1

An Underwater Acoustic Telemetry Modem for Eco-Sensing*

Ronald A. Iltis, Ryan Kastner, and Hua Lee Daniel Doonan, Tricia Fu, Rachael Moore and Maurice Chin

Department of Electrical and Computer EngineeringUniversity of California,

Santa Barbara, CA 93106-9560{iltis,kastner,lee}@ece.ucsb.edu

*This work was supported in part by the W.M. Keck Foundation and UCSB Marine Sciences Institute.

2

Dock

AquaNodes with acoustic modems/routers, sensors.

Dockside acoustic/RF comms and signal processing.

Cabled hydrophone array

Wi-Fi or Wi-Max link

CTD, currents, nutrient data to Internet. Adaptive sampling commands to AquaNodes.

WetNet Implemented with AquaNodes

Applications: Santa Barbara Channel LTER, Moorea Coral Reef LTER and many more.

3

Modem Alternatives• Commercial modems: (Benthos, Linkquest…)

– Too expensive, power hungry for Eco-Sensing. Proprietary algorithms, hardware.– M-FSK (Scussel, Rice 97, Proakis 00) does use frequency diversity, but requires coding to

erase/correct fades.• Navy modems:

– Need open architecture for international LTER community – precludes military products.• Direct-sequence, QPSK, QAM, coherent OFDM

– Great deal of work on DS, QPSK for underwater comms. But equalization, channel estimation are difficult. (Stojanovic 97, Freitag, Stojanovic 2001, 2003.)

• MicroModem: – Best available solution for WetNet. FSK/Freq. Hopping relies on coding to correct bad hops.– But can we do better? Less power? Wider bandwidth for lower uncoded symbol error rate

(SER)? • AquaNode modem: Uses Walsh/m-sequence signalling, matching pursuits channel

estimation.– Uses per-symbol frequency diversity.– Motivated by 802.15.4 (Zigbee), 802.11b m-ary quasi-orthogonal waveforms.– Achieves 133 bps data rate without need for equalization, accurate carrier phase tracking.– Battery life in months for reasonable transmit duty cycles.– Matching Pursuits only assumes channel constant over 22 msec.– Far superior to FSK in slow fading (Doppler spread < .1 Hz) scenario using Kalman filter

channel tracking.

4

Multipath/Doppler Spread References

• Long range shallow water multipath spread ~100 msec. (Kilfoyle and Baggeroer 00)

• 120 msec. spread at 48 nm, 5 msec. at 2nm shallow water (Stojanovic et. al. 94)

• Significant delay spread ~10 msec. 2-6 meter depth, 400-500m range. (Freitag et. al. JOE 01)

• 2.5 msec multipath spread, .5 Hz Doppler spread at 3km (6 to 30m depth) in Baltic. (Sozer et. al. 99)

• .67 msec. multipath spread for two-ray channel (Benson et. al. 00)

• Conjecture: A broad class of short range (< 500 m) shallow water channels exists with temporal multipath spread ~10 msec., Doppler spread < 1 Hz.

5

Walsh/m-sequence Signals

1 1 -1 1 -1 -1-1 1 1 -1 1 -1 -1-1-1 -1 1 -1 1 1 1

Tc = :2msec:

6

Motivation for Walsh/m-sequence Waveforms

• Wideband (5 kHz) yields frequency diversity.• 3 bits/symbol yields 10log3 = 4.8 dB coding

gain relative to binary FSK.• Does not require accurate phase tracking for

detection (c.f. QPSK, QAM.)• Time-guard band eliminates need for

equalization.• Sparse channel estimation easily implemented

via Matching Pursuits.

7

Wideband for Acoustic Comms -- Frequency Diversity Argument

• B Hz. Wideband signal can resolve multipaths Ts = 1/2B apart.• Classical RAKE receiver.

)(nr

k

L

kk

L

kks nE

1

*

1

2|2

*1 *

2 *3 *

L

sT sT sT

)(ns

8

Channel, Walsh/m-sequence Spectra

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Frequency (Hz.)

|H(f

)|

Channel Response

Walsh/m-seq. spectrumFSK Tones

9

Auto-Cross Correlation of Walsh/m-seq.

