Some Anons have said Nellie Ohr could only have been able to communicate within a limited area based in her "amateur" ham radio operators license (100 miles).
But what if she was not broadcasting "outward" but rather "upward"? - toward the MOON, bouncing the signal off the Moon to be picked up by a FOREIGN POWER(a Five Eyes country with maybe a rather large antennae array) Maybe Oz?
Earth–Moon–Earth communication (EME), also known as moon bounce, is a radio communications technique that relies on the propagation of radio waves from an Earth-based transmitter directed via reflection from the surface of the Moon back to an Earth-based receiver.
Current EME communications
A single sideband contact between IZ1BPN in Italy and PI9CAM at the Dwingeloo Radio Observatory. IZ1BPN's transmission is shifted up in pitch slightly to compensate for PI9CAM's transmission being shifted down by the Doppler effect. At the end of IZ1BPN's transmission you can hear the echo of his signal returning from the Moon at a lower pitch due to the Doppler effect.
Amateur radio (ham) operators utilize EME for two-way communications. EME presents significant challenges to amateur operators interested in weak signal communication. EME provides the longest communications path any two stations on Earth can use.
Amateur frequency bands from 50 MHz to 47 GHz have been used successfully, but most EME communications are on the 2 meter, 70-centimeter, or 23-centimeter bands. Common modulation modes are continuous wave with Morse code, digital (JT65) and when the link budgets allow, voice.
Recent advances in digital signal processing have allowed EME contacts, admittedly with low data rate, to take place with powers in the order of 100 Watts and a single Yagi–Uda antenna.
World Moon Bounce Day, June 29, 2009, was created by Echoes of Apollo and celebrated worldwide as an event preceding the 40th anniversary of the Apollo 11 Moon landing. A highlight of the celebrations was an interview via the Moon with Apollo 8 astronaut Bill Anders, who was also part of the backup crew for Apollo 11. The University of Tasmania in Australia with their 26-meter dish were able to bounce a data signal off the surface of the Moon which was received by a large dish in the Netherlands, Dwingeloo Radio Observatory. The data signal was successfully resolved back to data setting a world record for the lowest power data signal returned from the Moon with a transmit power of 3 milliwatts, about 1,000th of the power of a flashlight lamp.
Interestingly, the C_A was using "Moon Bounce" back in the Cold War to monitor the Soviet missile program's radio transmissions.
Search: C_A, Moon Bounce