Multiuser Communications Using Passive Time Reversal - CiteSeerX

IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007

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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 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). Index Terms—Active time reversal, decision-feedback equalizer (DFE), decision-feedback phase-locked loop (DFPLL), intersymbol interference (ISI), multiple-input–multiple-output (MIMO), multiuser communication, passive time reversal, time reversal communication.

I. INTRODUCTION

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ELIABLE, high data rate, acoustic communications in a time-varying multipath shallow-water environment is a highly challenging problem [1]. 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 Manuscript received April 11, 2007; accepted July 2, 2007. This work was supported by the U.S. Office of Naval Research under Grants N00014-05-10263 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 Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093-0238 USA (e-mail:[email protected]; [email protected]; [email protected]). T. Akal was with NATO Undersea Research Centre, La Spezia 19126, Italy. He is now with Marine Physical Laboratory, Scripps Institution of Oceanography, 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: [email protected]). M. Stevenson is with NATO Undersea Research Centre, La Spezia 19126, Italy (e-mail:[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. 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 system.

the ISI and compensate for the channel variations [2], [3]. These techniques, however, are quite demanding in terms of computational complexity, algorithm stability, and selection of channel parameters [4], [5]. Recently, a relatively simple time reversal approach has been introduced in UWA communications which involves using multiple transmit/receive transducers referred to as a time reversal mirror (TRM) [6]. Time reversal exploits spatial diversity to achieve spatial and temporal focusing in a complex environment such as a waveguide [7]–[9]. Temporal focusing (pulse compression) mitigates the ISI while spatial focusing achieves a high signal-to-noise ratio (SNR) at the intended receiver with a low probability of interception (LPI) elsewhere. The spatial focusing property enables a straightforward extension of the time reversal 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 [10]. Previous work on multiuser communications in shallow water applied multichannel decision-feedback equalizers (DFEs) exploiting spatial diversity to suppress ISI and multiuser interference [11], [12]. Note that our multiuser MIMO is distinguished from point-to-point single user MIMO explored in the wireless channel [13] and the UWA channel [14], [15] 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 [7]. Active time reversal communications [Fig. 1(a)] has been demonstrated in shallow water for both a single user [6], [16], [17] and multiple users

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Fig. 2. System model for passive (uplink) time reversal communications followed by an equalizer for the single user case.

[18]. Passive time reversal communications [Fig. 1(b)] has been demonstrated to date only for the single user case [7], [19], [20], [4]. The objective of this paper is to explore multiuser communications using passive time reversal. Although the temporal focusing achieved by time reversal reduces ISI significantly, there always is some residual ISI which results in a saturation of the performance [21]. 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 adaptive channel equalization which simultaneously eliminates the residual ISI and compensates for the channel variations [7], [16], [17], [5]. Indeed, it has been shown [17], [22] that the combination provides nearly optimal performance using the theoretical performance bounds derived in [21]. Throughout this paper, we will use the passive time reversal combined with adaptive channel equalization. Here, we will present examples of multiuser passive time reversal communications using data collected during the Focused Acoustic Fields 2005 (FAF-05) experiment. Section II reviews the theory behind multiuser passive time reversal communications including the receiver structure. Section III describes experimental setup followed by performance of multiuser communications carried out at ranges 4 and 20 km in 120-m-deep water. II. PASSIVE TIME REVERSAL First, we review passive time reversal communications for the single user case [7], [19] since a multiuser system is a straightforward extension of the single user system. The system under consideration is shown in Fig. 2 which includes a channel equalizer as a post-time reversal processor. When a signal is transmitted from a probe source (PS), the received signal on the th element of a receiver array is in the absence of additive noise where is the channel impulse response (CIR) and denotes

convolution. While active time reversal retransmits the time re[17], passive time versed version of the received signal reversal applies matched filtering at each receiver element with and combines them coherently such that

