Multiuser Communications Using Passive Time Reversal
ABSTRACT A recent paper (Song , IEEE Journal of Oceanic Engineering, vol. 31, no. 2, pp. 170-178, 2006) demonstrated multiple-input-multiple-output (MIMO) communications in shallow water using active time reversal where the time reversal array (i.e., base station) sent different messages to multiple users simultaneously over a common bandwidth channel. Passive time reversal essentially is equivalent to active time reversal with the communications link being in the opposite direction. This paper describes passive time reversal communications which enables multiple users to send information simultaneously to the time reversal array. Experimental results at 3.5 kHz with a 1-kHz bandwidth demonstrate that as many as six users can transmit information over a 4-km range in a 120-m-deep water using quaternary phase-shift keying (QPSK) modulation, achieving an aggregate data rate of 6 kb/s. Moreover, the same data rate has been achieved at 20-km range by three users using 16 quadrature amplitude modulation (16-QAM).
[show abstract] [hide abstract]
ABSTRACT: Progress in underwater acoustic telemetry since 1982 is reviewed within a framework of six current research areas: (1) underwater channel physics, channel simulations, and measurements; (2) receiver structures; (3) diversity exploitation; (4) error control coding; (5) networked systems; and (6) alternative modulation strategies. Advances in each of these areas as well as perspectives on the future challenges facing them are presented. A primary thesis of this paper is that increased integration of high-fidelity channel models into ongoing underwater telemetry research is needed if the performance envelope (defined in terms of range, rate, and channel complexity) of underwater modems is to expandIEEE Journal of Oceanic Engineering 02/2000; · 0.95 Impact Factor
[show abstract] [hide abstract]
ABSTRACT: High-speed phase coherent communications in the ocean channel are made difficult by the combined effects of large Doppler fluctuations and extended, time-varying multipath. In order to account for these effects, we consider a receiver which performs optimal phase synchronization and channel equalization jointly. Since the intersymbol interference in some underwater acoustic channels spans several tens of symbol intervals, making the optimal maximum-likelihood receiver unacceptably complex, we use a suboptimal, but low complexity, decision feedback equalizer. The mean squared error multiparameter optimization results in an adaptive algorithm which is a combination of recursive least squares and second-order digital phase and delay-locked loops. The use of a fractionally spaced equalizer eliminates the need for explicit symbol delay tracking. The proposed algorithm is applied to experimental data from three types of underwater acoustic channels: long-range deep water, long-range shallow water, and short-range shallow water channels. The modulation techniques used are 4- and 8-PSK. The results indicate the feasibility of achieving power-efficient communications in these channels and demonstrate the ability to coherently combine multiple arrivals, thus exploiting the diversity inherent in multipath propagationIEEE Journal of Oceanic Engineering 02/1994; · 0.95 Impact Factor
Article: Differences between passive-phase conjugation and decision-feedback equalizer for underwater acoustic communications[show abstract] [hide abstract]
ABSTRACT: Passive-phase conjugation (PPC) uses passive time reversal to remove intersymbol interferences (ISIs) for acoustic communications in a multipath environment. It is based on the theory of signal propagation in a waveguide, which says that the Green's function (or the impulse-response function) convolved with its time-reversed conjugate, summed over a (large-aperture) vertical array of receivers (denoted as the Q function) is approximately a delta function in space and time. A decision feedback equalizer (DFE) uses a nonlinear filter to remove ISI based on the minimum mean-square errors (mmse) between the estimated symbols and the true (or decision) symbols. These two approaches are motivated by different principles. In this paper, we analyze both using a common framework. We note the commonality and differences, and pros and cons, between the two methods and compare their performance in realistic ocean environments, using simulated and at-sea data. The performance measures are mean-square error (mse), output signal-to-noise ratio (SNR), and bit-error rate (BER) as a function of the number of receivers. For a small number of receivers, the DFE outperforms PPC in all measures. The reason for poor PPC performance is that, for a small number of receivers, the Q function has nonnegligible sidelobes, resulting in nonzero ISI. As the number of receivers increases, the BER for both processors approaches zero, but at a different rate. The modeled performance differences (in mse and SNR) between PPC and DFE are in general agreement with the measured values from at-sea data, providing a basis for performance prediction.IEEE Journal of Oceanic Engineering 05/2004; · 0.95 Impact Factor
IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007915
Multiuser Communications Using
Passive Time Reversal
H. C. Song, W. S. Hodgkiss, Member, IEEE, W. A. Kuperman, T. Akal, and M. Stevenson
Abstract—A recent paper (Song et al., IEEE Journal of Oceanic
Engineering, vol. 31, no. 2, pp. 170–178, 2006) demonstrated mul-
tiple-input–multiple-output (MIMO) communications in shallow
water using active time reversal where the time reversal array (i.e.,
base station) sent different messages to multiple users simultane-
ously over a common bandwidth channel. Passive time reversal es-
sentially is equivalent to active time reversal with the communica-
tions link being in the opposite direction. This paper describes pas-
sive time reversal communications which enables multiple users to
imental results at 3.5 kHz with a 1-kHz bandwidth demonstrate
that as many as six users can transmit information over a 4-km
range in a 120-m-deep water using quaternary phase-shift keying
(QPSK) modulation, achieving an aggregate data rate of 6 kb/s.
