No, that was the MiG-25P's Smerch-A1 (NATO FOX FIRE
), of ten years earlier. But!
However, many microwave engineers insist even now that vacuum-tube technology is perfectly practical and cost-effective for high-power microwave applications
By 1979, the MiG-25PD came about using a version of the MiG-23's Saphir-23 radar, using transisters and pulse-Doppler operation to provide a look-down / shoot-down capability. The -PD is the one that went abroad. But probably quite downgraded, as the Soviets did with many exports to Arab countries.
The MiG-31's Zaslon was actually the first electronically scanned phased array radar to enter service in the world. It's passive, so more like the PESA than the AESA, and pretty old by now for comparison, but in a way ahead of its time.
The movie is based on a novel of 1977, 5 years before the Foxhound became known to the West. The movie actually first wanted to use a Viggen (denied by Swedish government), later cover artwork depicted a MiG-25 version (close one), but I guess this wasn't enough "hollywood" (it was known by now, the MiG-25 wasn't that great). Firefox was based on a novel. If you have a novel about a Russian aircraft, and you know the MiG-15/17/19/21/23/25/27/29, what comes next? You can take 31 if it's more advanced, or fill in those blanks if it's not more advanced, like they did with MiG-28 in Top Gun.
If that story about the Russian pilot is true (I doubt it), then the guy is pretty stupid to think a Hollywood movie reflects US DOD intel. Any fabricated link between the movie's MiG-31 and the real MiG-31 is nonsense, IMHO.
Sure, the US overestimated Soviet capabilities all the time, technology and numbers-wise. but don't try to link that with fiction writing... It's funny though whenever they established the last thing was crap afterall, they were yet surprised and scared of the next thing. I think it's kinda like: overestimate -> get facts -> underestimate -> be surprised -> overestimate, etc.