Did our ancient ancestors sleep sitting up?

It would have been prudent for Neanderthal and Cro-Magnon man to sleep in a sitting up position. Weapons against animals that attacked them for food could be kept close by easily accessible before they had fire to keep them away. They would have put their backs against a stone wall of a cave more because of the room needed to accommodate their numbers and so sitting up sleeping solved at least 2 problems faced by our ancestors.