Signal Processing for

Underwater Communications

Milica Stojanovic millitsa@ece.neu.edu

Acknowledgments to the Office of Naval Research for supporting much of this research, and for the travel grant N62909-09-1-1024.

“If you cause your ship to stop and place the head of a long tube in the water

and place the outer extremity to your ear, you will hear ships at a great distance from you.“

(1490)

‘77 ‘85

Underwater wireless communications

Why?

Major scientific discoveries: cabled submersibles Cables are heavy, expensive, restrict motion (but offer high bandwidth) Applications: -ocean monitoring (climate, pollution, oil, fisheries, earthquakes,…) -underwater exploration (marine archaeology, natural resources, …) -search and survey (shipwrecks, mines, area mapping,…)

How?

Radio: ~100 Hz, very high attenuation (~m @ 10kHz) Optical: short distances (<100m), pointing precision Acoustical: a solution

What has been done?

Underwater telephone (WW2, analog SSB 8-11 kHz) DSP technology: acoustic modems (few kbps over few km) 70’s,80’s: noncoherent mod/demod commercially available 90’s: bandwidth-efficient mod/demod prototypes

What is next? More signal processing, networks.

Overview

communication channel

• single-carrier, multi-carrier • single-user, multi-user (SIMO/MIMO)

implications for networking

• attenuation and noise • multipath propagation

• time-variability

signal processing

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0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

distance [km]

optim

al fr

eque

ncy

[kH

z]

-10 logA(x,f)N(f)

fundamental limitation (also transducer)

Underwater acoustic channel: attenuation and noise

site-specific: man-made biological ice, rain seismic

noise= turbulence+ shipping+ surface+ thermal+ other

100

101

102

103

104

105

106

20

30

40

50

60

70

80

90

100

110

f [Hz]

no

ise

p.s

.d.

[dB

re

mic

ro P

a]

........ wind at 10 m/s

____ wind at 0 m/s

shipping activity 0, 0.5 and 1

(bottom to top)

10 log N(f)

~ 50 -18 log f

~ f2/100

“UWA=UWB”

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

frequency [kHz]

abso

rptio

n co

effic

ient

[dB

/km

]

10log a(f)

: spreading + absorption A(x,f)~xkax(f) (k:1-2)

10 log a(f) = 0.11 f2/(1+f2)+44 f2/(4100+f2)+0.000275 f2+0.003 dB/km, for f [kHz]

0 10 20 30 40 50 60 70 80 90 10010

0

101

102

103

104

distance [km]

B [kH

z] an

d C

[kbps

]

0 10 20 30 40 50 60 70 80 90 100110

120

130

140

150

160

170

distance [km]

P [dB

re m

icro Pa

]

capa

city

, ban

dwid

th, p

ower

: de

pend

ence

on

dist

ance

A “high-rate” acoustic system is inherently wideband (“UWA=UWB”)

System is band-limited, narrowband assumption does not hold.

Implications : • need bandwidth efficient modulation methods (coherent detection) • cannot use signal processing methods that rely on narrowband assumption (array processing, synchronization)

Fundamental difference between radio, acoustics:

f

~GHz

~MHz

f

~kHz

~kHz AF

RF

Absolute bandwidth may be “low,” but it is not negligible w.r.t. center frequency (e.g. 1 kHz @ 1 kHz, 5 kHz @ 10 kHZ, 20 kHz @ 30 kHz).

Underwater acoustic channel: multipath and time-variability

depth

c

surface layer (mixing) const. temperature (except under ice) main thermocline temperature decreases rapidly

deep ocean constant temperature (4 deg. C) pressure increases

Sound speed increases with temperature, pressure, salinity.

continental shelf (~100 m)

continental slice

continental rise

abyssal plain

land sea

surf shallow deep

tx

distance c

tx rx

Channel variation: large/small scale surface motion, internal waves, turbulence, fine changes in the sound speed profile.

multipath spread~ 10 ms, 100 ms coherence time~ 0.1 s, 1s?

