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62 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 25, NO. 1, JANUARY 2000
Communication Over Doppler Spread ChannelsPart I: Channel and Receiver PresentationTrym H. Eggen, Arthur B. Baggeroer, Fellow, IEEE, and James C. Preisig, Member, IEEE
AbstractScattering functions from several experimentsdemonstrate that acoustic underwater channels are doublyspread. Receivers used on these channels to date have difficultywith large Doppler spreads. A receiver to perform coherent com-munication over Doppler spread channels is presented in this firstpaper of two. The receiver contains a channel tracker and a lineardecoder. The tracker operates by means of a modified recursiveleast squares algorithm which makes use of frequency-domainfilters called Doppler lines. The decoder makes use of the channeltracker coefficients in order to perform minimum mean squareerror decoding. This first paper treats theory aspects whereas thesecond part presents implementation issues and results.
Index TermsAcoustic signal processing, adaptive systems, dig-
ital communication systems, Doppler spread, least squares.
I. INTRODUCTION
COMMUNICATION in the ocean by means of acousticsignals has been in use for several decades, and numeroussimulations have been carried out in the literature in order
to quantify capabilities and limitations. The attenuation of
acoustic waves is roughly proportional to the square of the
frequency [1], making the communication channel severely
bandlimited, which limits the achievable range. Communica-
tion channels may exhibit both dispersion in time (delay spread)
and frequency (Doppler spread); in this paper, we are partic-
ularly interested in the Doppler spread channels. Emphasisin early systems was on incoherent communication where
phase information of the signal is not used, and frequency shift
keying (FSK) is common [2], [3]. An overview of existing
configurations before 1984 can be found in [4]. During the last
eight or nine years, the feasibility of coherent communication
in the ocean has been demonstrated, but incoherent schemes
like MFSK are still widely used to gain robust communication.
The phase-coherent schemes require phase tracking of the
channel because the information is transmitted by means of
the signal phase. The most common modulation techniques
are phase shift keying (PSK) and quadrature PSK (QPSK).
Systems with this modulation are reported in [5][8]. With
this modulation, Doppler shift becomes an important issue.
One way to deal with this is to use adaptive delay taps and a
phase-locked loop (PLL).
Manuscript received October 17, 1999; revised November 4, 1999.T. H. Eggen is with Simrad AS, N-3191 Horten, Norway.A. B. Baggeroer is with the Massachusetts Institute of Technology, Cam-
bridge, MA 02139 USA.J. C. Preisig is with the Woods Hole Oceanographic Institution, Woods Hole,
MA 02543 USA.Publisher Item Identifier S 0364-9059(00)00994-8.
A large body of simulation studies is reported in many dif-
ferent periodicals and books. They cover all aspects of under-
water acoustic communication systems such as channel identi-
fication and tracking, coding, modulation techniques, and spa-
tial diversity combining. Simulations of acoustic channels with
emphasis on the communication aspect is given in [9] and [10]
and addresses the stability of the channel multipath and phase.
The multichannel receiver for both incoherent [11] and coherent
[6] communication is reported to give significant gain. These
involve both simulations and demonstrations in shallow-water
environments. The problem of optimally combining multiple
channels is also simulated in [12]. The combination of beam-forming and adaptive equalization is reported in [17] where ray
tracing is used to extract significant paths.
At the frequencies in question here, a ray representation of
the acoustic propagation is valid. A simple range-invariant ray
representation with a piecewise linear sound-speed profile is
used. The underwater communication channels are modeled
as linear time-variant (LTV) systems due to processes such
as tides, currents, moving transmitter/receiver/surface, and
internal waves. Thus, the receivers are often adaptive in order to
track the channel [13], [14], and a common adaptive algorithm
for this purpose is the recursive least squares (RLS) [ 15], [16].
