Integrating Ocean Acoustics and Signal Processing

Transcription

1 Integrating Ocean Acoustics and Signal Processing W.A. Kuperman and H.C. Song Marine Physical Laboratory, Scripps Institution of Oceanography University of California, San Diego 9500 Gilman Drive, La Jolla, CA , USA Abstract. The combination of ocean acoustical physics and signal processing has been the central theme of our research over the last twenty years. In particular, the thrust of our research has been in matched field processing, waveguide invariant physics, time reversal acoustics, acoustic communications, sensitivity kernel analysis, and correlation based noised processing. Common to all these areas is the complexity of the medium so that our research goals have been to either overcome the downside of the complexity or, more interestingly, actually utilize propagation and noise complexity and diversity in the extraction of signal and environmental acoustic information. We present examples emphasizing this common theme. Keywords: matched field processing, waveguide invariant, time reversal, sensitivity kernel, and correlation processing PACS: Pc, Kx, Jn, Ot, Dh, and Tj INTRODUCTION The structure of the shallow water acoustic field can enhance various signal processing goals. In particular, we review the relation between matched field processing and time reversal physics. Further, we show that the same ideas relating the latter lead to efficient self-adaptive underwater acoustic communication methods. Data from our experiments are used to demonstrate these results. MATCHED FIELD PROCESSING AND TIME REVERSAL In matched field processing (MFP) [1] we compare data received on an acoustic array with a propagation model for the purpose of locating a source and/or determining some properties of the propagation medium, the latter procedure often referred to as matched field tomography (MFT). Matched field uses a forward propagation model from a grid of candidate source locations whereas standard tomography per se usually involves an inverse procedure. In MFP the actual data model comparison can utilize various signal processing algorithms from linear processors such as a Bartlett processor to nonlinear or adaptive processors such as a Minimum Variance Distortionless Response (MVDR) processor. In any case, the comparison is done with replicas derived from an environmental acoustic propagation model whose fidelity is always limited by the environmental input to the model. Further, higher acoustic frequency data requires more accurate environmental input because of the order wavelength sampling of the acoustic medium. Overcoming these environmental (and other) uncertainties is the goal of robust MFP. Advances in Ocean Acoustics AIP Conf. Proc. 1495, (2012); doi: / American Institute of Physics /$

2 On the other hand a time reversal mirror (TRM) [2] receives signal from a source and then uses a set of sources co-located with the array of receivers to backpropagate a set of fields that focus at the original source location. The process is based on reciprocity and the time reversal symmetry of the linear acoustic wave equation. TRM is an experimental implementation in which the fields backpropagate in exactly the same medium as the forward propagation. In that sense, it works for any stationary environment since no knowledge of the medium is required. Further, since no model is used, localization (other than the focus is at the same place as the original source) with a simple implementation of a TRM cannot be done. Rather than experimental backpropagation, a model can be used but that procedure is just an unnormalized version of MFP [3]. However, what is interesting is that one can think of TRM as an existence theorem that if one had the exact knowledge of the medium no matter how complex, MFP would work. Further, we know from experiments that the TR focus can be accomplished after some time delay between receiving the data and retransmitting it. Hence, the process remains somewhat stable or robust while the ocean changes. The MFP Processor and the TRM Process Phase conjugation in the frequency domain corresponds to time reversal in the time domain. Hence, frequency domain MFP has its associated sidelobes so that coherent frequency synthesis MFP would be the appropriate analog to the TRM. In any event, we can work in either space knowing the coherent Fourier relation between the two. The fundamental equation for either frequency domain MFP or phase conjugation is b(r) = g + (r array ;r source )g(r array ;r) b mfp (r) 2 = w + (r)k data w(r) (1) where, the first expression correlates data on a receiver array to either a model calculation to, in the case of MFP, a candidate field position r or, in the TRM case, an actual physical back propagation initiated by the phase conjugated array data to all field positions. In the MFP case, the candidate position that coincides with the original source position has the highest amplitude whereas for the TRM, the backpropagated field focuses at the (probe) source. The second expression is an important representation of MFP where w are the replicas as obtained from a model calculation and K, the cross-spectral density matrix (CSDM) is the outer product of the data vector with its complex transpose (+). For the MFP case, the replica s can also be derived for an adaptive processor that is dependent on the model and the data itself, such as an MVDR processor (see Eq. 5). It is then clear that MFP requires and therefore is limited by model fidelity to the actual environmental acoustics scenario whereas a TRM is more or less a matched filter process that uses the environment to produce the data and the filter: more or less an autocorrelation process. Hence, TRM works but without a model, does not produce localization information; with a model, TRM is just MFP. Time reversal, though, provides an important physical understanding into MFP process in addition to having more direct useable applications as indicated in the acoustic communications (Acomms) section below. 70

