An experimental evaluation of the generalized sinusoidal frequency modulated waveform for active sonar systems.

This paper experimentally evaluates the Generalized Sinusoidal Frequency Modulated (GSFM) waveform, a generalization of the Sinusoidal Frequency Modulated (SFM) waveform. The Instantaneous Frequency (IF) of the GSFM resembles the time/voltage characteristic of a Linear Frequency Modulated (LFM) chirp waveform. Consequently, the GSFM possesses an Ambiguity Function (AF) that resembles a thumbtack shape. Practical sonar system design must consider two factors beyond the AF. The Spectral Efficiency (SE), defined as the ratio of energy in an operational frequency band to the total waveform energy, is another important metric for waveform design. The Peak-to-Average-Power Ratio (PAPR) quantifies how close the waveform is to constant amplitude. These measures predict a waveform's energy efficiency and ability to be accurately replicated on practical piezoelectric transducers, which have limits on both their bandwidth and maximum transmit power. This paper explores these design considerations for the GSFM waveform and evaluates its performance against a host of other well established waveforms using simulated and experimental acoustic data. The GSFM possesses superior SE, PAPR, and overall energy efficiency when compared to other thumbtack waveforms.

Spatial power spectral density estimation using a Welch coprime sensor array processor.

A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA product processor achieves an asymptotically unbiased spatial power spectral density (PSD) estimate using far fewer sensors than a conventional ULA beamformer, but at the expense of increased sidelobes and variance. Nonstationary underwater sonar environments often preclude increasing the number of snapshots required to achieve a desirable PSD variance. Bartlett's and Welch's methods improve PSD variance by O(K) at the expense of resolution without requiring additional snapshots by averaging uncorrelated PSD estimates obtained using K array segments. This paper proposes the Welch overlapping segment averaging product (WOSA-product) processor for coprime arrays to achieve unambiguous PSD estimates with desirable variance properties for passive direction of arrival estimation. The first two moments of the WOSA-product processor's spatial PSD estimate are derived in closed-form for spatially white Gaussian processes. Monte Carlo simulations verify the variance reduction predicted by the analytical derivation for white processes and planewave arrivals, and the effects of segment length on resolution, variance reduction, and peak sidelobe levels are discussed.

Spatial power spectral density estimation using a multitapered coprime sensor array minimum processor.

A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA Min processor achieves an asymptotically unbiased spatial power spectral density (PSD) estimate while approaching the variance of a ULA conventional beamformer. Nonstationary underwater sonar environments often preclude the number of snapshots required to achieve a desirable PSD variance. The multitaper method improves PSD variance by O(K) at the expense of resolution without additional snapshot cost by averaging uncorrelated PSD estimates obtained using a set of K orthogonal tapers. This paper proposes the multitapered Min processor to achieve unambiguous PSD estimates with desirable variance properties for passive beamforming scenarios. The probability density function and the first two moments of the MT-Min processor's PSD estimate are derived in closed-form for spatially white Gaussian processes. Simulations verify the variance reduction predicted by the analytical derivation for white processes and, by extension, for non-white processes. The multitaper method is then extended to an ad hoc mixture of Min and Product processors under constant noise plateau normalization that attenuates the spurious peaks occurring in the CSA PSD estimates in the presence of multiple planewave arrivals.

Processor dependent bias of spatial spectral estimates from coprime sensor arrays.

Coprime sensor arrays (CSAs) can estimate the directions of arrival of O(MN) narrowband plane wave sources using only O(M+N) sensors with the CSA product processor. Processing data from a finite aperture array effectively smears the true spatial power spectral density (PSD) with a kernel function determined by both the array geometry and the processing of the signals observed by the array. This paper examines the asymptotic behaviors of the kernel functions resulting from two different processors applied to a CSA sampling geometry in the limit of large aperture. The kernel functions of the product processed CSA and conventionally beamformed coprime sensor arrays (CBF CSA) are compared to the baseline of the kernel of a densely populated uniform line array (ULA) of similar aperture. At the limit of large aperture, the product processed CSA estimate is asymptotically unbiased like the ULA, while the CBF CSA estimate is not. The PSD estimates computed from the CSA processors are compared when spatially correlated Gaussian noise is an input to the array to highlight the bias issues.

Off-axis targets maximize bearing Fisher Information in broadband active sonar.

Broadband active sonar systems estimate range from time delay and velocity from Doppler shift. Relatively little attention has been paid to how the received echo spectrum encodes information about the bearing of an object. This letter derives the bearing Fisher Information encoded in the frequency dependent transmitter beampattern. This leads to a counter-intuitive result: directing the sonar beam so that a target of interest is slightly off-axis maximizes the bearing information about the target. Beam aim data from a dolphin biosonar experiment agree closely with the angle predicted to maximize bearing information.

