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Multi-carrier OFDMA-CDM has a range of advantages that make it ideal for high data rate wireless access system. In this paper, we propose a multi-user multi-service random access and channel assignment approach for the uplink communication of the mm wavelength multi-carrier OFDMA-CDM BWA system. The OFDMA-CDM 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 multi-service 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 are carried out to evaluate the system's performance.