# Underwater Messaging Using Mobile Devices

Tuochao Chen,⋄ Justin Chan⋄ and Shyamnath Gollakota  ⋄Co-primary student
authorsPaul G. Allen School of Computer Science & EngineeringUniversity of
Washington, Seattle, WA, USA<EMAIL_ADDRESS>
(2022)

###### Abstract.

Since its inception, underwater digital acoustic communication has required
custom hardware that neither has the economies of scale nor is pervasive. We
present the first acoustic system that brings underwater messaging
capabilities to existing mobile devices like smartphones and smart watches.
Our software-only solution leverages audio sensors, i.e., microphones and
speakers, ubiquitous in today’s devices to enable acoustic underwater
communication between mobile devices. To achieve this, we design a
communication system that in real-time adapts to differences in frequency
responses across mobile devices, changes in multipath and noise levels at
different locations and dynamic channel changes due to mobility. We evaluate
our system in six different real-world underwater environments with depths of
2-15 m in the presence of boats, ships and people fishing and kayaking. Our
results show that our system can in real-time adapt its frequency band and
achieve bit rates of 100 bps to 1.8 kbps and a range of 30 m. By using a lower
bit rate of 10-20 bps, we can further increase the range to 100 m. As
smartphones and watches are increasingly being used in underwater scenarios,
our software-based approach has the potential to make underwater messaging
capabilities widely available to anyone with a mobile device.

Project page with open-source code and data can be found here:
https://underwatermessaging.cs.washington.edu/

Underwater communication, ocean sciences, SOS beacons, mobile phones, smart
watches, underwater exploration

††journalyear: 2022††copyright: acmlicensed††conference: ACM SIGCOMM 2022
Conference; August 22–26, 2022; Amsterdam, Netherlands††booktitle: ACM SIGCOMM
2022 Conference (SIGCOMM ’22), August 22–26, 2022, Amsterdam,
Netherlands††price: 15.00††doi: 10.1145/3544216.3544258††isbn:
978-1-4503-9420-8/22/08††ccs: Networks Mobile networks††ccs: Applied computing
Environmental sciences††ccs: Human-centered computing Ubiquitous and mobile
devices

##  1\. Introduction

Each year, tens of millions take part in underwater activities like snorkeling
in lakes, rivers, and oceans (sno, 2022). Millions more participate in
recreational scuba diving in the United States alone (sta, 2022). Underwater
exploration is also important in observation of marine life, water pollution
and to document the biological, geological, and archaeological aspects of
underwater environments (exp, 2022). Effective communication during these
underwater activities is critical for safety and navigation (sig, 2022a, b,
2018). Hand signals are commonly used to communicate intention, convey
direction and maintain safety. In addition to the 10-20 signals commonly used
in recreational settings (sig, 2022a), professional divers use more than 200
hand signals to communicate with each other or with surface members of the
dive team (sig, 2022b). This includes information about oxygen level, aquatic
life or operations that require cooperation (sig, 2018). Given the number of
hand signals and their visual nature, however, this mode of communication is
ineffective in low-visibility scenarios (e.g., turbid waters) and is limited
in its communication range and reliability.

To address this problem, commercial efforts have designed hardware that
enables two-way text messaging to send from a set of pre-defined messages or
SOS beacons (com, 2008). DARPA also initiated the AMEBA effort to build custom
hardware that would enable divers to communicate at a low bit-rate with each
other via text messages or with nearby relay buoys (dar, 2016). These prior
efforts require custom hardware that is neither ubiquitous nor has the
economies of scale.

Figure 1. Mobile devices for underwater messaging.

In this paper, we take a different approach and explore if one can enable
underwater messaging capabilities on mobile devices like smartphones and
smartwatches. Smartphones are increasingly being used with diving-proof cases
($30-40) for underwater photography, video logging and in lieu of a dive
computer (cas, 2022b, a). These diving-proof smartphone cases are rated to
work at depths of 15-40 m depending on their price (pho, 2022a, b). The latest
smartwatches are also water-resistant and can be used during shallow water
activities like snorkeling (wat, 2019, 2022). Ideally, anyone with a mobile
device should be able to download a software app and communicate underwater
during snorkeling, recreational diving or scientific exploration, without
additional hardware. Such an approach would leverage the ubiquity of mobile
devices to democratize underwater communication and make it available to
anyone with a mobile device.111Recent reports note Apple’s R&D interest in
enabling iPhones to communicate in underwater environments (app, 2021, 2020).

We present AquaApp, the first software-only solution that enables underwater
acoustic communication and networking on commodity mobile devices. While the
most common communication modality on mobile devices is to use radios (e.g.,
Wi-Fi and LTE), these frequencies are not suitable for underwater
communication — 2.4 GHz Wi-Fi signals can attenuate as much as 169 dB per
meter in seawater (Dong et al., 2016; Lin et al., 2021). Our experiments show
that two smartphones separated by just a few inches in fresh water could not
connect using Wi-Fi or Bluetooth. Our solution instead is to leverages audio
sensors, i.e., microphones and speakers, that are ubiquitous in today’s
devices to enable acoustic underwater communication. In contrast to RF
signals, acoustic signals have much better propagation properties underwater
(Dong et al., 2016).

Figure 2. User interface of our messaging system on a phone within a water-
proof case.

Repurposing microphones and speakers on commodity mobile devices for
underwater communication is challenging for three reasons: (1) Unlike custom
hydrophone hardware that is specially designed to operate underwater, acoustic
sensors in smartphones and watches are designed for in-air operation and the
hardware components used can vary across device manufacturers. This results in
different frequency responses across devices (Fig. 3a,b). The transmit power
on these mobile devices is also typically limited compared to underwater
hydrophones. In addition, the severe multipath in underwater scenarios can
result in the signal strength varying by as much as 10-20 dB within a few kHz.
(2) Even with the same smartphone model used across users, the SNR profiles on
the forward and backward paths can be different (Fig. 3c,d), resulting in the
need to use different frequency bands on the two paths. (3) The bit rate can
vary an order-of-magnitude from 100 bps to 1.8 kbps with distance and
multipath, requiring an adaptation algorithm to minimize packet error rate.
However, mobility inherent to diving and snorkeling results in varying channel
across packets, making adaptation challenging. This requires a real-time
protocol to pick the correct bit rate before transmitting data, without
incurring significant overhead.

Figure 3. (a,b) Frequency selectivity underwater in a lake at a 5 m distance
across devices and locations. (c,d) Channel reciprocity on the forward and
backward path in (c) air and (d) water separated by 2 m.

At a high level, we use orthogonal frequency division multiplexing (OFDM) to
communicate underwater between mobile devices. Our real-time system adapts the
acoustic frequencies used to encode data in each packet transmission, as a
function of frequency response, distance and signal-to-noise ratio (SNR) of
each frequency bin. This ensures that when the devices are a few meters apart
and have a high SNR, the system adapts in real-time to use all the OFDM bins
to encode data and achieve a high bit rate. On the other hand, it uses a
smaller frequency band as the distance increases. This ensures that more power
is allocated to a right set of frequencies, thus, increasing the SNR and the
packet delivery rate.

