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A key research area in underwater acoustic (UWA) communication is the development of advanced modulation and detection schemes for improved performance and range-rate product. In this communication, we propose a variable-rate underwater data transmission system based on direct sequence spread spectrum (DSSS) and complementary code keying (CCK), particularly for shallow-water acoustic channels with severe multipath propagation. We provide a suboptimum receiver that consists of a bidirectional decision feedback equalizer (BiDFE) to cancel both postcursor and precursor intersymbol interference (ISI). We also develop iterative signal processing and time-reversal (TR) diversity processing to mitigate the effect of error propagation in BiDFE. We present performance analysis on bit error rate (BER) for different data rates. Our works show that this new variable-data-rate DSSS-CCK is a suitable candidate for UWA communications over varying channel conditions and distance.