Moreover, the same data rate has been achieved at 20-km range by
three users using 16 quadrature amplitude modulation (16-QAM).
Index Terms—Active time reversal, decision-feedback equal-
izer (DFE), decision-feedback phase-locked loop (DFPLL),
intersymbol interference (ISI), multiple-input–multiple-output
(MIMO), multiuser communication, passive time reversal, time
is a highly challenging problem . The bandwidth-limited
underwater acoustic (UWA) channel is characterized as doubly
spread: 1) delay spread due to multipath propagation and
2) Doppler spread due to environmental fluctuations and/or
relative motion between transmitter and receiver. The delay
spread causes the received symbols to suffer from intersymbol
interference (ISI). Over the last decade, much effort has been
directed at developing adaptive channel equalizers to remove
ELIABLE, high data rate, acoustic communications in
a time-varying multipath shallow-water environment
Manuscript received April 11, 2007; accepted July 2, 2007. This work was
supported by the U.S. Office of Naval Research under Grants N00014-05-1-
0263 and N00014-06-1-0128. Parts of this paper were presented at the MTS/
IEEE 2006 OCEANS Conference.
Associate Editor: R. C. Spindel.
H. C. Song, W. S. Hodgkiss, and W. A. Kuperman are with the Marine Phys-
ical Laboratory, Scripps Institution of Oceanography, University of California
at San Diego, La Jolla, CA 92093-0238 USA (e-mail:email@example.com;
T. Akal was with NATO Undersea Research Centre, La Spezia 19126, Italy.
He is now with Marine Physical Laboratory, Scripps Institution of Oceanog-
raphy, La Jolla, CA 92093-0238 USA, TUBITAK-MAN, Marmara Research
Center, Earth and Marine Science Research Institute, Kocaeli 41470, Turkey,
and Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY
10964-1000 USA(e-mail: firstname.lastname@example.org).
M. Stevenson is with NATO Undersea Research Centre, La Spezia 19126,
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/JOE.2007.904311
Fig. 1. MIMO time reversal communication systems: (a) active multiuser
(downlink) and (b) passive multiaccess (uplink). The multiple-element array on
the left-hand side (TRM) corresponds to a base station in a terrestrial cellular
the ISI and compensate for the channel variations , .
These techniques, however, are quite demanding in terms of
computational complexity, algorithm stability, and selection of
channel parameters , .
Recently, a relatively simple time reversal approach has been
introduced in UWA communications which involves using mul-
tiple transmit/receive transducers referred to as a time reversal
mirror (TRM) . Time reversal exploits spatial diversity to
such as a waveguide –. Temporal focusing (pulse com-
signal-to-noise ratio (SNR) at the intended receiver with a low
approach to multiple-input–multiple-output (MIMO) multiuser
communications, provided that the users are well separated in
range or depth from each other compared to the focal size in the
acoustic waveguide . Previous work on multiuser commu-
nications in shallow water applied multichannel decision-feed-
back equalizers (DFEs) exploiting spatial diversity to suppress
MIMO is distinguished from point-to-point single user MIMO
 where the single user employs multiple transmitters.
Multiuser time reversal communications can be implemented
in the following two ways: 1) active multiuser (downlink)
[Fig. 1] and 2) passive multiaccess (uplink) [Fig. 1(b)]. The two
approaches essentially are equivalent with the communications
link being in the opposite directions . Active time reversal
communications [Fig. 1(a)] has been demonstrated in shallow
water for both a single user , ,  and multiple users
0364-9059/$25.00 © 2007 IEEE
916IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007
Fig. 2. System model for passive (uplink) time reversal communications followed by an equalizer for the single user case.
. Passive time reversal communications [Fig. 1(b)] has been
demonstrated to date only for the single user case , ,
, . The objective of this paper is to explore multiuser
communications using passive time reversal.
