Analysis of High-Frequency Communication Channel Characteristics in a Typical Deep-Sea Incomplete Sound Channel

Abstract

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.

1. Introduction

Underwater acoustic channels are generally regarded as one of the most difficult communication channels nowadays [1]. Compared to radio frequency wireless communication, underwater wireless communication may suffer random fluctuation of the sea surface, internal waves [2], turbulence [3], and other complex physical phenomena. These phenomena increase the difficulty of high-speed and high-reliability underwater acoustic communication. The performance of underwater acoustic communication systems is further affected by multipath effects, Doppler frequency shifts, attenuation of sound wave transmission, and limited bandwidth [4]. Therefore, by studying the statistical and other characteristics of underwater acoustic channels, we can guide the design of underwater acoustic communication systems and develop robust underwater acoustic communication algorithms.

Many researchers have studied the spatiotemporal characteristics of underwater acoustic channels. Previous studies have focused on three characteristic channel parameters: amplitude, delay spread, and channel temporal coherence. As a basis for statistical channel modeling, the distribution of the envelope amplitude has been fitted to Rayleigh distribution [5,6,7], Rice distribution [8,9,10,11], lognormal distribution [12,13], K distribution [14,15], and Burr distribution [16]. Most of these studies analyze specific experimental data for statistical modeling of channel amplitudes and fading, providing references for channel prediction and channel tracking. Meanwhile, studies on delay spread have analyzed the average, maximum, and RMS delay spreads [17], which represent the expansion degree of a channel in the delay domain. Delay spread lasts several to hundreds of milliseconds in shallow-sea channels, extending to several or tens of seconds in deep-sea channels. RMS delay spread, which reflects the complexity of the channel structure, is reportedly more related to the performance of a communication system [18] and is adopted as the performance index in evaluations of channel models [19]. In 2023, Fan et al. introduced this parameter to reinforcement learning and proposed a new communication-strategy algorithm [20]. Meanwhile, the channel temporal coherence is a second-order statistic reflecting the fluctuations of a channel on a certain time scale. The performance of the adaptive equalizer depends on how well it adapts itself to the changing channel within the signal coherence time [21]. This parameter is essential for communication systems design and is commonly adopted [11,14,22,23,24,25] for characterizing temporal variation of channels.

Channel characteristics are usually investigated using the data of high-frequency and low-frequency experiments in shallow-sea zones and the data of low-frequency experiments in deep-sea zones. The channel characteristics of deep-sea high-frequency acoustic communications are rarely reported. At present, high-frequency acoustic communication has been adopted in the field of marine resource exploration, ecological environment monitoring, submarine observation network construction, underwater reconnaissance, and underwater robot cluster cooperation. High-frequency underwater acoustic communication technology with a short distance, high reliability, and high data rate is particularly important. However, there are some challenges in high-frequency underwater acoustic communication. Firstly, the spatial variation in temperature, salinity, and density determines the complex distribution of the sound speed profile. It causes the fluctuation of the sound field in the process of sound wave propagation. Secondly, the transmission loss of high-frequency sound waves is relatively large. Thirdly, multiple reflections of sound waves cause serious large-delay multipath effects. Fourthly, the relative motion of the transmitter and receiver and the dynamic marine environment make the phase of the received signal fluctuate randomly and the Doppler frequency shift and spread. On this basis, it is of great significance to study high-frequency underwater acoustic channels to overcome the challenges mentioned above. To this end, this paper analyzes the experimental data of a deep-sea communication experiment in the South China Sea. Adopting previously reported channel characteristic analysis methods, it investigates the spatiotemporal channel characteristics of the shadow zone and the direct-arrival zone in a shallow-depth transmitted high-frequency underwater acoustic channel. Theoretical explanations of the findings are also provided.

The main contributions of this paper are summarized below.

(1) The main arrival paths of the multipath and vertical structures of channels at different depths are analyzed in a deep-sea shallow-depth high-frequency transmitted scenario. The simulated channel impulse response (CIR) structure is consistent with the measured CIR structure, providing a basis for determining the arrival paths of the multipath in subsequent analysis. The path clusters of different channel arrival paths are distinguished to provide the amplitude distributions of different path clusters in the channels at different receiving depths. Meanwhile, the randomness degrees of the path clusters are evaluated in terms of the coefficient of variation.

