The missiles use pieces of the crackdown specific code.
If your base is hidden, the missile strike mission will spawn a wave of HK ships in the relevant continent region to attempt to locate it. Shooting those down will stop it. The seeking wave of ships only lasts about 2 days, and if they fail to locate your base, no missile strike will happen.
Take care that if your base is revealed by anyone, its location is available for all for future crackdowns and missile strikes. (F. Ex. Ratman swarms, bogey swarms).
You can defend your base from being located, by keeping is small(facilities add to the radar signature, large facilities add more), or building hideout shrouds. Or of course, shooting down everyone who gets close.
You can further build your bases in "dead UFO zones", zones in which UFOs do not like to patrol because of how the game works. I am not an expert in those, but in general, look for edges of regions. Two come to mind, the Panama Isthmus, and just SE of Lake Victoria in Africa.
The missile strike itself follows some rules. It never hits more than 3 buildings in a wave. This means that if your base has a connectivity of minimum 4, you will not lose all your facilities due to loss of connectivity. Missiles seem to also target buildings in construction. Missiles also hit buildings according to their missile attraction stat, so radar facilities and stills will draw more heat than say a burrow. This means that buildings with high attraction go on the periphery when planning the base, and do try to not rely on them for connectivity. This also means that if you feel a missile strike is incoming(due to the obvious HK wave), you can fool them by queuing building outposts everywhere. They are cheapish and have a relatively high missile attraction, and you can cancel them once danger has passed. Missiles also seem to like large buildings as well. Each missile hits a 'per square' basis not 'per facility' basis, so a hangar or plantation can be hit multiple times, wasting their shots.
Remember that a missile wave can have multiple strikes, so check your base and decoy outposts between strikes and put up new ones as needed.
Obviously AA defenses are just one solution.
