That would appear to be a "Cordless Rumblepad 2"?
http://support.logitech.com/en_us/product/cordless-rumblepad-2/faq#link_38032
There's some explanation re: the USB 2.4GHz adapters there, and some things that can cause conflicts.
If you simply don't have the receiver, then no, you cannot connect it via Bluetooth etc.
FWIW, I believe most of Logitech's receivers are interchangeable (ie if you had a wireless Logitch mouse and the receiver plugged in, you wouldn't need to plug an additional one for the controller).
If you don't have the receiver......my suggestion would be to try to find one, but I don't believe they're sold separately.
I would suspect that would then require you to buy the cheapest Logitech wireless product...