(1) where is the number of receiver elements and the term in the right bracket denotes the -function representing the summation of the autocorrelation of each CIR [23]. 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 requires knowledge of the channel which is measured by a channel probe signal at the beginning of each data packet. Here, we use the same linear frequency modulation (LFM) chirp for the probe signal and the symbol shaping (modulation) filter [7]. In this case, it is convenient to employ the demodulation filter as for both pulse compression and channel matched filtering simultaneously since are the directly measured channel responses. The performance of time reversal communications depends entirely on the behavior of the -function which involves the complexity of the channel (i.e., the number of multipaths), the number of array elements , and their spatial distribution. To minimize the ISI, it would be desirable to have a -function that approaches a delta function. In practice, however, there always is some residual ISI which results in saturation of the performance [7], [21]. 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 [19]. Here, we apply the time reversal approach

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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 h (t) on the VRA from each user (superscript j ). (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 fluctuations without compromising the data rate. Note that this approach is also referred to as the correlation-based DFE by Yang [5]. The impact of channel complexity and the number of receiver elements on the performance of time reversal communications is discussed theoretically in [22] while [7] and [5] address the impact of spatial diversity ( ) using at-sea experimental data. A. Time Reversal Combined With Channel Equalization Versus Multichannel Equalization The difference between the following two approaches is worth noting: 1) time reversal with adaptive channel equalization and 2) adaptive multichannel 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) typically 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-feedback equalization [2], [24], [25]. 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 [17]. 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 -function in (1) which assumes perfect matched filtering can be generalized to

(2) is the response of the channel at time to an imwhere pulse applied at time and denotes the initial measured CIRs. Then, the adaptive equalization implemented in approach 1) implicitly updates an estimate of the time-varying function resulting from the mismatch between and the actual time-varying channel responses . In approach 2), however, the estimates of the individual CIRs are updated either implicitly through the equalizer coefficients [2], [3] or explicitly estimated as in the channel-estimate-based decision feedback equalizers (CE-DFEs) [26], [27]. The -function tends to vary slower than the individual channel responses due to the self-averaging of the time reversal process as observed in our previous stability experiment [28] and longer duration data packets can be received and processed effectively. In addition, due to the relatively 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 computational complexity of the equalizer [7], [17], [5]. 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 decision-feedback phase-locked loop (DFPLL) [29], while in approach 2), the carrier phases of individual channels are jointly estimated with the equalizer tap gains to minimize the overall mean square error (MSE) [2]. The separation of phase tracking

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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.

interaction between PLL and DFE causes unnecessarily rapid channel updates even in a relatively time-invariant environment. Finally, the benefit of approach 1) is the much lower complexity as compared to approach 2) where its computational complexity grows significantly with an increase in the number of receiver elements . To mitigate the complexity of approach 2), a reduced-complexity multichannel equalizer has been developed exploiting the relationship between optimal diversity combining and beamforming [24], [26]. In contrast, the complexity of approach 1) with single channel equalization remains relatively the same since multichannel combining using time reversal has minimal computational burden (see [5, Fig. 12]). B. Multiuser Communications

Fig. 5. CIRs observed by the VRA1 from an SRA source at 96-m depth at 4-km range.

and channel equalization can be beneficial especially in fluctuating ocean environments since a rapid phase change is removed by the phase-locked loop (PLL), allowing for the DFE to focus mainly on the ISI. In fact, Yang [4] indicated that the nonlinear

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 [18]. 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 environment 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-

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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 16) and the data rate is 3 kb/s. (Right) Performance as a function of the number of receiver elements : (a) output SNR (4) along with input elements ( SNR (3) 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.

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TABLE I SUMMARY OF MIMO MULTIACCESS EXPERIMENTS SUCCESSFULLY CONDUCTED AT 4-km RANGE (VRA1). PERFORMANCE OF REPRESENTATIVE EXAMPLES (CIRCLED LETTERS) ARE DISPLAYED IN FIGS. 6–9

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The crosstalk between two users ( and ) can be quantified as a generalization of the -function defined in (1)

(3)

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 with each set of the CIRs followed by combining as 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 nature of acoustic propagation in the ocean [10]. Indeed, we have demonstrated multiple foci at up to six different depths simultaneously using active time reversal in an earlier experiment [30].

