bluetooth
I mainly do not know what is the problem.
The simplest way to do this is to study about bluetooth protocol, it physical layer. then you will find what band it is working in. then yoiu have to find what is the minimum required SNR in this system. then you will try to find or design a circuit that can receive, amplify and transmitte the input signal. This is the simplest way I think, Using a repeater.
you can use another approach in witch you will decode the receive message in your device and then you will code it again using bluetoth protocol. this technique is more advanced, better perfromance and also more expensive.
I hope it helped you.