Intensity evaluation of bottom backscattering between high-frequency underwater acoustic instruments and its experimental validation

A surface or underwater platform (e.g., a ship or a submersible) is usually equipped with multiple high-frequency underwater acoustic instruments to realize functions of communication, positioning, bathymetry observation, obstacle avoidance, object searching, etc. For instance, the acoustic system of the Jiaolong deep manned submersible includes 16 underwater acoustic instruments,^1,2 many of which operate simultaneously in some cases.^3,4 Running several acoustic instruments simultaneously can cause interference between the instruments, which may reduce the data quality. The effect of such interference varies according to the configuration, from slight disturbances to complete malfunctioning. Interference between underwater acoustic instruments can therefore be a severe problem and should be taken into account, especially for compact platforms, e.g., human-occupied vehicles, remotely operated vehicles, and autonomous underwater vehicles.

Many different methods have been developed to solve the interference problem, including time division multiplexing, frequency division multiplexing, advanced signal processing, and physical arrangement optimization. Time division multiplexing is widely used in practice. The interference problem can be solved by proper timing of the instruments and by controlling the triggering of each instrument's transmission.⁵ However, the efficiency of the platform's acoustic system will be lowered significantly if a large number of instruments are scheduled. Frequency division multiplexing is also useful. In some cases, the interference is not significant if the operating frequencies of the instruments are well separated, but more often, this method does not work due to harmonic distortions.⁵ Advanced signal processing techniques are receiving more and more attention because of their good performances. The interference can be suppressed significantly by using anti-interference waveforms and interference suppression algorithms.^6,7 Unfortunately, it is not available for off-the-shelf instruments, which are commonly used in acoustic system design for surface and underwater platforms. Physical arrangement optimization is a practical and efficient method^8,9 that can be applied to almost every platform equipped with multiple asynchronous instruments. Proper arrangement of the instruments can reduce the interference while at the same time keeping the acoustic system efficient. Therefore, in order to help optimize the arrangement of high-frequency underwater acoustic instruments from the perspective of acoustic system design for surface and underwater platforms, the present work aims to develop a practical method for evaluating the relative intensities of the interference signals corresponding to different instrument-to-instrument distances.

With the application of beamforming techniques and sidelobe-suppression techniques to high-frequency underwater acoustic instruments, the acoustic interference caused by direct-path signals is not significant in most cases. In the case considered here, therefore, the acoustic interference signal transmitted by an underwater acoustic instrument (referred to as “transmitter”) is scattered by the water bottom, before being received by another underwater acoustic instrument (referred to as “receiver”), as shown in Fig. 1(a).

The underlying theory for high-frequency (e.g., 100 kHz or higher) underwater acoustic instruments is mainly based on geometrical acoustics. The aim of the present work is to calculate the intensity $IR$ of the interference signal received by the receiver. For this purpose, the water bottom is divided into small patches. It is assumed that each patch scatters sound independently of the other patches and the total sound energy received by the receiver is obtained as a simple sum of the water-bottom patches' energy contributions. $IR$ can then be calculated by

where the subscript i denotes the ith patch $Pi$⁠, $ΔIP,i$ is the intensity of the sound wave scattered by the patch $Pi$⁠, $DR(θR,φR)$ is the directivity pattern of the receiver in terms of energy, and $θR$ and $φR$ denote the direction of the patch $Pi$ in a local spherical coordinate system centered at the acoustic center of the receiver R.