In the experimental results shown in Section III, the multiple transmitters are well separated in depth from each other to minimize the crosstalk. The multiple transmitters (users) are selected from the 29-element source/receive array (SRA) which we have used previously for active time reversal communications [18]. Although, in general, mutiple users are not expected to be positioned at the same range, this presents the most challenging scenario 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 allocation [29]. While high-quality spatial focusing requires a vertical array spanning the water column with many elements [8], this is not critical for just the single user case unless covert operation (low transmit level) also is desirable [7]. We will investigate the impact 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 multipaths) also is addressed by comparing the results at two different 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

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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.

Island off the west coast of Italy. The passive time reversal communications portion of the experiment reported in this paper was 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 [see Fig. 3(a)]. The SRA 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 19–21. Both the SRA and the VRA were moored for stable operation. 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

Table I summaries the multiaccess [see Fig. 1(b)] experiments conducted successfully at 4-km range (VRA1) (the letters refer to specific cases discussed in the text). An assortment of modulation 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 to 6. Gray coding was used in the mapping of symbols. Note that there is a tradeoff between the number of users and the order of constellations. 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

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Fig. 8. Cochannel interference for three different receiver array configurations (Table I, Case B): (a) M 32 and L 62 m (all elements), (b) M 16 and L 60 m (every other element), and (c) M 16 and L 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 F 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.

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chirp with a Hanning window, resulting in an effective 100-ms, 3–4-kHz bandwidth chirp. Note that this probe signal is identical to the one used for the active time reversal communications results reported in [18] and [17] and the duration of the chirp after compression (matched filtering) is 2 ms. Thus, the symbol rate was 500 symbols/s with an excess bandwidth [29] of 100% and the element data was sampled at 12 kHz. An example of the CIRs from the PS at 96-m depth at 4-km range is shown in 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 communications with a -function approaching a delta function. Multiuser time reversal communications requires measurement of CIRs (Green’s function) between each user ( ) and the receiving array elements ( ) for spatio–temporal matched filtering as shown in Fig. 3(b). For the single user case ( ), the information-bearing signal is preceded by a channel probe signal to estimate the CIRs. For the multiaccess case ( ), however, we adopt the same approach used in active MIMO multiuser communications [18] where a pulse is transmitted separately from each SRA element (emulating 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. Immediately 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.

Representative examples of scatter plots (circled letters from A to C in Table I) are displayed in Figs. 6–9 showing the performance 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 user in Figs. 1(b) and 3(a). An adaptive equalizer, either linear or nonlinear DFE, whichever yields better performance, has been applied. As in our previous results [7], [17], [18], a fractionally spaced equalizer (FSE) with feedforward tap spacing of was adopted ( 2 ms). The number of taps for the feedforward and feedback portions of the DFE are denoted by and , respectively. Note that implies a linear equalizer. The recursive least squares (RLS) algorithm has been used with forgetting factor of 0.99. For the case of multiple users (i.e., ), the scatter plots displayed use all receiving array elements 32 (62-m aperture) to achieve the best spatial focusing, and hence, minimal crosstalk. However, only the bottom 16 elements ( 16, 30-m array aperture) have been used for the single user case ( 1) with the highest order constellation (64-QAM) in Fig. 6 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 frequency 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 performance (i.e., 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 [7]. In addition, the performance improvement is minimal after around 17.

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TABLE II 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)

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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 18.

