The expression "RADAR" was first used around 1940 in the US, meaning "RAdio Detection And Ranging". There was little distinction at that time between systems which:
- detected radio signals transmitted by an enemy object, and tried to work out the location of that object
- detected radio signals from an enemy object and tried to read the data they contained, which might be encrypted
- transmitted a radio signal pulse from a friendly location, and detected any reflected signals from any unknown (and therefore likely enemy) objects, and tried to work out the location of the objects, what we would now refer to as the word which entered the English language as "radar" (no capitalisation)
Chain Home was developed in the UK in 1935, and went into operation in 1936 with five stations, in other words before the term RADAR was even coined. The overlap in technologies is shown by the radio transmitters, which were produced from the same model used by the BBC at a TV transmitter built around the same time.
These first radar stations were massive, using four towers 110m tall in a line 55m apart with the antennas strung between them to transmit the radio signal. There were a further four towers 73m tall some distance away which had the receivers to detect any signal reflected back by any approaching planes, up to 100 miles away. The stations used so much power from the National Grid that they couldn't transmit at the same time, so careful synchronisation between them occurred.
When Chain Home went into operation in 1936 there were five stations. By mid-war there were 40. Additionally, stations were developed with more antennas to provide better detection at certain heights. But they had one major flaw, caused by their huge size - they generated the signal in only one direction, out to sea. Once enemy planes passed over the stations, ie. were over Britain, Chain Home couldn't detect them. Nevertheless, by that time their height and direction had been closely plotted and ground observers and fighters scrambled to intercept them could keep the commanders informed of any changes. Nevertheless, smaller transmitters were developed at other sites that could be turned, and ultimately through 360 degrees. These proved better at direction finding, but were not as powerful. Chain Home remained in operation, supplemented by the new smaller sites, and a variant called Chain Home Low designed to detect planes flying low to the ground. Eventually there were about 100 static radar sites around the coast of Britain. Plus many other sites monitoring enemy radio transmissions, some attempting to locate where they were coming from (systems such as "huff duff" - high frequency direction finding), others recording the information in the signal for decryption/translation.
Developments of the radio transmitting/receiving technology were limited. But analogue computers were developed to automate the processes for working out where the planes were located, and CRT technology improved to plot locations on a screen. The radar transmitters/receivers were part of a massive operation, connected by their own telephone system back to central control rooms and to air bases, naval bases and army operated AA gun emplacements.
I saw nothing wrong with having 10 levels of static RADAR in a province in HOI3, to represent everything from a basic listening station, up to the complexity and scale of the systems in place in Britain by 1945, including Chain Home, the Dowding System, huff duff and Bletchley Park.