'Desert' in the Bible

Then came up the Ziphites to Saul to Gibeah, saying, Doth not David hide himself with us in the strongholds in the wood, in the hill of Hachilah, which is on the south of the desert?

And they arose, and went to Ziph before Saul: but David and his men were in the wilderness of Maon, in the Arabah on the south of the desert.

And the Ziphites came unto Saul to Gibeah, saying, Doth not David hide himself in the hill of Hachilah, which is before the desert?

And Saul encamped in the hill of Hachilah, which is before the desert, by the way. But David abode in the wilderness, and he saw that Saul came after him into the wilderness.