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There is an emerging need for high-rate underwater acoustic (UW-A) communication platforms to enable a new generation of underwater monitoring applications including video streaming. At the same time, modern UW-A communication architectures need to be flexible to adapt and optimize their communication parameters in real time based on the environmental conditions. Existing UW-A modems are limited in terms of achievable data rates and ability to adapt the protocol stack in real time. To overcome this limitation, we present the design, implementation, and experimental evaluation of a new high-rate software-defined acoustic modem (SDAM) with real-time adaptation capabilities for UW-A communications. We introduce new physical-layer adaptation mechanisms that enable either joint adaptation of communication parameters such as modulation constellation and channel coding rate or seamless switching between different communication technologies such as orthogonal-frequency-division-multiplexing and direct-sequence-spread-spectrum. The performance of the proposed SDAM has been evaluated in both indoor (water tank) and outdoor (lake) environments. We demonstrated that the SDAM achieves 104 kbit/s with bit-error-rate (BER) of 2 × 10-5, 208 kbit/s with BER of 10-3, and 260 kbit/s with BER of 10-2 in real time over a 200 m horizontal link at a very-shallow lake environment.