Although the temporal focusing achieved by time reversal re-
duces ISI significantly, there always is some residual ISI which
results in a saturation of the performance . Moreover, in a
fluctuating environment, the channel varies over time even in
the absence of relative motion, while time reversal assumes that
the channel is time invariant. The performance of time reversal
alone can be improved significantly in conjunction with adap-
tive channel equalization which simultaneously eliminates the
, . Indeed, it has been shown ,  that the combi-
nation provides nearly optimal performance using the theoret-
we will use the passive time reversal combined with adaptive
Here, we will present examples of multiuser passive time re-
versal communications using data collected during the Focused
Acoustic Fields 2005 (FAF-05) experiment. Section II reviews
the theory behind multiuser passive time reversal communica-
tions including the receiver structure. Section III describes ex-
perimental setup followed by performance of multiuser com-
munications carried out at ranges 4 and 20 km in 120-m-deep
II. PASSIVE TIME REVERSAL
single user case ,  since a multiuser system is a straight-
forward extension of the single user system. The system under
as a post-time reversal processor.
(PS), the received signal on the th element of a receiver array
in the absence of additive noise
convolution. While active time reversal retransmits the time re-
versed version of the received signal
reversal applies matched filtering at each receiver element with
and combines them coherently such that
, passive time
the right bracket denotes the -function representing the sum-
mation of the autocorrelation of each CIR . Note that
essentially is identical to the signal received at the probe source
in active time reversal
(see [17, eq. (1)]). The matched
filter processing in the frequency domain
quires knowledge of the channel
a channel probe signal at the beginning of each data packet.
for the probe signal and the symbol shaping (modulation) filter
tion filter as
and channel matched filtering simultaneously since
the directly measured channel responses.
The performance of time reversal communications depends
entirely on the behavior of the -function which involves the
the number of array elements
To minimize the ISI, it would be desirable to have a -function
that approaches a delta function. In practice, however, there al-
ways is some residual ISI which results in saturation of the per-
formance , . Moreover, the channel continues to evolve
over time in a dynamic ocean environment while time reversal
assumes that the channel is time invariant. Thus, time reversal
alone may require frequent transmission of a channel probe
signal at the expense of data rate to accommodate the channel
fluctuations . Here, we apply the time reversal approach
is the number of receiver elements and the term in
which is measured by
for both pulse compression
, and their spatial distribution.
SONG et al.: MULTIUSER COMMUNICATIONS USING PASSIVE TIME REVERSAL 917
Fig. 3. (a) Schematic diagram of multiuser communications using passive time reversal (see, also, Fig. 4). A subset of elements of the SRA is selected as multiple
users separated in depth which transmit information to the VRA. Time reversal approach requires knowledge of the CIRs ? ??? on the VRA from each user
(superscript ?). (b) Block diagram for a receiver separating signals from different users in passive time reversal communications.
combined with adaptive channel equalization to simultaneously
eliminate the residual ISI and compensate for channel fluctu-
ations without compromising the data rate. Note that this ap-
proach is also referred to as the correlation-based DFE by Yang
. The impact of channel complexity and the number of re-
ceiver elements on the performance of time reversal communi-
cations is discussed theoretically in  while  and  ad-
dress the impact of spatial diversity (
) using at-sea experi-
A. Time Reversal Combined With Channel Equalization Versus
The difference between the following two approaches is
worth noting: 1) time reversal with adaptive channel equaliza-
tion and 2)adaptivemultichannel equalization(e.g., [3,Fig.3]).
First, channel equalization in approach 1) is applied to a single
time series which is combined from multichannel data using
the time reversal concept (see Fig. 2), whereas approach 2) typ-
ically involves linear (feedforward) filters applied separately to
the individual channel data and these filters are jointly updated
and then followed by channel combining and decision-feed-
back equalization , , . Implementing single channel
equalization is obvious in active time reversal communications
where the channel equalization is applied to the signal received
at the focal (probe source) position . Note that approach
2) performs matched filtering implicitly as a component of the
linear filters whereas matched filtering is performed explicitly
in approach 1).
