Frequency-domain Beamforming Research Articles

Beamforming using the fractional fourier transform

We present a new method of beamforming using the fractional Fourier transform (FrFT). This method encompasses the conventional minimum mean-squared error (MMSE) beamforming in the frequency domain or spatial domain as special cases. It is especially useful for applications involving chirp signals such as signal enhancement problems with accelerating sinusoidal sources where the Doppler effect generates chirp signals and a frequency shift and active radar problems where chirp signals are transmitted. Numerical examples demonstrate the potential advantage of the proposed method over the ordinary frequency or spatial domain beamforming for a moving source scenario.

Localization of dolphin whistles through frequency domain beamforming using a narrow aperture audio/video array

Correlating the acoustic and physical behavior of marine mammals is an ongoing challenge for scientists studying the links between acoustic communication and social behavior of these animals. This talk describes a system to record and correlate the physical and acoustical behavior of dolphins. A sparse, short baseline audio/video array consisting of 16 hydrophones and an underwater camera was constructed in a cross configuration to measure the acoustic signals of vocalizing dolphins. The bearings of vocalizing dolphins were estimated using the broadband frequency domain beamforming algorithm for sparse arrays to suppress grating lobes of Thode et al. [J. Acoust. Soc. Am. 107 (2000)]. The estimated bearings from the acoustic signals were then converted to video image coordinates and a marker was placed on the video image. The system was calibrated both at an indoor tank and from an outdoor dock at UMass Dartmouth prior to field tests in a natural lagoon at the Dolphin Connection on Duck Key, FL. These tests confirmed that the system worked well within the limits of underwater visibility by consistently placing the marker on or near the whistling or echolocating dolphin. [Work supported by NSF Ocean Sciences.]

Frequency-domain partially adaptive array algorithm combined with CFAR technique

A frequency-domain partially adaptive beamformer is proposed to reduce the computational complexity of conventional frequency-domain adaptive beamformers. The proposed beamformer only adapts the weights that correspond to the frequency bins expected to contain interferences using a cell-averaging constant false alarm rate (CA-CFAR) processor. The false alarm rate is also changed adaptively to achieve optimum partial adaptation.

Multi-channel estimation of time residuals from broadband seismic data using multi-wavelets

Abstract We describe a new multi-channel procedure for estimating arrival time residuals from seismic array data. It incorporates aspects of three traditional array processing methods: frequency-domain beamforming, time-domain beamforming, and principal-component analysis. We start by applying the multi-wavelet transform to the data, which yields a suite of narrow-band seismograms. We use the multi-wavelet transform, instead of the windowed Fourier transform, for superior control over both the time and frequency resolution. We employ a beamforming procedure that uses principal component analysis on the transformed, time-aligned data. The values in the principal component vector and value pair are used to calculate a measure of coherence analogous to semblance. A measure of the misfit of the data to our plane-wave model is contained in the phase differences in the principal component vector. The phase differences can be converted directly to time residuals, but they are only resolvable to a fraction of the analyzing wavelength. Hence, our method is a staged process that moves from lower to higher analyzing frequency bands. We present two data examples that illustrate the wide range of spatial and temporal scales over which this approach can be applied. First, we determine time residuals for the deep-focus Bolivian earthquake of 1994 for a set of broadband stations spread over most of southern California. The time residuals had a range of 2 sec, and after their removal, we were able to stack the data to over 1.0 Hz. Second, we study a local event recorded by high-frequency sensors at an array in Turkmenistan with an aperture of less than 1 km. We found that the time residuals only had a range of 0.02 sec, but by removing them, we significantly improved the stack of the data for the arrival's dominant frequency.