3 FIGURE 1. Schematic of time reversal mirror (TRM) experiments in the Mediterranean performed jointly by NATO/SACLANTCEN and UCSD/SIO. The probe source (here, center frequency of 3.5 khz but lower and higher frequencies were also used) data at the vertical source/receiver (SRA), lower right panel is time reversed and retransmitted resulting in the focus (lower left panel) measured on a vertical array collocated with the probe source. The upper right panel indicates the modal interpretation of the TR focal process. We have conducted a series of propagation type TRM experiments [1,4-11] which are schematically summarized in Fig. 1. After performing the classical TR experiments depicted in Fig. 1 we have found that it is more useful to experimentally measure the transfer functions between sources and receivers and process these data for TR and other (MFP, Tomography, etc) analysis. Figure 2 depicts this experimental scheme [11] in which a signals from sources on a vertical array are individually transmitted to all elements of a receive array. The data can then be used for constructing TR foci, one way data can be combined with a model for MFP processing and/or for many other possibilities such as for inversion/tomography purposes. We have not been successful in the MFP version of the 3.5 khz experiment at the indicated range, but we have been able to perform analogous MFP to TRM processes at lower frequencies as shown in Fig. 3 indicating MFP is viable for less challenging lower frequency scenarios (given sufficient SNR). Note the relationship between frequency and channel complexity: the shorter the wavelength the greater the requirement in the space-time accuracy of the environment. One of the most environmentally complicated TR experiments we have performed has been the 3.5 khz range-dependent example shown in Fig. 4. We believe that the MFP analog of the TRM result in Fig. 4 at this point in time is not close to being feasible, but on the other hand, such an environment with and without additional water column variability does pose an extreme challenge for the research community. 71

4 FIGURE 2. Time reversal is implemented by individually transmitting signals to a receive array. These make up the transfer functions from the sources to all receivers. Data from a matrix of received signals can then be rearranged and time reversed and then correlated with the transmitted signals by using the originally measured transfer functions to the received array. One of the more prominent aspects of TR physics is the focal size that is related to the MFP resolution cell concept. Figure 5 is a schematic of the waveguide physics that determines focal (resolution) size. Resolution can be thought of as the resolution of an effective lens made from the images as shown. The size of the lens is related to the critical angle of the waveguide with tapering associated with attenuation. This resolution size is the same as the analogous MFP result. Typically, though we must include SNR in the MFP resolution through, for example, the Cramer-Rao bounds [12] that are a measure of the convexity of the CSDM with respect to the search parameters. The relevant question, then, is how does the construction of the CSDM impact the desired focal/resolution. 72

5 FIGURE 3. Experimental results for MFP at 450 Hz for a TRM scenario. The data is taken from the TR processing scheme illustrated in Fig. 2.The three processors are Bartlett, Minimum Variance Distortionless Response (MVDR) and White Noise Constraint (WNC). The WNC has typically been the most robust MFP processor for us. MFP Performance and the CSDM One of the main reasons we use the CSDM in narrowband passive MFP is that we are typically trying to localize a source from a random radiator and the CSDM is not a function of the actual phase of the source. The sample CSDM is constructed by summing complex outer-products of frequency domain data snapshots, K= # snapshots k =1 d k d +k (2) thereby also enhancing the SNR, assuming the source fields add coherently and the noise field less coherently. For adaptive processing, K must be invertible implying that one must, more or less, use at least the same number of snapshots as array elements. With sufficient snapshots, the eigenvectors of the CSDM are associated with individual sources only if each source remains within a resolution cell. However, since 73