Second, once the multichannel data is collapsed to a single
channel time series in approach 1) using the channel probe
signal at the beginning of the data packet, we only need to
deal with the
-function rather than the individual channel
responses. In a time-varying channel, the
which assumes perfect matched filtering can be generalized to
-function in (1)
pulse applied at time
CIRs. Then, the adaptive equalization implemented in approach
1) implicitly updates an estimate of the time-varying
function resulting from the mismatch between
actual time-varying channel responses
however, the estimates of the individual CIRs are updated either
estimated as in the channel-estimate-based decision feedback
equalizers (CE-DFEs) , . The -function tends to vary
slower than the individual channel responses due to the self-av-
eraging of the time reversal process as observed in our previous
received and processed effectively. In addition, due to the rela-
tively compact structure of
, the number of taps required for
the post-time reversal equalizer is much smaller than the case
with just an equalizer alone, thereby resulting in lower compu-
tational complexity of the equalizer , , .
Third, approach 1) builds up the input SNR by combining
multichannel data coherently which facilitates the operation of
the channel equalizer as a postprocessor as well as in carrier
recovery. In approach 1), phase tracking is carried out on the
single channel time series before the equalizer using a deci-
sion-feedback phase-locked loop (DFPLL) , while in ap-
proach 2), the carrier phases of individual channels are jointly
estimated with the equalizer tap gains to minimize the overall
mean square error (MSE) . The separation of phase tracking
is the response of the channel at time
to an im-
denotes the initial measured
. In approach 2),
918IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007
Fig. 4. Experimental area North of Elba Island, off the west coast of Italy. The VRA was deployed at two different ranges from the SRA in 120-m-deep water:
1) 4 km (VRA1) and 2) 20 km (VRA2). The sound-speed profile measured between the SRA and VRA1/VRA2 during the communications experiment, July
16–21, 2005, is also shown.
and channel equalization can be beneficial especially in fluctu-
by the phase-locked loop (PLL), allowing for the DFE to focus
mainly on the ISI. In fact, Yang  indicated that the nonlinear
interaction between PLL and DFE causes unnecessarily rapid
Finally, the benefit of approach 1) is the much lower com-
plexity as compared to approach 2) where its computational
complexity grows significantly with an increase in the number
ofreceiverelements .Tomitigate thecomplexityof approach
2), a reduced-complexity multichannel equalizer has been de-
veloped exploiting the relationship between optimal diversity
combining and beamforming , . In contrast, the com-
plexity of approach 1) with single channel equalization remains
versal has minimal computational burden (see [5, Fig. 12]).
B. Multiuser Communications
Multiuser communications using active time reversal has
been demonstrated recently where independent messages were
sent simultaneously from a TRM to multiple users (up to 3)
at 8.6-km range in 105-m-deep water . Similarly, passive
time reversal communications for the single user case can be
extended directly to multiuser communications by exploiting
the spatial focusing property of time reversal in a complex en-
vironment and linearity of the system. The schematic diagram
of multiuser communications using passive time reversal is
illustrated in Fig. 3. Each user transmits information simulta-
SONG et al.: MULTIUSER COMMUNICATIONS USING PASSIVE TIME REVERSAL919
Fig. 6. (Left) Scatter plot for a single channel (? ? 1) using 64-QAM (Table I, Case A): Ch#7 (96 m). The bit error rate (BER) is zero using the bottom 16
elements (? ? 16) and the data rate is 3 kb/s. (Right) Performance as a function of the number of receiver elements ?: (a) output SNR (?) along with input
SNR (?) and (b) BER (?). The receiver elements are selected from the bottom and there are no errors beyond the ? marked. Note that ? ? 6 provides reasonable
performance and after around ? ? 17 the improvement is minimal.
AT 4-km RANGE (VRA1). PERFORMANCE OF REPRESENTATIVE EXAMPLES
(CIRCLED LETTERS) ARE DISPLAYED IN FIGS. 6–9
neously to the receiver array denoted by vertical receiver array
(VRA) such that the signal transmissions among the multiple
users completely overlap both in time and frequency (with the
exception of the probe pulses). The signals from the various
users (superscript ) then are separated at the receiver array by
cross correlations of the received signals
of the CIRs
depicted in the block diagram of Fig. 3(b).
The spatial focusing capability of time reversal governs the
extent that the users will interfere with one another. The focal
size and sidelobe levels depend on the wavelength, the element
spacing, and the effective aperture of the array where the latter
is larger than the physical aperture due to the waveguide na-
ture of acoustic propagation in the ocean . Indeed, we have
demonstrated multiple foci at up to six different depths simulta-
neously using active time reversal in an earlier experiment .
with each set
followed by combining as
The crosstalk between two users (
a generalization of the -function defined in (1)
and ) can be quantified as
In the experimental results shown in Section III, the multiple
from the 29-element source/receive array (SRA) which we have
used previously for active time reversal communications .