Minimum variance distortionless response beamforming of acoustic array data

An array of hydrophones is towed below the sea surface so as to sample the underwater acoustic pressure field in both space and time, while a land-based array of microphones is used to sense the atmospheric acoustic environment which, at the time, was dominated by a single source of broadband energy. After transformation from the time domain to the frequency domain, the sensor outputs from each array are weighted and combined in the spatial domain (beamformed) so as to produce a frequency–wave number power spectrum, which displays the power spectral density distribution of the various signal and noise sources as a joint function of frequency and wave number. The frequency-domain beamforming (or spatial filtering) process enables both conventional and optimal estimation of the frequency–wave number power spectrum. The optimal spatial filtering technique used here is commonly referred to as the Minimum Variance Distortionless Response (MVDR) beamformer which requires inversion of the observed narrow-band cross-power spectral matrix at each frequency of interest. A comparison of the frequency–wave number power spectra estimated by the two spatial filtering techniques shows that the MVDR beamformer enables the various sources of acoustic energy to be more clearly delineated in frequency–wave number space. The MVDR beamformer is a data-adaptive spatial filter which is observed to suppress sidelobes, to enhance the spatial resolution of an array through narrower beamwidths, and to provide superdirective array gain at frequencies well below the design frequency of an array. By extending the processing to include the data from another type of towed array, it is shown that frequency–wave number analysis, when incorporated with MVDR beamforming, constitutes a powerful diagnostic tool for studying the self-noise characteristics of towed arrays.

A small towed beamforming array to identify vocalizing resident killer whales ( Orcinus orca) concurrent with focal behavioral observations

Investigations of communication systems benefit from concurrent observation of vocal and visible behaviors of individual animals. A device has been developed to identify individual vocalizing resident killer whales ( Orcinus orca) during focal behavioral observations. The device consists of a 2-m, 15-element hydrophone array, which is easily towed behind a small vessel, on-board multi-channel recorders, and real-time signal processing equipment. Acoustic data from the hydrophones are digitized and processed using broadband frequency-domain beamforming to yield frequency-azimuth (FRAZ) and “directo-gram” displays of arriving sounds. Based upon statistical analysis of independent portions of typical killer whale calls, the precision of the angle-of-arrival estimate ranges from ±0° to ±2.5° with a mean precision of ±1.5°. Echolocation clicks also are resolved precisely with a typical −6 dB mainlobe width of ±2.0°. Careful positioning of the array relative to the animals minimizes the effects of depth ambiguities and allows identification of individual sources in many circumstances. Several strategies for identifying vocalizing individuals are discussed and an example of a successful identification is described. Use of the array with resident killer whales did not interfere with vessel maneuverability, animal tracking, or behavioral sampling of focal individuals. This localization technique has promise for advancing the abilities of researchers to conduct unbiased behavioral and acoustic sampling of individual free-ranging cetaceans.

Superdirectivity design for a sphere-buffled microphone array

For the signal extraction from a diffuse sound field, the superdirecitonal microphone array seems to be more stable and more effective than the noise canceling microphone array system. In this research, for the sphere-baffled microphone array (SBM), the superdirectivity characteristic was designed by the frequency domain beamforming method and the complex least mean square algorithm. The frequency domain beamforming is a method for a broadband beamforming. There is a possibility of improvement of the directivity frequency characteristic. The SBM is an array which was embedded 36 elements on the rigid diffractive sphere of 8.84 cm radius. An advantage of SBM is its isotropy. When the directivity characteristic was fixed for a definite direction, only the shift coefficent can be used to change the mainlobe direction. This idea can be easily generalized into the three-dimensional mainlobe control. In a typical design calculation, for the beamwidth of −3 dB, 30° was achieved at the frequency 2 kHz. This characteristic is comparable to that of a larger size microphone, which is called a shotgun microphone.

Estimation of slowness vectors and their uncertainties using multi-wavelet seismic array processing

AbstractWe have developed a new seismic array data processing method to produce slowness vector estimates and an objective measure of their uncertainties in the form of statistical confidence intervals. The slowness vector, which is typically transformed into bearing and velocity, is a key parameter used for identifying seismic phases and for event source location. Our method, multi-wavelet beamforming, is closely related to both time-domain and frequency-domain beamforming. The major advantage of multi-wavelet beamforming is that it produces multiple estimates of the slowness vector that are approximately statistically independent. First, a set of wavelet transforms is applied to the data in a manner analogous to the use of the windowed Fourier transform. Next, for each wavelet transform, we calculate semblance, a measure of signal coherence, for a range of possible slowness vectors. Then, the slowness vector estimate associated with that transform is the vector that produces the largest semblance value. The multiple slowness vector estimates can be treated as samples from a probability distribution, whose “center” we estimate using the mean, the median, and an M-estimator. Uncertainty intervals are calculated for these estimators by applying the jackknife statistical method. The intervals for the mean estimator appear to be true statistical confidence intervals, but the estimates can be biased by a directional noise field in low signal-to-noise circumstances. The median estimates are less biased by a directional noise field but sometimes underestimate the uncertainty. The M-estimator produces less-biased estimates while appearing to estimate correctly their uncertainty.

