Irrigating deserts doesn't really work that well. The main problem is, that undistilled water always contains some ions, i.e. salts (it's got electrolytes!). If the main process for loss of water is evaporation these salts are left behind leading to salinization. You don't really want that.
If you want to fight desertification, then you must combat evaporation first, which you'd do for example with engineering the soil. Only after you've figured out how to make the soil keep the water, then you may start to thing about irrigation.
