Underwater Acoustic Communication Systems

This document presents a systematic treatment of underwater acoustic (UWA) communication principles and system design. Electromagnetic waves attenuate rapidly in seawater, making acoustics the primary modality for wireless underwater communication despite its challenging propagation characteristics.

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1. Introduction

Seawater is conductive, causing electromagnetic wave attenuation of approximately 4 dB/m at 1 MHz. Practical RF communication is limited to ranges under 10 m at frequencies above 100 kHz. Acoustic waves, conversely, propagate efficiently through water, enabling communication ranges from hundreds of meters to tens of kilometers depending on frequency and environmental conditions.

However, the underwater acoustic channel presents severe challenges: limited bandwidth, extensive multipath, large and variable propagation delays, and significant Doppler effects. Understanding these constraints is essential for effective system design.

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2. Acoustic Propagation Physics

2.1 Sound Speed

Sound speed in seawater varies with temperature (T), salinity (S), and depth (D):

c = 1449.2 + 4.6T − 0.055T² + 0.00029T³ + (1.34 − 0.01T)(S − 35) + 0.016D — Eq. (1)

Where c is in m/s, T in °C, S in ppt, and D in meters.

Typical values:

Environment	Sound Speed (m/s)
Surface, tropical	1540
Surface, temperate	1500
Deep ocean (4000m)	1545
SOFAR channel axis	1480

Table 1 Representative sound speed values.

2.2 Attenuation

Acoustic attenuation α (dB/km) is strongly frequency-dependent:

α(f) = 0.11f² / (1 + f²) + 44f² / (4100 + f²) + 2.75 × 10⁻⁴f² + 0.003 — Eq. (2)

Where f is in kHz. This expression (Thorp’s formula, modified) yields:

Frequency	Attenuation (dB/km)
1 kHz	0.06
10 kHz	1.0
50 kHz	10
100 kHz	35

Table 2 Acoustic attenuation versus frequency in seawater.

2.3 Spreading Loss

Geometric spreading follows:

TL_spread = k · 10 log₁₀(r) — Eq. (3)

Where k = 2 for spherical spreading (deep water), k = 1 for cylindrical spreading (shallow water duct), and k = 1.5 for practical intermediate cases.

2.4 Total Transmission Loss

TL = k · 10 log₁₀(r) + α(f) · r/1000 — Eq. (4)

Where TL is in dB, r in meters.

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3. Channel Characteristics

3.1 Bandwidth Constraints

The bandwidth-range product is fundamentally limited:

Range	Usable Bandwidth	Maximum Data Rate
100 m	100 kHz	100 kbps
1 km	10–50 kHz	10–50 kbps
10 km	2–10 kHz	1–5 kbps
100 km	0.5–2 kHz	100–500 bps

Table 3 Bandwidth-range tradeoffs in UWA systems.

3.2 Multipath Propagation

Acoustic signals arrive via multiple paths due to reflections from:

1. Sea surface: Dynamic, rough reflector causing scattering
2. Seabed: Frequency-dependent reflection coefficient
3. Thermoclines: Gradual refraction at sound speed gradients

Multipath spread τ_max depends on geometry:

Environment	Typical τmax
Shallow (h = 20m)	10–50 ms
Deep (h = 1000m)	1–10 ms
Vertical channel	50–200 ms

Table 4 Multipath delay spreads by environment.

The delay spread limits symbol rate:

R_s < 1 / τ_max — Eq. (5)

Or equalization is required.

3.3 Doppler Effects

The low sound speed makes Doppler shifts significant. For relative velocity v:

Δf / f = v / c — Eq. (6)

Platform Velocity	Doppler at 10 kHz
1 m/s	6.7 Hz
5 m/s	33 Hz
10 m/s	67 Hz

Table 5 Doppler shifts at acoustic frequencies.

A 33 Hz shift at 10 kHz represents a 0.33% frequency error—orders of magnitude larger than typical RF systems.

3.4 Channel Coherence

Parameter	Shallow Water	Deep Water
Coherence time Tc	10–100 ms	100–1000 ms
Coherence bandwidth Bc	10–100 Hz	100–1000 Hz
Doppler spread	0.1–10 Hz	0.01–0.1 Hz

Table 6 Channel coherence parameters.

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4. Modem Architecture

4.1 Signal Processing Chain

Transmit Path:

Stage	Function	Output
1. Source	Data generation	Bit stream
2. FEC Encoder	Error protection	Coded bits
3. Interleaver	Burst error protection	Reordered bits
4. Modulator	Symbol mapping	Complex symbols
5. Pulse Shaping	Bandwidth limiting	Baseband signal
6. DAC	Digital-to-analog	Analog waveform
7. Power Amp	Signal amplification	Acoustic drive
8. Transducer	Electrical-to-acoustic	Pressure wave

Receive Path:

Stage	Function	Output
1. Transducer	Acoustic-to-electrical	Analog signal
2. LNA	Low-noise amplification	Amplified signal
3. ADC	Analog-to-digital	Digital samples
4. Synchronization	Timing recovery	Aligned samples
5. Doppler Comp	Motion correction	Resampled signal
6. Equalizer	Multipath compensation	ISI-free symbols
7. Demodulator	Symbol-to-bit mapping	Soft bits
8. Deinterleaver	Reorder restoration	Ordered bits
9. FEC Decoder	Error correction	Recovered data

Table 7a Acoustic modem signal processing stages.