Simulation of fixed microphone arrays for directional hearing aids.

Microphone arrays with fixed optimum weights are known to suppress the background noise and reverberation that severely reduce the effectiveness of conventional hearing aids. By means of a general technique for digital frequency-domain implementation of optimum broadband arrays that was developed recently [C. Liu and S. Sideman, J. Acoust. Soc. Am. 98, 241-247 (1995)], a practically promising system is proposed to realize the arrays with the well-known sensitivity-constrained superdirective beamforming weights, and with five identical omnidirectional, cardioid, hypercardioid, or dipole microphones, respectively, in the endfire or broadside configurations, which were theoretically proposed by Stadler and Rabinowitz [J. Acoust. Soc. Am. 94, 1332-1342 (1993)]. The digital broadband frequency-domain beamforming system allows the broadband superdirective beamforming weights to be faithfully and independently applied to each frequency component of the signal. The practical application of this technique is demonstrated through computer simulation of the system in anechoic situations. Furthermore, its performance in simulated reverberant environments is evaluated.

Observation of an aircraft transit using a land-based acoustic array

A turbo-prop aircraft flew at a constant altitude and speed over and along the axis of a line array consisting of 15 microphones spaced 0.9 m apart. The acoustic data from the microphones were processed by a frequency-domain beamformer, which led to the acoustical Doppler effect being observed on the various output displays of the processor. Color displays showing the variation of the beamformer’s output power as a function of frequency and angle of arrival are presented here for a conventional beamformer, an adaptive beamformer, and an adaptive beamformer with a weight norm constraint. Adaptive beamforming maximizes the array gain resulting in the spatial leakage being lower and the widths of the beams being narrower when compared with conventional beamforming. Imposing an upper bound on the norm of the adaptive weight vector reduces the signal suppression that occurs in adaptive beamforming as a result of system errors. The observed variation of the Doppler shift in the propeller blade rate with the angle of arrival is compared with the variation predicted using an isospeed sound propagation model.

Optimal time-domain beamforming with simulated annealing including application of a p r i o r i information

A fast simulated annealing algorithm is developed for an optimal time-domain beamformer. The optimal beamformer has greater resolution than the standard frequency-domain beamformers, which discard information by averaging the data to form a correlation matrix and remove degrees of freedom by collapsing the number of unknown parameters. The optimal ambiguity function uses the data in raw form and depends on all of the unknown source parameters. This approach is practical with simulated annealing. A specialized simulated annealing algorithm is required to search for the source bearings and time series because the parameters are analogous to a mixture of substances with different freezing points. Examples are presented to demonstrate that the optimal beamformer can be enhanced significantly with a priori information and to illustrate the effects of source level and bandwidth, noise level, array size, and number of sources.

Slowness araising in the discrete radon transform:A multirate system approach to beamforming

Time-domain beamforming with an array of space-time samples is equivalent to performing a discrete Radon transform (DRT). The result is a function of slowness (inverse velocity) and time intercept. As a function of slowness, beamforming decimates each channel in proportion to its distance from the beamformer reference channel. This viewpoint allows the slowness bandwidth to be expressed as a function of the array spatial locations and the normalized temporal bandwidth of the received waveforms. These relationships determine the required temporal sample rate increase at each channel when interpolation beam-forming is used to avoid slowness aliasing. The conclusions regarding the slowness sampling density are applicable as well to frequency domain beamforming, where the beams must also be computed at discrete values of slowness. A polyphase filter structure is shown to be particularly suited to interpolation beamforming. Examples are presented showing the slowness aliasing that results if either the temporal bandwidths or the array spatial aperture are too large. The beamformer output energy averaged over a time window is shown to require twice the slowness sampling rate as the beamformer output itself.

