How to setup a wireless repeater to passively relay EAP Authentication?

Question

I need to connect to a wireless AP with my smartphone via EAP-AKA, but the AP signal is too weak.

Then I'm thinking of reconfiguring a router with DD_WRT firmware or maybe a Raspberry Pi, to act as a repeater between my mobile and the AP.

I made some search, but all the solutions I found require the repeater to authenticate to the AP via EAP, i.e. by setting a user and a password, and then connecting the client (phone) to the repeater. The problem is I don't have any user nor password, yet I'm allowed to authenticate with my credentials, which are stored on my mobile's SIM.

I need the repeater to relay passively the wireless frames at physical (or possibly MAC) layer, without authenticating by itself to the AP, and feed the responses back to my phone.

How can that be done with some Linux device?