4.2 Modulation Techniques

Modulation	Spectral Efficiency	Robustness	Complexity
FSK	Low (0.5 bps/Hz)	High	Low
DSSS	Very low	Very high	Medium
PSK/QAM	Medium (1–4 bps/Hz)	Medium	Medium
OFDM	High (2–6 bps/Hz)	Low	High

Table 7 Modulation scheme comparison.

4.3 Equalization Requirements

For coherent modulation, adaptive equalization compensates multipath:

y(n) = Σ h_k(n) · x(n−k) + w(n) — Eq. (7)

Equalizer length L must satisfy:

L ≥ τ_max · f_s — Eq. (8)

Where f_s is the symbol rate.

Decision-Feedback Equalization (DFE) is common:

Component	Purpose
Feedforward filter	Cancels precursor ISI
Feedback filter	Cancels postcursor ISI
Phase tracker	Compensates residual Doppler

Table 8 DFE equalizer components.

4.4 Doppler Compensation

Resampling corrects for motion-induced time compression/expansion:

r_comp(t) = r((1 + v/c)t) — Eq. (9)

Doppler estimation methods:

1. Preamble correlation: Compare received/transmitted preamble timing
2. Pilot tracking: Track known symbols distributed in packet
3. Blind estimation: Estimate from signal statistics

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5. Performance Specifications

5.1 Commercial Modem Comparison

Parameter	Short Range	Medium Range	Long Range
Frequency	20–50 kHz	10–30 kHz	5–15 kHz
Range	500 m	3 km	10 km
Data rate	10–30 kbps	1–10 kbps	100–1000 bps
BER	10⁻⁶	10⁻⁵	10⁻⁴
Power (TX)	5–20 W	10–50 W	20–100 W

Table 9 Commercial acoustic modem specifications.

5.2 Link Budget Example

For a 1 km horizontal link at 15 kHz:

Parameter	Value
Source level	180 dB re 1 µPa @ 1m
Transmission loss	−75 dB
Received level	105 dB re 1 µPa
Noise level (SS3)	65 dB re 1 µPa in band
SNR	40 dB
Required SNR (QPSK)	15 dB
Margin	25 dB

Table 10 Example UWA link budget.

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6. Network Architectures

6.1 Protocol Challenges

Challenge	Cause	Mitigation
Long propagation delay	1.5 ms/m (vs 3 ns/m for RF)	TDMA, scheduled access
Hidden terminal	Limited propagation	Carrier sensing unreliable
Half-duplex	Transducer reciprocity	Time-division protocols
Spatial uncertainty	Node mobility	Localization protocols

Table 11 UWA networking challenges.

6.2 MAC Protocol Approaches

Protocol	Throughput	Latency	Complexity
TDMA	Moderate	High	Low
CDMA	Low	Low	Medium
FDMA	Moderate	Low	Low
MACA-U	Variable	Variable	Medium

Table 12 MAC protocol comparison.

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7. Emerging Technologies

7.1 MIMO Acoustics

Spatial multiplexing using N_T transmitters and N_R receivers:

C = min(N_T, N_R) · B · log₂(1 + SNR/min(N_T, N_R)) — Eq. (10)

Practical challenges include transducer spacing (wavelengths at acoustic frequencies are large) and spatial correlation in confined channels.

7.2 Optical-Acoustic Hybrid

Modality	Range	Data Rate	Conditions
Acoustic	Long	Low	All
Optical (blue-green)	Short	High	Clear water

Table 13 Hybrid system characteristics.

Hybrid architectures use acoustic for command/control and optical for high-bandwidth data transfer at close range.

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8. References

1. Stojanovic, M. and Preisig, J., “Underwater Acoustic Communication Channels: Propagation Models and Statistical Characterization,” IEEE Communications Magazine, vol. 47, no. 1, pp. 84–89, 2009.
2. Chitre, M., Shahabudeen, S., and Stojanovic, M., “Underwater Acoustic Communications and Networking: Recent Advances and Future Challenges,” Marine Technology Society Journal, vol. 42, no. 1, pp. 103–116, 2008.
3. Urick, R.J., Principles of Underwater Sound, 3rd ed., McGraw-Hill, 1983.
4. Brekhovskikh, L.M. and Lysanov, Y.P., Fundamentals of Ocean Acoustics, 3rd ed., Springer, 2003.
5. Akyildiz, I.F., Pompili, D., and Melodia, T., “Underwater Acoustic Sensor Networks: Research Challenges,” Ad Hoc Networks, vol. 3, no. 3, pp. 257–279, 2005.