Underwater Acoustic Data Transmission in the Presence of Challenging Multipath Conditions and Shadow Zones: Sea Trial Analysis and Lessons Learned

Abstract

In comparison to traditional wired and wireless communication scenarios, the underwater channel is peculiar, being significantly more difficult for communication and presenting a unique set of features and impairments, thus necessitating special care in selecting ad hoc encoding and modulation technologies to achieve successful transmissions. This process can be aided by simulations, which can be effectively carried out only using a good, detailed channel model validated through sea measurements. This study presents the results of a sea measurement campaign run in May 2024 off the Gulf of La Spezia, Italy, characterized by challenging shallow water conditions and the presence of shadow zones. The collected data is then used to model a simulated channel as faithful as possible to the one experienced during the sea trial. The obtained channel is then used to carry out a comparison of different forward error correction (FEC) codes, highlighting each scheme’s performance in our working context. Conclusive results show that a satisfactory simulated channel was obtained and that a different choice of FEC schemes could have improved the performance of the underwater acoustic communication.

1. Introduction

In certain contexts, underwater acoustic signals are crucial communication enablers [1], and the only wireless transmission method that is available, since other popular technologies that are based on radio-frequency (RF), optical, or magneto-inductive (MI) signals are all affected by significant downsides. For example, the high conductivity of the water medium causes strong absorption of electromagnetic waves, hindering traditional RF-based communications [2], while optical communications are susceptible to water turbidity and any kind of obstacle or organic matter blocking the line of sight between nodes. Finally, MI communications suffer from a very limited communication range, leaving acoustic as the only viable communication technology for reliable medium-to-long-range underwater communication [3]. This technology can be applied to various fields, such as environmental research, diver support, aquaculture [4], and the military [5].

The several challenges posed by the underwater acoustic medium, which include colored environmental noise, strong and variable multipath in shallow waters, and non-negligible Doppler effects [1,6], make an accurate underwater channel model necessary. However, the current state of the art does not yet agree upon a common reference model, leaving many possibilities open about the different simulation strategies that can be employed. Some of these strategies include simulation tools, such as WOSS [7] and Bellhop [8], that can efficiently recreate some of the impairments of an underwater acoustic channel if configured with enough experimental data, which however tends to be scarce. Other strategies make use of replay channels such as the well-established Watermark benchmark [9] or the more recent Underwater Acoustic Channel Library [10], that are able to capture a faithful representation of the underwater channel but experience a lack of flexibility when replaying under configurations that differ from those used during the channel recording. Finally, it is worth mentioning that many of the remaining simulators in the literature [11,12,13,14], as well as some of our previous work [15,16,17], are more focused on the statistical evolution of the transmitted packets at the network layer instead of the link layer.

In this paper, we use the data collected during a challenging sea trial in order to create a synthetic channel model that builds upon the ray-tracing capabilities of Bellhop while adding meaningful environmental colored noise. In the considered deployment, the transmitter and receiver are static or exhibit only minimal low-frequency drift due to waves and mooring motion. Under these conditions, the Doppler shift is dominated by a small, slowly varying carrier-frequency offset (CFO) rather than by significant time-scaling effects. This residual CFO is effectively compensated by the synchronization mechanisms used in the modem (coarse CFO estimation followed by a phase-locked loop). Since no appreciable Doppler rate or time-stretching was observed in the experimental data, Doppler-induced distortion can be safely neglected in this scenario. All the experimental data has been collected during a measurement campaign carried out using the Leonardo research vessel (RV) in the Gulf of La Spezia (Italy). Environmental parameters were acquired using vertical casts with an Ocean Seven 310 conductivity–temperature–depth (CTD) sensor by Idronaut SRL, Brugherio, Italy [18]. The acoustic modem used was the Subsea Modem (SuM) by SubSeaPulse SRL, Padua, Italy [19], a device that had already been employed in previous shallow-water experiments [20,21]. SuM supports various single-carrier modulation schemes (phase-shift-keying, orthogonal frequency-division multiplexing, direct sequence spread spectrum, etc. …), as well as the JANUS modulation [22,23], where the employed implementation consists of a slightly modified version of the official reference (version 3.0.5) [24]. The availability of multiple modulation and coding schemes naturally enables future studies on adaptive modulation and coding strategies for the SuM modem. Physical-layer adaptivity has been widely explored in underwater acoustic communications to adjust transmission parameters to instantaneous channel conditions [5,25]. In order to support adaptivity, the current modem should be extended to support the per-frame adaptive selection of payload modulation and FEC. In future work, such parameters will be encoded in a header that uses a fixed, robust configuration.

