The radar horizon advantage
A missile flying at 5 m above the waves is below the radar horizon until it is within about 15 km of the ship. For a target moving at Mach 0.9, that's about 50 seconds of warning. At Mach 3, it's 15 seconds. The Sheffield had less than a minute. Many modern systems have even less.
Clutter and multipath
Even when above the horizon, the missile is in heavy sea clutter — waves reflecting radar energy back to the receiver. Multipath adds reflections from the sea surface, creating fading and ghost tracks. The missile itself is small, often with reduced RCS. Separating it from the background is one of the hardest problems in naval radar.
Defence layers
Modern ships use layered defence: long-range air-search radar (sometimes on a helicopter), mid-range tracking radar, short-range point-defence radar, and finally close-in weapon systems (CIWS) like Phalanx or Goalkeeper. Each layer has seconds to act. The missile-defence problem is a race between radar detection, fire-control solution and interceptor flight time.
Stealth skimmers and hypersonics
The next generation includes missiles with stealth shaping and ramjet propulsion at Mach 5+. Hypersonic sea skimmers compress the engagement timeline to seconds. Directed-energy weapons (lasers) and railguns are being developed precisely because conventional interceptors cannot close the distance fast enough. The race continues.