I have already Googled a bit, but I haven't found a list specifying the supported devices.
Is it possible to use Wi-Fi Direct on Samsung Galaxy Mini (GT-S5570B with Android 2.3.6 Gingerbread)? Is there a hardware limitation?
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WiFi Direct can be used on all Android devices. Android 4.0 and higher comes with this feature pre-installed.
If your device runs an older version of Android, you can find many apps in the Google Playstore to enable direct file sharing service over WiFi. Go for SuperBeam, Fast File Transfer, WiFi File Transfer, etc.