A frequency-domain beamforming algorithm for wideband, coherent signal processing

Coherent detection processors for sonar (e.g., matched filters for active systems) require continuous time series as input and have conventionally been coupled to delay-and-sum time-domain beamformers. As an alternative, we have extended the FFT beamforming technique to be functionally equivalent to a time-domain beamformer. The procedure utilizes the ‘‘analytic’’ representations of the hydrophone signals as input and produces continuous beam time series as output, thereby allowing for complete flexibility in post-beamformer processing. The method will be applicable when the array elements are uniformly spaced, and when a large fraction of the possible beams are to be computed. In such cases, the algorithm offers the following advantages relative to a conventional time-domain beamformer: (1) elimination of the need for a high input sampling rate to achieve acceptable beam patterns—the frequency-domain approach is insensitive to the sampling rate provided this exceeds the (bandpass) Nyquist rate; (2) reduction of high beam sidelobe levels due to dead or malfunctioning array elements—the response of missing array elements is readily estimated in the frequency domain by interpolating from the spectra of neighboring sensors; and (3) potential reductions in the computational load when the array is large or the center-frequency/bandwidth ratio of the signal is high. Using a general purpose array processor we have demonstrated near real-time evaluation of a complete beam set for a 128-channel linear array. Computer-generated ‘‘acoustic’’ data were used to confirm that the software preserves the envelope, spectrum, and temporal correlation properties of signals while yielding near-theoretical performance in reducing beam sidelobe levels.

Wideband, frequency-domain beamforming for coherent signal processing

Coherent detection processors for sonar (e.g., matched filters for active systems) require continuous time series as input and have conventionally been associated with delay-and-sum time-domain beamformers. As an alternative, we have extended frequency-domain beamforming techniques to retain the coherence of wideband signals and have demonstrated efficient software for computing continuous time-series beams for flexible postprocessing. Using computer-generated “acoustic-array” data, the beamformer was shown to preserve the envelope, spectrum, and correlation properties of signals while yielding near theoretical performance in reducing beam side-lobe levels. Advantages over a conventional delay-and-sum beamformer are: (1) elimination of the need for high input sampling rates to achieve acceptable beam patterns—the frequency-domain approach is insensitive to the sampling rate provided it exceeds the (band-pass) Nyquist rate; (2) reduction of high-beam side-lobe levels caused by malfunctioning array elements—the response of missing array elements is readily estimated in the frequency domain by interpolating from the spectra of neighboring sensors; (3) minimization of hardware requirements—all stages of signal processing (bandpass filtering, holefixing, beamforming, time-line reconstruction, and matched filtering) can be efficiently performed in a general purpose array processor.

Formulation of the maximum signal-to-noise ratio array processor in beam space

The maximum signal-to-noise ratio (SNR) processor as formulated by Edelblute et al. [J. Acoust. Soc. Am. 41, 199–206 (1967)] has proved extremely useful in the analysis and interpretation of sonar data. In a known noise field this processor uses an optimum set of weights (or shading coefficients) derived from the crosspower spectral matrix of receiver noise outputs. In this paper an alternative maximum SNR processor is derived. This processor transforms the outputs of a conventional frequency domain beamformer in such a way that the SNR in the transformed beam is maximized. Expressions for the transformation (i.e., the complex beam weights) and the resulting array gain are derived. Some general properties of the beam space formulation are discussed and conditions for its equivalence to the element space formulation of Edelblute et al. are determined. Examples using both simulated and sonar data are given to compare the beam and element space formulations.

The TAP III beamforming system

The Three-Array Processor (TAP III) beamforming system incorporating both wide-band time-domain beamforming and narrow-band frequency-domain beamforming is described. This paper briefly develops the beamforming theory and shows how the fast Fourier transform (FFT) is applied to accomplish frequency-domain beamforming. The frequency-domain beamformer operates in the frequency domain to form beams and power spectrum data over narrow frequency bands of interest. A real-time digital filtering technique is used to extract the narrow bands of interest from the broad-band input signal. The frequency-domain beamformer accomplishes real-time digital filtering and beamforming by using a high-speed array processor to do the complex calculations and data handling required by the algorithm. The time-domain beamformer operates in parallel with the frequency-domain beamformer to form up to 16 broad-band beams in the time domain. A programmable all-pass digital filter is used to create the fine time delays required by the time-domain beamformer.