0 20 40 60 80 100 120-0.5

0

0.5

1

Delay (Samples)

Wa

lsh

/m-s

eq

ue

nce

Co

rre

latio

nS

1,S

2 cross-correlation

S1 auto-correlation

10

Un-coded SER Improvement with Diversity

FSK in Rayleigh Fading

Binary Orthogonal with L-degree Diversity in i.i.d. Rayleigh Fading. Ideal RAKE – zero cross-correlation.

(J. G. Proakis 7.4.15)

P2 = 12+ E b

N 0

Union Bound

Pe < (Nw ¡ 1)P2¹ =

E bL N 0

2+ E bL N 0

Law of Large Numbers Interpretation – Normalized Channel Energy

E f j®k j2g= 1L

2EsP L

k=1 j®kj2 ! 2EsLE f j®k j2g= 2Es

P2 =

µ1¡ ¹

2

¶L L ¡ 1X

k=0

µL ¡ 1+k

k

¶ µ1+¹

2

¶k

11

Union Bound SER -- Frequency Diversity

10 11 12 13 14 15 16 17 18 19 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0

Pb

FSK

Orthogonal, diversity order =1

Orthogonal, diversity order =7

Orthogonal, diversity order =13

Orthogonal, diversity order =19

Orthogonal, diversity order =25

12

Received Signal Model

r(t) =N®X

p=1

®p(n)sm(n)(t ¡ ¿p(n)) +n(t)

Transmitted Walsh/m-sequence

Received signal

Nyquist-sampled equivalent vector signal

sm(n)(t) =Nw L pn ¡ 1X

i=0

(dm(n))ig(t ¡ iTc)

r(n) ¼N s ¡ 1X

l=0

f lsm(n)(l) +n(n) = Sm(n)f +n(n)

13

Matching Pursuits Channel Estimation

• Conventional LS estimate is “noisy” for sparse channels (Nf << components of f are nonzero.)

• Assume “minimum underspread” channel. Coefficients f are constant only during one symbol+time guard interval (22.4 msec.)

• Matching Pursuits (Mallat and Zhang, Cotter and Rao 02, Kim and Iltis 04) yields sparse channel estimates and is readily implemented in reconfigurable hardware (Meng et. al. DAC 05.)

r(n) ¼2Tsy

m

s (q1)f̂ q1

s(q2)f̂ q2

s(q3)f̂ q3

s(qN f)f̂ qN f

+

+

+

14

MP Algorithm

• Step 1 – Conventional LS, best fit.

Step k – Cancel previous k-1 detected paths, find qk

f̂ i = s(i)H r=jjs(i)jj2; i = 1;::: ;Ns

q1 = argmini

¯¯¯¯¯r̄ ¡ s(i)f̂ i

¯¯¯¯¯¯2

= argmaxi

jf̂ i j2jjs(i)jj2

rk = r ¡k¡ 1X

i=1

s(qi )f̂ qi

f̂ i = s(i)H rk=jjs(i)jj2

qk = arg mini6=q1 ;:::;qk ¡ 1

¯¯¯¯¯r̄k ¡ s(i)f̂ i

¯¯¯¯¯¯2

= arg maxi6=q1 ;:::;qk ¡ 1

jf̂ i j2jjs(i)jj2

15

GMHT-MP Algorithm• Decision on m(n) using Generalized Multiple Hypothesis Test

(GMHT)

m̂= argminm

½min

f :´ (f )=N f

jjr(n) ¡ Smf jj2¾

Numerosity constraint

GMHT has complexity Nw binom(Ns, Nf) due to numerosity constraint. For Nf = 12 paths, this requires 35x1015 LS channel estimates requiring matrix-vector multiplies!