(2) The study analyzes the spatial distribution of RMS delay spread, which is closely related to the communication performance. The instantaneous changes in RMS delay spread are investigated in the shadow zone and the direct-arrival zone. By elucidating the depth dependence of the fluctuations in average RMS delay spread, we can provide a parameter basis for communication decision algorithms.

(3) The study analyzes the channel temporal coherences at different depths in the shadow and direct-arrival zones, along with the temporal coherences of individual path clusters in different zones. This research component can guide the design of algorithms for channel tracking and channel equalization in deep-sea shallow-depth high-frequency transmitted communications.

The remainder of this paper is organized as follows. Section 2 introduces some brief information on the channel measurement experiment, and Section 3 defines the channel statistics (multipath amplitude, RMS delay spread, coefficient of variation, and channel temporal coherence). Section 4 analyzes the experimentally derived channel statistics and obtains the temporal and spatial characteristics of the channel. Section 5 concludes the study. Section 6 provides future work plans. Abbreviations part explains the abbreviations used in the paper.

2. Overview of the Experiment

The data of this paper were derived from a deep-sea communication experiment in the South China Sea conducted in July 2021. The experimental area is displayed in Figure 1.

O1 and S1 in Figure 1 are the transmitting and receiving points, respectively, and the range between them is 14.8 km. The sea floor between these points is relatively flat, with an approximate sea depth of 3790 m.

The receiving array consists of 44 self-recording hydrophones arranged at unequal intervals. The receiving depth ranges from 124 to 3605 m. Figure 2 is a schematic of the experiment.

The linear frequency modulation (LFM) signal has good autocorrelation performance and is not sensitive to Doppler, so it is usually used for channel estimation in underwater acoustic communication. In this experiment, LFM signals were transmitted by an underwater acoustic transducer suspended at a depth of 44.8 m from an experimental ship at point S1 in Figure 1. The center frequency of the transmitted signal was 10 kHz and the bandwidth was 4 kHz. Figure 3 shows the time-frequency diagram of the transmitted signal.

The duration of the LFM signal was set to 1 s and the time interval between adjacent LFM signals was 4 s. The transmitted signal consisted of 41 LFM signals. Figure 4 shows the sound speed profile measured during the experiment. The approximate depth of the sound channel axis was 1110 m. The sound speeds at the bottom and the surface were 1523 and 1544 m/s, respectively. As the sound speed at the sea surface was greater than that near the seabed, it was a typical incomplete sound channel. Incomplete sound channels commonly exist in the South China Sea, so it is of significance to study the channel characteristics in such a scenario.

The received signals were obtained from the hydrophones. The CIRs were obtained by processing the received data. Then, the vertical structure change, coefficient of variation, RMS delay spread, and temporal coherence of channels were analyzed according to the CIRs of different positions and times. Specific analytical methods are described in the next section.

3. Underwater Acoustics Channel Statistics

3.1. CIR

The CIR is obtained by correlating the received signal and the LFM signal in the frequency domain, as shown in Figure 5.

In Figure 5, $r(t)$ and $x(t)$ represent the received and the transmitted LFM signal, respectively. $R(\omega )$ and $X(\omega )$ denote the frequency responses of the processed received and transmitted signals, respectively. $h(t,\tau )$ is the CIR at sampling time $t$.

All processed signals and channels in Figure 5 and those mentioned below are in the discrete form. As a result, the output CIR can be written as $h(n{T}_{ch},m{T}_t)$, where $t=n{T}_{ch}$, $\tau =m{T}_t$, $n$ is the index of the received LFM signal, there are $N$ received LFM signals in total, and $m$ is the tap sampling index in the delay domain. $T_{ch}$ represents the sampling interval between adjacent CIRs, and $T_t$ represents the sampling interval between adjacent taps in an individual CIR.

