You compensate for a lack of sleep whenever there is the opportunity:
A five minutes break? You go to sleep. (In the military, five minute breaks tend to become 25 minutes breaks and even longer. Enough time for a little nap.)
During training, this isn’t such a big problem, because sooner or later, you will have some time off. In combat, however, weeks can pass before you’ll have the opportunity to sleep eight hours in a real bed.
When there is nothing to do (and it’s not explicitly forbidden), find yourself a place and have a nap. Even a couple of minutes of sleep do wonders and you will feel much better afterwards.
During my time in Kosovo, we often slept in our positions. One squad member stayed awake to warn us about sudden enemy movements while the rest of us were snoring away.
During battles, there is always a lot of down time. It’s either your side that is waiting for the signal to move forward, or it’s the enemy’s. Either way, there are endless hours which can be used to work on your sleep deficit.
The important thing is not to be too squeamish about your sleeping location (almost any place will do) and not to worry too much about what’s going on: There is nothing you can do anyway and worrying will just keep you awake.
Sleep whenever and wherever you can.
Caffeine, nicotine, willpower, chewing gum, and a whole plethora of stupid tricks.
One way I used on a regular basis during radio watch, was to keep a thumbtack in an empty pocket.
When I felt myself starting to nod off or getting fuzzy, I’d slap the tack.
A quick sharp pain has a marvelous way of keeping you from dozing off when you feel the sleep creeping up on you.
Short bursts of exercise helps as well. Doing some squats or push ups will shake the sleep off of you for a period of time.
But outside of the individual tricks, which are only good for short bursts of focus, you’ll crash whenever you can, and you’ll learn not give a damn about where.
I’ve taken twenty minute naps in mud holes, dusty floors, and piles of rubble that felt like I had slept for hours in a bed.
Also after deployments, my own sleep schedule was usually so screwed that I slept in a different room from my wife. This lasted until my sleep schedule evened back out to normal.