MP estimation requires Nw Ns!/(Ns-Nf)! = 1.7x1025 least-squares estimates, but these are scalar quanitities. MP also only requires one matrix-vector multiply when implemented using sufficient statistics. GMHT-MP thus has the form

m̂= argminm

njjr(n) ¡ Smf̂M P;mjj2

o

16

Sufficient Statistics MP Implementation(A. Brown and Y. Meng, DAC 05)

• Step 1: Matrix-vector multiply

v1 = SH r(n); A = SH S (look-up table)

q1 = argmaxi

jv1i j

2

A i ;i;

f̂ q1 =v1

i

A i ;i

v2 = v1 ¡ A (:;q1)f̂ q1

Step k: Does not require further matrix-vector multiplies.

qk = argmaxi

jvki j

2

A i ;i;

f̂ qk =vk

i

A i ;i

vk+1 = vk ¡ A (:;qk)f̂ qk

17

Reconfigurable Hardware MP-Core(Kastner, Meng, Brown)

Input( r, S, A, a ) Output( f ) // r : received signal vector // S : ],,,,[ 1 SNi SSSS

// A : ],,,,[ 1 SNk AAAA

// a : TNk S

aaaa ],,,,[ 1 // f : estimated channel coefficients MP( r, S, A, a ) 1 for i = 1, 2, …, SN // compute matched filter (MF) outputs 2 rSV T

ii 0 3 0if

4 0ig 5 end for 6 00 q // do successive interference cancellation 7 for j = 1, 2, …, fN

// update MF outputs 8

11

1

jj qqjj AfVV

9 for k = 0, 1, …, 1SN 10 k

jkk avg

11 kjkk gvQ *)(

12 end for 13 }{maxarg

11,...,,k

qqkkj Qq

j

14 jj qq gf

15 end for 16 return (f)

(c) Matching pursuit algorithm for channel estimation

CLB Block RAM IP Core (Multiplier)

* + -

*+

control control

(a) Matched filter (b) Multipath successive interference cancellation

1jqf

0

iV

kg

kg

kQ

kQ

jkV

iS iS

kA

ka

r

18

Note: 112 Nyquist samples/symbol + 112 samples for channel clearing.

MPCORE 1

MPCORE 2

MPCORE 7

MPCORE 8

AquaNode Modem Architecture

13X

k=0

r(k+n)c(k)

28X

k=14

r(k+n)c(k)

111X

k=98

r(k+n)c(k)

97X

k=84

r(k+n)c(k)

8X

k=1

b1(k)yk(n)

8X

k=1

b2(k)yk(n)

8X

k=1

b7(k)yk(n)

8X

k=1

b8(k)yk(n)

19

Matching Pursuits Channel Estimation

0 0.002 0.004 0.006 0.008 0.01 0.0120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mu

ltip

ath

Inte

nsi

ty P

rofil

e

Time (sec.)

True MIP

Matching Pursuits Estimated MIP

N = 12, Nf = 16, Es/N0 = 20 dB

20

Matching Pursuits SER – Fixed Order

14 15 16 17 18 19 20 21 2210

-4

10-3

10-2

10-1

Es/N

0

SE

R

AquaNode/GMHT-MP N =12 Nf =16

RAKE N =12 Nf =16

FSK/SFH N =12 Nf =16

21

Channel Order Estimation

• MDL and AIC yield overparameterized channel estimates. • Modified MDL uses penalty term increasing with SNR and

channel order, but requires optimization of penalty weight.• Heuristic algorithm: Stop when decrease in error is below a

threshold.

N̂f = k if¯¯¯¯¯

¯¯¯¯¯r(n) ¡

kX

i=1

s(qi )f̂ qi

¯¯¯¯¯

¯¯¯¯¯

2

> ¯

¯¯¯¯¯

¯¯¯¯¯r(n) ¡

k+1X

i=1

s(qi )f̂ qi

¯¯¯¯¯

¯¯¯¯¯

2

Typical values of are .95, .98.

22

SER Using Residual-Based Order Estimation

14 15 16 17 18 19 20 21 2210

-4

10-3

10-2

10-1

Es/N

0

SE

R

MP N =12 Nf =16

RAKE N =12 Nf =16

FSK/SFH N =12 Nf =16

Using Residual-BasedOrder Estimation = .98

23

Kalman Filter Channel Estimator• MP only requires channel constant over Tsym = 22.4

msec. Good solution for large Doppler spreads (> .1 Hz.)

