Direct-sequence spread spectrum is used for underwater acoustic communications between nodes, at least one of which is moving. At-sea data show that the phase change due to source motion is significant: The differential phase between two adjacent symbols is often larger than the phase difference between symbols. This poses a challenge to phase-detection based receiver algorithms when the source or receiver is moving. A pair of energy detectors that are insensitive to the phase fluctuations is proposed, whose outputs are used to determine the relationship between adjacent symbols. Good performance is achieved for a signal-to-noise ratio (SNR) as low as -10 dB based on at-sea data. While the method can be applied to signaling using short code sequences, the focus in this paper is on long code sequences for the purpose of achieving a high processing gain (at the expense of a low data rate), so that communications can be carried out at a low input SNR to minimize the probability of detection (P-D) by an interceptor. P-D is calculated for a typical shallow water environment as a function of range for several source levels assuming a broadband energy detector with a known signal bandwidth. [DOI: 10.1121/1.2996329]
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