AHC: War in Space

With a POD before 2016, how can we have human powers fighting battles against each other in Space? These do not need to be large scale, and could be something like satellites launching space based projectiles at ground targets or high-altitude fighters attacking enemy satellites. No extraterrestrials allowed, also.
In a conventional WW3 having US Anti Satellite Missiles might work, that was one of the last B58 missions before retirement
Yeah, I'm pretty sure a modern Great Power war (involving at least two of the US, China, or Russia on opposing sides) would probably see the use of anti-satellite weapons if things escalated beyond the skirmish level.