Which AP and switch are compatible with this wireless controller?
We need an AP for outdoor which one is the best and compatible with this equipment?
Depends on the firmware your controller is running. You can start with all APs that support 802.11ac wave 1 and APs that support CleanAir. Don't bother going "cheap" and getting APs that only support up to 802.11n because future firmware releases will no longer "support" them. So APs to look for are AP2700 and AP3700. Cisco will be releasing 3800 in the next few months.
For outdoor, I'd recommend 1552U.
How can i know the range of the AP?
Depends on the AP, the antenna and data rates. But if you left everything to it's default value, you should get about 40 metres in a single direction when running 802.11b and about 25 metres on 802.11a.
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