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Multi-carrier OFDM-CDMA has a range of advantages that make it ideal for high data rate wireless access system. In this paper, a cross-layer multi-service random access and channel assignment approach is proposed for the uplink communication of the mm wavelength multi-carrier OFDM-CDMA BWA system. The OFDM-CDMA solution and the iterative interference cancellation and detection are applied at the system's physical layer to support multi-user multi-service capabilities and to improve the robustness against the flat and frequency selective fading. The proposed scheme grants the uplink random access connections and allocates the radio resources to the active multiservice subscriber stations by using the cooperation between base station and subscriber stations, as well as the diversities in spreading codes, subcarriers, time in OFDM symbols, and time division multiplex. A MAC protocol and its connection and channel assignment procedures are described. Numeric simulations of the uplink BWA system with the proposed random access and channel assignment scheme are carried out to evaluate the system's performance.