The main contribution of this study is to analyze the results of a challenging sea trial and understand the observed peculiar behavior of obtaining a higher packet error rate at short distances with respect to longer ones by proposing a simulated channel model that behaves as close as possible to the real one. Subsequently, in order to understand which configurations could have increased the observed performance, the synthetic channel has been used as a testbed for comparing different forward error correction (FEC) schemes: previous work has already analyzed how the underwater acoustic context is peculiar and differs from traditional RF communications in ways also affecting the FEC scheme choice [26]. The obtained simulated channel confirms what was expected, and the results indicate that a precise FEC selection can offer some improvements in this challenging scenario.

The rest of this paper is structured as follows: Section 2 presents the La Spezia sea trial and the data collected during the measurement campaign. The section continues with an account of the transmission loss plots modeled using Bellhop. Section 3 presents the channel model used to simulate the sea trial conditions, and Section 4 validates the proposed approach. Finally, after a comparison of two sets of FEC schemes suitable for the transmission, Section 5 concludes this paper.

2. Sea Measurement Campaign

During the sea trial, both the JANUS waveform and phase-shift-keying (PSK) modulations were used and, in the latter case, a cascade of SEC-DED (72, 64) and Hamming (8, 4) [27] FEC codes was employed to protect the packet. The packet sizes chosen were 16 bytes for the JANUS modulation and 15 bytes for the PSK modulation. For the PSK modulation, an additional pseudo-random sequence of 64 bits is used as preamble for locking in the automatic gain control (AGC) and PLL at the receiver side, which is responsible for packet detection.

The results collected for the PSK communication experiments will include the following values:

• The received signal strength indicator (RSSI), estimated from the power of the packet preamble.
• The error vector magnitude (EVM), calculated over N packet symbols as

  $$EV{M}_{dB}=10{\log }_{10}\left({\displaystyle \frac{1}{N}}\sum _{i=1}^N{|r_i-{\widehat{x}}_i|}^2\right),$$

  (1)

  which measures the distance of each received symbol $r_i$ from its estimated constellation symbol ${\widehat{x}}_i$ and is indicative of the SNR of the channel.
• The packet delivery ratio (PDR), i.e., the percentage of demodulated and decoded packets that pass an 8-bit cyclic redundancy check (CRC).

Concerning JANUS, the experiment results will only include the PDR metric.

2.1. Sea Trial Description

The sea trials were conducted on 28–29 May 2024 in the waters off the Gulf of La Spezia, Italy; the referenced sea portion is an approximately 3 km long stretch of water located far off the Tyrrhenian coast, with a seabed depth of approximately 100 m. The surface water temperature was 20 °C and the sea state was 1 [28]. Environmental parameters were collected on site with an Idronaut Ocean Seven 310 CTD, as depicted in Figure 1.

The transmitting modem was deployed from the Leonardo RV, operated by the Italian Navy, and maintained at a constant depth of 5 m for all tests, while the receiver was deployed from a dinghy that moved to different positions in order to perform ranging trials (Figure 2).

The dinghy’s engine was shut down during each test to avoid noise, while the Leonardo RV was in silent mode. For the RV, the engine was only used for maintaining the ship position, keeping the noise to a minimum. Some occasional impairments included the traffic of nearby boats, with noise coming not only from their engines and movement but also from their echo sounders. The ranges between the transmitter and the receiver were measured using the radar of the Leonardo RV, ensuring precise positioning during the trials.

The transducers used in the experiments are listed in

Table 1. Transducers used with the SuM modem during the sea trial.

Model	TVR [dB re 1 μPa/V]	RVR [dB re 1 V/μPa]
Lubell LL916H	160 dB @ 10 kHz	−195 dB @ 10 kHz
Btech BT-28UF	150 dB @ 28 kHz	−191 dB @ 28 kHz
Aquarian AS-1	125 dB @ 40 kHz	−208 dB @ 40 kHz

and depicted in Figure 3.

