Yunfei Li

The frequency shift of multipath sound rays induced by the motion of a sound source in an ocean waveguide environment is a crucial factor affecting the detection capabilities of both active and passive sonar systems, as well as the quality of underwater communication. Therefore, investigating the sound field characteristics of a moving sound source in the SOFAR channel is of significant importance. By comparing the spectra of continuous-wave (CW) signals with pulse widths of 1 s and 15 s received by a vertical array in SOFAR channel, it was observed that the sound field of the moving source exhibits a stable spectral splitting characteristic. Two frequency shift bright lines in the vertical direction were identified, corresponding to two sets of sound ray paths. One set of sound ray paths corresponds to the direct sound and the first surface-reflected sound, and the other set of sound ray paths corresponds to the first seabed-reflected sound and the first surface- and seabed-reflected sound. This study revealed that the spectral splitting of the moving sound source’s sound field displays a distribution trend in a depth direction similar to that of the multipath delay structure. A multipath sound ray frequency shift calculation model, based on ray theory, was developed to explain and predict the vertical distribution pattern of spectral splitting in the sound field of a moving sound source. By combining the model with measured data, it was found that the spectral splitting arises from the frequency shift differences corresponding to multipath sound ray paths. Additionally, the frequency shifts for the D&S and B&SB ray paths are generally proportional to the cosine values of the initial grazing angles of the sound waves at the emission source and the cosine values of the horizontal azimuthal angle between the source motion direction and the receiver.

Continuous phase modulation (CPM), which is widely used in aviation telemetry and satellite communications, may help improve the performance of underwater acoustic (UWA) communication systems owing to its high spectral and power efficiency. However, applying conventional frequency-domain equalization (FDE) algorithms to CPM signals over time-varying UWA channels considerably degrades performance. Moreover, time-domain equalization algorithms often rely on excessive approximations for symbol detection, compromising overall reception. This study presents an iterative-detection–based time-domain adaptive decision feedback equalization (ID-TDADFE) algorithm that tracks channel variations through symbol-by-symbol detection. The symbol detection in ID-TDADFE fully considers the inherent coding gain of CPM signals can be cascaded with an adaptive equalizer, and enhances symbol detection performance by utilizing joint probability estimation. Numerical simulations with minimum-shift keying (MSK) and Gaussian MSK signals demonstrated that ID-TDADFE significantly improved communication performance over a time-varying UWA channel within one or two iterations. In a sea trial for experimental verification, ID-TDADFE reduced bit errors by 45.08% and 51.8% in the first and second iterations, respectively, compared to FDE.

Based on experimental data from the deep-sea sound channel axis in the Western Pacific, the statistical distribution law of cluster structure and channel delay spread characteristics are analyzed for three typical receiving depths near the sound channel axis in this paper. A ray theory-based underwater acoustic channel model is used to explain the variations in channel parameters over time and the receiving depth. The results indicate that the underwater acoustic communication channel at the channel axis depth over a 20-km range exhibits a clustered structure that depends on the emission angles of sound rays. For the amplitude characteristics, the amplitude of each cluster follows an inverse Gaussian distribution, with the maximum average amplitude observed when the receiver and transmitter depths are similar. The amplitude of each cluster fluctuation decreases as the receiving depth increases. Regarding delay spread characteristics, the delay spread of each cluster, as well as the maximum and root mean square delay spread of the channel, conform to a Gaussian mixture distribution. The mean and fluctuation of the delay spread parameters increase with the receiving depth. Variations in the cluster structure and channel delay spread characteristics above are primarily attributed to the time-varying sound speed along the propagation paths of sound rays emitted at small upward angles.

Gaussian minimum shift keying (GMSK) stands as a specialized form of continuous phase modulation, offering inherent benefits such as a constant envelope and inherent coding gain, which enhance both spectrum utilization and power efficiency within underwater acoustic (UWA) communication. To improve symbol detection performance, a novel iterative detection algorithm is introduced and integrated with frequency-domain equalization (FDE) and time-domain adaptive decision feedback equalization (TDADFE). ID-FDE employs the correlation function to assess the joint probability of both forward and backward information, which becomes particularly valuable within the first two iterations, culminating in a substantial enhancement of symbol detection performance. ID-TDADFE handles interference caused by time-varying UWA channels through symbol-by-symbol detection and second-order digital phase-locked loops. Moreover, it rectifies the input symbols of the feedback filter via the correlation function and prior information. Using the time-varying underwater acoustic channel model for simulation, the results show that for the time-invariant channel, iterative detection can significantly reduce the bit error rate (BER) in 2 iterations, which is about 1dB at a BER of 1 × 10−4. For the time-varying channel, after third iteration, ID-TDADFE displayed better BER performance compared to ID-FDE by approximately 1.7dB at a BER of 1 × 10−4.

Deep-sea acoustic communication has attracted widespread attention in recent years. Research on deep-sea acoustic communication channel characteristics is essential for the development and system design of deep-sea acoustic communication technologies. However, the structural and spatiotemporal characteristics of deep-sea high-frequency acoustic communication channels (unlike those of shallow-water acoustic communication channels) are poorly understood. Based on a channel measurement experiment in a typical deep-sea incomplete sound channel environment in the South China Sea, this paper analyzes the structural and spatiotemporal characteristics of high-frequency underwater acoustic channels in the direct-arrival and shadow zones. The channel multipath vertical structure, amplitudes of different path clusters, root mean square (RMS) delay spread, and channel temporal coherence are investigated at different depths. The randomness of different path clusters is quantified as the coefficient of variation. The channels in the shadow zone are characterized by a complex multi-path structure, high RMS delay spread, and low temporal coherence. On the contrary, the channels of the direct-arrival zone show multi-path convergence, low RMS delay spread, and high temporal coherence. Understanding the dynamic changes in these parameters can guide the statistical modeling of channels and the design of communication algorithms in different zones in deep-sea high-frequency acoustic communication scenarios.