(“anti-causal”)

0

5

10

15

-40

-20

0

20

40

0

0.2

0.4

0.6

0.8

time [s]delay [ms]

tx depth : 100 m, rx depth : 640 m

Channel # 6 : omnidirectional

Rate : 333 sps

Range : 110 nautical miles

0

5

10

15-50

0

50

0

0.2

0.4

0.6

0.8

time [s]delay [ms]

tx depth : 25 m, rx depth : 23 m

Channel # 8 : omnidirectional

Rate : 333 sps

Range : 48 nautical milestime [s]delay [ms]

tx depth : 8 m, rx depth : 3.5 m

Channel # 1 : directional

Rate : 500 sps

Range : 2 nautical miles

02

46

810

-10

-5

0

5

100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Examples: measured channel responses

There are no widely accepted statistical channel models.

Channel modeling (for signal processing)

tx rx

Each path in an acoustic channel acts as a (low-pass) filter.

(2) time-variation

Each path:

• length, delay • propagation loss A • reflection coefficient Γ

path filters: same shape, different gain

time variation: inherent, motion-induced (random, deterministic/unknown)

(1) time-invariant channel

Example Narragansett Bay, March 2008

400m

9-14m

3m 2m

8-18 kHz

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0 5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

tap magnitude

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(no motion of tx/rx)

Equivalent band-limited baseband discrete-path models

non-uniform tap spacing

uniform tap spacing

0 0.005 0.01 0.015 0.02 0.0250

0.5

1

1.5

2

2.5

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resp

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co

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nts

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ag

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de

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1

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30 ms @ 5 ksps = 150 symbols.

…respect the physics of the channel, and …

win-win

tx/rx: 1 km / 75 m fc=10 kHz, B=5 kHz

Motion-induced time-variation: the Doppler effect

t t+at f f+af

a=v/c

…respect the physics of thy channel …

• inherent Doppler spreading • motion-induced Doppler shifting (and spreading)

adaptive channel estimation (slow) synchronization (fast)

tacking θ(t) vs. e j θ(t)

time dilation/compression frequency offset

Implications: explicit synchronization is necessary.

comparable only to LEO satellite systems

v ~ m/s c=1500 m/s a~10-4

with or without intentional motion

Time variation:

0 2000 40000

2

4

mse

[symbol intervals]0 2000 4000

-1

-0.5

0

0.5

fd=-0.02106Hz

phase [rad]

[symbol intervals]

-2 0 2-2

-1

0

1

2out.scatter

Re

Im

receiver parameters : 500 sps

N=60 (T/2) M=60

Le=0.998 Lc=0.99Kf1=0.0005 Kf2=5e-05

K=10 P=3

Pe~0SNRout~18.58dB

inp. K

com- biner forward

forward + _ decision

feedback

adaptation algorithm

inp.1

inp.2 data out

sync.

filter coefficients

training data

data est.

Single-carrier systems

Ex. New England Continental Shelf, 50 n.mi, 1 kHz

Current achievements:

Point-to-point (2/4/8PSK;8/16/64QAM) •  medium range (1 km-10 km ~ 10kbps) •  long range (10 km – 100 km ~1kbps) •  basin scale (3000 km ~ 10bps) •  vertical (10 m~150 kbps, 3 km~15 kbps, 10 km~5 kbps)

Mobile communications AUV to AUV at 5 kbps

Multi-user communications five users, ~ kbps in 5 kHz band “the faster the better”

CDMA underwater?

Conventional assumptions do not hold: • ISI is not negligible • channel is not constant over one symbol Receiver design: • chip-rate filtering • chip-rate adaptation

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“chip hypothesis feedback” recovers processing gain.

Mobile experiments in 5 kHz band: direct sequence spread spectrum feasible at 15 knots.