The key to calculating $IR$ is to derive $ΔIP,i$⁠. For this purpose, consider first the sound propagation path from the transmitter to the patch $Pi$⁠. According to the transport equation in ray theory,¹⁰ the intensity $ΔIT$ of the sound wave received by the patch $Pi$⁠, can be written as follows:

where W denotes the sound power radiated by the transmitter, $DT(θT,φT)$ is the directivity pattern of the transmitter in terms of energy, $θR$ and $φR$ denote the direction of the patch $Pi$ in a local spherical coordinate system centered at the acoustic center of the transmitter T, $LT$ is the horizontal distance between T and $Pi$⁠, and $θT,0$ and $θT,N$ are the grazing angles at the water surface and bottom, respectively. Because the sound speed c varies with depth, it is usually assumed that the acoustic medium is divided into a set of homogeneous layers with a constant-gradient approximation to the sound speed in each layer. Let $zn−1$ and $zn$ (⁠$n=1,2,…,N$⁠) denote the upper and lower boundaries, respectively, of the nth layer. Then, according to the Eikonal equation in ray theory,¹⁰ 

where $gn=dc/dz=(cn−cn−1)/Δzn$ is the sound-speed gradient, $Δzn=zn−zn−1$⁠, $cn−1$ and $cn$ are the sound speeds at the upper and lower boundaries, respectively, and $θT,n−1$ and $θT,n$ are the grazing angles at the boundaries, as shown in Fig. 1(b). Combining Eq. (3) and Snell's law, $cos θT,n=cn cos θT,0/c0$⁠, $LT$ can be written as a function of $θT,0$⁠, $LT=LT(θT,0)$⁠. For the patch $Pi$⁠, $LT$ is known. The angular variable $θT,0$ as well as other angular variables in Eq. (3) can then be determined by applying inverse interpolation to $LT=LT(θT,0)$⁠. Furthermore, substituting Eq. (3) into Eq. (2),

Note that Snell's law, $cos θT,n=cn cos θT,0/c0$⁠, is used in the derivation of Eq. (4).

Then consider the sound propagation path from the patch $Pi$ to the receiver. Similarly, as shown in Fig. 1(a), $ΔIP,i$ can be derived from Eq. (4) by replacing $LT$ by $LR$⁠, $c0$ by $cN$⁠, $θT,0$ by $θR,N$⁠, $θT,N$ by $θR,0$⁠, $θT,n$ by $θR,n−1$⁠, and $θT,n−1$ by $θR,n$⁠, which yields

where $LR$ is the horizontal distance between $Pi$ and R, $θR,n−1$ and $θR,n$ (similar to $θT,n−1$ and $θT,n$⁠, respectively) are the grazing angles at the layer boundaries, and $φS$ is defined in Fig. 1(a). The variable $ΔWP,i$ denotes the sound power received by the patch $Pi$⁠, and is given by

where $ΔSP,i$ is the area of the patch $Pi$⁠. The factor $σb(θT,N,θR,N,φS)$ denotes the scattering cross section, and can be expressed as a sum of scattering contributions due to interface roughness and volume inhomogeneity.^11,12 The formulas for $σb$ are quite complicated, and the high-frequency bistatic scattering model¹³ and numerical algorithm¹⁴ presented in previous works are used in the present work.

Consequently, the intensity $IR$ of the interference signal can be calculated by using Eqs. (1), (3), (4), (5), and (6), as well as an equation for $LR$ which is similar to Eq. (3). It is worth mentioning that, the sound speed profile, $c=c(z)$⁠, and the directivity patterns, $DT$ and $DR$⁠, are the input parameters of the proposed method, and should be determined in advance. The calculation requires that the summation in Eq. (1) is performed over the water bottom. In practice, the summation region can be determined based on the footprints of the transmit and receive beams. In the present work, the transmit beam footprint is calculated by setting $θT,0$ equal to one-half the −3-dB beamwidth in Eq. (3), and the receive beam footprint is calculated in a similar manner. Note that the −3-dB beamwidth is a function of $φT$ for the transmit beam and a function of $φR$ for the receive beam. In most cases, high-frequency underwater acoustic instruments use narrow beams, and thus the summation region is not large. In addition, in some cases (e.g., $θT,0=π/2$ or $θR,N=π/2$⁠), the limiting expression for $ΔIP,i$ is used due to division by zero, which yields

where the arguments in $DT(θT,φT)$ and $σb(θT,N,θR,N,φS)$ are omitted for brevity.