• For Doppler spreads fd < .1 Hz, Kalman filter channel estimator is promising.

• Use decision-directed KF with process/measurement models

f(n+1) = ®f f(n) +w(n)

r(n) = Sm̂(n)f(n) +n(n)

m̂(n) = argminm

jjr(n) ¡ Sm̂f̂ (njn ¡ 1)jj2

24

Decision-Directed Kalman Filter

r(n)

jjr(n) ¡ S1f̂ (njn ¡ 1)jj2

jjr(n) ¡ S8f̂ (njn ¡ 1)jj2

m̂(n)min

Kalman Filter

Tsymf̂ (n+1jn)

f̂ (njn) = f̂(njn ¡ 1) +P (njn)SHm̂(n)

1¾2

n[r(n) ¡ S ^m(n)

f̂ (njn ¡ 1)]

P (njn)¡ 1 = P (njn ¡ 1)¡ 1 + 1¾2

nSH

^m(n)S ^m(n)

P (njn); f̂ (njn)

f̂ (n+1jn) = ®f f̂ (njn)

MP Initializationf̂ (1j0)

25

Union Bound Conditional SER• Analytic union bound SER speeds up KF simulations.• Pairwise error probability.

SNR decrease due to estimation error

P1;2 =12erfc

ÃjjS1f ¡ S2f̂ jj

¾n¡

jjS2(f ¡ f̂ )jj2

¾n jjS1f̂ ¡ S2f̂ jj

!

Pe <1

Nw

N wX

i=1

N wX

j =1

Pi ;j

26

Kalman Filter Channel Estimation

0 0.002 0.004 0.006 0.008 0.01 0.0120

0.05

0.1

0.15

0.2

0.25

0.3

0.35M

ulti

pa

th In

ten

sity

Pro

file

Time (sec.)

True MIP

Unconstrained Kalman Filter Estimated MIP

fd = .05 Hz

Eb/N

0 = 8 dB

27

Example SER Trajectory – Doppler Spread = .05 Hz

0 50 100 150 200 250 300 350 400 450 50010

-10

10-8

10-6

10-4

10-2

100

Pe

Symbol Number

Walsh/m-seq. Kalman Filter

Walsh/m-seq. A-priori known channelNoncoherent FSK

fd = .05 Hz

Eb/N

0 = 8 dB

28

Simulation/Analysis using Union Bound

2 3 4 5 6 7 8 9 10 11 1210

-8

10-6

10-4

10-2

100

Eb/N

0

Pe

WM seq. a-priori channel

WM Kalman filterFSK/FH

fd = .05 Hz

N = 12

29

Sonatech Transducer2 FeetSignal and Data Parameters

Data rate: 133 bps

Chip duration Tc = .2 msec.

Symbol duration Tsym = 11.2 msec.

Time guard interval Tc = 11.2 msec.

M-sequence length Lpn = 7 chips.

Walsh sequence length Nw = 8

Bandwidth = 5 kHz

Carrier Frequency fc = 25 kHz

Nominal range 100 – 300 m.

Power Consumption Overview

Load Tx State Rx State Sleep State

CPU 440 mW 440 mW .30 mW

CPU I/O 420 mW 420 mW .15 mW

Flash Memory 165 mW 165 mW .10 mW

Power Amp. 7.2 W .05 mW .05 mW

Battery Total 9.3 W 2.1 W 10 mW

Battery Life (Based on 20 amp-hours)

Tx Duty Cycle Rx Duty Cycle Days

.1% .2 % 624

.5% 1 % 189

1% 2% 101Power Amp and Transducer Matching Network

TI 2812 DSP with CompactFlash, ADC, DAC

30

Conclusions

• Walsh/m-sequence signaling exploits frequency diversity and yields lower uncoded SER than FSK.

• Matching Pursuits algorithm enforces sparse estimates, implemented in FPGA and DSP.

• Modem should be adaptive, using Kalman or MP channel estimation depending on sensed channel variation, velocity.

• Can a numerosity-constrained Kalman filter be developed? Better performance for fd > .1 Hz?

• First generation modem implementable in DSP, but second gen. will require DSP +FPGA.