Check, those signs inform people the area is used; and that "someone may arrive who will question their presence". Of course it depends on how many people are trying to get in there - simple "info" may be all you need, rather than yelling at folks. With luck it may be just a few people you need to inform, or assert rights to, and then "you're done".
One problem I have with putting up punitive signs. Every time I'm about to do it, I feel apprehension,,,, like then I'd be obliged to exaggerate the trespassing offenses so my guests (some who are friends of friends) don't think I'm just being a jerk. There's the insurance/liability issue too (I hate that too!).
A gate doesn't yell at guests, and what you say oosik is correct. But then you too - are forced to open it, close it, tell other folks what to do with it etc, EVERY TIME. I like the automatic gates too, but they announce that there may be valuables in there (plus the gate itself). I've settled on making my entrance "un-interesting" - not eye-catching. (with luck!)
Lots and lots of details to every 'entrance'!