Cross-layer design is a promising way to improve Quality of Services (QoS) by making use of the state information from different layers. In this paper, transmissions with random data arrival over fading channels are investigated. Probabilistic scheduling and adaptive modulation aware of both the queue state and the channel state are applied, hence we can formulate a Markov Decision Process. Based on its inherent Markov Reward Process, the average delay and power consumption are analysed and expressed by the steady-state probability distribution. We minimize the average delay given an average power constraint, so that by varying the power constraint, the optimal delay-power tradeoff curve is obtained. It is discovered that the optimization can be transformed into a linear programming. We further study the properties of the optimal scheduling policy and discover that it is threshold-based. These results are validated by numerical and Monte-Carlo simulations.
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