In order to validate the accuracy of the proposed method, a series of lake experiments were conducted. A prototype high-frequency underwater acoustic transducer was chosen as the transmitter, and a prototype acoustic Doppler current profiler (ADCP) was chosen as the receiver. The present work aims to evaluate the relative intensities of the interference signals corresponding to different distances between the transducer and the ADCP. The intensity of the signal transmitted by the transducer and received by the ADCP was therefore measured for various transducer-to-ADCP distances. During the experiments, the transducer was manually moved along the x axis, as shown in Fig. 2(a), while the position of the ADCP remained unchanged.

The beam patterns of the transducer and the ADCP were measured in anechoic tanks and provided by the manufacturers. The operating frequency range of the transducer was 200 to 400 kHz, and the beamwidth of the axisymmetric transmit beam was 10°. The operating frequency of the ADCP was 300 kHz. The ADCP used a conventional four-beam Janus configuration, and the beams were labeled as shown in Fig. 2(a). For each axisymmetric ADCP beam, the beam steering angle was 30° and the beamwidth was 4°.

Pulsed sinusoidal signals with a carrier frequency of 300 kHz were used in the experiments. The pulse repetition period was 200 ms, and the pulse duration was 4 ms. An analyzer (Type PXI, National Instruments) was used to generate signals for the transducer. The signals received by the ADCP were analyzed and recorded by the ADCP deck unit. Because the ADCP itself transmitted signals with a pulse repetition period of 1 s and a pulse duration of 40 ms during the experiments, a synchronizer (Type SSC-8, Boundary) was used to control the triggering of the transducer's transmission, so that the transducer transmitted signals for 500 ms every 1 s (duty factor of 50%). Consequently, the signals transmitted by the transducer and the ADCP were well separated.

An unpowered catamaran was chosen as the experimental boat and towed alongside a tugboat throughout the experiments, as shown in Fig. 2(b). The transducer and the ADCP, as well as two auxiliary instruments, i.e., a multibeam echo sounder (Type MS400, Hydro-tech Marine) and a sound velocity profiler (Type SVP1500, Hydro-tech Marine), were mounted on brackets, as shown in Fig. 2(c). These instruments were mounted at a depth of 0.45 m into the water. Two guide rails were used to enable the movements of the mounting brackets in the x-direction. Each mounting bracket was equipped with four stoppers to prevent the corresponding instrument from straying off the measurement position during data acquisition. The length of the guide rails was 4.3 m, allowing the maximum distance between the transducer and the ADCP to be 3.55 m.

The experiments were conducted in Qiandao Lake, which is a human-made, freshwater lake in China. A large number of paddy fields had been flooded to create the lake for a hydroelectric power station project, resulting in a flat lake bed. The experiments were carried out on windless, sunny days, so that the lake was calm during the experiments. The experimental data were collected at two experimental sites. There was a floating dock at each site. The tugboat was moored to the floating dock during the experiments, as shown in Fig. 2(b). The multibeam echo sounder was used to map the lake bed at the experimental sites in advance. The results indicated a flat but inclined lake bed. Accordingly, the heading of the experimental boat was adjusted carefully and then maintained by using buoys and tires (hung between the floating dock and the tugboat), so that the x axis was parallel to the lake bed plane in order to simplify the calculation. The inclination of the lake bed can then be denoted by the angle $θbed$ between the lake bed plane and the xy-plane, as shown in Fig. 2(a). It is worth mentioning that rotation matrices were involved in the calculation due to the inclination of the lake bed.

