How to scale PSD/Pwelch highest point to 0dB?

Hi,

I am currently using the pwelch function to simulate the spectrum of an OFDM signal.

Note: I used random numbers, QPSK modulation, zero padding and finally IFFT to obtain my OFDM signal.

   fsMHz = 80;
   Len = length(ofdm_signal); 
   [Pxx,f] = pwelch(ofdm_signal,[],[],Len,fsMHz);
   plot([-(Len/2):((Len/2)-1)]/1024,10*log10(fftshift(Pxx)));

Resulting in:

As you can see on the PSD axis, the highest point is at around -50dBr.

I also did some calculations and I came up with the following:

    Re = real(ofdm_signal);              % Real part of the signal.
    Im = imag(ofdm_signal);              % Imaginary part of the signal.
    Power = Re.*Re+Im.*Im;               % Calculating Power.
    AvgP = sum(Power)/Len;               % Calculating Average Power.
    AvgP_db = 10*log10(AvgP);            % Average Power in dB.
    PeakP = max(Power);                  % Calculating Peak Power.
    PeakP_db = 10*log10(PeakP);          % Peak Power in dB.
    PAPR_db = 10*log10(PeakP/AvgP);      % PAPR in dB.

    disp(['Average Power1 = ' num2str(AvgP)]);
    disp(['Average Power1 (dB) = ' num2str(AvgP_db)]);
    disp(['Peak Power = ' num2str(PeakP)]);
    disp(['Peak Power (dB) = ' num2str(PeakP_db)]);
    disp(['PAPR (dB) = ' num2str(PAPR_db)]);

Which resulted in:

      Average Power = 0.00024414
      Average Power (dB) = -36.1236
      Peak Power = 0.0020307
      Peak Power (dB) = -26.9235
      PAPR (dB) = 9.2001

What I want to know is whether there is a way to scale that PSD axis so that the highest point is around 0dB, as frequently used in theory. Here are some pictures of what I'm trying to do.

Please help me out here.

Looking forward to your answers.

Answer 1

[Honglei Chen]

You just need to normalize it, for example

plot([-(Len/2):((Len/2)-1)]/1024,10*log10(fftshift(Pxx/max(Pxx))));

and

AvgP_db = 10*log10(AvgP/max(AvgP))

[Jean-luc]

Thank you so much Honglei Chen.

What you're trying to tell me is that I need to normalize my average power too, right?

[Honglei Chen]

No, I'm just saying if you want to get 0dB, you can just normalize it. If you want the true average power, you should not normalize it. Sorry for the confusion.

Answer 2

[Wayne King]

Can't you just scale the PSD estimate, Pxx, by the maximum value?

You did not provide your OFDM signal, so I'll just create a signal here

Fs = 1000;
 t = 0:0.001:1;
 x = cos(2*pi*100*t)+randn(size(t));
 [Pxx,F] = pwelch(x,300,250,512,Fs);
 maxval = max(Pxx);
 Pxx = Pxx./maxval;
 plot(F,10*log10(Pxx))

[Jean-luc]

Thank you Wayne King, it didn't occurred to me to divide by the max value.

If you don't mind;

Why did you use window as 300 and nonoverlap as 250?