Some interesting stuff in the "official" Flarm document on Antenna placement
Q: What is the minimum required range for a timely warning?
A: When flying at or below 250 kt, a range of 2 nm (3 704 m) forward and 1 nm to the side and behind will give the pilots a warning at least 15 seconds before closest convergence. Any range beyond that may be useful for tactical purposes but it adds very little to safety. Calculation: Worst case below 10 000 ft is normally two aircraft converging at 250 kt each -> 500 kt closing speed -> 257 m/s For a 15 second warning -> 3 858 m -> 2.08 nm The profile of a glider when seen from straight ahead at 2 nm distance is about as thick as a human hair held at arm’s length; almost impossible to see... The FLARM Range Analyzer (see Section 3.1.1) indicates the recommended range for a typical GA aircraft.
Q: Can you tell me if my antenna installation will perform well?
A: No, we will not be able to predict how your particular installation will perform. You have better knowledge of the material used in your airplane than we do. Stick to the guidelines in this document and your installation should be OK for collision avoidance. If you want to get extended range, you will have to do some testing.
This document also has some background on the different antenna types which would also be relevant to PAW or ADSB systems....
https://flarm.com/wp-content/uploads/man/FTD-041-Application-Note-FLARM-Antenna-Installation.pdf