sum( signal * exp(1i*2*piFmod(i)/obj.Fs) ) )^2

Fp = abs( sum( signal * exp(-1i*2*piFmod(i)/obj.Fs) ) )^2

Answer 1

Seems to me that

signalPower(ii) = signalPower(ii) + abs(IQrx(ii-jj))^2;

Should be something more like:

signalPower(ii) = signalPower(ii) + abs(IQrx(ii-jj));

You might want to try something a bit simpler for the signal power like:

pwt=x'*x; % Power in time domain

where x is your windowed time series value. (inspiration from this link).