@Moon @pwm You don't need anything beyond a tiny stick and a ground plane for 1090ES.

Wavelength is: 299792458/1090000000 = 0.275 m. Quarter is 6.9 cm or 2.7". Four wires are perfect for a ground plane, you just bend them to match to the impedance of your coax or receiver. Usually it's 50 Ohm, so something like 43 degrees. That's all! I soldered mine to the actual connector and used it indoor on top of the receiver in a USB stand. See this photo:
https://zaitcev.livejournal.com/226449.html

In fact, don't even do that. Just take a wire from an Ethernet cable, cut to under 3 inch, plug it into the receiver with the connector upright. The receiver itself provides the ground plane.

The reason why this works is that airplane transponders are absurdly powerful. For example, my Garmin 333 is rated for 250 Watts. Not micro- or milli-watts. Watts! If your cellphone output that, it'd cook your brain in a minute.

So stop thinking about unnecessary complexities and focus on the whole system.