Our design has three key components:

  * •

Post-preamble feedback. In high-data rate systems (e.g., Wi-Fi), rate
adaptation is performed across packets since packet sizes are less than a
millisecond, and the channel coherent time is more than a few packets. In
contrast, our underwater acoustic system is low rate making packets much
longer and resulting in the channel changing between consecutive packets. To
do this, we perform per-packet adaptation by splitting the preamble/header and
data portions of each packet. Say Alice wants to send a packet to Bob. In our
design, Alice first broadcasts the preamble and header with Bob’s address and
stays silent for Bob’s feedback before transmitting the data portion of the
packet (Fig. 5). Bob estimates the SNR for each OFDM bin using the preamble,
runs a frequency adaptation algorithm and in real-time sends information back
to Alice, embedded in a single OFDM symbol. Alice uses this feedback to
transmit the data portion of the packet using the right frequency band.

  * •

Frequency band adaptation. Per-frequency rate adaptation is ideally performed
using the water-filling algorithm to allocate different power and modulation
to each OFDM bin (Rahul et al., 2009). In a low-data rate system, however,
conveying fine-grained feedback about 60 OFDM bins requires at least O(60)
bits which is a significant overhead. To minimize the feedback Bob sends back
to Alice, we design a low-overhead frequency band adaptation algorithm
(§2.2.2). At a high level, we first compute the SNR in each bin using the
received preamble. If not all the OFDM bins are above an SNR threshold, we
drop the lowest SNR bin and reallocate power to the remaining bins. We repeat
this process until we find the largest contiguous band where all frequencies
are above the SNR threshold. Bob sends back only information about the start
and end frequencies, $f_{start}$ and $f_{end}$, of this contiguous band.

  * •

Feedback encoding method. Bob encodes this feedback using a single OFDM
symbol. Our encoding method allocates all the power to the two OFDM bins
corresponding to the start and end frequencies, $f_{start}$ and $f_{end}$,
output by our frequency band adaptation algorithm. Alice can extract this
information by performing a sliding window and picking the top-2 OFDM bins
with the highest power. This is a reliable encoding method since all the
transmit power is being allocated to these two OFDM bins. Alice then uses this
band to send data by setting the OFDM bins outside it to zero.

We implemented our software system in real-time on the Android platform so it
can be used with various smartphone models and smart watches. Since underwater
multipath can have a large delay spread, we implement time-domain equalization
to reduce the cyclic prefix duration to only 7% of the OFDM symbol. To address
mobility, we use differential coding across consecutive OFDM symbols to reduce
errors (§2.3). We also design a carrier sense based MAC protocol to support a
network of multiple underwater mobile devices (§2.4). Using our communication
system, we implement a messaging app where users can transmit one of the 240
common messages. Finally, by using a lower bit rate, we design a longer-range
SoS beacon messaging system.

We evaluate our system in six different real-world underwater environments.
Our findings are as follows.

  * •

Our system adapts the frequency band to achieve bit rates of 100 bps-1.8 kbps
at distances up to 30 m. The bit rate scales with distance and multipath. By
reducing the bit rate to 10-20 bps, our system can increase its range to 100
m.

  * •

Our real-time adaptation algorithm reduces the average packet error rate (PER)
from 38-70% to 3% compared to fixed bandwidth schemes across 5 to 30 m.

  * •

Our system achieves a PER of 4% and 7% in the presence of slow and fast
motion. Further, it adapts its frequency band to operate reliably with
different phone orientations.

Contributions. The last few decades have shown that software can bring
technology to the masses more rapidly than custom hardware. We present the
first acoustic-based system that enables underwater messaging on commodity
mobile devices, using only software. To this end, we designed a communication
system that in real-time adapts to variations in frequency responses across
mobile devices, changes in multipath due to mobility and SNR variations from
severe frequency diversity, to minimize packet error rate. We evaluated our
system in underwater environments and built a messaging app that allows users
to send messages and SoS beacons. Finally, by making our system code publicly
available at publication, we believe that this work has the potential to make
underwater communication technology accessible to everyone with a mobile
device, by just downloading software.

Figure 4. Underwater ambient noise measurements. Normalization is done across
plots in the same graph.

##  2\. System Design

We first characterize the properties of acoustic signals from mobile devices
in water. We then present our real-time protocol as well as our data encoding
and decoding algorithms. We open-source our code and data at
https://underwatermessaging.cs.washington.edu/.

###  2.1. Characterizing mobile devices in water

We characterize the acoustic properties of commodity smart devices (e.g.,
phones, watches) in underwater scenarios.

Frequency selectivity. As the speakers and microphones differ between smart
devices, the frequency selectivity of an acoustic signal can vary between
different transmitting and receiving phones. To evaluate this, we selected
four different smart devices: Samsung Galaxy S9, Google Pixel 4, OnePlus 8
Pro, and Samsung Galaxy Watch 4. We placed each device pair underwater 5 m
away from each other. We placed each smartphone in a waterproof pouch (pou,
2022) and submerged the device to a depth of 1 m in a 2 m deep lake. The
transmitter sends a 1–5 kHz chirp with a duration of 500 ms. Fig. 3a shows
that the frequency response varies between device pairs. It is uneven and
exhibits deep notches with the frequencies where notches occur varying across
device. The plot also shows that the frequency response diminished above 4
kHz, which suggests that acoustic communication above this frequency on mobile
devices may be challenging.

Next, we fix the transmitting and receiving smart devices to both be a Samsung
Galaxy S9. We repeat the same experiment as before at a distance of 10 m. Fig.
3b shows the variation in frequency response as a result of the multipath
characteristics at the different locations. Specifically, we observe that
multipath causes the notches of the response to occur at different
frequencies. Thus the frequencies ideal for underwater communication may vary
with location.

Channel reciprocity. Next, we analyze the frequency response of the forward
and backward channel in air and underwater. We use two smartphones of the same
model (Samsung Galaxy S9) and measure the frequency response of a 1–3 kHz
chirp with a 1 s duration. The first phone is set to send a chirp to the
second phone, and two seconds later, the second phone sends a chirp back to
the first phone. We separate the phones by 2 m and perform the measurement
over the air and underwater. In Fig. 3c we see that the frequency response of
the chirp sent over the air is similar across both phones. However, the
frequency response of the chirp underwater in Fig. 3d differs significantly.
This suggests that the optimal frequencies for communication are different for
the forward and backward channel. So an explicit feedback signal would need to
be sent from the receiving device to the transmitting device.

Ambient noise. Finally, we measure underwater ambient noise as recorded on
different smart devices for five seconds at the same location. Fig. 4a shows
the ambient noise across these devices for different frequencies. Each noise
profile is normalized to the maximum amplitude across all measured
frequencies. The plot shows that across devices, the amplitude of noise is
high below 1 kHz. Furthermore, noise can also be seen at higher frequencies up
to 4.5 kHz. In our measurement location, underwater noise was due to the sound
of water flowing and the movement of air bubbles. Additionally, the plot shows
that the noise profiles vary across smartphones. We also measured the level of
ambient noise at different locations using a Samsung Galaxy S9. Fig. 4b shows
that the level of noise between 0–6 kHz can vary by 9 dB between locations.
This is expected as the amount of water flowing or other acoustic interference
will vary across locations. Across both these experiments, the high noise
level below 1 kHz suggests that acoustic communication in that frequency range
may be challenging. This suggests that we need to measure both signal strength
and noise across frequencies to determine the right frequencies.

Design requirements. So our requirements are:

  * •

Works across smart devices with different frequency responses. Our system
should work across speakers and microphones on smart devices with different
frequency responses.

