What the radar has to do
A long-range ballistic missile launches, burns for 3-5 minutes, releases its warhead in space, then the warhead reenters at 6-8 km/s. Detection must happen during boost. Tracking must continue through the midcourse phase, where decoys are released. Discrimination — real warhead vs decoy — happens in the last 60 seconds. The interceptor has roughly 30 seconds to hit.
The big radars
The US Sea-Based X-band radar (SBX), a 50-metre dish on an oil rig, can track a baseball at 4,000 km. The PAVE PAWS phased arrays at Cape Cod and Beale AFB watch for SLBM launches across the oceans. Russia's Don-2N in Moscow is a four-faced pyramid the size of a small mountain. Each is a multi-billion-dollar national asset.
Hit-to-kill, not explode-near
Modern interceptors don't use warheads. They rely on kinetic kill — direct collision at closing speeds of 15+ km/s. The interceptor's own seeker takes over from ground radar in the final seconds. It must see a re-entering warhead glowing in the upper atmosphere and adjust its course down to the last metre. Hitting a baseball with a baseball from across the country, at 15 times the speed of sound.
Why nobody is confident
BMD test records range from credible (Israel's Arrow, US Aegis SM-3 against medium-range targets) to unconvincing (US Ground-Based Midcourse Defense against ICBMs, ~50% success in scripted tests). Decoys, manoeuvring re-entry vehicles, hypersonic glide vehicles and saturation attacks all complicate the problem. Every BMD system protects against some threats, none protects against all.