Experiment: • range: 2.5 km • center frequency: 33 kHz • chip rate: 19,200 chips/sec • four users, up to 2.5 kbps • spreading factor (15-255)

L=15 L=255

Tc …

… …

…

T=LTc

Tc~1/B B fixed T grows with L “processing gain” ≠ L

0 50 100 150 200 250 3000

5

10

15

20

25

30

35

spreading factor L

outp

ut S

NR

[dB

]

CHF

SDF L

Multi-carrier systems

FFT

FFT

c o m b i n e r

c o m b i n e r

.

.

.

.

.

.

in 1

in M

1

K

1

K

dec

dec

out 1

out K

goal: low-complexity processing (post-FFT)

f …

B=KΔf

Δf

f

fkfk(1+a)

transfer function of the channel

Problem:

Motion-induced Doppler distortion in a wideband system: non-uniform frequency shifting across the signal bandwidth

a=v/c

OFDM: +equalization -frequency offset

Pre-processing (initial synchronization)

ap’(n)fk<<Δf

t T=1/Δf

Tg OFDM block OFDM block OFDM block Tg Tg

guard interval ~ multipath spread tx

rx

rx after resampling by (1+a’’)

t

t

t

n=0 n=1 n=2 n=3

Trade-offs

Implications: have to estimate/track large number of phases.

 “optimal” number of carriers: greatest for which post-FFT processing is still possible.

want large K … but this means small Δ f / large T, i.e. more vulnerability to residual frequency offset / inherent time-variation

T=10 ms, B=10 kHz K=100 T=50 ms, B=20 kHz K=1000

some numbers: Tcoh~0.1 ms; Tmp~10 ms

time-variation: • phase offset • ICI

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Buzzards Bay, 2.5 km, 24 kHz

A simple approach to “Doppler” tracking

• estimate the Doppler factor a’(n) • use this (single) estimate to compute all K phases

K=1024

OFDM: channel estimation

K coefficients (system parameter)

FFTK

J (out of L) coefficients (channel parameter)

transfer function Hk(n)

impulse response hl(n)

• non-adaptive: each block detected independently: need L pilots per block (~TmpB) • adaptive: each block detected using knowledge from previous block

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channel sparsing: keep J strongest taps only. J/L

L/K J/K

Panama City Beach, 1 km, 12 kHz

• Adaptive synchronization enables decision-directed operation (no null subcarriers)

• Decision-directed operation enables full-size channel estimation (low pilot overhead)

• Sparsing eliminates unnecessary estimation noise.

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Pushing performance limits: MIMO OFDM (for spatial multiplexing gain)

Increasing K increases block duration (T=K/B); ICI arises.

Increasing MT increases cross-talk between channels, size of the estimator; MIMO channel estimation becomes more difficult.

Q: What is the performance limit? Does it “depend on the weather?”

Want: MT , K as large as possible.

R/B = MT/ (1+TgB/K) symbols/sec/Hz

(MT≤K/L)

Work in progress: MIMO channel estimation, ICI equalization, pulse-shaped MCM, … Experiment: 4-tx, Martha’s Vineyard, 1 km, 10 kHz (nudging 10 bps/Hz)

channel: statistical characterization (for simulation, performance bounds)

tx: adaptive modulation / power control (channel state prediction) spectrum shaping, coding,…

rx: adaptive receivers (single- and multi-carrier; single- and multi-input) model-based processing (e.g., path-specific Doppler)

networks: efficient and scalable protocols on all layers topologies, architectures (“typical applications?”) capacity?

Open problems

system integration and optimization: from data compression to navigation (and back)

Underwater networks

0 10 20 30 40 50 60 70 80 90 10010

0

101

102

103

104

distance [km]

B [kH

z] and

C [kbp

s]

0 10 20 30 40 50 60 70 80 90 100110

120

130

140

150

160

170

distance [km]

P [dB re

micro P

a]

The case for relaying… d/N

d

(d/N)/c

L/R

n-1

n

t

t

delay per hop

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number of hops

cost (e

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[dB

]

d=10,20,30,40,50 km

K’0=120 dB

SNR0=20 dB

power and bandwidth improve with # hops

min. w.r.t. N

delay penalty negligible if bit rate adjusted to distance.

capacity depends on distance … is the case for signal processing.