6 the length of each snapshot depends on the FFT process, the frequency resolution of the narrowband processing also effects the collection of snapshot within a resolution cell. That is, building a CSDM when sources cross resolution cells results in MFP degradation performance ( eigenvector spillage ). The interesting corollary to this argument is that a higher resolution, longer arrays or extreme narrowband processing may degrade performance because the high resolutions restricts the number of useful snapshots of a moving source. One potential fix for the overly resolved CSDM is to use subaperture processing [13] in which an array is separated into lower resolution subaperture whose individual array processed outputs are further processed coherently. FIGURE 4. Time reversal at a 10 km range in an upslope environment. The focus is of order.5 meters in vertical extent indicating that the TR focusing process in this particular case is related adiabatic propagation and hence to the set of modes at the receive array corresponding to the higher spatial frequencies shown in the upper right panel of Fig. 1. Another constraint on accumulating data for the CSDM is transit time, particularly for a horizontal array. For a moving source, the total number of snapshots is not only constrained by the resolution cell size, but in order for the signal to be coherently processed across the array, a snapshot must contain all the components of the signal within, say, the endfire transit time of the snapshot, T=L/c where L is the array length 74

7 and c the sound speed. Since the snapshot time is the inverse of the bandwidth, B we can approximate the restriction as B < c 8L (3) This ultimately translates into a relation between the FFT processing that provides the frequency domain snapshot data and the above cell size resolution constraints. Time Reversal, MFP, Ocean Variability and the Waveguide Invariant Ocean variability is another limiting factor in the construction of the CSDM. For example, TR experiments have shown, depending on frequency, that foci degrade over time when the same data is used at a TRM but retransmitted at later times. The time scale of this degradation is related to the ocean variability and it is, to some extent, this variability that a robust MFP algorithm must tolerate. To some extent, the impact of this variability can be related to the waveguide invariant. Experiments have shown that the concept of the waveguide invariant can be applied to shifting the focal range by retransmitting the TRM data at a shifted frequency [4]. The waveguide invariant describes the trajectory of intensity inteference maxima (or minima) in range-frequency space. If instead of intensity, one uses either the complex product of TRM data and propagation which is actually the TR process or the complex product of a model replica with data, one obtains the trajectory of the focal range or the localization peaks/sidelobes in MFP [14], respectively, relative to the unshifted focus or localization parameters. Actually, a generalized form of the waveguide invariant expression [15-18] is δr r 1 δω β ω + γ δh = 0,β = 1, γ = 2 (4) β h where, r is the focal (localization) shift, ω is angular frequency, h is a waveguide depth or channel width, β is the waveguide invariant taken as unity for shallow water, and γ is an analogous quantity relating the range shift to the channel in channel width [16, 19]. Since the top of the thermocline fluctuates due to internal wave activity, there is a variable channel width that should cause TR focal shifts in range and/or degradation in the analogous MFP result. Indeed, the generalized invariant-based ideas have been used to construct a robust processor based on multiple frequency constraint [10] in analogy to other multiple constraint formulations for robustness [20-21]. More generally, combining some of the ideas discussed above provides further guidance for array processing. In summary of MFP is problematic because we lack complete knowledge of the environment whereas TR is a an accurate process that, by itself (with a model) typically only reveals physical processes but not search parameters. Coherent broadband MFP of is even more problematic than the narrowband case, but TR clearly 75

