Time-variant Adaptive Passive Time Reversal Equaliser and a

Perspective for Environmental Focusing Method

Lussac P. Maia, Ant

onio Silva and S

ergio M. Jesus

SiPLAB-DEEI-FCT, University of Algarve, Campus de Gambelas, PT-8005-139, Faro, Portugal

Keywords:

Digital Underwater Acoustics Communications, Passive Time Reversal, Coherent Signalling, Environmental-

based Equalisation, Matched Field Processing, Time-variant Channel Modelling.

Abstract:

High digital data throughput in Underwater Acoustic Communications (UAComm) is a challenging sub-

ject, specially in shallow water where the channel is a wave-guide causing multipath propagation and where

Doppler effect usually occurs due to relative source-receiver motion jointly to ocean dynamics. The source

and receiver sensors can be used for telemetry in point-to-point underwater communications or as nodes of an

underwater acoustic network within the scope of oceanic research observatory or offshore activities. However,

channel tracking is required for reliable digital underwater communications between the sensors, which is a

hard task due to the complicated propagation of acoustic waves in the ocean. Equalisation is often required

to perform a compensation method aiming to overcome the inter-symbol interference (ISI) caused by multi-

path propagation. The motivation of this work is to propose a compensation method deploying the adaptive

passive time-reversal (ApTR) equaliser, aiming to perform ISI mitigation jointly to Doppler compensation

in time-variant channels. The beneﬁt given by ApTR processing would be the performance improvement in

underwater communications between an active sensor and a vertical line array of receiver sensors, relying in

well-succeed time-variant channel impulse response estimation. Furthermore, this position paper discusses the

perspective of use an environmental focusing method for channel estimation within the ApTR equaliser, based

on the idea that a set of oceanic acoustic physical parameters – which are generally estimated in low-frequency

matched ﬁeld processing problems like geoacoustic assessment, ocean tomography and source localization –

could be conveniently used for channel compensation in high frequency underwater communications using

a carefully chosen search space of replicas. The results are two fold: in one hand the equalisation shall im-

prove the UAComm system, and in the other hand, the best match of channel parameters consequently yields

a reﬁned local environmental assessment.

1 INTRODUCTION

The use of high data rate signalling for UAComm

is a challenging subject studied by the scientiﬁc

community, ﬁnding applications in point-to-point

(P2P) communications and underwater acoustic net-

works (UAN) used for, e.g., offshore activities

and oceanic reasearch observatories (Vilaipornsawai

et al., 2014). The complicated acoustic propagation

in ocean waveguide channels makes hard the task

of establish high rate data troughput between two

node sensors, maily because of multipath propagation

and Doppler distortion, often requiring equalisation.

The equaliser can use channel estimates in the signal

processing to reach compensation for time-frequency

distortion imposed by the variable channel, aiming

to mitigate ISI and improve communications perfor-

mance.

Any channel estimation technique must deal with

frequency selective attenuation, time dispersion from

multipath propagation and frequency dispersion due

to Doppler effect. Further, the use of coherent sig-

nalling is desirable for high data throughput because

of its improved bandwidth efﬁciency, a desired char-

acteristic in the UAComm system design consider-

ing the bandwidth limitation imposed by the ocean

channel. Additionally, one can note that conventional

equalisers do not use acoustic physical parameters of

the ocean channel, at least in a direct form. This is

not speciﬁcally a design requirement, but at ﬁrst look

one could expect to explore more incisively those pa-

rameters, because they rule the physics of propaga-

tion in the channel. This work proposes to deploy

the adaptive passive time reversal (here after named

ApTR) for achieve channel equalisation in P2P wire-

less underwater communication, using single-input-

103

P. Maia L., Silva A. and M. Jesus S..

Time-variant Adaptive Passive Time Reversal Equaliser and a Perspective for Environmental Focusing Method.

DOI: 10.5220/0005330901030108

In Proceedings of the 4th International Conference on Sensor Networks (SENSORNETS-2015), pages 103-108

ISBN: 978-989-758-086-4

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

multiple-output (SIMO) structure as required by pas-

sive time reversal technique.

