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!