  * •

Robust to multipath across different locations and distances. Underwater
environments can have challenging multipath due to reflections from the
surface, floor and from the coast. Our system should be robust to these
effects.

  * •

Tolerates mobility. Strong water currents or waves can cause devices to drift
away quickly or toward each other within a few seconds, resulting in Doppler
shifts. Our system should be able to work in these real world environments.

  * •

Adapts to different noise profiles across environments. The underwater
environments can suffer from significant noise from ships, boats and animals.
Loud sounds outside the water such as airplanes or helicopters also contribute
to the noise.

###  2.2. Post-preamble feedback protocol

Fig. 5 shows our protocol that splits the packet into preamble/header and
data. Alice first sends the preamble and the receiver ID. Alice remains silent
for feedback from Bob but keeps its OFDM symbol timer ON. The preamble is
composed of eight OFDM symbols from 1 to 4 kHz. When Bob detected this
preamble, we first check the ID. It then runs our SNR estimation algorithm on
the preamble for each subcarrier between 1-4 kHz, which it uses in our
frequency band adaptation algorithm. Instead of a fine-grained adaptation for
each bin, we select a contiguous band and send back only the start and end
frequencies of this band to reduce overhead. Alice uses this information to
encode bits within this selected frequency band and transmits data to Bob. To
do this, Alice transmits the data symbols at the beginning of the next OFDM
time interval as determined by its OFDM symbol clock. This ensures that the
preamble synchronization performed by Bob can also be used for data. The first
OFDM symbol in the data transmitted by Alice however is a known training
symbol to track changes in channel since preamble transmission. In practice,
the post-preamble silence period at Alice is assigned zero values to keep the
speaker buffer full. This ensures that the symbol timing can be maintained for
data symbols. Bob uses cross-correlation and energy detection in every OFDM
symbol interval to detect the arrival of the first known data symbol from
Alice. Bob can use the preamble to synchronize the data symbols since the
propagation time for preamble and data symbols is similar. Note that safe
human motion under water is usually lower than $1-2m/s$ (Wojtków and Nikodem,
2017) and the time interval between the preamble and data transmission in
Alice side is several OFDM symbols (including feedback propagation, processing
time). Assuming the interval is 5-symbol, the change in the propagation time
is only 0.6% of the OFDM symbol duration.

Figure 5. Protocol sequence diagram.

####  2.2.1. Preamble design

The preamble has three purposes: packet detection, symbol synchronization, and
channel estimation. For a real-time system, the preamble design and detection
algorithm have two main requirements: detection robustness and low
computational burden. Linear frequency modulation (LFM) signals and cross-
correlation-based detection are proposed for underwater communication (Xie et
al., 2009; Pec et al., 2017; Thottappilly, 2011). However, in our real-world
experiments, LFM was not robust enough at long distances or with severe
multipath. We instead use a data-aided approach (Nasir et al., 2010) where we
fill the OFDM bins with a CAZAC sequence. These sequences have a very good
auto-correlation property and have unit Peak to Average Power Ratio (PAPR)
(Wen et al., 2006). Further, the good autocorrelation properties of a CAZAC
sequence also makes it suitable to be used for channel estimation (Zhang et
al., 2020). We concatenate eight such identical OFDM symbols and multiply each
with a PN sequence with different signs ([-1, 1, 1, 1, 1, 1, -1, 1]), to
provide steeper fall off to the correlation timing metric and alleviate the
side-lobes problem for a more robust detection and accurate synchronization
(Wen et al., 2006).

Preamble detection and synchronization. Our detection algorithm is composed of
two parts: coarse detection and fine-grained detection. The coarse detection
algorithm applies cross-correlation between the received signal and preamble.
In the presence of a preamble, this results in a correlation peak. However,
the cross-correlation peak varies with SNR and spiky noise like underwater
bubbles could also cause a very high correlation peak. To address this, we
also use sliding correlation (Nasir et al., 2010) where instead of calculating
the correlation between the transmitted preamble and received signal, we apply
a sliding window on the received signal and divide the sliding windows into 8
segments each the length of an OFDM symbol. Then we multiply each segment by
the PN sequence and calculate the correlation between the two nearby segments.
Finally, we sum them up and divide the sum by the received energy within this
sliding window. When the real preamble arrives, the sliding correlation would
have a high peak ($>0.6$). The peak height of this normalized sliding
correlation is not sensitive to SNR changes. Moreover, spiky noise is unlikely
to have this specific encoded data pattern and thus its sliding correlation
value is low ($<0.2$).

for  _$L\leftarrow N_{0}$ to $1$_ do

for  _$m\leftarrow 0$ to $N_{0}-L$_ do

$\displaystyle SNR_{min}=\min_{m\leq k<m+L}\\{SNR_{k}+\lambda\cdot
10log_{10}(\frac{N_{0}}{L})\\}$

if  _$SNR_{min} >\epsilon_{SNR}$_ then

$n\leftarrow m+L-1$

return $(m,n)$

Algorithm 1 Frequency band selection algorithm

However, the sliding correlation method increases computational burden. So we
perform the sliding correlation on the candidate signals only after the coarse
detection. In addition, we increase the step size of sliding correlation to 8
to balance the computational burden and synchronization resolution. When a
valid preamble is detected, we select the peak index in the sliding
correlation curve as the beginning of the preamble for synchronization. Even
if our preamble structure can improve the peak prominence in sliding
correlation, a synchronization offset is still inevitable, which may affect
OFDM data transmission quality (Nasraoui, 2015). As described later, we use
time-domain equalization in our decoder and a cyclic prefix in our encoder to
address this issue.

####  2.2.2. Frequency band adaptation algorithm

Our frequency band adaptation algorithm is composed of two main steps.

SNR estimation per frequency bin. We use the 8 OFDM symbols in the preamble to
estimate the channel. We compute the SNR for each subcarrier by applying
frequency-domain channel estimation. Specifically, we denote the transmitted
data in subcarrier $k$ of the eight preamble symbols by a vector $x(k)$ and
the received data in subcarrier $k$ of 8 training symbols by a vector $y(k)$.
We apply a minimum mean square error (MMSE) estimator to compute the channel
response $H(k)$ for each subcarrier $k$. We then compute the SNR in the
$k^{th}$ bin as,
$SNR_{k}=20log_{10}\frac{\|H(k)x(k)\|_{2}}{\|y(k)-H(k)x(k)\|_{2}}$

Frequency band selection. Our goal is to find the optimal frequency range
based on the SNR distribution between 1-4 kHz. The basic idea is that we drop
the bin with the lowest SNR and reallocate power to the remaining bins until
the SNR in all remaining bins surpass the preset SNR threshold. Say, there are
totally $N_{0}$ bins between 1-4 kHz, and the estimated SNR in the $k^{th}$
bin is $SNR_{k}$. When we only select bins between $m$ and $n$, the power in
the discarded bins could be re-allocated to the remaining bins. Hence, the SNR
value in the remaining bins increases by $10log_{10}(\frac{N_{0}}{L})$, where
$L=n-m+1$. So, our optimization problem is as follows,

$\displaystyle\max_{m,n}\quad L=n-m+1$
$\displaystyle\begin{array}[]{r@{\quad}r<EMAIL_ADDRESS>10log_{10}(\frac{N_{0}}{L})>\epsilon_{SNR},\forall k\in[m,n]\\\ \end{array}$

where $\epsilon_{SNR}$ is the preset SNR threshold (in our implementation we
set $\epsilon_{SNR}$ to 7). $\lambda$ is a conservative factor between 0 to 1
(we select it empirically to 0.8), since in real-world implementation the
power re-allocation is not exact. We set, $\epsilon_{SNR}$ and $\lambda$, a
bit conservatively since we need to account for imperfect SNR estimation and
because the channel may still change due to mobility. $m$ and $n$ from the
above optimization give us $f_{begin}$ and $f_{end}$.

