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In most of the existing works on cognitive radio (CR) systems, the spectrum sensing and the cross-layer scheduling are designed separately. Specifically, the sensing module first determines whether or not a channel resource is available for the CR system based on the sensing information. The scheduling module then schedules the data transmission of different users on the available channels based on the hard-decision sensing information (HSI). In this paper, we shall propose a joint crosslayer and sensing design and study its performance advantages over the aforementioned traditional decoupled approaches. We shall consider the downlink transmission of an OFDMA-based secondary system sharing the spectrum with primary users using cognitive radio technology. We shall rely on the joint design framework to optimize a system utility, which adapts the power allocation and the subcarrier assignment across the secondary users (under a average interference constraint to the primary users) based on both the channel state information (CSI) and the raw sensing information (RSI). In addition, we shall also propose a distributed implementation for the cross-layer sensing and scheduling design using primal-dual decomposition approach. Simulation results reveals the substantial performance gain of the proposed joint design over the conventional CR systems.