Coherence factor in Delay-And-Sum-Beamformer: Triangle Inequality
No idea what CF is. But:

Just looking at it, the first equation looks wrong. It depends on N. The second equation looks like 'the average of the signal, squared, divided by the average of the signal squared.'

It looks less funny, with the N gone, if you first take the average, then the average of the squares, then compute average^2/avgsqrs.

Also, it is not clear what your second equation means. It should be:

$$
sum(signal)^2/(N*sum(signal^2))
$$