Figure 6. Data encoding and decoding.

####  2.2.3. Encoding feedback

We encode the frequency bins $f_{begin}$ and $f_{end}$, in a single OFDM
symbol by assigning all the power only to the two corresponding bins. By
allocating all the power from the transmitter into two frequency bins, Alice
can still decode the feedback signal reliably even when channel estimates of
the backward path from Bob to Alice are unknown. Specifically, Alice can
decode the signal by extracting the frequencies with the top-2 SNRs. The OFDM
symbol from Bob would arrive at Alice after a delay of around a round-trip
time. Since this specific OFDM symbol is effectively the same as transmitting
two frequency tones, Alice performs an FFT over a sliding window with the same
length as the OFDM symbol. The sliding window computation is performed up to
the maximum round trip time corresponding to 30 m, to search for Bob’s OFDM
symbol.

###  2.3. Data transmission

Multi-path can be severe under water due to reflections from the surface,
floor and other objects (Stojanovic, 2008b) causing inter-symbol interference
(ISI). To address ISI without sacrificing bit rate, we apply time-domain MMSE
equalization instead of increasing the cyclic prefix. Dynamic channel changes
due to motion of humans, waves and other underwater objects is another
challenge. Even within a packet, the channel for the first OFDM symbol may
differ from the last symbol, which may deteriorate the equalizer’s
performance. Here, describe our encoding and decoding mechanisms to address
these issues.

####  2.3.1. Data encoding.

Alice encodes the transmitted bits and generates OFDM symbols between
$f_{begin}$ and $f_{end}$. The duration of each OFDM symbol is 960 samples (20
ms duration and 50 Hz subcarrier spacing with 48000 kHz sampling rate). We
also add a 67 sample cyclic prefix ($6.9\%$ overhead).

  * •

Convolutional coding. We first apply 2/3 convolutional coding with constraint
length $K=7$ to encode data bits. These codes are widely used in GSM and
satellite networks (Halonen et al., 2004; Butman et al., 1981).

  * •

Interleaving bits. The next step is to assign the coded bits to OFDM symbols.
Our algorithm has two main rules: (1) assign bits to OFDM bins between
$f_{begin}$ and $f_{end}$ and set the remaining bins to zeros and (2)
interleave the bits to avoid consecutive bit errors which could cause
unresolved errors after convolutional decoding. Our empirical observations
show that bit errors usually happen in the OFDM packets at a specific
subcarrier or nearby two subcarriers. Our interleaving strategy is to first
fill one symbol until all selected subcarriers in this symbol have bits, and
then fill the next symbol to avoid consecutive bit errors in a single
subcarrier. Within a symbol, after assign a bit in a subcarrier, we leave some
subcarriers for the next bit with a step size is one-third of the selected
bins. If we use less than three bins then this defaults to not using
interleaving.

  * •

Differential coding. In our system, we use differential encoding across
consecutive OFDM symbols to alleviate the time-varying channel effects.
Specifically, say the data in subcarrier $k$ of symbol $i-1$ is $y_{i-1}(k)$
and $b$ is a coded bit intended for transmission. Then, we apply differential
coding by setting the data in subcarrier $k$ of the next symbol $i$ as,
$y_{i}(k)=y_{i-1}(k)\bigoplus b$. Thus, the bit is encoded as an XOR between
two consecutive OFDM symbols. Since channel variations across two consecutive
symbols is small, differential coding provides resilience to channel
variations, as long as the coherence time is larger than one OFDM symbol.

After assigning the bits to the OFDM subcarriers, we demodulate the bits in
each subcarrier using BPSK and use IFFTs to generate the time-domain OFDM
signal.

####  2.3.2. Data decoding.

To decode data, Bob first applies a 128 order FIR bandpass filter, with a
passband of 1–4 kHz, on the received signal to filter out ambient noise.

  * •

MMSE Equalization. Time domain equalization utilizes the equalizer
coefficients to recover the transmitted signal and address inter-symbol
interference (ISI). The equalizer coefficients is estimated using preset
training symbols and the MMSE algorithm. The communication channel model can
be written as $y=h*x+n$, where $x$ is the transmitted signal, $y$ is the
received signal, $h$ is the channel coefficient vector with length $L$, and
$*$ is the convolution operator. The time-domain equalization model can be
written as, $\hat{x}=g*y$, where $\hat{x}$ is the recovered signal, $y$ is the
received signal, and $g$ is the equalizer coefficient with length $L$. MMSE
equalizers (Schniter, 2008) minimize the mean square error between the
transmitted signal and the recovered signal, i.e. $\min\|\hat{x}-x\|_{2}^{2}$.
In our system, a known training symbol is appended to the front of the data
symbols. We utilize this training symbol to estimate our MMSE equalizer with
the channel length $L$ of 480 samples. Finally, we apply the estimated
equalizer to each received OFDM data symbol for transmitted signal recovery.

  * •

Differential & convolutional decoding. After equalization, we apply an FFT on
each symbol and acquire the data in the frequency bins. We calculate the phase
difference of two consecutive symbols on each OFDM bin within the frequency
range of our frequency band adaptation algorithm. By measuring the phase
difference, we can extract the coded bits, 0 or 1. We then re-interleave the
bits following the order of the pre-determined interleaver. Finally, we use
the Viterbi algorithm with constraint length 7. This provides maximum
likelihood values for the data bits.

We note the following points about our design.

  * •

Doppler shifts. A concern is that motion could also cause Doppler shifts,
leading to inter-channel interference (ICI) within the OFDM symbol. Since our
system mainly focuses on underwater human communication, the safe motion speed
for humans during scuba diving is usually slower than 1 m/s (Wojtków and
Nikodem, 2017). Even if the transmitter and receiver are moving in opposite
directions, their relative speed is 2 m/s. The typical underwater acoustic
speed is 1500 m/s. This results in a Doppler shift of around 5 Hz at our
maximum operational frequency. We however note that our OFDM subcarrier
spacing is 50Hz, which is much higher than this Doppler shift and thus does
not cause significant ICI.

  * •

Encoding ID and ACKs. We use a single frequency in the OFDM symbol to encode
device ID as well as the ACKs. Specifically, ACKs are encoded by assigning the
OFDM bin corresponding to 1 kHz to denote successful packet reception. This
mechanism is reliable and does not require a long preamble since it assigns
all the transmit power to a single OFDM bin. We also encode the device ID
using the different subcarriers in the OFDM symbol. We have a total of 60
subcarriers and when the device transmits the OFDM symbol encoding its ID, it
allocated all the power to the corresponding subcarrier. This limits the
number of devices in our local network to 60 users, which may be acceptable
for underwater human activities like scuba diving and snorkeling. These IDs
can be assigned using the app across devices in-air.

Figure 7. Different experimental environments. (a) Bridge: a quiet
environment. (b) Park: A busy location with boats and kayaks passing by
regularly. (c) Lake: a busy and noisy location by a fishing dock with animals
and other water activity. (d) Beach: a waterfront with a length around 100 m
for long range experiments. (e) Museum: a highly occupied location used to
dock ships and boats with a depth of 9 m for depth experiments. (f) Bay: a
location with 15 m depth for deeper water experiments.