Although, in general, mutiple users are not expected to be posi-
tioned at the same range, this presents the most challenging sce-
nario such that the received signals are completely overlapped
both in time and frequency. The multiple users will transmit at
equal power and we did not attempt to optimize the power allo-
While high-quality spatial focusing requires a vertical array
spanning the water column with many elements , this is not
critical for just the single user case unless covert operation (low
transmit level) also is desirable . We will investigate the im-
pact of spatial diversity (i.e., the number of array elements and
their distribution in space) on the multiuser communications.
The impact of channel complexity (e.g., the number of multi-
ranges, 4 and 20 km.
III. EXPERIMENTAL RESULTS
A time reversal experiment was conducted jointly with the
NATO Undersea Research Center in July 2005, north of Elba
920IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007
Fig. 7. Scatter plots for six channels (? ? 6) using QPSK (Table I, Case B): Ch#2 (110 m), Ch#7 (96 m), Ch#15 (74 m), Ch#17 (68 m), Ch#20 (60 m), and
Ch#25 (46 m). The aggregate data rate is 6 kb/s.
carried out in a flat region of 120-m-deep water as shown in
Fig. 4. The SRA had 29 transducers spanning a 78-m aperture
with 2.786-m element spacing [seeFig. 3(a)]. TheSRA covered
the water column from 34 to 112 m. A 32-element VRA was
deployed at two different ranges north of the SRA, spanning
the water column from 48 to 110 m with 2-m spacing: 1) 4 km
(VRA1) during July 16–18 and 2) 20 km (VRA2) during July
ation. The sound-speed profile measured between the SRA and
VRA1/VRA2 is also shown in Fig. 4 and indicates a very stable
environment below 30 m.
A. Range 4 km
conducted successfully at 4-km range (VRA1) (the letters refer
to specific cases discussed in the text). An assortment of mod-
ulation schemes were employed from binary phase-shift keying
(BPSK, 1 b/symbol) up to 64 quadrature amplitude modulation
(64-QAM, 6 b/symbol) while the number of users varies from 1
there is a tradeoff between the number of users and the order of
The source level of each element of the SRA was 179 dB re
1 Pa. The probe signal
was a 150-ms, 2.5–4.5-kHz LFM
SONG et al.: MULTIUSER COMMUNICATIONS USING PASSIVE TIME REVERSAL921
Fig. 8. Cochannel interference for three different receiver array configurations (Table I, Case B): (a) ? ? 32 and ? ? 62 m (all elements), (b) ? ? 16 and
? ? 60 m (every other element), and (c) ? ? 16 and ? ? 30 m (bottom-half array). Each plot is normalized with respect to the maximum and the corresponding
performances are given in Table II. Plot (a) displays minimal cochannel interference providing the best performance as seen in Fig. 7. Plot (b) displays significant
cochannel interference resulting in decoding failure denoted by ? in Table II) for two channels: Ch#20 and Ch#17. Specifically, Ch#20 suffers from the cochannel
interference from Ch#2 while Ch#17 is corrupted by both Ch#2 and Ch#7, as observed from the two columns indicated by arrows. On the other hand, configuration
(c) still provides successful decoding for all six channels with the overall BER of 1.7% in Table II.
chirp with a Hanning window, resulting in an effective 100-ms,
to the one used for the active time reversal communications re-
sults reported in  and  and the duration of the chirp after
compression (matched filtering) is
rate was 500 symbols/s with an excess bandwidth  of 100%
and the element data was sampled at
Fig. 5 indicating a complicated multipath structure. The delay
spread is about 90 ms resulting in an ISI of 45 symbols. The
complexity of the channel is beneficial for time reversal com-
munications with a -function approaching a delta function.
Multiuser time reversal communications requires measure-
ment of CIRs (Green’s function)
( ) and the receiving array elements ( ) for spatio–temporal
matched filtering as shown in Fig. 3(b). For the single user
), the information-bearing signal is preceded by a
channel probe signal to estimate the CIRs. For the multiaccess
), however, we adopt the same approach used in
active MIMO multiuser communications  where a pulse
is transmitted separately from each SRA element (emu-
lating a user) in a round robin fashion and received on the VRA
with a time delay (see [18, Fig. 1]). This approach facilitates
capturing the channel response matrix between the source and
the receiver array (
) almost instantaneously. Thus, we
can choose various numbers of users at different depths. Im-
mediately after the round robin transmission, independent data
streams from each users are transmitted to the VRA without a
channel probe signal. The communication sequence was 9.8 s
long with 4900 symbols for the multiuser case, while it was
9.4 s long with 4700 symbols for the single user case with a
probe signal in the preamble.
