Is there any compatibility issue while using wifi-direct between different cell phone vendors? I was trying to transfer a file via my LG optimus L9 (T-mobile) wifi-direct to my friend's Samsung galaxy S3, it got connected successfully however shortly after sending initialization, I got an error "Sending Failed".

then I tried the other way i.e. Recieving, but no success.

Later, I have tried with my another friend's Samsung galaxy Note, but no success.

nobody around having LG device with wifi-direct feature.

Can someone tell why is that going wrong?
Why don't you try using a 3rd party implementation just as Izzy suggested. My ROM doesn't have that feature so I typically use Fast File Transfer. It's a great app and only the host phone needs it. Currently it doesn't work with host HTC phones though.