This paper addresses the problem of carrier frequency synchronization and time-varying channel equalization in the uplink of a broadband multi-user wireless communication system employing an oversampled perfect reconstruction filter bank (OPRFB) transceiver structure for multi-carrier modulation. Based on the maximum likelihood (ML) principle, a pilotaided joint estimator of the carrier frequency offsets (CFO) and channel equalizer coefficients of the multiple users is proposed. The performance of the new estimator is examined for various subband allocation schemes by means of numerical simulations under realistic conditions of operation. For mobile users with time-varying fading channels, we also study the effect of using different distributions of pilots over time. Our results show that the proposed estimator can provide accurate estimates of the unknown CFO and channel parameters, which in turn can be used to design effective compensation mechanisms.