8 works. The juxtaposition of TR and MFP experiments and analysis may provide further guidance to improve MFP processing. One area in ocean acoustics where TR has particular utility, though, is acoustic communications. FIGURE 5. The range and depth Rayleigh resolution is depicted in the upper panel. In the low panel, the image representation of waveguide is used to show the analogous resolution. An (nonexistent) ideal waveguide with perfectly reflecting boundaries would have images of infinite extent in the vertical; the critical angle of the waveguide limits the size of the effective aperture and the bottom attenuation acts as a taper. UNDERWATER ACOUSTIC COMMUNICATION Underwater acoustic (UWA) channels are characterized by large multipath spreads resulting in intersymbol interference (ISI) that degrades the quality of the received signal and requires compensation (i.e., channel equalization). The time varying nature of the multipath also requires continuous tracking of receiver parameters necessary for demodulation. An additional factor is that the available bandwidth in UWA channels is limited due to severe frequency-dependent attenuation of the physical medium. Consequently, high spectral efficiency (an information rate per Hz) is critical for achieving significant data rates, suggesting a phase-coherent system design along with high-order constellations [22]. Over the last decade time reversal (TR) [23] has been studied extensively for phasecoherent communication as an alternative to the use of multichannel decisionfeedback equalizers (M-DFEs) in UWA environments [24]. TR, either active [25] or passive [26], exploits spatial diversity to achieve spatial and temporal focusing in rich multipath environments (e.g., shallow water), albeit not perfect. Temporal focusing (pulse compression) mitigates ISI. When subsequently cascaded with a single channel 76

9 decision-feedback equalizer (DFE) to remove the residual ISI, referred to as a TR- DFE, TR communication can provide nearly optimal performance (similar to M- DFEs) in theory [27]. Considered in this paper, passive TR (uplink) as illustrated in Fig. 6 essentially is equivalent to active TR (downlink) with the communications link being in the opposite direction, which is presented in this paper. The channel response h i (t) includes the shaping pulse, transmit filter, channel impulse response, and receive filter. FIGURE 6. Block diagram for passive time reversal equalization for a single user case (uplink). Time reversal combining is based on knowledge of the channel responses h i (t), i = 1,, M and is followed by a single channel equalizer to remove the residual ISI. Extension to Time-varying Environments Time reversal (TR) communications requires knowledge of a channel (provided by a channel probe or training symbols) and that the channel be time-invariant or slowly varying. However, underwater acoustic channels often are characterized as dynamic (time-evolving), highly dispersive, and sparse. This is especially true of the highfrequency regime (e.g., khz) typical for acoustic telemetry as shown in Fig. 7. FIGURE 7. Temporal evolution of the channel response at two different receiver depths during the KAM08 experiment (12-20 khz): (a) 62.5 m and (b) 80 m. The source is at 57 km depth and 4 km range. The temporal variability and sparseness of he channel are evident. The delay spread is up to ~10 ms, resulting in the ISI spanning about 50 symbols for a symbol rate of 5 ksymbols/s. The color scale is in decibels. 77

10 Recently the time reversal approach has been extended to time-varying channels in passive (uplink) scenarios [28]. The basic idea is to implement it on a block-by-block basis such that within each block the channel remains time-invariant and subsequently is updated using detected symbols (decision-directed mode). It was shown that a potential benefit of this block time reversal approach is elimination of an explicit phase tracking algorithm required for phase-coherent communications except during the initial training period. This was accomplished by a combination of a smaller block size and adaptive channel estimation on a symbol-by-symbol basis. The most recent channel estimates then were applied as matched filters to the immediately following block, leaving just the incremental phase evolution. The proposed time reversal approach without explicit phase tracking has been demonstrated using the FAF-06 experimental data (11-19 khz) collected in shallow water off the west coast of Italy as shown in Fig. 8 [29]. Note that the vertical receive array (VRA) shown in Fig. 8(a) corresponds to a base station in wireless channels. (c) FIGURE 8. (a) Schematic of FAF-06 communication experiment (11-19 khz). A 16-element vertical receive array (VRA) was deployed in 92-m deep water. A single element at 39-m depth is selected from a 12-element transmit array (Topas) deployed to the seafloor in 46-m deep water at 2.2 km range. (b) An example of the channel response received by the VRA. (c) Scatter plot for 32-QAM (quadrature amplitude modulation) with a data rate of kbits/s. The output SNR is 22.8 db. Further, using the KAM08 experimental data (12-20 khz) collected in ~100-m deep shallow water, off the west coast of Kauai, HI, three different block-based TR approaches also were investigated: (1) without explicit phase tracking, (2) with phase tracking, and (3) exploiting channel sparsity. In addition, the TR approaches were compared to a conventional adaptive multichannel equalizer [9]. It was found that approach (3) in general provides the best performance among them along with robustness. MIMO/Multiuser Communication An additional benefit of TR is that the spatial focusing property facilitates multiuser or multi-access communications without the explicit use of time, frequency, or code division (e.g., coded-division multiple access (CDMA)) that inevitably sacrifices data 78

