Cyclostationary Feature Detector: Performance doesn't vary with Change in SNR

Question

I have Implemented Cyclostationary detector for spectrum sensing in AWGN channel in Matlab but I am getting vague result. As it performance doesn't vary with change in SNR. Its very strange result for me. I don't know what mistake I am doing in it. I am attaching my codes please have look and comment. Here I am finding cyclostationary feature of signal for its detection. Firstly I tried to Out FFT of a signal then shift its frequency by +alpha of tranform and -alpha to its conjugate. Then I multiplied both to taken sum of all. Thats how all theory explain about cyclostationary feature detection I will very grateful if somebody can help me in this.

function Pd=Cyclo_AWGN(Pf,snr_avg,n,N,Sim_Times)

% Pf= Probablity of false alarm  
% n= length of data
% N= length of fft
% Sim_Times= Iteration


ln=0:n-1;

Over_Num = 0;

Th_awgn= sqrt(-2*log(Pf)/n);         % threshold

for kk = 1:Sim_Times


     phi= randi([-180,180],1,n);
     phi=phi*2*pi/360;
     x=sin(0.32*pi*ln+phi);
     Recv_Signal = x;                                              % Recived Signal


    Noise_awgn = randn(1,n)+1i*randn(1,n);
    AvgPower_Noise_awgn=sum(abs(Recv_Signal).^2)/snr_avg;          %average power of noise  
    std_Noise_awgn = sqrt(AvgPower_Noise_awgn); 
    Noise_awgn = std_Noise_awgn*Noise_awgn;



    norm_signal_awgn = Recv_Signal/std_Noise_awgn;  %Normalized signal sample
    norm_noise_awgn =   Noise_awgn/std_Noise_awgn; %Normalized Noise sample

    Recv_sig_awgn =  norm_signal_awgn + norm_noise_awgn;  % Normalized received signal for detection



    X=zeros(2*N+1);
    Y=zeros(2*N+1);

    Ts=1/N;

    for f=-N:N

         d=exp(-j*2*pi*f*ln*Ts);
         xf= Recv_sig_awgn.*d;
         n_r=n:-1:1;
         X(f+N+1)=sum(xf(n_r));
         Y(f+N+1)=conj(sum(xf(n_r)));   
    end

   alpha=10;
   f=5;
   f1=f+floor(alpha/2)+(floor(-((N-1)/2)):floor((N-1)/2));
   f2=f-floor(alpha/2)+(floor(-((N-1)/2)):floor((N-1)/2));

   S(kk)=sum(X(f1+N+1).*Y(f2+N+1))/N;

   S(kk)=abs(S(kk))/n;

    if S(kk)>Th_awgn
        Over_Num = Over_Num +1;                         %decide 1 or 0, present or absent
    end


end

Pd = Over_Num / Sim_Times;                             % Simulated Pd}

Answer 1

You need to take this one step at a time. I see errors in the signal generation as well as the statistic calculation.

First, ensure that you are creating a cyclostationary signal! I ran the signal-generation code in the function above, and also looked at it. It looks like a random phase modulation. Try first to generate a signal you know is cyclostationary, like BPSK or analog AM.

Second, you tried a cycle frequency of 10. But it looks like you are using (implicitly) a sampling rate of 1 (at least in the signal-generation part), which is fine. But then alpha must lie in the interval [-1,1].

Third, rewrite the code to more clearly separate the signal generation, spectral correlation function estimation, and detection-statistic calculation. Make sure that the spectral correlation function is first being estimated correctly before you try to put it in a loop for Pd/Pfa calculation.

Have a look at Chapter 18 of the book "Cognitive Radio Technology", Second Edition. The end of the chapter has some exercises that might help you fix up your code.

Good luck!

Answer 2

In many cases you know the value of cycle frequency in advance, because you know some things about the signal you are trying to detect (such as the symbol rate).

When you don't know any cycle frequencies, you can perform an exhaustive search, but not all algorithms are suitable for this task for computational reasons. I've supplied lots of helpful information on this, as well as on the issue of generating a suitable test signal, on my blog at cyclostationary.wordpress.com.