Easy to describe, VERY hard to pull off
ILS is a pretty robust system (Which is why we've been using it for this long)
Also, it's not actually 2 overlapping signals. The guidance is achieved with a single radio beam at a certain carrier frequency (The frequency dialed in by the pilot and noted on the charts) modulated with 2 sidebands at 90 and 150 Hz offsets. By using a phased antenna array, one sideband is received stronger on one side of the center line, the other sideband on the other side of the centerline.
There's a very good manual with explanations for a Thales ILS system on the FCC website here and also a shorter and slightly more readable (for me anyway) post on Stackexchange here
Also, good luck overpowering a 15W ILS system with directional phased array antennas with a simple handheld. It's potentially possible, but I very much doubt anyone would be able to do so anywhere closer to the airport (where there's actually a second antenna system transmitting an overlapping signal to cancel out potential side-lobes in the longer range signal) where it actually matters most. (At that point the monitoring systems of the ILS system would probably conclude there is a problem, report an error and stop transmitting.
I also have my doubts an attacker knows the aircraft position (especially close in to the runway) precisely enough to generate a smooth signal. ILS systems are surprisingly precise, to the point where airports prefer airlines NOT use autoland to touchdown because it pummels the tarmac to absolute shreds in a very small zone. Manual approaches smear this beating out over a much larger zone. If an attacker doesn't generate his signal to within a few meters accuracy the receiver system on the aircraft is going to act noticeably weird (And remember he has to match the relationship/modulation depth between 2 sideband signals, not just a certain signal timing)