###  2.4. MAC protocol

In a typical use case, we expect our network to be operating in a low load
scenario where not all transmitters send data at the same time. However, to
support multiple devices that may operate at the same time, we also use
carrier sense, similar to Wi-Fi, as a means of mediating access to the channel
between multiple transmitters. We implement our carrier sense in realtime
using energy detection by measuring the average energy level in the 1–4 kHz
band, which is the frequency range used for communication in our system. We
perform this measurement every 80 ms. Prior to transmission, each phone
measures if the energy level on the channel exceeds a predefined threshold. If
it detects that the energy level exceeds the threshold, the phone waits for a
random backoff period that is defined in multiples of the packet duration.
During this backoff period, the phone continues to listens to the channel. If
it detects energy on the channel during this backoff period, it will increase
the backoff time by the duration of one packet to ensure the backoff period
will not elapse while a packet is being transmitted on the channel. After this
additional time has elapsed, the phone will again check if the energy on the
channel is below the threshold. After the remainder of the backoff time has
elapsed and the channel is idle, the phone is then clear to send a packet. The
threshold is computed by measuring the average noise level for a few seconds
in each environment before use.

We note two points: 1) In addition to energy detection, Wi-Fi receivers also
use preamble detection as part of carrier sense, which we could also
incorporate to improve noise resilience. 2) Our post-preamble feedback
mechanism can be considered as a light-weight version of RTS-CTS. So we can
add a preamble to Bob’s feedback which could be used in lieu of a CTS message
to address the hidden terminal problem. Our current implementation does not
include either features.

##  3\. Evaluation

Our communication system has been implemented to run on Android devices with
preamble detection running continuously in real-time. The runtime to execute
our channel estimation, frequency adaptation, and feedback decoding algorithm
are each on average 1–2 ms on a Galaxy S9. Our decoder can perform
equalization and Viterbi decoding for each symbol in less than 20 ms, which is
the duration for an OFDM symbol. Fig. 2 shows our app interface where users
can select from a list of 240 messages corresponding to hand signals used by
professional divers. Users can filter the list of messages based on eight
different categories. Additionally, the 20 most commonly used hand signals are
displayed more prominently for selection by users. Pictorial representations
of hand signals are included for reference in the app. The size of our data
packet is 16 bits, 24 bits after applying a 2/3 convolutional code. With this,
users can choose to send two hand signals in a single packet.

Our system also encodes a user’s 6-bit ID into an SoS beacon using frequency-
shift keying. Specifically, we encode a 0 bit with a single frequency tone
$f_{0}$ and a 1 bit with a single frequency tone $f_{1}$. We design our system
to support data rates of 5, 10, and 20 bps and use frequencies in 1.5–4 kHz to
transmit these beacons over longer ranges. Using this scheme we may also
encode an 8-bit hand signal, which can be transmitted in around a second at
these rates.

We evaluated our system in four underwater environments with different
multipath effects and noise levels (Fig 7).

  * •

Bridge. Under the water of a bridge with a horizontal distance of 20 m. This
is a quiet location with still waters.

  * •

Park. By the waterfront of a park with a length of 40 m. This is a busy
location with boats and strong currents.

  * •

Lake. Fishing dock by lake with a 30 m length. The lake had a 5 m depth. This
is a busy location with people fishing and kayaking.

  * •

Beach. The length of the water here is around 100 m.

  * •

Museum. This location has a depth of 9 m. This is a highly occupied location
used as a dock for different boats and ships.

  * •

Bay. This location has a depth of 15 m. There were a lot of waves at this
location and experiments were performed on a kayak.

Figure 8. BER measurements are from distances of 5, 10, and 20 m with
bandwidth of 1-4 kHz.

BER versus SNR. First, we evaluate our decoding algorithm by computing the BER
at different subcarrier SNRs. Given the frequency fading nature of underwater
links, BER can be different at each of the OFDM subcarriers depending on its
SNR. In these experiments we use our real-time implementation on two Samsung
Galaxy S9 phones. In all experiments, the phone speaker is set to its maximum
volume. The phones were placed in a waterproof case and submerged at a depth
of 1 m using a selfie stick as an extension pole. We perform the experiments
at a distance of 5, 10, and 20 m at the bridge location. At each distance, we
configure the transmitter to send a total of 500 OFDM symbols on the
subcarriers between the 1–4 kHz and the modulation scheme for each subcarrier
is set to BPSK. We computed the BER as the fraction of mistakenly decoded bits
(without coding) to the total transmitted bits over 500 symbols. Fig. 8 plots
the BER curve obtained in our experiments in comparison to the theoretical
curve for BPSK. The plot shows that the empirical data for our design follows
a similar trend to the theoretical estimates.

Figure 9. Effect of different environments. (a) CDF of bitrates selected by
our algorithm. (b,c) Example frequency responses from two locations. Dashed
lines indicate the range of selected frequencies by our algorithm. (d) A PER
value computed using all packets at each location for our system and fixed
bandwidth schemes.

Effect of different environments. We evaluate our system in three locations:
the bridge, park, and lake. These range from quiet and still to noisy and
busy, and capture a diversity of environmental effects. We report the bitrate
picked by our real-time algorithm and the PER of our system at 5 m.

During the experiment, our system runs in real-time where the transmitting
smartphone first sends the preamble and header to the receiver. The receiver
continuously listens for the preamble, when it detects it, performs SNR
estimation on each OFDM subcarrier, runs our frequency band adaptation
algorithm and sends back $f_{begin}$ and $f_{end}$ frequencies to the
transmitting phone in a single OFDM symbol. The transmitting phone then sends
data using OFDM subcarriers between $f_{begin}$ and $f_{end}$. Each data
packet contains 2 bytes of data (24 bits after applying a 2/3 convolutional
code) on the selected OFDM frequency bins. This is more than sufficient to be
able to encode the range of hand signals used by professional divers. We
compare the performance of our frequency adaptation scheme to fixed-rate
bandwidth schemes, where the transmitting phone sends the same bits using a
fixed bandwidth of 1–4 kHz, 1–2.5 kHz and 1–1.5 kHz, which correspond to 60,
30, and 10 OFDM bins respectively. This procedure was set to repeat 100 times
at each of the three locations tested. Every 25 packets, we would pause
measurements on the smartphone, retrieve it from the water, and submerge it
again, until all 100 packets were transmitted. Even if one bit error occurs at
the decoder output, we mark it as an erroneous packet. Fig. 9a shows that the
selected bit rate varies across location as well as runs. Within the same
location, the selected bitrate changes as the multipath changes with time. The
average selected bitrate was highest at the bridge location which is likely
because the environmental noise and water currents are lowest in this setting.
In comparison, at the park and lake environments, people fishing and kayaking
nearby may have affected the channel, resulting in a selection of lower
bitrates. Fig. 9b,c shows an example received frequency spectrum in the bridge
and lake locations. The dashed lines indicate the range of frequencies
selected by our algorithm for sending data. In contrast to the bridge
location, the spectrum at the lake location exhibit more frequent and deeper
dips. In the lake location, the wall and pillars underwater would reflect the
acoustic signals resulting in more frequency selectivity.

