The Aircable implements the SPP (Serial Port), DUN (Dial-Up Networking), LAN (Local Area Network) and OBEX Bluetooth profiles. I don't believe that a cell phone will talk to any of those, and I doubt that it would send Caller-ID information on any of them. It normally sends Caller-ID over HFP (Hands Free).
I think you'd have to roll your own Bluetooth doohickey that would listen on HFP for just the Caller-ID info and then spit that out over the serial port. But then you have to ask if the cell phone would support both that and the regular headset/hands-free kit attached at the same time.
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Bitt Faulk