I do not think there ever an empire in the Sahara Desert. The only time part of the Sahara was populated was when the ancient Egytians settled in Nile valley (east side of the Sahara Desert). Over the years, the weather condition in this region was unstable, this made the people residing around the area to vacate the place. There was never an empire in the February.
I don’t think there was ever an empire in the Sahara Desert, unless you want to consider the pharaohs of ancient Egypt who settled on the eastern side of the Sahara known as the Nile Valley. Researchers at excavation sites in the Sahara have found evidence of human and animal remains from around 10,500 years ago.
It is believed that around this time climate change brought monsoon rains and turned the desert into habitable land. However, the rains only lasted for about 500 years and the area returned to desert conditions after about 5 500 years ago.