Amature Telescope Maker, but I quit before it was complete.
The goal of SETI is not to decode the signals, it's just to see whether they are there.
In order for it to be a genuine LGM signal it has to be more than just a carrier, it has to have some non natural occuring signal. Carl Sagan's favorite LGM beacon was a series of prime numbers of pulses which could be AM'd, FM'd or PSK'd or even on off modulated onto a carrier.
There simply aren't any natural narrowband radio sources in the relevant channels. In the bands that we use for communications, Earth is at least 1000 times brighter than any natural source in the galaxy. You can't hear the sun with a transistor radio, even though it subtends an area far larger with respect to your radio than any antenna you're likely to listen to.
So you believe that at 107.9 MHZ, from 50 light years away, the earth, or sources on the earth, emits more signal than the sun? No Way.
I can't say whether that's a good frequency to use, but I'm certain there are frequencies where the Earth would be brighter at 50 light years than the sun at 1 A.U. But even if there weren't, you could still pick out the Earth.
The two-sided coin is that you have to pick the right frequencies to see the signal in the first place. That introduces the difficulty of looking at millions of channels simultaneously, but it also allows you to rule out natural sources. A natural source will cover a very broad band, so many contiguous channels will be active simultaneously. The sun will look nothing like the Earth.
Finding such a signal is not like trying to find a needle in a haystack; it's more like trying to find a needle in a swimming pool full of pudding. The odds may be small that you find it in any given mouthful, but in the right mouthful its presence will be unmistakable.
This is where you are completely wrong. The scintillation of the interstellar medium will pretty much "chew" up any modulation (other than on/off), so SETI is doing just that. Looking foe an extremely narrowband CW signal (no information or modulation needed). And when I say narrow, I mean in the .8 Hz range. Just the fact a .8 Hz narrowband signal exists, denotes an artificially generated signal.