Passive time-reversal (pTR) – and its frequency

domain version named passive phase conjugation

(PPC) (Gomes et al., 2008) – is inspired in active

time-reversal (TR) which compensates the channel

exploring the retro-focusing propagation property of

the wave equation in wave-guide. The TR concept

was ﬁrst demonstrated in underwater acoustics by

(Parvulescu, 1961). In its passive version the process-

ing can be performed synthetically, exploring spa-

tial and temporal diversity of the acoustic channel by

software setup. Nonetheless, the conventional pTR

equaliser requires to estimate the channel impulse re-

sponse (CIR) which is usually obtained by an ini-

tial channel probe, being unable to track for channel

variability along the data transmission. The ApTR

equaliser is designed to overcome this problem. Fur-

ther, it is proposed for investigation the environmental

focusing method aiming to estimate the time-variant

channel during the data transmission, performing cor-

relation between the observed channel and carefully

chosen replicas in a data bank which is pre-computed

for a restrict area using time-variant high-frequency

acoustic propagation model.

Section II describes the theoretical background for

time-variant UAComm channel modelling. Section

III presents the ApTR, including a preliminary test

in simulated ocean waveguide channel, and discuss

the environmental focusing method. The conclusion

is presented in the Section IV.

2 THEORETICAL BACKGROUND

2.1 CIR Modelling for UAComm

Acoustic propagation in shallow water performs mul-

tiple paths, causing ISI that contributes to errors in

demodulation. Additionally, ocean dynamics and

relative motion between source and receiver cause

time-frequency dispersion, requiring compensation

for Doppler distortion. Under the time-invariant chan-

nel assumption, the ray tracing acoustic propagation

model is suitable for UAComm, because it allows to

range-dependency, have fast computation and use the

inﬁnite-frequency approximation from the ray theory

in the solution of the Helmholtz equation. However,

there are naturally temporal variations in the ocean

channel that make the time-variant approach neces-

sary for more realistic CIR modelling.

The work of (Rodriguez and Silva, 2012)

presented the Time-Variable Acoustic Propagation

Figure 1: Bi-static scattering geometry (full line and dash-

dot line) and mono-static geometry (ﬁne dot line).

Model (TVAPM) that can simulate underwater acous-

tic propagation in time-variant channel using sequen-

tial runs of the Bellhop model (Porter, 2011). The

set of sequential runs of the ray model aims to build

a matrix that provides information about the time-

variant CIR and implements Doppler distortion to

simulate the received signal. The fundamental as-

sumptions to the dynamic propagation simulations

with TVAPM are: source and array can be placed any-

where in a three-dimensional box limited by speciﬁed

bathymetry and by a pressure release surface which

can include a wind-driven surface model (JONSWAP

spectrum model was used in this work); a transmitted

signal is speciﬁed as input; linear velocities can be at-

tributed to both source and array and the correspond-

ing positions are updated progressively along trans-

missions. This model was used in the present work to

perform time-variant CIR simulations and link them

to a coherent UAComm model containing the ApTR

equaliser.

2.2 Doppler Distortion in Wave-guide

The Doppler distorted signal can be computed for

each path of the multipath propagation through the in-

sertion of a compression factor (β

). This factor per-

forms compression/expansion in time and frequency

shift (with compression/expansion in the correspond-

ing spectrum) in the signal.

Figure 1 shows the bi-static scattering geometry

scenario (Ziomek, 1995), where the signal transmitted

by a moving source (T) is reﬂected in a moving point

scatterer (S) and received in a moving receptor (R).

The velocity vectors for the transmitter, receiver and

point scatterer are

and

respectively; ˆn

t,p

and

ˆn

r,p

are the unity vectors in direction of propagation of

the transmitted and received waves, respectively, for

each path.

The time compression factor β

for a single path

in the bi-static scattering geometry (paths 1 and 2) is

SENSORNETS2015-4thInternationalConferenceonSensorNetworks

104

(Ziomek, 1995; Gomes et al., 2008)

(1 −

• ˆn

t,p

/c)(1 −

• ˆn

r,p

/c)

(1 −

• ˆn

r,p

/c)(1 −

• ˆn

t,p

/c)

− 1 (1)

where c is the sound speed in the medium, the sym-

bol • denotes dot product and

• ˆn

x,p

represents the

projection of a given velocity vector (

) in

the ray path direction. The same expression is valid to

compute the mono-static geometry (path 0), just con-

sidering that

is null and ˆn

r,0

is equal to ˆn

t,0

The compression factors (β

for the direct path,

for the free surface reﬂected path and β

for the

bottom reﬂected path) represent the compression (or

dilation) suffered by the signal when travelling to the

receiver through each path.

