the Prophet (may Allah's peace and blessings be upon him) used to sleep at the beginning of the night and rise at its end to pray. [Al-Bukhari]
"كان النبي -صلى الله عليه وسلم- يَنَام أول اللَّيل، ويقوم آخره فَيُصلِّي. [صحيح.] - [متفق عليه.]"