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IOTL, first operational SAM was Nike Ajax produced in 1953, after 8 years of development.

Important harbingers of SAM were late WWII radar proximity fuses, photodiode-triggered guns of German interceptors, early unguided rockets, radio-guided glide bombs, and acoustic-homing torpedoes.

Could the work of SAM development be done faster in other historical circumstances, ideally with crude hardware of interwar period? If such development is possible, how it could be done?

I imagine roughly following possibilities for earlier SAM implementations:
1) Passive radar homing (either in beam-riding or true bistatic configuration)
2) Radio command homing
3) Photodiode homing
4) Bolometer homing
5) Animal-assisted homing (insects or pigeons as servo, in combination with 1-4)
6) Radar proximity fuses, in combination with 1-4
7) Active radar homing
8) Wire guided missile
9) Other ideas?

I think the passive radar homing was theoretically possible with the 1940 year tech.
Warhead would have 2 pairs of tube-based phase difference detectors tuned to slightly different frequencies, and catching the reflection from target, which is illuminated by separate ground radar. Phase detectors are controlling missile`s 4 tail planes. As soon as signal exceeds set threshold (either because the missile enter the radar beam or comes close to target), the warhead is detonated. The active part of radar must be huge installation to have a decent directive in decimeter wave range, and is steered semi-mechanically. For example, by remote-controlled motors turning variable resistors in RC phase-shiftier circuits feeding individual Yagi emitters of antenna field.
System will be heavy and unreliable though.
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