3.2. Cluster Amplitude and Coefficient of Variation

Each path cluster may contain multiple rays, which appear as different taps in the CIR. Here, the amplitude of the path cluster is not the maximum peak of the path cluster because the phase of the arrival rays is time variable for the same delay, causing large fluctuations in the maximum peak. Instead, the amplitude of each path cluster is characterized by energy averaging. For this purpose, we introduced a threshold $T_m$ and calculated the cluster amplitude $A_k$ of the $k\mathrm{t}\mathrm{h}$ path cluster as follows [11]:

$$A_k(n)=\sqrt{\frac{1}{M_k}{\displaystyle \sum _{m_k=1}^{M_k}{h}^2(n,\{m_k|\frac{\left|h(n,m_k)\right|}{\max (\left|h(n,m_k)\right|)}\ge T_m\})}},$$

(1)

Equation (1) calculates the RMS of several adjacent taps, satisfying $\left|h(n,m_k)\right|/\max (\left|h(n,m_k)\right|)\ge T_m$ in the $k\mathrm{t}\mathrm{h}$ path cluster. $A_k(n)$ is the amplitude of the $k\mathrm{t}\mathrm{h}$ path cluster at the $n\mathrm{t}\mathrm{h}$ sampling time. $M_k$ is the total number of taps satisfying the threshold condition in the $k\mathrm{t}\mathrm{h}$ path cluster, and $m_k$ is the tap index of the $k\mathrm{t}\mathrm{h}$ path cluster. The time interval between two adjacent taps must exceed the time resolution.

There are some path clusters in the channels of the shadow and direct-arrival zones with extraordinarily small amplitudes. Path clusters with amplitudes below a threshold can be ignored because their energies negligibly contribute to the CIR. These path clusters can be treated as noise in communication systems. The selection criterion of a channel path cluster is given by

$$\frac{A_k(n)}{\max \left\{A_k(n\left)\right|k=1,2,\dots ,K\right\}}\ge T_c,$$

(2)

where $K$ is the total number of path clusters, and $T_c$ is the threshold of the ratio between the $k\mathrm{t}\mathrm{h}$ path cluster in a channel and the maximum energy cluster in a channel. The $T_c$ in the shadow and direct-arrival zones was initially set to empirical values of 0.1 and 0.05, respectively.

After determining the number of path clusters in the channel, we evaluated the arrival paths of these clusters based on the simulation results. The path clusters with different arrival paths were separated for statistical analysis post-processing.

As mentioned above, the randomness degrees of the different clusters are quantified by their coefficients of variation, defined as

$$D_k=\frac{\sqrt{\frac{1}{N}{\displaystyle \sum _{n=1}^N{\left(A_k(n)-\overline{A_k}\right)}^2}}}{\overline{A_k}}.$$

(3)

In Equation (3), $A_k(n)$ represents the amplitude of the $k\mathrm{t}\mathrm{h}$ path cluster in the channel obtained at the $n\mathrm{t}\mathrm{h}$ sampling time, and $\overline{A_k}=1/N{\displaystyle {\sum }_{n=1}^N{A}_k(n)}$. Equation (3) computes the standard-to-mean deviation of the amplitude of $k\mathrm{t}\mathrm{h}$ path cluster over $N$ CIRs.

3.3. RMS Delay Spread

In wireless communication, the RMS delay spread is referred to as the multipath spread and provides a good measure of time dispersion of the channel [26]. This parameter can reflect the complexity of the channel. In this paper, instant and average RMS delay spread of the channels were measured. The instant RMS delay spread is defined as [27]

$${\tau }_{RMS}(n)=\frac{1}{f_s}\sqrt{\frac{{\displaystyle \sum _{t=1}^{M_{tap}}{(m_t-\overline{m})}^2{\left|h(n,m_t)\right|}^2}}{{\displaystyle \sum _{t=1}^{M_{tap}}{\left|h(n,m_t)\right|}^2}}},$$

(4)

where $M_{tap}$ denotes the number of taps, and $f_s$ is the sample rate. $m_t$ is the tap index used for calculating the RMS delay spread. The average delay spread $\overline{m}$ is determined as

$$\overline{m}=\frac{{\displaystyle \sum _{t=1}^{M_{tap}}{m}_t{\left|h(n,m_t)\right|}^2}}{{\displaystyle \sum _{t=1}^{M_{tap}}{\left|h(n,m_t)\right|}^2}},$$