Consider a transmitted bandpass signal ˜s(t) with

carrier angular frequency ω

and low-pass equivalent

signal s(t) containing the information bit sequence

a(n) shaped by the pulse shape p(t) sampled at the

symbol interval T

, as follows:

˜s(t) = Re{s(t)e

jω

}; s(t) = a(n)p(t − nT

) (2)

The Doppler distorted bandpass signal ˜s

(t) is the

sum of the distorted path signals, which consider the

Doppler compressional factor β

in each path p to

perform time compression/expansion and frequency

shift:

˜s

(t) =

∑

Re{s((1 + β

)t)e

jω

(1+β

} (3)

Using baseband equivalent notation, the received

noiseless signal for a single path can be represented

as the convolution of the path distorted signal s

(t)

with the single path impulse response g

(ν). Perform-

ing algebra manipulation, the time-variant channel

impulse response in the p-th path is given by (Gomes

et al., 2008):

(t, µ) =

1 + β

(

µ + β

1 + β

jω

1+β

(t−µ)

(4)

with

(t) =

s(t − µ)h

(t, µ)dµ (5)

In the i-th hydrophone, the time-variant CIR is:

(t, µ) =

∑

p,i

(t, µ)δ(t − µ

p,i

) (6)

3 APTR EQUALISER

The passive time-reversal technique performs for

each channel the correlation between the reverse-

conjugated estimated CIR and the observed CIR. The

sum over the channels will yield a function that allows

for a straightforward analysis of the performance of

passive time-reversal based equalisers.

Considering a time-variant channel impulse re-

sponse h

(t, µ) and its estimate

(t, µ), where i is the

hydrophone index of a vertical line array, t denotes

time and µ denotes delay, the Q(t,µ)-function is the

summation along the array of the cross-correlation

function between the CIR and the corresponding esti-

mate, as follows

Q(t, µ) =

∑

∗

(t, −ν)h

(t, µ − ν)dν (7)

For the time-invariant case, since the CIR do not vary

along time, the variable t can be suppressed. Consid-

ering the usual assumptions of pTR, that the sensor

array spans the most energetic area of the water col-

umn for the normal mode orthogonality to hold,

Q(t = 0, µ) ' δ(t = 0, µ) (8)

The pTR output signal is given by

z(t) =

∑

i=1

(t) =

Q(µ)I(t − µ)dµ (9)

where I(t) contains the information data signal a(t)

and the auto-correlation of the pulse shape p(t) used

in the transmitted signal and the receiver, as follows

I(t) =

a(µ)R(t − µ)dµ (10)

and

R(t) =

∗

(−µ)p(t − µ)dµ (11)

Since the ApTR adaptive processing is completely

done in the Q-function, equation (9) represents (as

well for the pTR case) the ApTR output signal.

3.0.1 Static CIR and Conventional pTR

Usually the conventional pTR equaliser obtains the

estimated CIR by an initial probe. In static channel

case, considering the usual assumptions of pTR, the

equation (7) have impulse-like shape and it is valid

the relation (8).

3.0.2 Time-variant CIR and Conventional pTR

For the time-variant case with pTR using initial chan-

nel estimate, the function Q(t, µ) becomes

Q(t, µ) =

∑

∗

(0,−ν)h

(t, µ − ν)dν (12)

and due to the h

(t, µ) variability there will be mis-

match between the CIR and the corresponding esti-

mate. It results that, as time goes by, the impulse-like

shape is lost and the ISI increases.

Time-variantAdaptivePassiveTimeReversalEqualiserandaPerspectiveforEnvironmentalFocusingMethod

105

Figure 2: Time-variant ApTR equalizer block diagram.