The largest number of users is accommodated in Fig. 7 where six users ( 6) transmit information to the receiving array simultaneously using QPSK modulation, achieving an aggregate 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 interference between channels shown in Fig. 8 for the following three different array configurations: (a) 32 and 62 m (all elements), (b) 16 and 60 m (every other element), and (c) 16 and 30 m (bottom-half array). The corresponding performances are given in Table II in terms of BER and output SNR with denoting the array aperture. The

Fig. 10. CIRs observed by the VRA2 from an SRA source at 88-m depth at 20-km range.

cochannel interference is evaluated from the -function in (3) using the measured CIRs provided by a round robin transmission. 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., ] indicating more energy in the lower half channels (at deeper depths) in a downward-refracting profile. On the other hand, the cochannel interference is shown on the off-diagonal points whose value represents the maximum of the cross correlation (i.e., ) between a pair of users . As expected, the best performance in Fig. 7 is achieved by configuration (a) which shows minimal cochannel interference

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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 (4) along with input SNR (3) 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.

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TABLE III SUMMARY OF MIMO MULTIACCESS EXPERIMENTS SUCCESSFULLY CONDUCTED AT 20-km RANGE (VRA2). PERFORMANCE OF REPRESENTATIVE EXAMPLES (CIRCLED LETTERS) ARE DISPLAYED IN FIGS. 11–13

a receiver array (or base station) can assess the cochannel interference 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 channels (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). B. Range

in Fig. 8(a). The increase in cochannel interference is noticeable in Fig. 8(b) and (c) when reducing the array elements by half ( 16), while configuration (b), using every other element to keep the aperture, indicates significant cochannel interference between low and high channels separated in depth. Not surprisingly, the six-user communications based on the array configuration (b) results 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 in Fig. 8(b). In both channels, the sidelobe levels are just about 5 dB below from the main focus on the diagonal. On the other hand, configuration (c) with 16 (bottom half) still provides successful decoding for all six channels with the overall BER of 1.7%. This example illustrates that

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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 2 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

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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 20 (40-m aperture). in depth at 20-km range. The BER is 0 for

exploits channel complexity for spatial focusing to minimize cochannel interference in multiuser communications. In general, lower channel complexity affects the time reversal approach adversely. While the number of equalizer taps can be smaller, the performance of time reversal communications deteriorates with a decrease in channel complexity [22] since the -function has higher sidelobes both in time and space. The impact of lower complexity on multiuser communications is significant in two respects. First, the focal size increases with range resulting from lower complexity (fewer modes) as described in [10], 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 communications at 20-km range has been successful for only up to three users. In an attempt to further reduce the crosstalk, we alternated the LFM probe signals such that one channel uses an upsweep chirp while the other uses a downsweep chirp exploiting the orthogonality between the two.

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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.

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Since most of the energy is captured by the receiver elements at deeper depth in Fig. 10, we will use only the bottom 20 elements ( 20, 40-m array aperture) for processing in this section. In addition, the transmit channels (users) are selected from the elements toward the bottom of the SRA since the lower 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 specific 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

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of users ranged from one to three. Representative examples of scatter plots (circled letters from D to F in Table II) are displayed 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 user ( 16 elements constellation (64-QAM). Only the bottom (30-m aperture) are processed resulting in almost error-free performance. The impact of spatial diversity is shown in Fig. 11 in terms of output SNR and BER as a function of . Note that at least 7 receivers are required for reasonable performance corresponding to an input SNR of 18 dB and the performance improves minimally after around 20. Multiaccess communications for two users ( 2) is displayed in Fig. 12 using 8-PSK modulation and 20 (40-m aperture). Note that the two channels are separated by only about 10 m in depth (90 and 101 m) at 20-km range and achieve errorfree performance. The BER increases slightly to 0.2% when 16 (not shown). The maximum aggregate data rate ob3) is 6 kb/s using 16-QAM modutained with three users ( 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).

