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This paper focuses on the problem of ensuring quality of service (QoS) to 4G network users. An adaptive cross-layer (ACL) strategy, that jointly optimizes the parameters of physical (PHY) and medium access control (MAC) layers using queueing theory, is proposed and applied to mobile user communications in an OFDM-based wireless network. PHY and MAC layers are referring to IEEE 802.16 standard, supporting, respectively, different modulations and the automatic repeat request (ARQ) protocol. PHY and MAC layer parameters are here optimally combined by ACL strategy to meet the QoS requirements. The main contribution of the paper is the evaluation of the impact of mobility on ACL strategy performance, by using an accurate channel model that accounts for shadowing effects. The simulation results show that the ACL strategy outperforms non-adaptive or single-layer strategies, in terms of bandwidth savings. Also, ACL strategy is able to guarantee the requested QoS in the different mobility scenarios with different degrees of performance.