We use theframework of a doubly spreadchannel [18] to clas-
sify underwater communication channels. This means that thereceived signal is dispersed in both time and frequency. Under-
water communication channels depend on sound propagation
conditions, channel geometry, and boundary conditions. Thus,
one encounters delay spread, doubly spread, and Doppler spread
channels. The results in this paper are in the scenarios where the
carrier is around 20 kHz with bit rates not exceeding 10 kbit/s
and a range of a few kilometers. Both shallow and deep-water
channels are considered.
The context of this paper is coherent communication using
QPSK modulation in channels that have more severe Doppler
spread than delay spread in the sense that common receivers
are able to compensate for the delay spread but not the Doppler
spread. This paper is part I of two papers treating this problem.We present the LTV channel model and measured channels in
Section II. The receiver makes use of frequency-domain filters
called Doppler lines presented in Section III. An adaptive re-
ceiver suited for doubly spread channels using a modified RLS
with a time update step is presented in Section IV. This re-
ceiver is specialized to the Doppler spread channel in Section
V. This section also contains a brief simulation example with
Doppler spread data comparing a decision feedback equalizer
(DFE) with the receiver presented herein. The work presented
in part I is summarized in Section VI. In part II [ 19], the results
0364-9059/00$10.00 2000 IEEE
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64 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 25, NO. 1, JANUARY 2000
Fig. 1. 3 dB contours of the cross-ambiguity function from four differentunderwater communication channels. Upper left: Arctic Ocean. Upper right
and lower left: Newport, RI. Lower right: Bahama Islands.
TABLE ICHARACTERISTICS OF THE DIFFERENT
UNDERWATER COMMUNICATION CHANNELS
is heaving, yielding the Doppler spread, and the return around
2 ms is the direct path. The return around 4 ms is consistent with
the travel time for a surface bounce. In the lower left panel, the
suspended source is moving vertically due to significant heave
and roll of the surface vessel. The received signal level was ob-
served to be very sensitive to source depth. Thus, it is believedthat a sound channel is present, and this is also suggested by ac-
companying sound speed profiles taken at the location the same
day. In the lower right panel, the communication takes placebetween a surface vessel and a bottom-mounted receiver. The
energy around 4 ms is the direct path and the severely spread
cluster around 25 ms is believed to be a surface bounce. The
transmissions were carried out in sea state 45.
All transmissions use QPSK modulation. There is a large
variation in the channels: The upper left panel shows a delay
spread (LTI) channel, the right panels are doubly spread chan-
nels, and the lower left panel is a Doppler spread channel. The
characteristics in terms of delay and Doppler spread are so dif-
ferent that one can hardly hope for one particular communica-
tion system serving all these channels appropriately. The em-
phasis is on the channels similar to the lower left and upper
Fig. 2. The channel has scatterers at different ranges with different velocitiesso that the composite channel is time-variant.
right panels of Fig. 1, where the Doppler spread is a significant
problem.
B. Channel Model
The underwater communication channel is now modeled as
a linear time-variant system. Some of the sources of the time-variation are mentioned in Section I. Since QPSK modulation is
used, the transmitted symbols are
(8)
The modified delay-Doppler-spread function [20] is
our channel model where the modification is to allow the
delay-Doppler-spread function to be a slowly varying function
of time. The discrete representation of our channel is thus
(9)
where
output of the channel;
Delay-Doppler-spread function which is the
scattering amplitude at lag and Doppler
for time ;
input to the channel;
number of signal returns;
zero mean measurement noise with variance ;
energy in each symbol;
Doppler spacing.The notation in the index of the sum of (9) means that
there are pairs of ; there is no assumption on the distri-
bution of these points. Thus, the model contains doubly spread,pure delay spread, and pure Doppler spread channels that may
be sparse in both delay and Doppler. A physical interpretation
is shown in Fig. 2. This is a channel with scatterers at different
ranges moving with different velocities in order to give dif-
ferent Doppler shifts. Thus, the communication channel is time
varying from symbol to symbol.
