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In cognitive radio (CR) networks, the end-to-end transmission-control protocol (TCP) performance experienced by secondary users is a very important factor that evaluates the secondary user perceived quality of service (QoS). Most previous works in CR networks ignore the TCP performance. In this paper, we take a cross-layer design approach to jointly consider the spectrum sensing, access decision, physical-layer modulation and coding scheme, and data-link layer frame size in CR networks to maximize the TCP throughput in CR networks. The wireless channel and the primary network usage are modeled as a finite-state Markov process. Due to the miss detection and the estimation error experienced by secondary users, the system state cannot be directly observed. Consequently, we formulate the cross-layer TCP throughput optimization problem as a partially observable Markov decision process (POMDP). Simulation results show that the design parameters in CR networks have a significant impact on the TCP throughput, and the TCP throughput can be substantially improved if the low-layer parameters in CR networks are optimized jointly.