AES-GCM for Securing Bluetooth Low Energy Application
Using GCM with a long term fixed key is dangerous; if you repeat the nonce, you can leak the authentication piece.

Instead, what I would suggest is that you use AES-SIV instead.  It doesn't have the problems with repeating a nonce.  It is more complex, and slower, however it is far better suited if you have to use a long term key.