Do you have a timer set to beep each minute during a call? Or 15 seconds before you reach a 10-minute or other pre-set limit? My old LG had that feature - you may have set it inadvertently.
Another possibility is a low battery indicator.
This sounds a lot like the 'minute beep' settings. Go to 'Settings & Tools>Sound Settings>Service Alerts>Minute Beep. Then turn off. This feature alerts you 10 seconds before the end of every minute during a call.
Please advise if this resolves your issue!
I've got a new Note 4, same beep-beep noise . during calls, good call on "minute minder" fix, don't remember why I turned it on, but now it's off!