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Severe cochannel interference in wireless cellular networks significantly affects users at cell edges. We propose a cost-effective cochannel interference avoidance (CIA) medium access control (MAC) scheme to improve network performance. For CIA-MAC, base stations judged as severe interferers transmit randomly and the transmission is controlled by wireless channel states to optimize the overall network performance while maintaining proportional fairness among users. Conditions for triggering CIA-MAC are derived and two simple trigger mechanisms are obtained. The CIA-MAC scheme requires low signaling overhead and only minor changes to the existing mobile systems. Simulation results show that the proposed scheme, CIAMAC, significantly outperforms traditional approaches through the avoidance of severe cochannel interference as well as the exploitation of multiuser diversity through cross-layer design.