May I introduce you to: the Log-periodic dipole array antenna[0], allowing quite a broad response range with decent directionality in a single antenna. There's probably a practical limit to just how broadband you can make one, but just from a quick search I found one commercially-available antenna[1] that covers 120mhz-2.5ghz, for example.
Another approach is a phased rx array, could even be as few as 2 antennas, and from that you get a bearing too.