We tested several transmission configurations, summarized in

Table 2. Transmission configurations.

Carrier Frequency	Modulation	Bandwidth
10 kHz	BPSK	1200 Hz
10 kHz	JANUS	2600 Hz
10 kHz	JANUS	4160 Hz
28 kHz	BPSK	1200 Hz
28 kHz	BPSK	2400 Hz
28 kHz	QPSK	1200 Hz
28 kHz	QPSK	2400 Hz
28 kHz	JANUS	6500 Hz
40 kHz	BPSK	1200 Hz

. Although the JANUS standard specifies five operational bands spanning the 4.960–31.250 kHz frequency range, it is common practice in experimental research to implement JANUS on non-standard frequencies. For this reason, in order to perform a controlled comparison with some of the BPSK transmissions, we set the JANUS carrier frequency to 10 kHz for some experiments while using the standard E band (i.e., 28 kHz of carrier frequency and 6.5 kHz of bandwidth) for the remaining ones.

The number of experiments was constrained by vessel availability, weather conditions, and the cost of at-sea operations, preventing repeated measurements under controlled or replicated channel conditions. As a result, the dataset reflects the specific channel realizations encountered during the trial and is not enough for a comprehensive statistical characterization across varying SNR levels.

2.2. Sea Trial Results

In this section, the observed data is presented. The experimental data is compared against the estimated transmission loss derived from the Bellhop acoustic propagation model [8], implemented using the Acoustic Toolbox [29] and fed with the collected environmental data.

Unfortunately, due to the short cable lengths of the transducers used in the sea trial, the depth at which the transducers were positioned is not ideal. In fact, it corresponds to the point of maximum measured sound speed, as can be seen in Figure 4. This resulted in a sound propagation that bends faster towards the sea bottom, and such challenging conditions are probably one of the main reasons for the low packet reception rate experienced on May 28 and 29. In addition, it is worth noting that the SSP measured on May 28 was acquired in the afternoon, when the surface water layer had been warmed by solar radiation. This heating effect is clearly visible in the corresponding profile, which shows higher sound speed values near the surface. Conversely, the SSP on May 29 was obtained in the morning, when the surface layer was still relatively cool, resulting in lower sound speed values in the upper part of the water column.

Regarding the Bellhop configurations used, the seabed was assumed flat and homogeneous (no granulometry variations), and the directional radiation patterns of the three employed transducers were taken into account. The sea trial measurements are overlaid on the transmission loss diagrams, where the x and y axes correspond to, respectively, the range and depth, and each point corresponds to a reception event. Every point is associated with a color intensity on a red scale colormap that reports the transmission loss, which is an indicator of the measured PDR: brighter red indicates a higher received power and so an expected higher PDR, thus summarizing how successful each experiment has been.

Figure 5 depicts the transmission results obtained with the Lubell LL916H operating at a carrier frequency of 10 kHz with a source level around 180 dB re 1 µPa @ 1 m. As expected, JANUS proved to be more robust than BPSK, achieving a PDR higher than 70%.

Notably, as shown in Figure 6, Figure 7 and Figure 8, performance metrics are higher at roughly 2000 m than at shorter ranges. We explain this with the phase and temporal structure of the arrivals. Although the incident energy is higher near the transmitter, the sound waves often follow multiple paths with relative delays that produce a substantial phase offset at the receiver. This phase dispersion causes partially or completely destructive interference, reducing the net coherent received amplitude and impairing demodulation and packet detection performance. At around 2000 m, in contrast, arrivals tend to be more clustered in phase (i.e., have smaller relative phase differences), resulting in predominantly constructive summation and an increased coherent signal level. As detailed in Figure 9, Bellhop is able to reproduce this trend. Figure 9a,c show the modulus of the reconstructed channel impulse response $h\left(t\right)$ at, respectively, 700 m and 2000 m of distance from the transmitter, where it is possible to see the arrival clusters. Figure 9b,d show instead the sum of all the arrival taps within the time of a symbol duration, which corresponds to roughly 10 ms. These two last figures compare, for each cluster C, its actual modulus that suffers from destructive interference (i.e., $|{\sum }_{i\in C}h\left(t_i\right)|$), with the maximum achievable one, obtained with perfect phase alignment (i.e., ${\sum }_{i\in C}\left|h\left(t_i\right)\right|$). Even though the RMS delay spread computed from the channel impulse response is smaller at 700 m (9.72 ms) than at 2000 m (13.93 ms), this metric does not take into consideration the phase of the arrivals which may result in destructive multipath, as we observed during the sea trial (and as highlighted in Figure 9).