3.0.3 Time-variant CIR and ApTR

The ApTR, instead of estimating the CIR only at the

time of a initial probe, estimates the time-variant CIR

along the data frame, making possible to maintain the

impulse-like shape of the Q(t,µ)-function. In such

conditions, the validity of relation (8) is kept and ISI

is mitigated. Under the ideal case, it is assumed that

the estimated (simulated) time-variant CIR matches

perfectly with the observed CIR. However, more re-

alistic approach requires to estimate the time-variant

channel using a suitable method. This question is di-

cussed in subsection 3.1.

Figure 2 shows the ApTR equaliser block dia-

gram. The signal s(t) containing the information se-

quence is transmitted through the time-variant chan-

nel and the received signals are processed in the

ApTR equalizer, such that the sum of the processed

channels generates the ApTR output signal z(t), over

which the coherent demodulation yields the estimated

message.

3.1 Environmental Focusing

A well-known technique that employs acoustic prop-

agation modelling is matched ﬁeld processing (MFP).

It performs correlations between replicas of acoustic

pressure ﬁeld from a propagation model with the ob-

served ﬁeld in a receiver array, aiming to estimate an

speciﬁc set of physical parameters. It was ﬁrstly pro-

posed by (Hinich, 1973). Generally the searched pa-

rameters aims to solve three classes of problems: pas-

sive source localization, matched ﬁeld inversion for

geoacoustic parameters and ocean acoustic tomog-

raphy to perform estimation of water column sound

speed proﬁle (or the closely related ocean temperature

ﬁeld). Important benchmarking in MFP are found in

(Bucker, 1976; Tolstoy et al., 1991; Jesus, 1993; Bag-

geroer et al., 1993).

The environmental focusing method for ApTR

equalisation proposed in this work is inspired in the

focalization technique (Collins and Kuperman, 1991),

used in MFP for source localization. Focalization,

which simultaneously focuses and localizes, elimi-

nates the stringent requirement of accurate knowledge

of the ocean-acoustic environment by including the

environment in the parameter search space. The idea

of environmental focusing in UAComm is to create a

data bank of carefully chosen channel replicas (search

space) that reaches the CIR with best acoustic ﬁtness,

which should update the ApTR ﬁlters. Generally, it is

quite difﬁcult to accurately model the ocean channel.

Therefore, to make it a less rigid requirement, it is

used this focusing method aiming to reach the replica

that best matches the observed channel, instead of use

an outdated initial probe. In fact, this method does

not use the initial probe to be performed during the

signal transmission. The method is based in careful

pre-computation (and at large number) of time-variant

channel replicas for a speciﬁc restrict area, acting

as a probe-independent process (just as it happens

in MFP). The success in channel tracking using the

replicas data bank strongly depends of how well the

channel variability was inserted in the search space.

For example, it is known that even small changes

in the source/receiver positions cause corresponding

changes in acoustic ﬁeld that severely affect the de-

modulation of coherent UAComm signals, then the

pre-computed search space must contain replicas that

track such geometrical variability in a ﬁne scale. It

can be expected considerable high computational cost

in this procedure and for that reason it is need at least

a coarse knowledge of the environmental/geometric

physical parameters of the local where the system

is employed. The inﬂuence of acoustic propagation

physical parameters must be investigated, because its

understanding strongly contributes to build a suitable

search space of replicas. It should not be deliberately

performed a brute force method for choosing the a

priori sets of parameters aiming to avoid the corre-

sponding huge computational cost. The area where

the UAComm system will be employed must be anal-

ysed, being another basis for reasonable selection of

a priori candidates.

This environmental focusing method proposed for

ApTR equalisation is intended to be investigated and

extensively tested by the author in future work. It

is expected that the well-succeed experience of low-

frequency MFP technique could be advantageously

used in model-based adaptive passive time-reversal

equalisation for high-frequency (i.e., 3–50 kHz band)

underwater communications. An evidence that the

cases are similar also resides in the fact that in both

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106

Figure 3: Scenario used in the preliminary test with

TVAPM integrated to the UAComm model.

problems the same wave equation with boundary con-

ditions must be solved. The results would yield the

set of acoustic physical parameters that comes from

the best ﬁt between replicas and the observed CIR,

being the process performed for each channel corre-

sponding to each receiver sensor of the vertical line

array. Such replicas with best ﬁtness should be used

to feed the respective ApTR ﬁlters and the sum over

the channels yields the equalised output signal.