The WSSUS assumption is broken when the delay-Doppler-
spread function is time varying. For this reason, we use a quasi-
WSSUS assumption allowing for time variation in the delay-
Doppler-spread function . Thus, the physical interpretation
given below is not in general valid but, as the following numbers
show, it is useful in our scenario. A typical symbol rate is 1000
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EGGEN et al.: COMMUNICAT ION OVER DOP PL ER SP RE AD CHANNEL S PART I: CHANNEL AND RE CEIVER P RES ENTATION 6 5
symbol/s so that a symbol extends 1500/1000 m = 1.5 m when
the sound speed is 1500 m/s. A Doppler shift of 5 Hz at 20 kHz
carrier means a scatterer speed of 0.38 m/s. Data are transmitted
in packets of typical length 2 s. The scatterer moves 0.38 2 m
= 0.76 m in this time. Thus, the scatterer is within one symbol
length (=1.5 m) during the entire transmission. This is the as-
sumption that makes the physical interpretation of Fig. 2 useful
and (9) valid. It should be used with care since it is obviouslynot satisfied for a higher Doppler, higher symbol rate, or longer
packet length. The time variation enters this scenario through
the motion of the scatterer.
It is noted that the channel model (9) is WSSUS only when
in (4) (in which case ). Therefore, the relation-
ships between the scattering function, cross-ambiguity function,
and delay-Doppler-spread function in (7) are true only in this
limiting case.
Now a state space description for a system, aiming at deriving
a recursive estimate of the state space vector, is defined as
... (10)
The state space model for is given by
. . .
(11)
where
. . .
(12)
and is a vector ofnoise values. The expression in (10) ismerely
a way to collect the characterization in a single variable
which is the input delay-spread function [20]. According to theAR(1) model (4)for thechannel evolution, we write thefirst part
of (11). The last expression of (11) is a rewriting of (9). The first
expression of (12) is a vector of transmitted symbols, and it is
called the observation vector . This may seem counterintu-
itive since are the transmitted, and not the observed,
data. However, in the state space description of (10)(12), the
unknown quantity is the channel and the receiver must es-
timate this quantity. The covariance of the system noise
is diagonal. The physical interpretation of this is that the scat-
tering processes at different (delay, Doppler) cells are uncorre-
lated. The quantity is the scattering strength at delay and
Doppler . The description in (11) and (12) is the basis for the
Fig. 3. The FFS Doppler line.
receiver that is presented in Section IV. In Section V, this re-
ceiver is specialized to Doppler spread channels. It contains a
time-dependent device called a Doppler line which is intro-
duced now.
III. DOPPLER LINES
The doubly spread underwater communication channel
exhibits both time- and frequency-dispersive fading which are
caused by the Doppler and delay spread of the medium and by
the transmit/receive platforms. Both delay spread and Doppler
spread are forms of dispersion, and there is a close connec-
tion between channels exhibiting delay spread and channels
exhibiting Doppler spread: If the time domain and frequency
domain are considered as dual domains, the delay and Doppler
spread channels may be thought of as duals. This concept of
duality is treated in depth in [27], and the reader should see this
reference for definitions and implications of duality.
The notion of a filter is often used for a device that makes
a weighted sum of differently delayed versions of a signal.
The name delay line is used for this device and Dopplerline for the device that makes a weighted sum of differently
Doppler-shifted versions of the signal. They are both filters
but in dual domains. We now look at some of the features
of Doppler lines, and connect them to their duals the more
frequently encountered delay lines. For this purpose, let us
assume a purely Doppler spread channel model with constant
. The channel model (9) with
yields
(13)
Note that the model (13) implies a time-variant channel. It is
therefore expected that the device needed to compensate this
channel is time-variant. Thus, the Doppler line is a time-variant
gain unlike its dual the delay line.
Consider the Doppler line in Fig. 3. The structure is similar to
that of a finite impulse response (FIR) delay line, and the only
difference is that the Doppler shift is used in place of the delay.