2 ms. Thus, the symbol
12 kHz. An example
between each user
Representative examples of scatter plots (circled letters from
A to C in Table I) are displayed in Figs. 6–9 showing the per-
formance of multiuser passive time reversal communications.
The channel number annotation in the figures refers to the SRA
transducer (numbered from the seafloor to surface) emulating a
nonlinear DFE, whichever yields better performance, has been
applied. As in our previous results , , , a fractionally
spaced equalizer (FSE) with feedforward tap spacing of
was adopted (2 ms). The number of taps for the feedfor-
ward and feedback portions of the DFE are denoted by
, respectively. Note that
The recursive least squares (RLS) algorithm has been used with
forgetting factor of 0.99.
For the case of multiple users (i.e.,
displayed use all receiving array elements
ture) to achieve the best spatial focusing, and hence, minimal
crosstalk. However, only the bottom 16 elements (
30-m array aperture) have been used for the single user case
where there was no cochannel interference, showing error-free
performance. Since each symbol represents 6 b in this case, the
data rate is 3 kb/s with a 1-kHz bandwidth at the carrier fre-
quency of 3.5 kHz. The performance improvement in terms of
output SNR also is shown in Fig. 6 as a function of the number
of receiver elements
as well as the BER. Note that there is
a minimal number of elements required for reasonable perfor-
6), indicating the existence of a threshold for
the input SNR. For lower order constellations such as BPSK,
just two or three elements will be sufficient . In addition, the
performance improvement is minimal after around
implies a linear equalizer.
), the scatter plots
32 (62-m aper-
922IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007
Fig. 9. Scatter plots for three channels (? ? 3) with different modulations
(Table I, Case C): 8-QAM for Ch#2 (110 m), QPSK for Ch#10 (88 m), and
BPSK for Ch#25 (46 m). The BER is 0 for ? ? ??.
The largest number of users is accommodated inFig. 7 where
six users (
6) transmit information to the receiving array
simultaneously using QPSK modulation, achieving an aggre-
gate data rate of 6 kb/s with almost error-free performance.
The impact of spatial focusing and sidelobe levels on multiuser
communications can be illustrated from the cochannel interfer-
ence between channels shown in Fig. 8 for the following three
different array configurations: (a)
(all elements), (b)
ment), and (c)
corresponding performances are given in Table II in terms of
BER and output SNR with
denoting the array aperture. The
60 m (every other ele-
30 m (bottom-half array). The
BERS OF SIX-CHANNEL MULTIACCESS COMMUNICATIONS AT 4-km RANGE
(TABLE I, CASE B) FOR THREE DIFFERENT ARRAY CONFIGURATIONS
CORRESPONDING TO FIG. 8. THE TOTAL NUMBER OF BITS IS 9600
WITH THE OUTPUT/INPUT SNR SHOWN BELOW THE BERS. ?
INDICATES DECODING FAILURE WHICH OCCURS AT
CH#20 AND CH#17 FOR CONFIGURATION (B)
Fig. 10. CIRs observed by the VRA2 from an SRA source at 88-m depth at
cochannel interference is evaluated from the -function in (3)
using the measured CIRs provided by a round robin transmis-
sion. Note that channels 11 and 22 of the SRA were not active
during this time and each plot is normalized with respect to the
maximum (i.e., 0 dB). The diagonal points represent the energy
focused at each channel [i.e.,
in the lower half channels (at deeper depths) in a downward-re-
fracting profile. On the other hand, the cochannel interference
is shown on the off-diagonal points whose value represents the
As expected, the best performance in Fig. 7 is achieved by
configuration (a) which shows minimal cochannel interference
] indicating more energy
SONG et al.: MULTIUSER COMMUNICATIONS USING PASSIVE TIME REVERSAL923
Fig. 11. (Left) Scatter plot for a single channel (? ? 1) using 64-QAM (Table II, Case D) when only the bottom 16 elements (? ? 16) are used for processing
(30-m aperture). (Right) Performance as a function of the number of receiver elements ?: (a) output SNR (?) along with input SNR (?) and (b) BER (?). The
receiver elements are selected from the bottom. Note that reasonable performance requires at least ? ? 7 and the performance improvement is minimal after
around ? ? 15.