3.2 Simulated CIR Test

The following test shows the results from UAComm

simulation using TVAPM to model time-variant CIR.

The test uses simulated channels for feeding the

corresponding ApTR ﬁlters, so that the ideal case

is achieved (i.e., best possible match between esti-

mated CIR and observed CIR). Even though no up-

date through focusing method is done yet, the simula-

tion results will show the Doppler compensation and

equalisation being performed by the ApTR.

Figure 3 shows the scenario considered in this test.

The moving source (the star with big circle marks

the initial position) and the static array (small circle)

are positioned inside a 3-D environmental-based box

with range-dependent bottom bathymetry. The upper

surface is computed inside the TVAPM with wind-

driven model using spectrum JONSWAP (Rodriguez

and Silva, 2012), direction 090 degrees, intensity 10

m/s . The runs were done with the sound source ac-

tive sensor developing the velocities of 0 m/s, 0.4 m/s

and 1 m/s. BPSK signals were transmitted with a

carrier frequency 10 kHz. The data frame contained

1024 symbols with bit rate 1000 bit/s. The results

show that the ApTR ﬁlters achieved the compensa-

tion for Doppler effect and the equalisation. Figure 4

shows the received constellations after be processed

by conventional pTR (plottings in the ﬁrst column),

after be processed by ApTR (plottings in the second

column) and after be processed by ApTR with rota-

tion lock (plottings in the third column). Each line of

plottings, from top to bottom, corresponds to the runs

with source velocities 0, 0.4 and 1 m/s, respectively.

In the case of received signal constellation for the

pTR equaliser, the clouds expand themselves rotat-

ing, in ring-like form. This strong distortion is caused

by the Doppler effect from the source motion along

the transmission. In the case of the received con-

stellation after the ApTR equaliser the dense clouds

clearly indicate the Doppler compensation and equal-

isation. Column 2 still shows that constellation ro-

tation still occurs (for the clouds as a whole) after

the ApTR processing. It is an effect from the cross-

correlation between Doppler distorted CIR. Substitut-

ing the time-variant CIR of equation (4) and (6) into

the Q-function of the equation (7) and performing the

integral, one can note that the result contain a remain

phase factor (not showed), which causes the constel-

lation clouds rotation. This was solved performing

the tracking of the constellation rotation angle using

the short m-sequence probe which was previously in-

serted in the frames for time synchronization. The

estimated constellation angle is then used to correct

the rotation, yielding the results showed in column 3.

4 CONCLUSION

The ApTR processor was proposed to perform equal-

isation jointly to Doppler compensation, aiming to

mitigate ISI and improve performance in coherent un-

derwater acoustic communications links whose sen-

sors are in SIMO conﬁguration. The adaptive proce-

dure requires a method to update the equaliser ﬁlters

with the time-variant CIR estimates. In this sense,

the environmental focusing method was suggested for

investigation, inspired in the low-frequency matched

ﬁeld technique, exploring the understanding about the

inﬂuence of acoustic propagation physical parameters

for channel modelling, since they rule the physics of

the acoustic propagation in the ocean channel.

Using suitable replicas of realistic environment,

reached from well-tuned modelling that considers

some a priori coarse information relative to the spe-

ciﬁc area where the system is used, the estimates of

time-variant CIR feed the ApTR ﬁlters. As results are

expected to achieve environmental-based equalisation

of communications signalling and reﬁned local envi-

ronmental assessment. The corresponding UAComm

performance improvement could beneﬁt P2P commu-

nications or the link between two UAN nodes.

Time-variantAdaptivePassiveTimeReversalEqualiserandaPerspectiveforEnvironmentalFocusingMethod

107

(a) pTR (b) ApTR (c) ApTR + rotation lock

Source-velocity = 0 m/s

Source-velocity = 0.4 m/s

Source-velocity = 1 m/s

Figure 4: Constellations for moving source and wind-driven modelled surface. Column (a): pTR; Column (b): ApTR without

constellation angle correction. Column (c): ApTR with constellation angle correction.

ACKNOWLEDGEMENTS

This work was funded under the Foreign Courses

Program of MB, PCExt-Port219/EMA. The authors

would like to thank the valuable research support

from SiPLAB-FCT team, University of Algarve.

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