How to use router as an interface antenna with an odroid

There is still a way to do it with mobiles using their cellular networking features but it is far more complicated. In GSM days it was doable (check openbts project), and there are a few more recent ones for HSPA/LTE.
You will likely have trouble to meet regulatory requirements with such devices.
I would stick with video recognition, or better (cheaper) attach rfid tags to the carts and baskets.