AT 20-km RANGE (VRA2). PERFORMANCE OF REPRESENTATIVE EXAMPLES
(CIRCLED LETTERS) ARE DISPLAYED IN FIGS. 11–13
in Fig. 8(b) and (c) when reducing the array elements by half
16), while configuration (b), using every other element
between low and high channels separated in depth. Not surpris-
ingly, the six-user communications based on the array configu-
ration (b) results in decoding failure denoted by
for two channels: Ch#20 and Ch#17. Specifically, Ch#20 suf-
fers from the cochannel interference from Ch#2 while Ch#17
is corrupted by both Ch#2 and Ch#7, as observed from the two
columns indicated by arrows in Fig. 8(b). In both channels, the
the diagonal. On the other hand, configuration (c) with
(bottom half) still provides successful decoding for all six chan-
nels with the overall BER of 1.7%. This example illustrates that
in Table II
a receiver array (or base station) can assess the cochannel inter-
ference between users given the CIRs from each users.
Finally, Fig. 9 demonstrates the flexibility of time reversal
communications such that different modulation schemes
(8-QAM, QPSK, and BPSK) can be employed for different
users to improve the quality of the communication depending
on the channel and the transmit energy, assuming that some
channel characterization feedback is available to the users. For
example, the receiving array could request the upper two chan-
nels (users) at shallower depth in Fig. 7 to transmit data with
lower order constellations (e.g., BPSK). In addition, Ch#17
and Ch#20 in the previous example [Table II, configuration (b)]
can be requested to stop transmissions for power saving when
using the array configuration (b).
Multiuser communications was carried out at much longer
range by redeploying the VRA at 20-km range (VRA2) as
shown in Fig. 4. Initially, we used the same probe signal used
at 4-km range (150-ms, 2.5–4.5-kHz LFM with a Hanning
window). However, the pulse did not yield sufficient SNR at
20-km range since the higher order modes were absorbed at
longer ranges. To increase the matched filtering gain of the
chirp, we doubled the length of the chirp from 150 to 300 ms.
Note that duration of the chirp after compression is still
ms dictated by the bandwidth of the chirp (1 kHz). An example
of CIRs from the PS at 88-m depth at 20-km range is shown
in Fig. 10. As compared to Fig. 5 at 4-km range, clearly there
are fewer modes (or rays) with a delay spread of about 20-ms
spanning just ten symbols of ISI. Normally, a smaller amount
of ISI would be desirable for typical multichannel equalization,
but this is not the case for the time reversal approach which
924IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007
Fig. 12. Scatter plots for two channels (? ? 2) using 8-PSK (Table II, Case
E): Ch#5 (101 m) and Ch#9 (90 m). The two channels are separated just 10 m
in depth at 20-km range. The BER is 0 for ? ? 20 (40-m aperture).
exploits channel complexity for spatial focusing to minimize
cochannel interference in multiuser communications.
approach adversely. While the number of equalizer taps can be
smaller, the performance of time reversal communications de-
teriorates with a decrease in channel complexity  since the
-function has higher sidelobes both in time and space. The im-
pact of lower complexity on multiuser communications is sig-
resulting from lower complexity (fewer modes) as described in
, requiring multiple users to be separated farther away from
each other. Second, the sidelobe levels outside the focal region
increase with lower complexity, resulting in more interference
(crosstalk) from other users. As a result, multiuser communi-
cations at 20-km range has been successful for only up to three
the LFM probe signals such that one channel uses an upsweep
chirp while the other uses a downsweep chirp exploiting the or-
thogonality between the two.
Fig. 13. Scatter plots for three channels (? ? 3) with Ch#1 (113 m), Ch#5
(101 m), and Ch#10 (88 m) using 16-QAM modulation (Table II, Case F). The
overall BER is 1.5% for ? ? 20 and the aggregate data rate is 6 kb/s.
Since most of the energy is captured by the receiver elements
at deeper depth in Fig. 10, we will use only the bottom 20 el-
20, 40-m array aperture) for processing in this
section. In addition, the transmit channels (users) are selected
order modes excited by sources at deeper depths can propagate
to longer ranges with minimal attenuation.