At a distance of more than 2.2 km, instead, no packets were received due to the clear presence of a shadow zone caused by the downward propagation of sound in the water medium. As can be seen in Figure 6, Figure 7 and Figure 8, at around 3 km, the sound bounces off the seabed, marking the midpoint of the shadow zone, as it then propagates upwards, reaching the end of the shadow zone at approximately 4 km.

Figure 10 shows the transmission results obtained with the Aquarian AS-1 transducer, operating at a carrier frequency of 40 kHz and a source level of around 155 dB re 1 µPa @ 1 m. The maximum reception range for successfully received packets was approximately 350 m with BPSK as modulation and a 1200 Hz occupied bandwidth.

3. Synthetic Channel

In this section, we present a model for reproducing the channel conditions observed during the sea trial that uses a combination of environmental noise measurements and the output of the Bellhop ray-tracer program in order to improve the faithfulness of the simulations of different underwater acoustic channels.

Synthetic Channel Model

The simulation pipeline is presented in Figure 11, where the experimental data, collected during the sea trial, is used for recreating the effects of multipath and colored additive noise on a recorded packet transmission of our own choice.

For every physical channel that we want to recreate, we use the Bellhop ray-tracing program to generate the channel impulse response using the available information about CTD measurements, transducer positions, center frequency, and polar patterns. The output generated by Bellhop consists of a group of pairs $(t_i, A_i)$ that represent, respectively, the time of arrival and the complex amplitude of each ray that reaches the receiver. In order to create a discrete version of the channel impulse response, the time of the first arrival $t_0$ is subtracted from each time $t_i$, thus accounting for the propagation time of the channel, and the resulting difference is then divided by the modem sample period T and rounded to the nearest integer, yielding $n_i=\lfloor (t_i-t_0)/T\rceil$ as the formula for obtaining the discrete channel indices. The resulting discrete channel impulse response function $h\left[n\right]$ is then defined as non-zero only for the indices $n_i$, where in these instances we have $h\left[n_i\right]=A_i$, and is used in a convolution with the signal representing the packet transmission.

In order to improve the faithfulness of the synthetic channel, we extracted a portion of samples from the recordings and used it as a source of additive noise. The extracted samples were taken from the few tens of seconds before each transmission and thus represent a portion of noise similar to the one experienced by the packets during the actual sea trial. The noise was then amplified by a parameter $\alpha$ which was tuned empirically via a parameter sweep in order to minimize the absolute difference between the number of detected packets resulting from the simulation and the one experienced in the sea trial. The parameter $\alpha$ was directly related to the SNR that characterizes the simulation, and was used to capture some of the effects that Bellhop was not able to model, such as the mismatch in the quality of the transducers used for the sea trial recording and the one used for data reception. Finally, the resulting signal was attenuated by a factor $\gamma =\sqrt{E_r/E_s}$ in order to match the average energy-per-sample of the recorded transmission, where $E_r$ and $E_s$ are the average energies-per-sample of, respectively, the recorded and the synthetic signal.

RSSI and EVM were not considered in the choice of $\alpha$ due to the fact that the former depends not only on the propagation characteristics of the environment but also on the non-calibrated transducers used in the sea trial, while the latter is available only for the correctly decoded packets, significantly reducing the number of samples that could be analyzed.

