Re: Correlation Estimator corr_est_cc "threshold" meaning

Achilleas,

Thank you for the detailed analysis of the threshold parameter - I know I have been tripped up using this block in the past and made various workarounds to have a settable threshold.  It is probably worth updating the documentation and parameter descriptions in the code so that users - just created an issue (https://github.com/gnuradio/gnuradio/issues/4273) in the github tracker so we don't lose sight of this.

Thanks,

Josh

On Fri, Feb 19, 2021 at 8:34 PM Achilleas Anastasopoulos <anastas@umich.edu> wrote:

Hi all,

I have been playing a bit with the "corr_est_cc" block and I was banging my head to understand the meaning of the parameter "threshold".

In all examples it seems to be a number VERY close to 1.

The documentation is cryptic:

" Threshold of correlator, relative to a 100% correlation (1.0). Default is 0.9."

Upon inspection of the code it is clear that there is a mixup between the 

quantities "threshold" and "1-probability of false alarm".

The code defines

d_pfa = -logf(1.0f-threshold);

which is clearly not the intended use: the pfa cannot be the log of something!

In fact, what is meant is that

===>     THRESHOLD = -logf(PFA);  

The smaller the PFA the larger the threshold should be.

This explains why we need to put a number close to 1 as "threshold" (which is actually 1-PFA).

Further down the code it shows how THRESHOLD is meant to be used:

float detection = 0;
for(int i = 0; i < noutput_items; i++) {
        detection += d_corr_mag[i];
 }
 detection /= static_cast<float>(noutput_items);
 detection *= d_pfa;   <========================

Clearly, the average magnitude is evaluated and then it is multiplied by "d_pfa"

which is meaningless, unless (as mentioned above) you interpret this as

detection *= THRESHOLD;

To summarize:

-------------------

What is shown as "pfa" in the code is actually a THRESHOLD

What is shown as "threshold" in the code is actually 1-PFA.

The user actually inputs 1-PFA (erroneously named "threshold").

I hope this will help anyone having similar issues understanding how this block works.

best

Achilleas