The boxes with the multipliers in Fig. 3 are mixers both sup-
plying the next mixer and the local weight with its output. This
structure is called the finite frequency spread (FFS) Doppler
line. The FFS is the dual of the FIR because, in the same way as
an FIR delay line has finite impulse response, as will be shown
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66 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 25, NO. 1, JANUARY 2000
Fig. 4. The convolutionof thetwo signals yieldsthe outputof theFFS Dopplerline. Z ( k ) has period N so that ( k 0 k ) repeats.
below, its dual the FFS has finite frequency spread. The picture
in Fig. 3 is written as
(14)
and it corresponds to time-selective fading [28]. By taking the
discrete time discrete frequency Fourier transform, assuming
with being window length, one obtains
(15)
where and have period . Thus, the time-selective
fading results in a frequency spreading. The nonzero support ofis . If is a single frequency so that
for , the situation is as shown in
Fig. 4. It is found from (15) that
(16)
and, from Fig. 4, it is seen that no aliasing takes place if
. Thus, the single frequency has been spread on the
finite interval of width and thereby this Doppler line gets the
name FFS. The aliasing requirement constrains the bandwidth
of but for practical communication channels and signals
so that this constraint is not severe.
There is also a counterpart to an IIR filter called the infinitefrequency spread (IFS) Doppler line. It is given by
(17)
It is clear that, for the discrete signals used here, (17) inevitably
yields aliasing because may be nonzero for arbitrary large
. Thus, the second part of (17) is the motivation for the name
infinite frequency spread. This equation is the same as for
Fig. 5. Receiver built up of separate channel tracker and equalizer.
an IIR filter with as input and as output. Further
discussion of Doppler lines and their properties is found in [23].
IV. GENERAL RECEIVER
Both the channel and the data in our model (9)
are unknowns in a realistic situation. Thus, the receiver must
both track the channel and decode the data. The receiver archi-
tecture in Fig. 5 is motivated by this. It is built according to ademand for simultaneous channel tracking and coherent signal
combining to reduce dispersion in both time and frequency. In
order to achieve an initial estimate of the channel, a training se-
quence, which is a sequence of symbols that is known to the re-
ceiver, is used. In addition to the training sequence, a short syn-
chronization sequence is prepended to the unknown data. When
these symbols are processed, the receiver enters the tracking
mode. In this mode, it tracks the channel variation by using
previously decoded symbols as the channel input. The order
of operation of the receiver in Fig. 5 is Receive synchroniza-
tionTraining modeTracking mode. This approach as-sumes that the decoding is correct or else the channel input is
not known. When the decoding is incorrect, the estimation ofthe channel response degrades, and this in turn gives more in-
correctly decoded symbols. The impact of this effect is analyzed
in part II [19] of this paper.
A. Channel Tracker
The algorithm for channel tracking is a modified RLS with
a time update step yielding a recursive estimate of and a
recursive equation for the estimated error covariance of .
The regular RLS algorithm is given in [15], and it can be shown
that it minimizes a weighted sum of the errors
given by
(18)
The output of the decoder is the soft symbol estimate ,
and this is passed through a quantizer yielding the symbol es-
timate according to a minimum distance rule. In the case
of QPSK, the quantizer assigns to the closest of the four
valid symbols in (8). When the forgetting factor , the RLS
is identical with a Kalman filter [15], [16] for the system with
state space description
(19)
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EGGEN et al.: COMMUNICAT ION OVER DOP PL ER SP RE AD CHANNEL S PART I: CHANNEL AND RE CEIVER P RES ENTATION 6 9
provided that the inverse in this expression exists. Note the
connection to our channel model: the delay-Doppler-spread
function introduced in (9) is interpreted as the scattering
amplitude at whereas the recursive channel tracker in
the case of a purely Doppler spread channel is approximately
a sliding window Fourier transform as shown in (32). This
means that the tracked coefficients are the contribution to the
delay-Doppler-spread function within a frequency band givenby the Fourier transform resolution. This is the interpretation
of in this section.
B. Receiver Using IFS Doppler Lines
We now show that the minimum mean square error (MMSE)
receiver for a Doppler spread channel is the IFS Doppler line.