The input parameters of the proposed method were measured in advance. Then the mounting brackets for the auxiliary instruments were dismounted from the guide rails before the experiments. The bathymetric parameters were measured by the multibeam echo sounder. The water depth measured from the most vertical beam was 51.1 m at site 1 and 14.0 m at site 2. The inclination angle $θbed$ was 0.5° at site 1 and 31.1° at site 2. The sound speed profiles were measured by the sound velocity profiler, and were characterized by a negative gradient, as shown in Fig. 2(d). Due to the difficulty of in situ measurements, the sediment geoacoustic parameters of the lake bed were assigned typical values for the lake-bed type “silt” according to previous geological surveys. The model of the scattering cross section and the parameters for “silt” used in the present work are described in Ref. 13.

Figure 3(a) illustrates a representative plot showing 300-kHz intensity versus time for the acoustic signals received by the ADCP during a pulse repetition period of the ADCP. The data of Fig. 3(a) correspond to 0.55 m (i.e., the minimum transducer-to-ADCP distance), beam A, and site 1. Due to the configuration of the ADCP deck unit, data were recorded only during the first 600 ms of each pulse repetition period (i.e., 1 s). Due to the use of the synchronizer, the transducer transmitted signals only during the time interval between 250 and 750 ms, and hence the pulses and echoes were well separated. It can be seen that the direct-path pulses transmitted by the transducer were significant. This might be caused by the sidelobes, because no sidelobe-suppression technique was applied to the transducer. It can also be seen that the intensities of the second echoes were much smaller than those of the first echoes, and the signal-to-noise ratios of the third and higher-order echoes were so low that these echoes could not be observed and analyzed. This suggests that first echoes might contribute significantly to interference between high-frequency underwater acoustic instruments.

The intensities of the first echoes were measured and then compared with theoretical predictions. Forty echoes were recorded for each transducer-to-ADCP distance (0.55–3.55 m in steps of 0.1 m). Echoes were not recorded for several distances due to the mechanical structures of the mounting brackets. Distorted echoes (approximately 10% of the total) were excluded by using an algorithm that checked echo shapes. Figures 3(b) and 3(c) indicate the intensities of the first echoes at site 1 and site 2, respectively. The normalization process of the ADCP deck unit was not provided by the manufacturer, and thus the relative intensities were obtained. For all four ADCP beams, the predicted intensities were normalized to the same value, i.e., the predicted intensity corresponding to a distance of 0 m and beam A, so that the differences between the intensity curves corresponding to different beams remained unchanged. In order to better compare the measured and the predicted intensities, there was one overall normalization factor for the measured intensities setting the average intensity for all four ADCP beams to be the same for the measured and the predicted intensities.

Figures 3(b) and 3(c) show good agreement between the measured and the predicted intensities. The mean absolute error was 1.1 dB for site 1 and 1.5 dB for site 2. The 95% confidence intervals (CI) were generally less than 3 dB (i.e., ±1.5 dB), indicating the consistency of the experimental results. It was worth mentioning that the differences between the intensity curves corresponding to different beams were also well predicted. In addition, the intensity varied more rapidly at site 2 where the inclination angle was greater and the water depth was shallower. Some patterns could be observed in the measured data that do not show up in the theoretical model. The patterns might be caused by the water current which might change the position of the floating docks very slightly.

This work presents a practical method for evaluating the relative intensity of interference between high-frequency underwater acoustic instruments. The mathematical basis of this method is a combination of ray theory and the high-frequency bistatic scattering model for water bottoms. A series of validation experiments were conducted in a lake. The relative intensity of the interference signal transmitted by a high-frequency underwater acoustic transducer and received by an ADCP was measured. The agreement between the measured and the predicted intensities demonstrated the validity of the proposed method. This method can be used in acoustic system design for surface and underwater platforms. It can be used to calculate the relative intensities of the interference signals between high-frequency underwater acoustic instruments corresponding to different instrument-to-instrument distances, thereby helping optimize relative position between the instruments to reduce the interference. This would be expected to contribute to acoustic compatibility between high-frequency underwater acoustic instruments and help improve the instruments' performances.

This work was supported by the National Natural Science Foundation of China Grant No. 11904330 and the Major Project of Science and Technology of Hainan Province Grant No. ZDKJ2019002.