(5)

The amplitude of one tap should satisfy Equation (2). The delay interval between two adjacent taps must be greater than or equal to the time resolution. The average RMS delay spread is defined as

$$\overline{{\tau }_{RMS}}=\frac{1}{N}{\displaystyle \sum _{n=1}^N{\tau }_{RMS}}(n).$$

(6)

3.4. Temporal Coherence Coefficient

The time variation of the channel is defined in terms of the temporal coherence, which describes the coherence degree of the channel within a certain time. The temporal coherence is defined as [23]:

$$\rho (n,\Delta n)=〈\frac{{\displaystyle \sum _{m=1}^M{h}^{*}(n,m)h(n+\Delta n,m)}}{\sqrt{{\displaystyle \sum _{m=1}^M{\left|h(n,m)\right|}^2{\displaystyle \sum _{m=1}^M{\left|h(n+\Delta n,m)\right|}^2}}}}〉,$$

(7)

where $〈\cdot 〉$ denotes the ensemble average over time sampling index $n$. $h(n,m)$ and $h(n+\Delta n,m)$ denote the CIRs measured at time sampling index $n$ and $n+\Delta n$, respectively. $M$ denotes the number of taps used in the calculation and $*$ denotes the conjugation operation.

4. Analysis of the Experiment Data

In this section, we use the statistical parameters defined in Section 3 to study the channel characteristics of the shadow zone and the direct-arrival zone. We focus on the following four channel characteristics.

4.1. Vertical Structure Change in Channel

The arrival paths of different path clusters were determined for subsequent characterization of the path clusters. Based on the number of reflections from the sea bottom and the sea surface, the path clusters were divided into the direct path cluster (D), surface path cluster (S), bottom path cluster (B), surface–bottom path cluster (SB), bottom–surface path cluster (BS), and surface–bottom–surface path cluster (SBS). The deep-sea high-frequency sound field can generally be simulated using Bellhop [28], which simulates the channel vertical structure and determines the arrival paths of a multipath of experimental channels, thus providing physical support for the analysis.

The measured sound speed profile and the environmental parameters (see

Table 1. Parameters used in the simulation.

Environmental Parameters	Value
Frequency range (kHz)	8–12
Transmitter depth (m)	44.8
Range between transmitter and receiver (km)	14.8
Receiver depth (m)	124–3605
Sea depth (m)	3790

for a partial list) were input to Bellhop. The absorption loss, density, and sound speed of the sea bottom were set to empirical values. The simulated sound field over a horizontal range of 25 km is shown in Figure 6.

As shown in Figure 6, an obvious boundary between the direct-arrival and shadow zones appeared. At a range of 14.8 km, it was at a depth of around 3400 m. The contributions of path clusters to the channel depend on their receiving depths. The arrival paths of path clusters of different channels were identified by comparing the experimental and simulation results. Then, the structural characteristics of the channels at different receiving depths were analyzed at 14.8 km.

The CIR was simulated using the Fourier frequency domain synthesis algorithm [29]. The transmitted source level was ignored and the actual sea bottom and sea surface parameters were different from those input to the simulation. The simulation results provided only the vertical changes in the channel structure rather than the absolute channel amplitudes. The simulation was intended only to guide the identification of the path clusters of the actual channel. The experimentally and numerically obtained vertical structure changes in the channel in the distance of 14.8 km are compared in Figure 7.

As shown in Figure 7, the vertical structures of the simulated channels and the measured channels were the same. Five path clusters with different arrival paths (S, B, SB, BS, and SBS, listed in order of arrival) appeared in the shadow zone. The relative delays between the path clusters changed with the receiving depth, but the sequence of the arrival path clusters remained. In the bottom part of the sea, where the direct-arrival zone is, except for the above path clusters, there was also D, and D arrived before S.

Figure 8 shows the details of some clusters. As shown in Figure 8a, the delay between SB and B decreased when the depth increased. This is because the distance difference between B and SB became smaller. Figure 8b shows that, when the receiving depth was greater than 3405 m, D started to arrive, and it arrived before S. As the depth increased, the relative delay between the two path clusters increased and the expansion and absorption losses of D also increased with the depth; hence, the energy of D decreased.