Given the signalmodel(27) and the estimateof in(30), the
transmitted data sequence is estimated by using the MMSE
criterion. T hus, and are assumed to be known,
and the task is to find . By the Gaussian noise assumption,the probability density for conditioned on and the set
of all is complex Gaussian and given by
(33)
The MMSE receiver for is obtained by minimizing the
exponent of (33) which yields
(34)
This amounts to dividing the current sample with a com-
plex gain and then choosing the closest symbol. It corresponds
to the IFS Doppler line of (17).
C. Receiver Using FFS Doppler Lines
There is nothing that prevents the denominator of (34) from
going arbitrarily close to zero. This is a potentialweakness remi-
niscent of the characteristic of a zero forcing equalizer [25]. One
way to introduce robustness in the zero forcing equalizer is to
constrain it to be an FIR filter. Motivated by this, the FFS-basedreceiver is introduced. Given , an FFS Doppler line can also
be used for decoding in a similar manner. In order to show this,
we use the MMSE criterion and, in addition, require the receiver
to be an FFS Doppler line as in (14). The coefficients of
this receiver are found by performing
(35)
where
(36)
Fig. 8. Decoding of a typical sparse underwater communication channel withmany symbol intervals between the returns and the returns at different Dopplershifts. The second return is from a surface swell with much longer period than
the packet length, so that a Doppler shift rather than a spread is the result.
In this case, the coefficients are given by [24]
(37)
for
(38)
Thus, the Doppler line is a central part of the receiver in the case
of a Doppler spread channel, and this is also true in the doublyspread case [24].
The emphasis in this work is on Doppler spread channels. The
Doppler lines are used in Section V. We show in Section V-B
that for a purely Doppler spread channel the MMSE receiver is
an IFS Doppler line. The FFS Doppler lines may also be used
as a more robust alternative, as shown in this section.
D. Simulation Example
Part II of this paper contains examples of decoding both sim-
ulated and real data from Doppler spread channels. In order to
further motivate the use of a Doppler-line-based receiver, a sim-
ulation example is included here in part I as well. A scenario issimulated where the channel response is constructed from two
rays with different Doppler shifts. It occurs as a result of trans-
mitter or receiver relative motion, and also when one of the rays
interacts with an ocean surface that has a long swell.
The upper left panel of Fig. 8 shows the resulting sparse com-
munication channel with different Doppler shifts on the two
widely spaced returns. The channel parameters are delays at (8,
28) ms and Doppler shifts at (0, 4) Hz. These parameters are the
outputs of a simulation of the sound field at the receiver using
raytrace. The physical parameters are summarized in Table II.
The three panels in Fig. 8 show the results; the 3-dB contours
of the ambiguity function (6) are shown in the upper left panel,
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70 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 25, NO. 1, JANUARY 2000
TABLE IITHE PARAMETERS USED FOR SIMULATING THE ENVIRONMENT YIELDING THE
DOPPLER SPREAD DATA
Fig. 9. Performance of the DFE receiver with a PLL on a Doppler spreadsignal. The predicted symbols in the right column and the MSE decision errorin the right column for a two-path signal with, respectively, 0, 1, and 2 Hz
difference in Doppler between the paths in the upper, middle, and lower panels.
complex values of the TU-RLS taps as given by (21) in
the upper right panel, and the estimates of the decoded symbols
from (23) are plotted in the lower left panel. The SNR is
15 dB and the training sequence duration is 512 symbols. The
training sequence is used both to compute the cross-ambiguity
function and to achieve initial convergence of the TU-RLS. The
#taps, tracking is the channel tracker dimension of (9), the
#taps, inversion is the FIR filter order of (22), the SNR
is the ratio , lambda is the exponential weighting factor
of the TU-RLS (21) and # errors in is the ratio of trans-
mitted to erroneously decoded symbols. The TU-RLS containsonly two taps and the estimated symbols are based on a signal
combiner with eight taps. This scenario is the result when one
direct path and one surface-reflected path are present, and the
ocean surface has a swell with a period significantly longer than
the packet length.