11 throughput to ensure multiuser separability at the detectors [31]. Provided that multiple users are well-separated in range and depth from each other compared to the focal size in a complex environment, each user can transmit information simultaneously to the passive time reversal receive array which corresponds to a base station. Similar to ISI, however, spatial focusing is not perfect and crosstalk among users or multi-access interference (MAI) cannot be eliminated completely using the conventional TR approach. Consequently, an adaptive TR approach has been developed that mitigates the MAI by exploiting knowledge of the channel from each user j at the base station [32]. Adaptive TR followed by a single channel DFE has been applied successfully to various examples of multiuser communication data collected in shallow water environments [33] (see Fig. 9) and recently extended to time-varying channels in conjunction with the successive interference cancellation (SIC) approach [34]. (a) (b) (c) FIGURE 9. (a) Schematic of FAF-06 experiment for multiuser communication (11-19 khz). A 16- element vertical receive array (VRA) was deployed in 92-m deep water. Multiple elements are selected from a 12-element transmit array (Topas) deployed to the seafloor in 46-m deep water at 2.2 km range. Scatter plots for a two-user case using 32-QAM: (b) user 1 and (c) user 2. The symbol rate is 5 ksymbols/s with a 7.5 khz bandwidth. The output SNRs are 18.7 and 20.5 db, respectively. The aggregate data rate is 50 kbits/s with BER of 0.23%. Adaptive Time Reversal The adaptive filter w i j (t), i = 1,, M for a user j was developed to minimize the crosstalk between users. Define a column vector d j as the collection of channel responses in the frequency domain between a user j to the M -element array, d T j = H j j 1 ( f ) H M ( f ) where T denotes the transpose operation. The filter response at each frequency f for focusing the array on user j is given by w j w j = R 1 d j d j R 1 d j, where R = d k d k + σ 2 I (5) where denotes the complex conjugate operation. Note that R is a cross spectral density matrix (CSDM) exploiting knowledge of the channel from each user at the base station and σ 2 is a small diagonal loading for matrix inversion with I being an identity matrix. The optimal weights w i j (t) are calculated for all frequencies in the transmitted band, transformed back to the time domain, and time- k 79

