Recommended readings from the Kalahari Bushmen:
E.Marshall Thomas: 'The Old Way' and also 'The Harmless People'
Nice and very readable.
Your ancestors came from the African savanna. They scavenged for carcasses of already killed animals, cracked open their bones and ate the marrow, and ate the brain from the skulls. This calorie dense, DHA dense, AA dense food allowed them to develop larger more metabolically demanding brains. As the climate changed and they expanded to other parts of Africa they probably began to incorporate more tubers, fish, and wild game. After they had invented the technology needed to be effective hunters they probably ate about every type of wild game (and not just the muscle meat) as well as whatever they could gather.
How dry is dry? Find out what grows there and that will tell you. Egypt is desert but they have the nile and could grow water loving crops all along it. YOu will need to know more about your particular desert and what your culture did to survive there. Some deserts have close to no plants and others have lots of ruminants, cactus, scrub, and even some fruit. Locally, the natives ate a lot of wild animals and also washed the poisons out of acorn meal and baked biscuits. Limited seasonal fruit was available and many herbs and plants could be found in the riparian areas.