Fig. 9d plots the PER obtained for our system, as well as the three fixed
bandwidth schemes at the three environments. The plot shows that the PER for
the fixed bandwidth schemes increases in response to larger multipath in the
environment. The PER is larger in the lake environment which exhibits the
highest variability in the received spectrum. In contrast, the PER of our
system remains low across all three locations with an average value of 1%. The
PER obtained by our system is also lower than those obtained by the fixed
bandwidth schemes at the park and lake location.

Figure 10. Effect of depth. (a) CDF of selected coded bitrate. (b) PER our
system compared to fixed bandwidth schemes. A PER value is computed at each
depth location using all packets sent at the location.

Effect of different depths. Multipath can change at different depths — close
to the surface, multipath interference from the surface of the water can be
strong. Similarly, close to the bottom of the water body, it may experience
significant multipath from the floor. We perform our experiments in the museum
location, which had a total depth of 9 m. Our experiments were performed at a
fixed horizontal distance of 5 m between the two smartphones.

Fig. 10a shows the bitrates selected by our system for three depths of 2, 5
and 7 m and Fig. 10b shows the PER. The PER for our system and the 0.5 kHz
fixed bandwidth scheme was highest at a depth of 2 m when the phones are close
to the water surface. For the 1.5 and 3 kHz fixed bandwidth scheme, the PER
was highest at a depth of 7 m when the phones are close to the bottom of the
lake. These results suggest that the environments at a depth of 2 and 7 m are
the most challenging multipath environments. This is likely because there are
more objects for the signal to reflect from at the surface and bottom of the
lake including ducks, fish, and kayaks. At all depths, our system obtained
significantly lower PERs than the fixed bandwidth schemes.

Figure 11. Testing in deeper waters. (a) CDF of selected coded bitrates. (b)
Waterproof casing rated for a depth of 15 m. Figure 12. Range evaluation. (a)
CDF of selected bitrates. (b,c) BER and PER of our system versus fixed
bandwidth schemes. A PER value is computed from all packets at the location.
(d) Longer ranges using lower bit rates. Figure 13. (a,b) Our system uses a
smaller band in response to increased attenuation at larger distances.

Testing in deeper waters. To evaluate our system at deeper depths, we
performed an experiment at the bay location with a total depth of 15 m and
submerged the phones to a depth of around 12 m. We note that 12 m is in the
range of depths associated with basic recreational scuba dives (dep, 2022). In
this experiment, we used a different waterproof pouch (cas, 2022a) (Fig. 11b)
which was rated to work at a maximum depth of 15 m. We note that this pouch
was made of a hard plastic casing (polycarbonate and thermoplastic
polyurethane) which attenuated the sound more than the thin flexible plastic
material (polyvinyl chloride) used in the pouch for other experiments. We
positioned the transmitter and receiver phone on either side of a two-person
kayak (3.5 m length), and weighed down the phones using a pouch of sand to
ensure the phones would submerge underwater. Fig. 11a shows that the median
bitrate selected by our system at a depth of 12 m was 133 bps. This suggests
the phones are able to communicate even at these deeper depths and with a hard
plastic casing.

Range evaluation. We perform our range evaluation in the lake location since
it had a comparatively long distance of 30 m. We performed our measurements at
a depth of 1 m, which as we note in the previous evaluation, has empirically
more challenging multipath at the lake location. The phones were submerged
into the water using a rope, which caused the phone to sway and rotate slowly
during measurements, i.e., the phones were not static.

Fig. 12a shows the bit rate after coding selected by our system at different
distances. The plot shows that the selected bitrate generally decreases with
distance, with the largest drop occurring between 5 and 10 m. At a distance of
5 m and 30 m, the median selected bitrate was 633.3 and 133.3 bps
respectively. In Fig. 12b we also show the BERs for the coded bits transmitted
at different distances for our frequency adaptation scheme and the fixed
bandwidth schemes. The BERs for the fixed adaptation schemes increase quickly
with distance. This is because the fixed schemes will continue to naively
transmit bits on low SNR subcarriers and increase the likelihood of bit
errors. This is clearer in Fig. 12c where we plot the PERs for these schemes
over distance. The plots show that the PER for the fixed adaptation schemes
reach 100% when using a fixed bandwidth of 1.5 and 3 kHz. In contrast, our
frequency adaptation scheme has a PER of 7% at a distance of 30 m. This
demonstrates that to minimize PER it is essential to pick the appropriate
frequency band since even with a fixed low bandwidth of 0.5 kHz, it is likely
that some of the frequencies in this narrowband signal are in a deep fade
resulting in sustained packet losses despite using coding. In contrast, our
real-time adaptive system picks a conservative set of frequencies depending on
the frequency profile and SNRs as shown in Fig. 13 which allows it to minimize
the packet error rate.

In the above design, each OFDM symbol had a 20 ms duration, limiting the
minimum symbol rate to 50 bps. To further reduce the bit rate, we increase the
symbol duration to 50, 100 and 200 ms and use a single frequency within each
symbol to encode data. This results in a bit rate of 20, 10 and 5 bps
respectively, which may result in a longer range. To evaluate this, we perform
our experiments in the beach location. Testing was performed at a fixed depth
of 1 m. We compute BER as the number of bits that were correctly decoded over
all the bits transmitted at each location at each of the three bit rates. Fig.
12d shows the uncoded BER of our system up to a distance of 113 m. The plot
shows that the BER is less than 1% for bitrates of 5 and 10 bps up to the
maximum tested distance of 113 m. This demonstrates that our system enables
communication between smartphones underwater at long ranges albeit at lower
bit rates. We also note that a bit rate of 10 bps is sufficient to transmit
SoS beacons which would be important at these long ranges during underwater
activities. Similarly transmitting a 8 bit packet that is sufficient to encode
the 200 hand signals can also be done in around a second after accounting for
coding.

Figure 14. Effect of mobility. (a) CDF of selected bitrates in a static
scenario versus one of the smartphones moving slow ($2.5m/s^{2}$) and fast
($5.1m/s^{2}$). (b,c) PER and uncoded BER of our system versus other
configurations.

Effect of mobility. We perform mobility evaluation in the lake location at a
fixed horizontal distance of 5 m and at a depth of 1 m. In this experiment, we
measure system performance when the phones are static, and when the
transmitting phone is moving slowly and moving quickly. To do this, we move
the phone horizontally back and forth, and vertically up and down. Since the
phone is attached to the rope, the phones will also rotate randomly during the
movement. During these measurements, the raw accelerometer readings on the
phone after compensating for gravity were on average, $2.5$ and $5.1m/s^{2}$
for slow and fast motion, respectively.

In Fig. 14c, we calculate the uncoded BER with and without differential
coding. Specifically, for received packets without differential coding, we
only apply the equalizer to each OFDM symbol and compare the decoded bits with
the original bits. The plot shows that with mobility, the BER without
differential coding increases rapidly and easily surpass $10\%$. When we apply
differential coding, the BER decreases dramatically and could still keep
around $1\%$ in the fast motion scenario. Fig. 14a shows the CDF of the coded
bitrate across these three mobility scenarios. We see that the coded bitrate
is highest in the static situation with a median bitrate of 640 bps. In
contrast, the median bitrates in the slow and fast moving case decrease to 433
and 336 bps respectively. Fig. 14b shows that our PER increases from 1.2 to
7.6% as mobility increases.