12 reversed, yielding a set of adaptive time reversal filters w i j ( t) which replace the conventional time reversal filter h i j ( t) shown in Fig. 6. Synthetic Aperture Communication (SAC) While our understanding of underwater acoustic communications has improved over the last two decades, communications involving mobile assets (e.g., Gliders and AUVs) remains quite challenging. First, the slow propagation speed of acoustic waves (e.g., 1500 m/s) makes Doppler effects significant even for a relatively slow moving platform (e.g., 4 kts). Due to the broadband nature of underwater acoustic communication signals, Doppler due to source motion requires resampling of the received signal. Moreover, the Doppler is time-varying and the temporal variability of underwater acoustic channels induces additional Doppler spreading. Second, underwater acoustic systems typically operate at low signal-to-noise ratios (SNR) and thus require some form of spatial diversity (e.g., array) to enhance SNR and mitigate channel fading effects. We are concerned with point-to-point coherent communication between a moving source and a single fixed receiver where spatial diversity is obtained from a virtual horizontal array generated by relative motion between them, referred to as synthetic aperture communications (SAC). It was motivated by our initial investigation into the feasibility of SAC in shallow water using the 2-4 khz frequency band [35]. In that work, simple on/off keying was employed to minimize complexity and not require coherent demodulation. Furthermore, the motion was almost transverse resulting in a small Doppler shift. In that case, diversity appeared to have come from the data being collected in an azimuthally inhomogeneous environment coupled with temporal channel variations between transmissions. (c) FIGURE 10. (a) Schematic of a synthetic aperture communication (FAF-04) between a moving source towed at about 4 kts at 70-m depth and a fixed receiver at 72-m depth. (b) The first five channel responses (envelope) spaced 1-min (~120 m) apart. (c) Communication signal transmitted by the towed source during the SAC FAF-04 experiment. Each 10-s data packet denoted by {a,b,a,c,d} consists of a channel probe followed by a 9-s communication sequence. Five data packets are concatenated together to form a single 50-s-long transmission with data packet a used twice. Based on the initial results reported in [35], we advanced our understanding of SAC by analyzing the data from two experiments (FAF-04 and FAF-06) where transmissions were carried out in different frequency bands: (1) 2-4 khz and (2) 8-20 khz. Case (1) involved BPSK coherent modulation, radial motion (significant Doppler), and transmission design suitable for SAC (i.e., interleaving) (see Fig. 10) whose performance is shown in Fig. 11 (left). On the other hand, Case (2) explored a higher frequency regime permitting the use of a large bandwidth with high-order constellations up to 8-PSK, achieving the potential of a high transmission rate. The receiver employed is time reversal diversity combining followed by a single channel decision-feedback equalizer (DFE) (TR-DFE) with frequent channel updates to accommodate the time-varying channel due to the coupling of space and time in the presence of motion [36]. 80

13 The performance of high-frequency coherent SAC during the FAF-06 is displayed in Fig. 11 (right) in terms of output SNR versus the number of receptions combined (M) for three different modulations using the full bandwidth available (8-20 khz) as well as the result using only half the bandwidth (8-14 khz) is included for comparison purposes. Note that the performance improves with coherent combination of multiple transmissions (M) and remains consistent for a given M over different modulations. In particular, 8PSK modulation can provide an effective data rate of 30/M kbits/s. In addition, the performance of 8PSK using the bandwidth available (*) shows better performance (1-2 db) over 8PSK using the full bandwidth at the expense of lower transmission rate, indicating a trade-off between data rate and performance [36]. FIGURE 11. Performance of synthetic aperture time reversal communications versus the number of transmissions combined (M) in terms of output SNR: FAF-04 (left) and FAF-06 (right). For FAF-04 (BPSK), ambient noise recorded separately is added to lower the input SNR to about 3 db such that each transmission alone results in poor performance. For FAF-06, three different modulations using the full bandwidth available (8-20 khz) are shown while 8-PSK modulation using only half the bandwidth (8-14 khz) also is displayed for comparison purposes. ACKNOWLEDGMENTS The research reported here was supported by the U.S. Office of Naval Research. REFERENCES 1. A.B. Bageroer et al., IEEE J. of Oceanic Eng. 18, (1993) 2. W.A. Kuperman et al., J. Acoust. Soc. Am. 103, (1998) 3. W.A. Kuperman and D.R. Jackson, Ocean Acoustics, Matched-Field Processing and Phase Conjugation in Imaging of Complex Media with Acoustics and Seismic Waves, Topics Appl. Phys. edited by Fink et al., Springer-Verlag Berlin Hiedelberg, 2002, pp H.C. Song et al., J. Acoust. Soc. Am. 103, (1998) 5. W.S. Hodgkiss et al., J. Acoust. Soc. Am. 105, (1999) 6. H.C. Song et al., J. Acoust. Soc. Am. 105, (1999) 7. J. Kim et al., J. Acoust. Soc. Am. 109, (2001) 8. S. Kim et al., J. Acoust. Soc. Am. 110, (2001) 9. J.F. Lingevitch et al., J. Acoust. Soc. Am. 111, (2002) 10. S. Kim et al., J. Acoust. Soc. Am. 114, (2003) 81

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