Well, how hard can it be to produce a missile? In my opinion, it's not that dificult.

I think that a good idea for making an AA missile, would be to make it radar directed, becuase that would make the rocket a lot less heavier and you would be able to leave the "brains" of the rocket in the ground.

you would need the following systems:

1) directions: the rocket would need an electronic system that translates the radio signals into a specific wing movement wich would be controlled by another electronic system.

This DIY design could be adapted for that purpose https://www.youtube.com/watch?v=qnUfsLCa8h8

2) radio comunication: there would have to be a radio reciever inside the rocket and an radio emition system in the ground to allow comunication between the rocket and the computer.

3) radar system: you could adapt these DIY design https://www.youtube.com/watch?v=rh6UxpzHlJI

4) computer: The computer would have to be programed to recognice and tag an object percieved by the radar. Then, it would also have to recognice the rocket on the radar and controll the directions of it. This, would requiere a somewhat complex programing done by an ingeneer.

5) impulse: The impulse system could be independant from any controll and can be compleatly mechanic.

6) warhead: The computer would be programed to detonate the war head at a specific distance from it's target.

All in all, I think it would be reasonably hard and it woud requiere a lot of testing, but the end resoult could be devastating. Never the less, there are other kinds of DIY missile technology that woulkd be a lot easier and efective, for diferent purpuses. For example, a ground to ground DIY cruise missile, like the one this guy trayed to build. Apparently it costed less then 5000 dollars to make it... http://www.interestingprojects.com/cruisemissile/missilemanbook.shtml