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Let's consider baseband complex signal like this:

example of baseband signal

red: real part of signal

blue: magnitude^2

green: mean value of magnitude^2

as you can see, there are a lot of peaks but only one has value greater than 10. From definition PAR=Ppeak/Pmean... question is what would be Ppeak in this case? Max(pepeak) could be taken, but intuition tells that this extreme peak could be casual interference and isn't significant (could be hard clipped without significant signal degradation). Another possibility would be some averaging of Ppeaks, but which peaks should be considered in this case (just all greater than Pmean)?

Andrew123
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1 Answers1

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The OP's intuition is correct, using the absolute maximum signal as the "peak" may be unfair in terms of actual signal degradation if it occurs very infrequently. For this reason PAPR is often presented as a complementary cumulative distribution function (CCDF) showing the probability on the vertical axis of signals having a PAPR greater than a threshold represented on the horizontal axis. We can then report a PAPR at a given probability as a more useful comparison of different systems or modulations, crest factor reduction schemes etc...

I demonstrate this in the plot below for OFDM (and showing how the distribution closely approximates a Gaussian). Here we see that the PAPR at a 10E-5 probability is close to 10.5 dB:

CCDF

My Python code used to create this ccdf is below:

def ccdf(x):
    papr = np.arange(0,12,.1)   # dB vector of PAPR values
    x = np.array(x)
    power = x*np.conj(x)
    power_ratio = power / np.mean(power)
    pdb = 10*np.log10(power_ratio)
    results=[]
    for level in papr:
        results.append(np.count_nonzero(pdb>level)/len(x))
    return papr, results

Neil Robertson wrote a nice blog article on the Peak to Average Power Ratio and CCDF which you can find here: https://www.dsprelated.com/showarticle/962.php

Dan Boschen
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