Move the alarm clock and any other plugged-in items at least 6' away from your head. This includes the plug cord itself. No piece of anything running on A/C power within 6' of the head. This does not include the wall outlet itself (unless the issue does not improve after doing this first step).
Include your cell phone (whether charging or on, the only exception is off or not charging) in this group, as it is sending and receiving a signal whenever it is on.
Report back after trying this for several nights.