Multiplicative and min processing of experimental passive sonar data from thinned arrays.

Sparse arrays reduce the number of sensors required to achieve a specific angular resolution by using sensor spacing greater than the half-wavelength. These undersampled sparse arrays require processing algorithms to eliminate aliasing ambiguities. Thinned arrays are sparse arrays whose sensor positions lie on an underlying equally spaced grid. Using data from a shallow water passive sonar experiment, this paper investigates two thinned array geometries (coprime and nested) along with two processing algorithms (multiplicative and min). Coprime and nested arrays consist of two interleaved Uniform Line Arrays (ULAs) where one or both of the ULAs are undersampled. Multiplicative and min processors combine the outputs of the conventionally-beamformed subarrays to estimate the spatial spectrum. While these nonlinear processors can suppress aliasing, they are often plagued by high sidelobes and cross term interference. This paper presents sparse array designs for a shallow waveguide that require 33% fewer sensors than a fully-sampled ULA and provide significant sidelobe attenuation. Experimental data analysis reveals that cross term interference dominates the spectral estimates for the coprime and nested multiplicative processors and the coprime min processor. The nested min processor outperforms its sparse counterparts due to its ability to contend with coherent multipath in the environment.

Comparing the effect of aperture extension on the peak sidelobe level of sparse arrays.

The reduced number of sensors in sparse arrays create high peak sidelobe levels (PSLs). This letter compares the PSLs of minimum redundancy arrays (MRAs), minimum hole arrays (MHAs), and co-prime sensor arrays (CSAs) (conventionally beamformed and product processed) with fully populated uniform linear arrays (ULAs) as a function of aperture using both numerical simulations and experimental data. This letter finds that PSLs of MRAs, MHAs, and conventionally processed CSAs are much higher than the ULA PSL and are largely insensitive to aperture extension. In contrast, CSA product processing decreases the PSL with increasing aperture, eventually matching the ULA PSL.

Dynamic Substrate for the Physical Encoding of Sensory Information in Bat Biosonar.

Horseshoe bats have dynamic biosonar systems with interfaces for ultrasonic emission (reception) that change shape while diffracting the outgoing (incoming) sound waves. An information-theoretic analysis based on numerical and physical prototypes shows that these shape changes add sensory information (mutual information between distant shape conformations <20%), increase the number of resolvable directions of sound incidence, and improve the accuracy of direction finding. These results demonstrate that horseshoe bats have a highly effective substrate for dynamic encoding of sensory information.

Generalized min-max bound-based MRI pulse sequence design framework for wide-range T1 relaxometry: A case study on the tissue specific imaging sequence.

This paper proposes a new design strategy for optimizing MRI pulse sequences for T1 relaxometry. The design strategy optimizes the pulse sequence parameters to minimize the maximum variance of unbiased T1 estimates over a range of T1 values using the Cramér-Rao bound. In contrast to prior sequences optimized for a single nominal T1 value, the optimized sequence using our bound-based strategy achieves improved precision and accuracy for a broad range of T1 estimates within a clinically feasible scan time. The optimization combines the downhill simplex method with a simulated annealing process. To show the effectiveness of the proposed strategy, we optimize the tissue specific imaging (TSI) sequence. Preliminary Monte Carlo simulations demonstrate that the optimized TSI sequence yields improved precision and accuracy over the popular driven-equilibrium single-pulse observation of T1 (DESPOT1) approach for normal brain tissues (estimated T1 700-2000 ms at 3.0T). The relative mean estimation error (MSE) for T1 estimation is less than 1.7% using the optimized TSI sequence, as opposed to less than 7.0% using DESPOT1 for normal brain tissues. The optimized TSI sequence achieves good stability by keeping the MSE under 7.0% over larger T1 values corresponding to different lesion tissues and the cerebrospinal fluid (up to 5000 ms). The T1 estimation accuracy using the new pulse sequence also shows improvement, which is more pronounced in low SNR scenarios.

Support for the beam focusing hypothesis in the false killer whale.

The odontocete sound production system is complex and composed of tissues, air sacs and a fatty melon. Previous studies suggested that the emitted sonar beam might be actively focused, narrowing depending on target distance. In this study, we further tested this beam focusing hypothesis in a false killer whale. Using three linear arrays of hydrophones, we recorded the same emitted click at 2, 4 and 7 m distance and calculated the beamwidth, intensity, center frequency and bandwidth as recorded on each array at every distance. If the whale did not focus her beam, acoustics predicts the intensity would decay with range as a function of spherical spreading and the angular beamwidth would remain constant. On the contrary, our results show that as the distance from the whale to the array increases, the beamwidth is narrower and the received click intensity is higher than that predicted by a spherical spreading function. Each of these measurements is consistent with the animal focusing her beam on a target at a given range. These results support the hypothesis that the false killer whale is 'focusing' its sonar beam, producing a narrower and more intense signal than that predicted by spherical spreading.

