Great idea!
Also, since we have never seen a Predator win, when do they go home after hunting some humans? It isn't after one kill, we know that much. We also know they take stuff from their victims as seen by the Elder Predator in Predator 2 who has the ancient flintlock.
So imagine this Predator, already being out in the desert for months. We know they like heat, but he also has to deal with sandstorms and stuff. These sandstorms have had some effect on his equipment after being there for a while. His camo doesn't work like it used to. His bio helmet vision is kinda glitchy, So he is in his regular armor like we know from the previous films, but he's also wearing some scarfs, or robelike poncho things, that he gathered from his trophies to wear, making him look all kinds of badass. Maybe some (but not too many) pieces of equipment from US armed forces. Like he has somehow fixed those panoramic night vision goggles (like they use in Zero Dark Thirty) to his bio mask.
You know, some stuff that enhance his abilities, but not like he's suddenly wearing army fatigues or something.