Brumby
Major
is very interesting and recently I went through modern (1995+) warships within a large range of displacements -- irrespective how the ship is formally classified, from half of a thousand tons of the Skjolds to some six and half thousands of the Huitfeldts -- so that the USN LCS was somewhere in the middle (by the way, I was surprised what some Navies were able to pack into less than 1500 tons) and I might've missed something, but the closest seems to be the Incheon-class; it doesn't have "over the horizon anti-aircraft missiles" either and is similar in size
There is a document I came across recently written by Robert Work titled : "The Littoral Combat Ship - How
we got here and why" It is a 64 page document which covers the complete history of the program and offers significant insight into why the program ended up the way it is today. It also discusses how the LCS would fit into Naval doctrine, CONOP and potential mission sets and would provide a reference point when looking at it from the standpoint of a Frigate. Highly recommended reading if you have an interest in the LCS program. Link to document provided below.