He doesn't want to wait till heaven . . . Paul also says he wants to know the fellowship of sharing in His sufferings , becoming like him in his death. But we have to think deeper. I don't think Paul is saying that he wants to suffer. Paul understands that following Christ will inevitably bring some suffering.
Obedience is costly.
So what is Paul seeking. He desires to receive and to react to the sufferings of this world in the same manner that Jesus did. He wants to face the sufferings and even death with the same kind of perspective that Jesus had. Paul wants to face the trials of life not as a threat, but as an opportunity to grow and testify of the Savior's goodness and love. He wants to have that same confidence in God that Christ had.