Effect of phone orientation. For this evaluation, we ran our system at the
bridge environment with a fixed distance of 5 m and a depth of 1 m. The phones
were submerged with the screen facing towards the water surface, and were
first set so the speaker and microphones of each phone are directly facing
each other. We rotate one phone in the azimuth angle from 0 to 180° in
increments of 45°. Fig. 15a shows that the median bitrate decreases with phone
orientation from 1067 bps at 0° to 567 bps at 180°. Fig. 15b shows that while
the fixed bandwidth schemes have a higher PER at large angles, our frequency
adaptation scheme achieves a low PER. This is because our system is able to
select a better frequency band and adapt to the channel at different
orientations.

Channel stability and SNR. We take a closer look at the effects of mobility
from the perspective of channel stability and SNR. Mobility has two effects on
our system: (1) the channel may change between the preamble and the data
symbols, leading to a different bandwidth selection and, (2) the channel
between the first and the last data symbol may be different. For the second
effect, as shown in Fig. 14(c), differential coding addresses the channel
changes within the data packet. Here, we investigate the stability of the
underwater channel between the preamble and data symbols in different motion
scenarios. In our system, Alice first transmits a preamble to Bob and Bob
selects the bandwidth. To verify the channel stability and its effects on SNR,
instead of transmitting the data symbols, we configure Alice to transmit
another preamble; Bob used the bandwidth from the first preamble to compute
the SNRs of the corresponding OFDM bins using the second preamble. Now, we can
evaluate the effect of channel stability on our bandwidth selection algorithm.
Specifically, when the SNRs in some of the subcarriers within the selected
bandwidth are very low, packet errors can happen. Hence, we select the minimum
SNR computed using the second preamble within the selected bandwidth as the
metric to evaluate the performance of our bandwidth selection algorithm.

Figure 15. Effect of phone orientation. (a) CDF of selected bitrates for
different azimuth offsets between a pair of smartphones. (b) PER at a distance
of 5 m for our system and other fixed frequency band schemes.

We performed this experiment at a horizontal distance of 10 m at the lake
location when both phones were held static, and when moving them at slow and
fast speeds similar to our mobility evaluations. The x-axis in Fig. 16
represents the experiment index number, and the y-axis is the minimum SNR
computed using the second preamble within the selected bandwidth. The dashed
SNR line of 4 dB is the reference for subcarrier quality evaluation (4 dB may
cause 1% BER according to the SNR-BER curve).

Figure 16. Channel stability and SNR. For consecutively transmitted pairs of
preamble signals separated by the feedback duration, the figure shows the
minimum SNR computed using the second preamble over the bandwidth picked from
the first preamble. We run these experiments in (a) static scenarios and with
(b) slow and (c) fast motion. The dashed line at 4 dB marks the SNR threshold
at which BER will theoretically be at 1%, representing the threshold for a
stable communication link. Figure 17. Effect of OFDM subcarrier spacing. CDF
of selected bitrates for different subcarrier spacing values at a distance of
(a) 5 and (b) 20 m. (c) PER for our system at different subcarrier spacings.

In the static scenario, the minimum SNRs are high, likely due to the
conservative parameter settings used in our bandwidth adaptive algorithm. In
the slow and fast motion scenario, the fluctuation of the minimum SNR values
increase and sometimes the bad subcarriers appear in the bandwidth selection
algorithm, leading to an increasing PER during fast motion. Despite the
existence of channel variance with motion, two components in our system help
alleviate the effects of mobility and keep the PER low: (1) the conservative
parameter settings of our bandwidth adaptive algorithm with a high SNR
threshold and conservative factor $\lambda$ allows for some room for safe
bandwidth selection albeit the inaccurate SNR estimation due to mobility. Due
to these conservative settings, only a small proportion of packets would pick
up the bad subcarrier (¡4 dB). (2) In scenarios where our conservative
parameters can fail when the change of channel is very large, convolution
coding helps reduce the bit errors. However, when channel drastically changes
leading to more deep drops in the selected bandwidth, packet error can occur,
which accounts for the increasing PER during fast motion. In future work,
further improvements can be used to make the bandwidth selection algorithm to
be even more conservative, which can lead to lower data rates. Another
approach to improving the PER is to apply non-linear equalization techniques,
which perform better for signal recovery in poor channels with severe
distortion (Paliwal et al., 2016).

Effect of OFDM subcarrier spacing. Next, we perform experiments with three
different OFDM subcarrier spacing: 50 Hz (length of OFDM symbol is 20 ms), 25
Hz (40 ms), and 10 Hz (100 ms). We do not select the OFDM subcarrier spacing
lower than 10 Hz due to Doppler shifts as described in §2.3. We perform these
experiments in the lake location at a horizontal distance of 5 m and 20 m.
During the experiment, for each subcarrier spacing, the OFDM symbol length in
the preamble is kept the same as the length of data OFDM symbol to maintain
the same frequency resolution. Fig. 17(c) shows that at 5 m, all the PERs are
around 1%. At 20 m, the PER with 50 Hz spacing increases to 4.6%, while PERs
for 25 Hz and 10 Hz spacings are lower than 1%. Smaller subcarrier spacing can
improve PER because (1) smaller spacing can provide high-resolution SNR
estimation and more accurate bandwidth selection and (2) smaller spacing can
also improve the equalization performance due to the higher frequency-
resolution in the training symbol.

Effect of air in water-proof case. To evaluate this, we first expelled as much
air as we can from the water-proof case before putting the phones into the
water and then measure the frequency response. We then filled the case with
air before putting the phones in the water and then analyzed the frequency
response. Fig. 18 shows that even if the frequency response of the two curves
has some difference, the average power within 1-4 kHz was not significantly
different.

Preamble & feedback signal evaluation. We also perform preamble evaluation in
the lake location at a depth of 1 m. We transmit 180 preambles at each
distance and evaluated the probability that our system could successfully
detect the preamble. Our measurements show that our detection rate defined as
the fraction of detected and transmitted preambles was 0.99, 1.0, 1.0 and 0.96
at 5, 10, 20 and 30 m. We also measured our system’s ability to correctly
decode the feedback signal containing the result of our frequency adaptation
algorithm at all the above distances. Frequency error rate is computed as the
fraction of feedback signals where the decoded frequencies did not match the
transmitted values. Across all tested distances, the error rate was around
0.01, i.e., 1 in 100 packets across all these distances. This is because we
allocate all the power to these two frequencies making the signal strength
much higher which allows reliable decoding even with frequency fading. In the
cases where there are errors, the system confuses it to the adjacent OFDM
bins.

MAC protocol evaluation. Finally, we measure the effectiveness of carrier
sense at supporting multiple devices underwater. We consider two network
deployments with four phones (three transmitters, and one receiver) and three
phones (two transmitters, and one receiver) placed underwater in the bridge
location at a depth of 1 m at distances in the range of 5-10 m from the
receiver. As mentioned before, we expect that not all devices will be
transmitting continuously underwater. But to test the effectiveness of carrier
sense in a heavily used network, we configure the transmitters to send
continuously after a random backoff period of multiple seconds, up to a
maximum of 120 packets per transmitter. We repeat the experiments with and
without carrier sense.

