I would try restoring the device to factory settings and testing for a few phone calls. If the calls work fine, try restoring from your backup. If the problem returns then there is something in your backup that may be corrupt and you'd need to return the the factory settings option. If the problem still exists after restoring to factory settings then you'll need to have it diagnosed at an Apple Store.
Restore your iPhone, iPad, or iPod to factory settings - Apple Support
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support