Table III summaries the multiaccess experiments conducted
successfully at 20-km range (VRA2) (the letters refer to spe-
cific cases discussed in the text). As in the 4-km range case, an
assortment of modulation schemes were employed from BPSK
(1 b/symbol) up to 64-QAM (6 b/symbol), while the number
SONG et al.: MULTIUSER COMMUNICATIONS USING PASSIVE TIME REVERSAL925
of users ranged from one to three. Representative examples of
scatter plots (circled letters from D to F in Table II) are dis-
played in Figs. 11–13 showing the performance of multiuser
communications at 20-km range. First, performance of a single
) case is illustrated in Fig. 11 using a higher order
constellation (64-QAM). Only the bottom
(30-m aperture) are processed resulting in almosterror-free per-
formance. The impact of spatial diversity is shown in Fig. 11 in
terms of output SNR and BER as a function of
7 receivers are required for reasonable performance
corresponding to an input SNR of 18 dB and the performance
improves minimally after around
Multiaccess communications for two users (
played in Fig. 12 using 8-PSK modulation and
10 m in depth (90 and 101 m) at 20-km range and achieve error-
free performance. The BER increases slightly to 0.2% when
16 (not shown). The maximum aggregate data rate ob-
tained with three users (
3) is 6 kb/s using 16-QAM modu-
lation as shown in Fig. 13 with an overall BER of 1.4%. The
transmitters are positioned at depths of 88, 101, and 113 m,
respectively (about 12-m separation).
. Note that at
2) is dis-
Multiuser communications using passive time reversal has
been demonstrated using two moored arrays (SRA and VRA)
separated in range by 4 and 20 km in 120-m-deep water.
Assuming that multiple users are distributed in depth at the
same range, multiple channels are chosen from the SRA ele-
ments to transmit information simultaneously to the VRA. The
32-element VRA spans the water column from 48to 110 m. Ex-
perimental results at 3.5 kHz with a 1-kHz bandwidth suggest
that as many as six users can transmit information over a 4-km
range using QPSK modulation, achieving an aggregate data
rate of 6 kb/s. Moreover, the same data rate has been achieved
at 20-km range by three users (12-m separation in depth) using
16-QAM modulation and the lower 20 elements of the VRA
(40-m array aperture).
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926IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007
H. C. Song received the B.S. and M.S. degrees in marine engineering and naval
architecture from Seoul National University, Seoul, Korea, in 1978 and 1980,
respectively, and the Ph.D. degree in ocean engineering from the Massachusetts
Institute of Technology, Cambridge, in 1990.
From 1991 to 1995, he was with Korea Ocean Research and Development
Institute. Since 1996, he has been with the Marine Physical Laboratory, Scripps
robust matched field processing, and active sonar systems.
Dr. Song is a Fellow of the Acoustical Society of America.
W. S. Hodgkiss (S’68–M’75) was born in Bellefonte, PA, on August 20, 1950.
He received the B.S.E.E. degree from Bucknell University, Lewisburg, PA, in
1972 and the M.S. and Ph.D. degrees in electrical engineering from Duke Uni-
versity, Durham, NC, in 1973 and 1975, respectively.
From 1975 to 1977, he worked with the Naval Ocean Systems Center, San
Diego, CA. From 1977 to 1978, he was a faculty member at the Electrical En-
gineering Department, Bucknell University, Lewisburg, PA. Since 1978, he has
been a member of the faculty of the Scripps Institution of Oceanography, Uni-
versity of California at San Diego, La Jolla, and on the staff of the Marine Phys-
ical Laboratory. Currently, he is the Deputy Director, Scientific Affairs, Scripps
Institution of Oceanography. His current research interests are in the areas of
plications of these to underwater acoustics and electromagnetic wave propaga-
Dr. Hodgkiss is a Fellow of the Acoustical Society of America.
W. A. Kuperman worked at the Naval Research Laboratory, the SACLANT
Undersea Research Centre, La Spezia, Italy, and most recently, at the Scripps
Institution of Oceanography of the University of California at San Diego, La
Jolla, where he is a Professor and Director of the Marine Physical Laboratory.
He has done theoretical and experimental researchin ocean acoustics and signal
T. Akal was a Principal Senior Scientist at SACLANT Undersea Re-
search Center, La Spezia, Italy, where, over the past 33 years, he has been
leading research projects related to underwater acoustic and seismic prop-
agation and marine sediment acoustics. Currently, he is collaborating with
TUBITAK-MAN, Marmara Research Center, Earth and Marine Sciences
Research Institute, Kocaeli, Turkey, the Marine Physical Laboratory, Scripps
Institution of Oceanography, University of California at San Diego, La Jolla,
and the Lamont-Doherty Earth Observatory of Columbia University, Palisades,
M. Stevenson graduated from the U.S. Naval Academy, Annapolis, MD, and
Scripps Institution of Oceanography, University of California at San Diego, La
He joined the Acoustic Branch of the Space and Naval Warfare Systems
Center. Currently, he is the Project Leader for focused acoustic field studies
at the NATO Undersea Research Centre, La Spezia, Italy. His past research in-
cludes design and deployment of acoustic measurement arrays under the Arctic
icecap and in coastal, shallow-water environments.