For desert driving you need a larger foot print that is why you reduce the pressure in your tires by atleast 10psi. So if you run on 30psi, your desert running should be 20psi.
The idea is to increase the foot print by an inch. A simple way to do it is to place a brick or anysort of marking object, an 3/4 inch away from the side wall & start to deflate. When the side wall touches the object, that's your pressure to run.
As for portable compressors, there are lots of them available in the market. Dont go for a foot pump as that would take you an hour easily to inflate back. The electronic ones that are recommended are AirMan, Dayga Devalt etc etc. Dont worry if you get a chinese one, it serves the purpose doesnt it & its cheap to replace.
Like we have Shershah (used part market) you guys have Bilal Gunj (Lhr) and Sultan Ka Koh (Rwp), you can get 'Dayga' style compressors that fit on to the vehicle. These can fill up 5 tires at a time.
One can always choose to inflate using the AC too.