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The IEEE 802.11e EDCA function differentiates traffics via parameterized backoff mechanism. However, many studies shown that QoS cannot be assured by only using the EDCA MAC layer function. Cross-layer controls are proven to be generally essential in QoS management. Moreover, unlike legacy DCF functional having specification and description language (SDL) descriptions in the standard, EDCA does not have standard SDL specifications. Therefore, we propose the SDL behavior model of the EDCA with cross-layer interface (EDCA-XLI) so that students and researchers are able to practice their cross-layer design of real-time applications in wireless networks. We demonstrate the deduction processes to show how the legacy DCF specifications are extended into EDCA-XLI. We call the deductions the morphisms from the DCF to the EDCA-XLI. The message sequence chart (MSC) simulations and a fuzzy QoS control implementation example show that the EDCA- XLI SDL not only realize the behavior defined in the IEEE 802.11e standard but also support generic cross-layer signaling design including receiving and feedback signals to protocols at different layers.