Kernel + system image. Modem has no effect on wifi. Any firmware base should work with a 5 GHz router.
Actually... CONGRATULATIONS! You just found a Hellraiser bug! (Well, not a bug, but something Hellraiser doesn't handle right now.)
There are country code entries in nvram_net.txt and nvram_net.txt_murata in /system/etc/wifi. To be able to see most 5 GHz frequencies used in the USA, you need to change the ccode in nvram_net.txt from GB to ALL and in nvram_net.txt_murata from GB to US. (Actually you might need to only do one of these, I need to chat with garyd9. Thank him for this - he just recently dealt with this issue on his Galaxy Note.) The above instructions apply to XWLA1 - If you make the above changes, it SHOULD see all 5 GHz APs in the USA. I9100 bases can see 5 GHz routers - but unlike the 2.4 GHz band where foreign countries only have a few extra bands we don't, for 5 GHz the bands are almost (but not quite) completely nonoverlapping. Changing the country code setting fixes this.
(I just tested this. Stock XWLA1 can't see my 5 GHz AP, with the above changes it can.)
With XWLA1, turning on wifi should at worst not hurt your battery, and in many cases will actually improve battery life.
Well it does suck the juice when I leave wifi on but no biggie since i always kill it when I dont use it
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