Mouth gape angle has little effect on the transmitted signals of big brown bats (Eptesicus fuscus).

Bats perform high-resolution echolocation by comparing temporal and spectral features of their transmitted pulses to the received echoes. In complex environments with moving prey, dynamically adapting the transmitted pulses can increase the probability of successful target representation and interception. This study further investigates the adaptive vocal-motor strategies of big brown bats (Eptesicus fuscus). During stationary target detection experiments, echolocation sounds were simultaneously recorded with high-speed, infrared video to examine the relationship of mouth position and movement to pulse characteristics among bats. All three bats produced strobe groups, but the proportion and frequency characteristics of the strobe group pulses differed for individual bats. Additionally, mouth gape angle had little effect on the emitted pulse characteristics, which suggests that laryngeal mechanisms drive changes in emitted pulses.

Cognitive adaptation of sonar gain control in the bottlenose dolphin.

Echolocating animals adjust the transmit intensity and receive sensitivity of their sonar in order to regulate the sensation level of their echoes; this process is often termed automatic gain control. Gain control is considered not to be under the animal's cognitive control, but previous investigations studied animals ensonifying targets or hydrophone arrays at predictable distances. To test whether animals maintain gain control at a fixed level in uncertain conditions, we measured changes in signal intensity for a bottlenose dolphin (Tursiops truncatus) detecting a target at three target distances (2.5, 4 and 7 m) in two types of sessions: predictable and unpredictable. Predictable sessions presented the target at a constant distance; unpredictable sessions moved the target randomly between the three target positions. In the predictable sessions the dolphin demonstrated intensity distance compensation, increasing the emitted click intensity as the target distance increased. Additionally, as trials within sessions progressed, the animal adjusted its click intensity even from the first click in a click train, which is consistent with the animal expecting a target at a certain range. In the unpredictable sessions there was no significant difference of intensity with target distance until after the 7th click in a click train. Together, these results demonstrate that the bottlenose dolphin uses learning and expectation for sonar gain control.

A deterministic compressive sensing model for bat biosonar.

The big brown bat (Eptesicus fuscus) uses frequency modulated (FM) echolocation calls to accurately estimate range and resolve closely spaced objects in clutter and noise. They resolve glints spaced down to 2 µs in time delay which surpasses what traditional signal processing techniques can achieve using the same echolocation call. The Matched Filter (MF) attains 10-12 µs resolution while the Inverse Filter (IF) achieves higher resolution at the cost of significantly degraded detection performance. Recent work by Fontaine and Peremans [J. Acoustic. Soc. Am. 125, 3052-3059 (2009)] demonstrated that a sparse representation of bat echolocation calls coupled with a decimating sensing method facilitates distinguishing closely spaced objects over realistic SNRs. Their work raises the intriguing question of whether sensing approaches structured more like a mammalian auditory system contains the necessary information for the hyper-resolution observed in behavioral tests. This research estimates sparse echo signatures using a gammatone filterbank decimation sensing method which loosely models the processing of the bat's auditory system. The decimated filterbank outputs are processed with [script-l](1) minimization. Simulations demonstrate that this model maintains higher resolution than the MF and significantly better detection performance than the IF for SNRs of 5-45 dB while undersampling the return signal by a factor of six.

Optimum array design to maximize Fisher information for bearing estimation.

Source bearing estimation is a common application of linear sensor arrays. The Cramer-Rao bound (CRB) sets a lower bound on the achievable mean square error (MSE) of any unbiased bearing estimate. In the spatially white noise case, the CRB is minimized by placing half of the sensors at each end of the array. However, many realistic ocean environments have a mixture of both white noise and spatially correlated noise. In shallow water environments, the correlated ambient noise can be modeled as cylindrically isotropic. This research designs a fixed aperture linear array to maximize the bearing Fisher information (FI) under these noise conditions. The FI is the inverse of the CRB, so maximizing the FI minimizes the CRB. The elements of the optimum array are located closer to the array ends than uniform spacing, but are not as extreme as in the white noise case. The optimum array results from a trade off between maximizing the array bearing sensitivity and minimizing output noise power variation over the bearing. Depending on the source bearing, the resulting improvement in MSE performance of the optimized array over a uniform array is equivalent to a gain of 2-5 dB in input signal-to-noise ratio.

Trading detection for resolution in active sonar receivers.

