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In this paper, we consider a broadband secondary transmitter-receiver pair which interferes with N narrowband primary users and study the effect of cognition and cooperation on the maximum stable throughput. In our study we focus on four transmission protocols as well as two channel types, i.e., flat fading and frequency selective fading. In the cooperative protocols, the broadband transmitter relays the packets of the primary users which have not correctly decoded at the primary receiver. The analysis includes random packet arrivals at the transmitters which may impact on the maximum stable throughput. Moreover, sensing errors at the secondary user are considered. In this paper, we derive the exact stability region for non-cooperative protocols and inner bounds for cooperative ones. The results reveal that depending on the channel states, the cooperative protocols may provide significant performance gains over non-cooperative protocols. Numerical results indicate that in the frequency selective channel, independent and simultaneous parallel transmissions in the available subbands are preferred, while in the flat fading channel, a non-parallel transmission in the total available bandwidth is recommended. In part II of our paper, we investigate the impact of cognition and cooperation on the delay performance of the protocols introduced in this paper.