The adaptive DFE with a PLL (see, e.g., [6]) is unable to
decode the case shown in Fig. 9 because thetotal Doppler spread
is too large. If there is no swell on the surface, the channel is LTI,
and the DFE decodes correctly. The right column of this figure
shows the predicted symbols for channels where the first return
is at 0 Hz as in Fig. 8 and the second return is at 0, 1, and 2 Hz
in the upper, middle, and lower panels, respectively. The left
column shows the MSE in the predictions. This example shows
decoding for a case where the Doppler spread contains discrete
tones,i.e., a numberof Doppler shiftsat differentdelays. Results
with continuous Doppler spread, discrete Doppler spread at the
same delay, and real data are presented in part II of this paper.
VI. CONCLUSION
Underwater communication channels are modeled as LTV
systems. The delay-Doppler-spread function is used to obtain
a model of the channels in this work. The scattering function
is used for channel characterization, and it is estimated from
the cross-ambiguity function. The channels obtained from real
data at various sites show significant dispersion in both time and
frequency. The receiver suggested for some of these channels
consists of a channel tracker, linear decoder, and quantizer; a
modified RLS algorithm that is used in the channel tracker is
presented. The most important modification is that the Doppler
is allowed to be different on each tap, and this enables effi-
cient tracking of Doppler spread. The receiver is constructed
to allow for the demodulation of signals which pass throughdoubly spread channels. In this paper, the concentration is on
Doppler spread channels. The concept of Doppler lines, which
are frequency-domain filters, is presented and used in the re-
ceiver. Part II of this paper contains results from using this re-
ceiver on real data as well as performance analysis.
ACKNOWLEDGMENT
The authors thank J. Catipovic, M. Johnson, and D. Nagle
for the use of some of the data in Fig. 1. Work carried out in the
MIT-WHOI joint program.
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York, NY: Wiley, 1969.
Trym H. Eggen was born in Oslo, Norway, on May 14, 1963. He receivedthe M.S. degree in electrical engineering from the Norwegian Institute of Tech-nology in 1987 and the Ph.D. degree from the Massachusetts Institute of Tech-nology, Cambridge, in 1997.
He is currently with the signal processing group at Simrad AS, Horten,Norway. His research interests are in the areas of communications, arrayprocessing, and adaptive algorithms.
Arthur B. Baggeroer (S62M68SM87F89)received the B.S.E.E. degree from Purdue University,West Lafayette, IN, in 1963 and the Sc.D. degreefrom the Massachusetts Institute of Technology(MIT), Cambridge, in 1968.
He is currently Ford Professor of Engineering andthe Secretary of the Navy/Chief of Operations Chairfor Ocean Science in the Departments of Ocean En-gineering, and Electrical Engineering and Computer
Science at MIT.
James C. Preisig (S87M91) received the B.S. degree in electrical engi-neering from theU.S. Coast GuardAcademy in 1980, theS.M. and E.E. degreesin electrical engineering from the Massachusetts Institute of Technology (MIT),Cambridge, in 1988, and the Ph.D. degree in electrical and ocean engineeringfrom the MIT/Woods Hole Oceanographic Institution (WHOI) Joint Programin Oceanography and Oceanographic Engineering, Woods Hole, MA, in 1992.
Prior to joining WHOI as a Scientist, he was a Visiting Assistant Professor inthe Department of Electrical and Computer Engineeringat Northeastern Univer-sity, Boston, MA, and a Visiting Investigator at WHOI. His research skills arein adaptive signal processing, signal propagation modeling, and numerical opti-mization.He currentlyappliestheseskillsin three researchprograms. Thefirst isthe development of a better understanding of the effect that environmental fluc-tuations have on propagation acoustic and electromagnetic signals, the second isto use this understanding to develop adaptive signal processing algorithms withimproved performance characteristics, and the third area is the development ofcomputationally robust and numerically efficient techniques for implementingnew adaptive algorithms.
Dr. Preisigis a memberof theSensor Array Processing Technical Committee.