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In order to support the diverse quality of service (QoS) requirements for differentiated data applications in broadband wireless networks, advanced techniques such as space-time coding (STC) and orthogonal frequency division multiplexing (OFDM) are implemented at the physical layer. However, the employment of such techniques evidently affects the subchannel-allocation algorithms at the medium access control (MAC) layer. In this paper, we propose the QoS-driven cross-layer subchannel-allocation algorithms for data transmissions over asynchronous uplink space-time OFDM-CDMA systems. We mainly focus on QoS requirements of maximizing the best-effort throughput and proportional bandwidth fairness, while minimizing the upper-bound of scheduling delay. Our extensive simulations show that the proposed infrastructure and algorithms can achieve high bandwidth fairness and system throughput while reducing scheduling delay over wireless networks.