Table 2. The ratio of the amplitude of different path clusters to the maximum energy path cluster at different receiving depths.

Rd (m)	D	S	B	SB	BS	SBS
605		0.186	1	0.521	0.350	0.303
1405		0.219	1	0.574	0.241	0.246
2405		0.549	0.858	1	0.168	0.162
2605		0.804	1	0.880	0.054	0.039
3505	1	0.460	0.118	0.084	0.008	0.007
3605	1	0.561	0.222	0.100	0.009	0.008

shows the ratios between the amplitude of different path clusters and the maximum amplitude of all arrived arrival clusters at six different depths. When the depths were shallower than 2405 m, the amplitude ratios of all path clusters except for D, of which there was none at these depths, were greater than the threshold. According to Equation (2), all of the path clusters’ energy contributes to the channel. The amplitude ratios of BS and SBS decreased with depth. When depths were greater than 2605 m, the two ratios were smaller than the threshold. Hence, their energy contributions to the channel were negligible.

It is worth mentioning that, due to the fluctuation of the sea surface, S may suffer severe time variance. Sometimes the ratio of S is smaller than the threshold and its energy contribution to the channel is negligible. Figure 9 shows an example where the time variance of S was more obvious than that of other clusters. During the first 32 s, the amplitude of S was very small, making the ratio smaller than the threshold. But at 48 s and 160 s, the amplitude was on the same level as the maximum cluster.

The above analysis clarifies different structural characteristics in the CIRs of the shadow and direct-arrival zones. In the shadow zone, S was affected by random fluctuations of the sea surface and experienced serious energy loss at large grazing angles. In some instances, the energy of S dropped to negligible levels. At most depths, the path clusters that contributed to the channel were B, SB, BS, SBS, and possibly S. But where the depth was greater than 2605 m, the energy of BS and SBS dropped down to a level that made them negligible.

The path clusters in the direct-arrival zone were D, S, B, and SB. Because D was affected only by water absorption during propagation, its energy was higher than that of the other clusters. The amplitudes of BS and SBS, with large transmission losses, violated Equation (2), and their energy contributions to the channel were negligible.

4.2. Coefficient of Variation of the Cluster Amplitudes

The coefficient of variation, which is closely related to the statistical characteristics of the channel amplitude, can quantify the randomness of different path clusters. It provides a basis for subsequent channel statistical modeling [11] and guidance for equalizer designs in deep-sea communication.

This subsection analyzes the amplitudes of different path clusters in the channel. A stable path cluster in a channel should have a narrow amplitude distribution. A wide distribution implies that the cluster is influenced by random factors that enlarge its fluctuations and enhance its randomness.

The path clusters contributing non-negligibly to the channel at six typical depths were selected and separated for analysis. Figure 10 shows the amplitude distributions of the individual path clusters.

The coefficients of variation of the different path clusters at different depths are listed in Table 2.

As shown in

Table 3. Coefficients of variation of the path clusters at different depths.

Rd (m)	D	S	B	SB	BS	SBS
605		0.328	0.047	0.258	0.284	0.202
1405		0.270	0.029	0.278	0.160	0.121
2405		0.492	0.063	0.256	0.156	0.137
3105		0.434	0.060	0.334
3505	0.193	0.274	0.061	0.330
3605	0.132	0.333	0.034	0.314

, in both zones, the path clusters related to the sea surface presented high coefficients of variation, indicating a high degree of randomness. The fluctuation of the sea surface led to variations in grazing angle and ultimately changed the energy loss of the path clusters interacting with the sea surface. Meanwhile, the bubbles generated by wind and waves introduced many scattering paths to the path clusters.

The coefficient of variation of B was very low in both zones, indicating that B was stable. During the experiment, the movement of the transducer and the receiver was small and the sea bottom was approximately flat, so the grazing angles between the rays in B and the sea bottom were almost constant. Therefore, the energy loss of B was consistent over a certain period of time and the amplitudes were very stable.

In the direct-arrival zone, the amplitude distribution width and coefficient of variation of D were between those of the sea surface-related clusters and B. The amplitude of D was very sensitive to phase changes, leading to a wide amplitude distribution and high coefficient of variation.