[7] H. Song, W. Hodgkiss, W. Kuperman, W. Higley, K. Raghukumar, T. Akal, and M. Stevenson, “Spatial diversity in passive time reversal communications,” J. Acoust. Soc. Amer., vol. 120, pp. 2067–2076, 2006. [8] W. A. Kuperman, W. S. Hodgkiss, H. C. Song, T. Akal, C. Ferla, and D. Jackson, “Phase conjugation in the ocean: Experimental demonstration of an acoustic time-reversal mirror,” J. Acoust. Soc. Amer., vol. 103, pp. 25–40, 1998. [9] C. Feuillade and C. Clay, “Source imaging and sidelobe suppression using a time-domain techniques in a shallow-water waveguide,” J. Acoust. Soc. Amer., vol. 92, pp. 2165–2172, 1992. [10] S. Kim, G. F. Edelmann, W. A. Kuperman, W. S. Hodgkiss, H. C. Song, and T. Akal, “Spatial resolution of time-reversal arrays in shallow water,” J. Acoust. Soc. Amer., vol. 110, pp. 820–829, 2001. [11] M. Stojanovic and Z. Zvonar, “Multichannel processing of broadband multiuser communication signals in shallow water acoustic channels,” IEEE J. Ocean. Eng., vol. 21, no. 2, pp. 156–166, Apr. 1996. [12] M. Stojanovic and L. Freitag, “Multiuser undersea acoustic communications in the presence of multipath propagation,” in Proc. IEEE OCEANS Conf., 2001, pp. 2165–2169. [13] G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., vol. 6, pp. 311–335, 1998. [14] S. Roy, T. Duman, L. Ghazikhnian, V. McDonald, J. Proakis, and J. Zeidler, “Enhanced underwater acoustic communication performance using space-time coding and processing,” in Proc. MTS/IEEE OCEANS Conf., Tokyo, Japan, 2004, pp. 26–33. [15] D. Kilfoyle, J. Preisig, and A. Baggeroer, “Spatial modulation over partially coherent multiple-input/multiple-output channels,” IEEE Trans. Signal Process., vol. 51, no. 3, pp. 794–804, Mar. 2003. [16] G. Edelmann, H. Song, S. Kim, W. Hodgkiss, W. Kuperman, and T. Akal, “Underwater acoustic communication using time reversal,” IEEE J. Ocean. Eng., vol. 30, no. 4, pp. 852–864, Oct. 2005. [17] H. Song, W. Hodgkiss, W. Kuperman, M. Stevenson, and T. Akal, “Improvement of time reversal communications using adaptive channel equalizers,” IEEE J. Ocean. Eng., vol. 31, no. 2, pp. 487–496, Apr. 2006. [18] H. Song, P. Roux, W. Hodgkiss, W. Kuperman, T. Akal, and M. Stevenson, “Multiple-input–multiple-output coherent time reversal communications in a shallow water acoustic channel,” IEEE J. Ocean. Eng., vol. 31, no. 1, pp. 170–178, Jan. 2006. [19] D. Rouseff, D. Jackson, W. Fox, C. Jones, and J. R. Dowling, “Underwater acoustic communications by passive-phase conjugation: Theory and experimental results,” IEEE J. Ocean. Eng., vol. 26, no. 4, pp. 821–831, Oct. 2001. [20] J. Flynn, J. Ritcey, D. Rouseff, and W. Fox, “Multichannel equalization by decision-directed passive phase conjugation: Experimental results,” IEEE J. Ocean. Eng., vol. 29, no. 3, pp. 824–836, Jul. 2004. [21] M. Stojanovic, “Retrofocusing techniques for high rate acoustic communications,” J. Acoust. Soc. Amer., vol. 117, pp. 1173–1185, 2005. [22] H. C. Song and S. Kim, “Retrofocusing techniques in a waveguide for acoustic communications,” J. Acoust. Soc. Amer., vol. 121, pp. 3277–3279, 2007. [23] T. Yang, “Temporal resolutions of time-reversed and passive-phase conjugation for underwater acoustic communications,” IEEE J. Ocean. Eng., vol. 28, no. 2, pp. 229–245, Apr. 2003. [24] M. Stojanovic, J. A. Capitovic, and J. G. Proakis, “Reduced-complexity spatial and temporal processing of underwater acoustic communication signals,” J. Acoust. Soc. Amer., vol. 98, pp. 961–972, 1995. [25] Q. Wen and J. Ritcey, “Spatial diversity equalization applied to underwater communications,” IEEE J. Ocean. Eng., vol. 19, no. 2, pp. 227–241, Apr. 1994. [26] M. Stojanovic, L. Freitag, and M. Johnson, “Channel-estimation-based adaptive equalization of underwater acoustic signals,” in Proc. IEEE OCEANS Conf., Seattle, WA, 1999, pp. 985–990. [27] J. C. Preisig, “Performance analysis of adaptive equalization for coherent acoustic communications in the time-varying ocean environment,” J. Acoust. Soc. Amer., vol. 118, pp. 263–278, 2005. [28] W. S. Hodgkiss, H. C. Song, W. A. Kuperman, T. Akal, C. Ferla, and D. R. Jackson, “A long range and variable focus phase conjugation experiment in shallow water,” J. Acoust. Soc. Amer., vol. 105, pp. 1597–1604, 1999. [29] J. Proakis, Digital Communications. New York: McGraw-Hill, 2001, pp. 347–352. [30] P. Roux, W. Kuperman, W. Hodgkiss, H. Song, T. Akal, and M. Stevenson, “A non-reciprocal implementation of time reversal in the ocean,” J. Acoust. Soc. Amer., vol. 116, pp. 1009–1015, Jun. 2004.