This paper proposes an active sonar receivers that offers a smooth trade-off between detection and resolution. A matched filter is the optimal detector of known signals in white Gaussian noise but may fail to resolve the targets if the time separation of targets is less than the mainlobe width of the autocorrelation function of the transmitted signal. An inverse filter achieves optimal resolution performance for multiple targets in the absence of noise, but amplifies the noise outside the signal bandwidth in a manner that makes it impractical in many realistic scenarios. The proposed active sonar receiver, the variable resolution and detection receiver (VRDR) combines the matched and inverse filter properties to achieve a smooth trade-off between detection and resolution. Simulated receiver operating characteristics demonstrate that for a range of dipole sonar targets, the performance of the VRDR is superior to the matched and inverse filter, as well as another previously proposed bandlimited inverse filter.

Designing nonuniform linear arrays to maximize mutual information for bearing estimation.

Estimating the bearing of a narrowband sound source using a towed horizontal array is a common array processing problem. This paper designs nonuniform linear symmetric arrays of fixed apertures for estimating the bearing of a sound source. Specifically, the hydrophone spacings for a symmetric linear array are chosen to maximize the upper bound on the mutual information between the true bearing and the estimated bearing in spatially white noise. The arrays maximizing the mutual information while nulling the forward endfire direction look significantly different from the uniform arrays commonly used in towed systems. Arrays maximizing mutual information are helpful when bearing estimation is considered as a quantization problem to assign the source to the correct partition. The optimal partitions for the array are designed using the Lloyd algorithm with an inner product distortion metric based on maximizing the likelihood function of the observations. In these approaches, increasing the mutual information and optimizing the partitions should reduce the probability of error (P(e)) in choosing the partition containing an unknown source. Simulation results with MAP and ML estimators demonstrate that the optimum arrays and partitions proposed here have a much lower P(e) than the uniform array and uniform partitions.

Information theory analysis of Australian humpback whale song.

Songs produced by migrating whales were recorded off the coast of Queensland, Australia, over six consecutive weeks in 2003. Forty-eight independent song sessions were analyzed using information theory techniques. The average length of the songs estimated by correlation analysis was approximately 100 units, with song sessions lasting from 300 to over 3100 units. Song entropy, a measure of structural constraints, was estimated using three different methodologies: (1) the independently identically distributed model, (2) a first-order Markov model, and (3) the nonparametric sliding window match length (SWML) method, as described by Suzuki et al. [(2006). "Information entropy of humpback whale song," J. Acoust. Soc. Am. 119, 1849-1866]. The analysis finds that the song sequences of migrating Australian whales are consistent with the hierarchical structure proposed by Payne and McVay [(1971). "Songs of humpback whales," Science 173, 587-597], and recently supported mathematically by Suzuki et al. (2006) for singers on the Hawaiian breeding grounds. Both the SWML entropy estimates and the song lengths for the Australian singers in 2003 were lower than that reported by Suzuki et al. (2006) for Hawaiian whales in 1976-1978; however, song redundancy did not differ between these two populations separated spatially and temporally. The average total information in the sequence of units in Australian song was approximately 35 bits/song. Aberrant songs (8%) yielded entropies similar to the typical songs.

Sound-diffracting flap in the ear of a bat generates spatial information.

Sound diffraction by the mammalian ear generates source-direction information. We have obtained an immediate quantification of this information from numerical predictions. We demonstrate the power of our approach by showing that a small flap in a bat's pinna generates useful information over a large set of directions in a central band of frequencies: presence of the flap more than doubled the solid angle with direction information above a given threshold. From the workings of the employed information measure, the Cramér-Rao lower bound, we can explain how physical shape is linked to sensory information via a strong sidelobe with frequency-dependent orientation in the directivity pattern. This method could be applied to any other mammal species with pinnae to quantify the relative importance of pinna structures' contributions to directional information and to facilitate interspecific comparisons of pinna directivity patterns.

Information entropy of humpback whale songs.

The structure of humpback whale (Megaptera novaeangliae) songs was examined using information theory techniques. The song is an ordered sequence of individual sound elements separated by gaps of silence. Song samples were converted into sequences of discrete symbols by both human and automated classifiers. This paper analyzes the song structure in these symbol sequences using information entropy estimators and autocorrelation estimators. Both parametric and nonparametric entropy estimators are applied to the symbol sequences representing the songs. The results provide quantitative evidence consistent with the hierarchical structure proposed for these songs by Payne and McVay [Science 173, 587-597 (1971)]. Specifically, this analysis demonstrates that: (1) There is a strong structural constraint, or syntax, in the generation of the songs, and (2) the structural constraints exhibit periodicities with periods of 6-8 and 180-400 units. This implies that no empirical Markov model is capable of representing the songs' structure. The results are robust to the choice of either human or automated song-to-symbol classifiers. In addition, the entropy estimates indicate that the maximum amount of information that could be communicated by the sequence of sounds made is less than 1 bit per second.