They didn't. Various mobile nuclear C3 assets were created and/or modernized, GWEN was started, etc. We didn't need the precise equivalent because we chose a di

They didn't. Various mobile nuclear C3 assets were created and/or modernized, GWEN was started, etc. We didn't need the precise equivalent because we chose a different route: redundant mobile command assets and a great deal of effort into preserving the Presidency (the office, not the person) at least until the combatant commanders had launch authority delegated to them. FWIW, the US used to have launch code broadcast rockets. The early ones were housed in dedicated sounding rockets. Later, radio "warheads" were secretly dispersed among the Minuteman fields. We no longer use them because there are enough reliable nodes to get the word out even while under attack (e.g. Milstar). Fun fact: missile command centers fitted to support the command rockets had a voice console where a crew member would read the current go codes into a microphone to be recorded on the "warhead" just before launch. Try not to stutter!