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In this paper, a single element receiver for short-range shallow water communication is proposed as an alternative to costly beamformer structures by utilizing state-of-the-art iterative demodulation techniques. The proposed receiver structure employs an adaptive decision feedback equalizer (DFE) and bit interleaved coded modulation with iterative decoding (BICM-ID) in conjunction with adaptive Doppler compensation. The performance of the proposed receiver is compared with an iterative receiver employing turbo-coded BICM (turbo-BICM) and a noniterative receiver employing a Reed-Solomon (RS) code. Experimental results show that the performance of a coding scheme strongly depends on the ability of the adaptive DFE to equalize the time-varying channel. It is also shown that under severe channel conditions the RS code, which is capable of correcting burst errors, fails to give acceptable performance even in the case where perfect decisions were fed back into the DFE. It is, therefore, established that the BICM-based receivers, i.e., turbo-BICM and convolutional BICM-ID, outperform the non-BICM-based receiver. Furthermore, it has been established that there exists a fundamental tradeoff between the Doppler correction factor and the receiver performance. In practice, a large Doppler correction factor is required to compensate for severe Doppler effects, however, it leads to noise enhancement in the system. The critical result is that although the proposed convolutional BICM-ID receiver matches approximately the performance of turbo-BICM, it exhibits lower implementation complexity and reduced memory requirements, attributes that are attractive for robust high data-rate underwater acoustic modems.