The Radar dome, as its name suggests, was the primary structure responsible for providing radar feed in the Second World War, used by both the Soviet Union and the Allied Forces. Its most striking feature was the giant dome that housed the radar antennae, set on a concrete foundation, in which all the electronic and computer equipment required to operate the radar was housed.
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The Radar Dome gives you an overhead view of the battlefield when fully powered. - Red Alert manual(src)
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The dome was constructed so that it would continue to function even when severely damaged. The only requirement was that continuous power supply was present. Without it, the radar ceased to function. After the war, with the refinement of radar and communications technology, the equipment was integrated with the communications centers during First Tiberium War, which took over the role of radar uplink units. In Red Alert Universe, Allies integrated it with Airforce Command Headquarter and the Soviets replace them with Radar Tower during Third World War
As a note, in the ending stages of the war, as the Allies developed GPS satellite technology, their tech centers took over the role of the radar dome when the satellite was launched.