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Underwater acoustic sensor networks can be employed by a vast range of applications, retrieving accurate and up-to-date information from underneath the water surface. Although widely used by radios in terrestrial sensor networks, radio frequencies do not propagate well underwater. Acoustic channels are therefore employed as an alternative to support long-distance and low-power communication underwater, even though such channels suffer from long propagation delay and very limited bandwidth. In this paper, we investigate the impact of the large propagation delay on the throughput of selected classical MAC protocols and their variants, and show that protocols need to be revised to accommodate large propagation delay in order to achieve good throughput. We then introduce a propagation-delay-tolerant collision avoidance protocol named PCAP and show that by taking into account the propagation delay, PCAP offers higher throughput than the protocols that are widely used by conventional wireless communication networks.