Shifted sideband beamformer

A fundamentally different time domain beamformer structure is described which can be used to process bandpass sensor signals efficiently. The beamformer operates directly on complex, frequency translated, single sideband representations of the input signals to obtain a similar representation of the beam output. Such representations are typically obtained by complex demodulation of the signals to facilitate the use of bandwidth sampling procedures. This new technique, which is referred to as the shifted sideband beamformer, is functionally a time-domain beamformer but it combines attributes of both time-domain and frequency-domain beamforming. Shifted sideband beam-forming has the advantage that beamformer vernier delay and throughput requirements depend on the frequency content of the translated band rather than of the original band. This paper discusses the potential hardware savings associated with shifted sideband beamforming in terms of analog to digital conversion, cable bandwidth, digital processing and, also, signal conditioning hardware. The impact of delay quantization on beam-pattern structure is compared for a shifted sideband and a conventional digital implementation. Beamformer throughput is also analyzed for both implementations. A further reduction in the beamformer throughput requirement is demonstrated by the use of digital interpolation in conjunction with the shifted sideband beam-forming concept.

Comparison of shifted sideband and conventional beamforming techniques

For many array configurations the exact time delays required for beamsteering impose prohibitingly large sample rate requirements on digital beamformer implementation. This necessitates the use of approximate time delays to achieve moderate sample rate requirements. For conventional beamformer implementations this degrades the sidelobe structure of the beampatterns. This degradation is also experienced by shifted sideband beamformers (SSB) which utilize frequency translated single sideband representations of the input signals [J. Acoust. Soc. Am. 64, S116(A) (1978)]. However, since beamsteering is performed on translated signals rather than on the original signals, degradation of the beampattern for the SSB is less sensitive to absolute time-delay errors than for the conventional approach. This result is supported analytically and by examples. The phase shift beamformer, a limiting case of both a frequency domain beamformer and the SSB, is considered. Beamsteering errors experienced by the phase shift beamformer at frequencies other than that for which it was designed are discussed. Analytical results and examples are presented which demonstrate that these errors can be eliminated with the SSB.

Shifted band beamformer: Theory and concept

This paper introduces a fundamentally different beamformer structure which can be used to process bandpass sensor signals.The beamformer operates directly on frequency translated versions of the input signals to compute a frequency translated version of the beam output. This new technique, which is referred to as the shifted band beamformer, is functionally a time domain beamformer but it combines attributes of both time and frequency domain beamforming. It is especially compatible with systems where the sensor data is initially basebanded to facilitate the use of bandwidth sampling procedures. Beamformer vernier delay and throughput requirements are relaxed since the delay quantization and beam output rate depends on the highest frequency component of the basebanded signal rather than that of the bandpass signal. The shifted band beamformer can also use interpolation [R. G. Pridham and R. A. Mucci, “A Novel Approach to Digital Beamforming,” J. Acoust. Soc. Am. 63, 425–434 (1978)] to achieve further hardware savings. Relationship between the new structure and frequency domain beamforming is also discussed.

Vertical directionality of low-frequency ambient noise in the ocean

Using a 532-m-long vertical array suspended near the sound channel axis, the vertical directionality of ambient noise in the 10–50-Hz frequency band was measured at a location about 200 miles southwest of San Diego. The outputs from 20 hydrophones, configured as a nonuniform spaced array, were digitized for later beamforming. The frequency domain beamforming produced beam noise level versus direction for 200 discrete frequencies, separated by about 0.2 Hz, covering the band from about 10–50 Hz. At times when there were no ships in the immediate vicinity of the array, the noise in the 20–50-Hz interval was concentrated in a near horizontal direction with most of the noise included in the angular segment from −14° to +14° with respect to the horizontal. Below about 20 Hz this strong, near-horizontal lobe of high noise appears to diminish with decreasing frequency. In many instances in the 10–15-Hz band, the noise no longer shows the strong concentration near the horizontal but instead appears to be almost isotropic. [Work supported by ONR.]