In this subsection, the coefficient of variation was used to quantify the randomness of the amplitude of a single-arrival cluster. In both the shadow and direct-arrival zones, a single channel comprised a set of stable path clusters and a series of random path clusters. The path clusters related to the sea surface were affected by random fluctuations and scattering from the sea surface, which introduced amplitude and phase fluctuations and numerous micro-paths that increased the randomness of the clusters. In contrast, the sea bottom interface was not notably changed within a few minutes of the experiment, which led to B being stable.

4.3. RMS Delay Spread

RMS delay spread assesses the complexity of the channel structure and characterizes the dispersion of propagation delay. The instant and average RMS delay spreads were calculated with Equations (4) and (6), respectively.

Figure 11a,b present the instant RMS delay spread temporal variations at depths shallower and greater than 500 m, respectively, and Figure 11c shows the average RMS delay spread as a function of the receiving depth. The average RMS delay spread fluctuated greatly at depths shallower than 500 m, and the instant RMS delay spreads at depths of 144, 246, and 328 m varied widely over time. Figure 12 shows representative three-dimensional amplitude variations of the CIR at depths of 144 and 246 m.

The CIRs at both depths contained S, B, SB, BS, and SBS. At a depth of 144 m (Figure 12a), the energy of the channel was almost entirely contributed by B, SB, BS, and SBS. The energy contribution of the channel mainly came from the last four path clusters, with a relatively small delay before 116 s. The approximate instant of RMS delay spread at 144 m ranged from 0.2 to 0.3 s. After 116 s, the energy of the S was increased by fluctuations of the sea surface, which changed the grazing angle of the rays in S. The energy contribution ratios of the path clusters to the channel differed from those of the previous sampling period. When the sampling time reached 116 s, S was added to B, SB, BS, and SBS with short relative delay, and the instant RMS delay spread increased. The average RMS delay spread at 144 m was 0.32 s.

At depths shallower than 500 m, the maximum value of the average RMS delay spread was 0.51 s at 246 m. As shown in Figure 12b, S highly contributed to the energy of the CIR at most sampling times and was separated by a large relative delay from the other path clusters. Consequently, the average RMS delay spread was high at 246 m. When the energy contribution of S (with a higher relative time delay than the other four path clusters) was lowered by sea surface fluctuations, the average RMS delay spread was low; otherwise, increased.

The average RMS delay spread decreased when the receiving depth increased to depths below 500 m. Figure 13 shows representative three-dimensional plots of the CIR amplitudes at depths of 805 and 905 m.

The arrival paths of the path clusters at both depths were the same as those at depths shallower than 500 m. The path clusters were S, B, SB, BS, and SBS. However, most of the energy of the channel at 805 m was contributed by B and SB, which presented small relative delays. BS and SBS provided low-energy contributions.

When the receiving depth increased to 1505 m, S (with a larger relative delay than the other path clusters) gradually gained energy and contributed more strongly to the CIR. Moreover, the relative delay difference between the last two path clusters and the two middle path clusters increased. As BS and SBS also contributed to the energy of CIR, the average RMS delay spread increased with increasing receiving depth.

As the energies of B and SB increased, their contributions became more concentrated in the delay domain below 1505 m. As the energy contributions of S, BS, and SBS to the channel were small, the RMS delay spread decreased with increasing energies of B and SB. As shown in Figure 14, when the depth reached 1905 m, the energies of both clusters decreased from those at 1805 m. The decreased energy contributions of these two path clusters increased the average RMS delay spread at this depth. Below 1905 m, the average RMS delay spread fluctuated the same way as the fluctuations at depths near the sea surface. As the receiving depth increased, the expansion and absorption losses of B decreased and the energy contributions of other path clusters (except for SB) related to the sea surface decreased; accordingly, the average RMS delay spread decreased between 1905 and 2605 m.

In the 2605–3305 m range of receiving depths, the energy of the channels was sourced from S, B, and SB. The energy contribution of S to the channel was also small at these depths. As most of the energy was provided by B and SB, the RMS delay spreads at these depths were very small (~0.1 s).

