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UnderWater Acoustic Sensor Networks (UW-ASNs) consist of sensors and Autonomous Underwater Vehicles (AUVs) performing collaborative monitoring tasks. In this article, UWMAC, a distributed Medium Access Control (MAC) protocol designed for UW-ASNs, is introduced. The proposed MAC protocol is a transmitter-based Code Division Multiple Access (CDMA) scheme that incorporates a novel closed-loop distributed algorithm to jointly set the optimal transmit power and code length. CDMA is the most promising physical layer and multiple access technique for UW-ASNs because it is robust to frequency-selective fading, it compensates for the effect of multipath at the receiver, and it allows receivers to distinguish among signals simultaneously transmitted by multiple devices. UW-MAC aims at achieving three objectives, i.e., guarantee i) high network throughput, ii) low channel access delay, and iii) low energy consumption. It is demonstrated that UW-MAC simultaneously achieves these three objectives in deep water communications (where the ocean depth is more than 100 m), which are usually not severely affected by multipath. In shallow water communications, which may be heavily affected by multipath, it dynamically finds the optimal trade-off among these objectives according to the application requirements. UW-MAC is the first protocol that leverages CDMA properties to achieve multiple access to the scarce underwater bandwidth, while other protocols tailored for this environment have considered CDMA merely from a physical layer perspective. Experiments show that UW-MAC outperforms many existing MAC protocols tuned for the underwater environment under different architecture scenarios and simulation settings.