4. FEC Optimization

To validate the synthetic channel, we performed a number of simulations that captured a subset of the sea trial. In particular, we focused on six experiments, performed on May 29, which all considered a BPSK transmission of 51 packets of 15 bytes each, using a carrier frequency of 28 kHz and a 1.2 kHz bandwidth. Out of the six experiments, it is worth mentioning that only experiments number 33, 42, and 48 resulted in some packets being received, while in experiments number 55, 56, and 65, no packets were detected. For this reason, only the first three experiments were used for validating the synthetic channel, while the other three were used for additional testing of the FEC configurations. Specifically, in addition to the Hamming and SEC-DED codes used in the sea trial, the SuM modem allowed us to select Reed–Solomon and convolutional codes of different rates: the former is more effective for a small number of bytes and for burst errors, while the latter is more suited for longer packets and is therefore out of the scope of this study. An interleaver was used in all cases except for the Reed–Solomon FEC, which is already robust against burst errors.

Figure 12 shows a comparison between the statistics of the received packets between the synthetic channel and the actual sea trial. While the single addition of multipath is not always enough to recreate the conditions experienced in La Spezia, the addition of the recorded noise results in a much closer representation, even if it does not perfectly match the channel realization. The only peculiar case is expressed by experiment number 42 where, as shown in Figure 12b, any introduction of noise degrades the channel more than necessary. For this reason, and only for this particular experiment, we consider the sole introduction of multipath.

Starting from the developed synthetic channel, we decided to evaluate different error correction schemes to improve the packet reception probability under conditions as similar as possible to those observed in the sea trial. The compared configurations consist of the cascade of SEC-DED (72, 64) and Hamming (8, 4) codes used during the sea trial against a single layer of a well-optimized Reed–Solomon (255, 223) [30] code with symbols defined over GF($2^8$) (i.e., the Galois Field of $2^8$ elements). These FEC schemes exhibit well-known computational characteristics. Hamming and SEC-DED codes require only $O\left(n\right)$ XOR operations for syndrome computation and correction. Reed–Solomon decoding, instead, has complexity $O(n\times t)$ over $GF\left(2^8\right)$, where t is the number of correctable symbols. For $n=255$ and $t={\displaystyle \frac{n-k}{2}}={\displaystyle \frac{255-223}{2}}=16$, the overall decoding cost is therefore on the order of $O(255\times 16)\approx 4\times {10}^3$ operations per codeword. Since operations in $GF\left(2^8\right)$ can be implemented via lookup tables and bitwise arithmetic, this complexity is easily manageable on low-power embedded platforms. For the short blocks and moderate constraint lengths used here, all schemes were verified to operate in real time even on a low-power Raspberry Pi Zero, indicating that decoding latency and computational load are not limiting factors for the configurations tested in this sea trial.

Figure 13 shows the improved results obtained by using Reed–Solomon as the packet FEC, where the number of successful decodings increases by roughly 29% in experiment 48, which remains the most impressive. This increase in performance is due to some rather unique properties of this type of code, where the unit of error is no longer the single bit but rather a symbol. Using this structure, any burst error generated by the channel that is contained within a symbol boundary results in a single erroneous symbol at the decoder. Another useful property of Reed–Solomon codes is that they are able to successfully reconstruct a code word whenever any number of symbols are corrupted, up to half the number of parity symbols generated during the encoding process. Thus, looking at the implementation that we are using, the symbols are aligned with the single bytes of the codeword and the number of parity symbols is fixed at 32, leaving any combination of 16 or fewer erroneous bytes correctable.

Figure 14 shows the improvement related to the change in the FEC configurations for the transmitted packets. Here, it is worth mentioning that the tuning parameter $\alpha$ has been purposefully fixed to a value that would permit the reception of some amount of data. Thus, these results obtained in a modified simulation environment may not fully represent the behavior of these codes under real sea trial conditions.

5. Conclusions

In this paper, we presented the data collected from a sea trial conducted in the Gulf of La Spezia, Italy, under challenging propagation conditions. Data analysis showed the presence of shadow zones that hindered communication, especially when PSK modulation was used. Starting from the measured data, we used the Bellhop ray-tracer in order to reconstruct the multipath fading of the channel and attempted to recreate the environmental colored noise based on the sea trial recordings. Overall, using the measured data, we could successfully create a synthetic channel model able to reproduce a communication behavior close to what has been experienced in the sea trial at the cost of a tuning parameter that requires manual adjusting. Finally, the channel was used for comparing different FEC schemes for packet protection. Results show that, even if the channel conditions experienced were challenging, using a stronger Reed–Solomon code for protection would have increased the reception rate at the receiver side.