At receiving depths within the direct-arrival zone (>3405 m), the energy of the channels was sourced from D, S, B, and SB. The relative delays of these four path clusters were very small and essentially converged. The energy of the channels in this zone was mainly sourced from D, with no interface loss. Therefore, the average RMS delay spread was very low (<0.1 s).

The above analysis led to the following conclusions:

(1) At depths shallower than 500 m in the shadow zone, the average RMS delay spread largely fluctuated under the influence of sea surface fluctuations.

(2) When B majorly contributed to the channel in the shadow zone, the depth-dependent fluctuations in the average RMS delay spread were caused by energy changes in this cluster.

(3) At depths greater than 2605 m in the shadow zone, the energies of BS and SBS in the channels were small and could not satisfy Equation (2). Therefore, the energy of the channel was sourced mainly from B and SB, with small relative delays, and the RMS delay spread was relatively low (~0.1 s).

(4) Within the direct-arrival zone, the path clusters converged and the energy of the channel was mainly sourced from D, with no interface loss. The channel structure was simple and the average RMS delay spread was low (<0.1 s).

4.4. Channel Temporal Coherence and Cluster Analysis

This subsection distinguishes and identifies the path clusters with different arrival paths and analyzes the temporal coherence of channels and single-path clusters. Single-path clusters were separated using the method in [11].

During the experiment, the transmitting ship drifted while the receiving hydrophone array was anchored to the sea bottom by a sinker. The relative motion of the transmitter and receiver caused a Doppler frequency shift in the received signal. The experimental records revealed constant speed and direction of the ship during the measurement period. The Doppler frequency shift in the received signals was removed as described in [14]. The temporal coherence of channels at different receiving depths was then calculated using Equation (7). The temporal coherence results at different receiving depths are shown in Figure 15.

At the shallow depths of the shadow zone (depths shallower than 500 m), the temporal coherence of the channel usually remained at 0.2 throughout the CIR measurement period. The coherence at 246 m was selected for further analysis (see Figure 16).

As is shown in Figure 16a, clusters arrived in the order of S, B, SB, BS, and SBS, and all of them provided clear contributions to the channel. Figure 16c indicates that the temporal coherence of all path clusters related to the sea surface was very low due to the fluctuation of the sea surface. Meanwhile, the temporal coherence of B declined slowly over time. Clusters with high randomness that contributed more energy to the channel led to low temporal coherence at shallow depths in the shadow zone.

As the receiving depth increased, B and SB, with high energy contributions to the channel, had an obvious influence on the temporal coherence of the channel.

The temporal coherence of the channels differed between the depths of 1805 m and 1905 m, as shown in Figure 17b and Figure 18b. Based on Figure 17a and Figure 18a, it was determined that the main energy of the channel at both depths was mainly sourced from B and SB, but the energy contributions of B and SB were more similar at the former depth than at the latter depth. At 1905 m, the main energy source of the channel was SB, with higher randomness than B. Figure 17c and Figure 18c indicate that the temporal coherence of B exceeded 0.98 at 1805 m but decreased with time at 1905 m, respectively. Considering a coherence coefficient of 0.5 as the evaluation standard, the channel coherence time at 1805 m reached 160 s. The clusters related to the sea surface exhibited poor temporal coherence because random scattering paths were introduced by sea surface fluctuations.

At depths greater than 2605 m in the shadow zone, the propagation distances of the rays in B were shorter than those at shallow depths, so the expansion and absorption losses were reduced. In most cases, B and SB dominated the energy contributions to the channel. Stable B, with high contribution to the channel, led to higher temporal coherence of the channel, which led to higher temporal coherence (0.5–0.6) of the channel than (0.2–0.5) at shallow receiving depths in the shadow zone.

In the direct-arrival zone at depths beyond 3405 m, the temporal coherence largely increased to 0.6–0.8. The additional contribution from high-energy high-temporal-coherence D with no interface loss led to the high channel temporal coherence in this zone. The main energy contributions to the channels of this zone were D, S, B and SB. The three-dimensional plot of the CIR and the temporal coherence analyses at 3405 m are given in Figure 19.