IV. CONCLUSION 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 elements to transmit information simultaneously to the VRA. The 32-element VRA spans the water column from 48 to 110 m. Experimental 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). REFERENCES [1] D. Kilfoyle and A. Baggeroer, “The state of the art in underwater acoustic telemetry,” IEEE J. Ocean. Eng., vol. 25, no. 1, pp. 4–27, Jan. 2000. [2] M. Stojanovic, J. A. Capitovic, and J. G. Proakis, “Adaptive multichannel combining and equalization for underwater acoustic communications,” J. Acoust. Soc. Amer., vol. 94, pp. 1621–1631, 1993. [3] M. Stojanovic, J. A. Capitovic, and J. G. Proakis, “Phase-coherent digital communications for underwater acoustic channels,” IEEE J. Ocean. Eng., vol. 19, no. 1, pp. 110–111, Jan. 1994. [4] T. C. Yang, “Differences between passive-phase conjugation and decision-feedback equalizer for underwater acoustic communications,” IEEE J. Ocean. Eng., vol. 29, no. 2, pp. 472–487, Apr. 2004. [5] T. C. Yang, “Correlation-based decision-feedback equalizer for underwater acoustic communications,” IEEE J. Ocean. Eng., vol. 30, no. 4, pp. 865–880, Oct. 2005. [6] G. Edelmann, T. Akal, W. Hodgkiss, S. Kim, W. Kuperman, and H. Song, “An initial demonstration of underwater acoustic communication using time reversal mirror,” IEEE J. Ocean. Eng., vol. 27, no. 3, pp. 602–609, Jul. 2002.

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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 Institution of Oceanography, University of California at San Diego, La Jolla. His research interests include time-reversed acoustics, underwater communications, 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 University, 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 Engineering Department, Bucknell University, Lewisburg, PA. Since 1978, he has been a member of the faculty of the Scripps Institution of Oceanography, University of California at San Diego, La Jolla, and on the staff of the Marine Physical Laboratory. Currently, he is the Deputy Director, Scientific Affairs, Scripps Institution of Oceanography. His current research interests are in the areas of signal processing, propagation modeling, and environmental inversions with applications of these to underwater acoustics and electromagnetic wave propagation. Dr. Hodgkiss is a Fellow of the Acoustical Society of America.

IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 4, OCTOBER 2007

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 research in ocean acoustics and signal processing.

T. Akal was a Principal Senior Scientist at SACLANT Undersea Research Center, La Spezia, Italy, where, over the past 33 years, he has been leading research projects related to underwater acoustic and seismic propagation 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, NY.

M. Stevenson graduated from the U.S. Naval Academy, Annapolis, MD, and Scripps Institution of Oceanography, University of California at San Diego, La Jolla. 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 includes design and deployment of acoustic measurement arrays under the Arctic icecap and in coastal, shallow-water environments.