An OFDM wireless communication system with an access point and a plurality of remote user terminals estimates an uplink channel. The access point receives training symbols transmitted by the user terminals. Each training symbol includes pilot symbols associated with phase offset estimation OFDM sub-carriers. The phase offset estimation sub-carriers include subsets of sub-carriers associated with each respective user terminals. Each subset is used exclusively by the associated user terminal during channel estimation. The channel estimation sub-carriers are used by all user terminals. For each terminal the access point estimates symbol-specific phase offsets specific to the user terminal using the received pilot symbols associated with the user specific subset of the phase offset estimation sub-carriers. The access point also estimates the uplink channel using the user-terminal-symbol-specific phase offset estimates and the received symbols.