The temporal coherence of the channels was high (>0.7) due to D, with its high temporal coherence (>0.85) and high energy contribution to the channel. B displayed the highest temporal coherence (Figure 19c), as observed previously, indicating that B was more stable than the other channels. The temporal coherence of path clusters related to the sea surface was lower than that of D and B. These path clusters related to the sea surface were considered random clusters.

It is worth mentioning that the phase changes of all clusters in the direct-arrival zone were high-energy clusters, and their phase changes could be analyzed over time [11]. Figure 20 plots the temporal phase changes of different path clusters (relative to the initial signal-sampling time) at 3405 m.

D and B exhibited less phase fluctuation than S and SB. Sea surface fluctuations changed the grazing angles of the paths in S and SB, thereby randomizing their phase changes. The slow phase changes of D in the direct-arrival zone explain the obvious amplitude changes but high temporal coherence of D in this zone.

The above analysis led to the following conclusions:

(1) The temporal coherence was very low (0.2–0.6) in the shadow zone but very high in the direct-arrival zone, which received high-energy path clusters (0.6–0.8).

(2) At different depths, random fluctuations of the sea surface always deteriorated the temporal coherence of clusters related to the sea surface, but the temporal coherence of B was consistently high.

(3) The temporal coherence of a single-path cluster affected the temporal coherence of the channel only when the cluster obviously contributed to the channel. A path cluster with high randomness largely contributed to the channel energy and degraded the temporal coherence of the channel.

5. Conclusions

Based on the data of a high-frequency underwater acoustic communication experiment, this paper studied and analyzed the channel characteristics of a typical deep-sea incomplete channel under the shallow-depth high-frequency transmitted condition.

The deep-sea field zone was divided into the direct-arrival zone and the shadow zone, and the channel characteristics were obviously different in the two zones. In the direct-arrival area, from the perspective of communication, the focus was mainly on the path clusters, such as D, S, B, and SB. The channel structure was relatively simple and stable, the RMS delay spread was usually less than 0.1 s, and the temporal coherence was 0.6–0.8.

On the contrary, in the shadow zone, there was no D. In addition to S, B, and SB, the contribution of BS and SBS was non-negligible. The channel structures were more complex, and the channel temporal variations were more obvious than those in the direct-arrival zone. The RMS delay spread ranged from 0.1 s to 0.6 s, and the temporal coherence was between 0.2 and 0.6.

Different path clusters were separated and their randomness was analyzed. D and B were the most stable, and their temporal coherence stayed above 0.8 within 160 s. Their coefficients of variation were less than 0.2. On the contrary, the temporal coherence of the surface-related paths clusters decreased significantly. Their coefficients of variation were generally larger. In most of the cases, the coefficients of variation were greater than 0.2.

Table 4. Different and same characteristics of channels in two sound field zones.

Sound Field Zone	Different Characteristics	Same Characteristics
Shadow zone	1. The channel path clusters contained B and SB and may have contained S, BS, and SBS. 2. The channel RMS delay spread ranged from 0.1 s to 0.6 s. 3. The channel temporal coherence ranged from 0.2 to 0.6.	1.The coefficients of variation of the path clusters related to the sea surface were high (>0.1). On the contrary, the coefficient of variation of B was low (<0.1). 2. The temporal coherence of B was much higher than that of other path clusters, and the temporal coherence of sea-related path clusters was very low. 3. The phase fluctuation of B was smaller than that of other path clusters.
Direct-arrival zone	1. The channel path clusters contained D, S, B, and SB. The energy of BS and SBS was negligible. 2. The channel RMS delay spread was less than 0.1 s 3. The channel temporal coherence ranged from 0.6 to 0.8.

is listed below to summarize the channel characteristics of the shadow zone and the direct-arrival zone in the communication scenario of this paper.

Understanding these characteristics of high-frequency deep-sea channels can provide guidance for the development of communication algorithms and system design in typical communication scenarios.

6. Future Work

On the one hand, the relationship between these channel characteristics and communication parameters such as the bit error rate and the maximum communication rate will be further studied. On the other hand, the formation mechanism of the resolvable intrapaths of different path clusters in this communication scenario will be analyzed, and appropriate modeling methods of different path clusters will be proposed.