We measure the fraction of collisions for each of the transmitter. To
calculate this fraction, we first logged the timestamps at when the
transmitting phones sent a packet. Packets that were transmitted within one
packet duration of each other was marked as a collision. The fraction of
collisions in the network was defined as the number of packets that were
involved in a collision divided by the total number of packets sent by all
transmitters (dotted horizontal lines). Fig. 19 shows that without carrier
sense, the collision rate in the three transmitter network is high with an
average of 53%, however, our carrier sense mechanism is able to reduce this to
an average of 7%. The figure shows a similar collision reduction for the two
transmitter network from 33% to 5%.

Figure 18. Effect of air in waterproof case.

##  4\. Related work

Underwater networking is an active research area where topics across the
network stack continue to be explored for custom acoustic modems and sensor
networks (Al Guqhaiman et al., 2021). There is also prior work in localization
and ranging (Monteiro and Martí, 2020; Domrese et al., 2014), which is not in
scope of our work. Below we describe the prior work in more detail.

Acoustic modem hardware. Since acoustic signals propagate well underwater,
unlike RF, the common approach is to design custom acoustic modem hardware and
use custom amplifiers at high power to achieve long ranges. Given the lack of
economies of scale, much of this hardware can be expensive or not as
accessible as in-air radios. All prior works that present underwater network
simulators (Demirors et al., 2015; Demirors et al., 2016; Chitre et al., 2014)
or protocol stacks (Potter et al., 2014; Petrioli et al., 2015; Calabrese et
al., 2012) use custom hardware with amplifiers and (de)modulators. Recent work
integrates a custom acoustic modem with software radios (e.g., USRPs) to
design a software-defined platform for underwater networking research
(Sklivanitis et al., 2014; Noh et al., 2015). The closest to our work is
iSonar (Restuccia et al., 2017) that designs a custom acoustic OFDM modem
hardware that can connect to the smartphone using its audio jack. In addition
to requiring additional hardware, it neither supports band adaptation nor is
evaluated with mobility. In contrast, we design the first underwater acoustic
communication system that operates on mobile devices without any additional
hardware.

Modulation, rate adaptation and MAC protocols. Prior work makes contributions
at the physical and MAC layers. (Stojanovic, 2008a; Tao et al., 2018; Schott
et al., 2021) have analyzed various modulation techniques. There has also been
work on underwater channel estimation for OFDM (Ouyang et al., 2021; Trubuil
et al., 2014), the use of pilot symbols to track channel estimates within a
packet (Tabba, 2020; Kumar and Kumar, 2020), Doppler estimation (Mason et al.,
2009; Trubuil and Chonavel, 2012; Hwang and Schniter, 2007) and bit rate
adaptation (Su et al., 2015; Alamgir et al., 2020; Teixeira et al., 2015;
Shankar and Chitre, 2013; Sadeghi et al., 2017; Pelekanakis and Cazzanti,
2018) for underwater sensor networks. Various hardware MAC protocols (Al
Guqhaiman et al., 2021) have also been explored in prior work. There have also
been interest in cognitive underwater spectrum access (Yonggang et al., 2008;
Bicen et al., 2012; und, 2021). All this existing work has been designed for
custom underwater hardware. In contrast, we design adaptation algorithms and
protocols that can run on commodity mobile devices and operate with a large
diversity of frequency responses across hardware.

Underwater sensor networks/IoT. Underwater sensor networks have been an active
research area and uses custom sensor hardware (Peng et al., 2009; Xiao, 2009).
Recent work has designed novel IoT hardware that uses backscatter
communication (Liu et al., 2013; Kellogg et al., 2014) and acoustic energy
harvesting to design battery-free underwater wireless sensors
(Ghaffarivardavagh et al., 2020; Jang and Adib, 2019). Recent work has also
designed creative hardware to communicate across the water and air interface
(Tonolini and Adib, 2018; Carver et al., 2020). Optical approaches have also
been proposed for short-range underwater communication at 1–2 m (Liu et al.,
2021). We build on this sensing work but focus instead of using commodity
devices to enable underwater communication capabilities without additional
hardware. Further, in contrast to prior work that is designed for underwater
sensors, our goal is to enable humans to message underwater using their smart
devices.

In-air acoustic communication. Prior work has used smartphones to enable
acoustic communication and tracking in air at close ranges (Nandakumar et al.,
2013; Wang et al., 2016; Lee et al., 2015; Santagati and Melodia, 2015; Wang
and Gollakota, 2019; Nandakumar et al., 2016). However enabling underwater
communication using smartphones is challenging for multiple reasons, 1)
multipath in underwater environments can be more severe in comparison to in
air, 2) even the frequencies that can be used on the forward and backward
paths can be different underwater (see §2.1), 3) in-air acoustic systems have
a limited communication range of a few meters. Designing an underwater
communication protocol that can adapt for a wide range of bit rates and
achieve much longer range requires designing a different system.

Figure 19. MAC protocol with multiple transmitters.

##  5\. Discussion

We discuss various system-level aspects of our system.

Battery life. To measure the power consumption of our system, we considered a
setup with two Samsung Galaxy S9 smartphones as the transmitter and the
receiver. We ran our system continuously at maximum sound volume with the
screen on and found that the battery power reduced by 32% after a duration of
4 hours. This is sufficient for the application of recreational scuba diving,
which have a maximum recommended dive time less than this (pad, 2022b, a).

Messaging latency. A question that the reader may have is if the bit rates in
our design are sufficient for underwater messaging. Since typing underwater
may be uncomfortable, our app interface has the user select from one of 240
messages, which translates to around 8 bits (and 12 bits after coding). It
takes close to half a second to send this message at 25 bps. At 1 kbps, we can
even send a 50 character message in half a second.

Range versus power. The range achieved by custom hydrophones depends on their
transmit power. Commercial hydrophones that have a kilometer or more range
typically have a high transmit power (Ghaffarivardavagh et al., 2020). The 30
m range for messaging and 100 m range for SoS beacons that we achieve with
mobile devices is sufficient for many recreational and professional underwater
activities.

Audibility. Underwater acoustic modems use a range of frequencies from
multiple kHz to 100s of kHz. Our results show that 1-4 kHz is the optimal set
of frequencies for use on commodity smart phones and watches. These are in the
audible range of human hearing, which is also true for some of the commercial
modems that operate in 7-17 kHz (low, 2018; Borden and DeArruda, 2012). Also
note that human hearing underwater occurs through bone conduction rather than
through the air pocket in the ear canal (Qin et al., 2011). As a result, some
prior studies observe that human hearing extends to ultrasonic frequencies
underwater (Qin et al., 2011; bon, 2016). While fish and sharks have limited
sensitivity for frequencies far above 10 kHz (Popper, 2003; Chapuis et al.,
2019), sea mammals, e.g., dolphins, seals, and whales are highly sensitive to
frequencies up to 150 kHz (Ketten, 1994, 1992). Transmissions from every
acoustic modem are assumed to be audible to sea mammals in the vicinity
(Schott et al., 2021).

##  6\. Conclusion

The last few decades have shown that software-based solutions can transform
industries and bring technology to the masses more rapidly than custom
hardware. We present the first acoustic system that uses software to bring
underwater communication capabilities to commodity mobile devices. We believe
that since our system can be downloaded as a mobile software app on billions
of devices, it can help democratize underwater communication and has the
potential to be used by tens of millions of people who participate in
underwater activities like scuba divers and snorkeling every year.

Acknowledgments. The researchers are funded by the Moore Inventor Fellow award
#10617 and the National Science Foundation. We thank our shepherd, Haitham
Hassanieh, and the anonymous reviewers for their feedback on our submission.

This work does not raise any ethical issues.

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