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Cognitive radio (CR) is the key enabling technology for an efficient dynamic spectrum access. It aims at exploiting an underutilized licensed spectrum by enabling opportunistic communications for unlicensed users. In this work, we first develop a distributed cognitive radio MAC (COMAC) protocol that enables unlicensed users to dynamically utilize the spectrum while limiting the interference on primary (PR) users. The main novelty in COMAC lies in not assuming a predefined CR-to-PR power mask and not requiring active coordination with PR users. COMAC provides a statistical performance guarantee for PR users by limiting the fraction of the time during which the PR users' reception is negatively affected by CR transmissions. To provide such a guarantee, we develop probabilistic models for the PR-to-PR and the PR-to-CR interference under a Rayleigh fading channel model. From these models, we derive closed-form expressions for the mean and variance of interference. Empirical results show that the distribution of the interference is approximately lognormal. Based on the developed interference models, we derive a closed-form expression for the maximum allowable power for a CR transmission. We extend the min-hop routing to exploit the available channel information for improving the perceived throughput. Our simulation results indicate that COMAC satisfies its target soft guarantees under different traffic loads and arbitrary user deployment scenarios. Results also show that exploiting the available channel information for the routing decisions can improve the end-to-end throughput of the CR network (CRN).