Superdirective Array Research Articles

A superdirective array of phase shift sources

A superdirective array of audio drivers is described, which is compact compared with the acoustic wavelength over some of its frequency range. In order to minimize the overall sound power output, and hence reduce the excitation of the reverberant field when used in an enclosed space, the individual drivers are made directional by using phase shift enclosures. The motivating application for the array is the enhancement of sound from a television, in a particular region of space, to aid hearing impaired listeners. The design is initially investigated, using free-field simulations, by comparing the performance of 8 monopoles, 8 phase shift loudspeakers, and a double array of 16 monopoles, with a contrast maximization formulation. The construction and testing of an array of 8 drivers is then discussed, together with its measured response in an anechoic environment. The result of using acoustic contrast maximization is then compared with a least squares formulation, which demonstrates that the performance of the least squares solution can be made similar to that given by acoustic contrast maximization in this application, with a suitable choice of the target field.

A Multiport Impedance-Matching Feed Network for Directional Antennas

The proposed multiport impedance-matching feed network simultaneously optimizes the operating bandwidth and gain of a two-element superdirective antenna array. Maximum directivity of an N-element isotropic radiator approaches N2 as the element spacing approaches zero. Additionally, the operating bandwidth of superdirective antenna arrays is narrowband. Utilizing a multiport impedance-matching network will increase the operating bandwidth. Special consideration is required in designing the circuit so that the losses introduced by the matching network do not significantly degrade the absolute gain of the antenna array.

Design of Robust Superdirective Arrays With a Tunable Tradeoff Between Directivity and Frequency-Invariance

Frequency-invariant beam patterns are often required by systems using an array of sensors to process broadband signals. If the spatial aperture is shorter than the involved wavelengths, using a superdirective beamforming is essential to get an efficient system. In this context, robustness of array imperfections is a crucial feature. In the literature, only a few approaches have been proposed to design a robust, superdirective, frequency-invariant beamformer based on filter-and-sum architecture; all of them achieve frequency-invariance by imposing a desired beam pattern. However, the choice of a suitable desired beam pattern is critical; an improper choice results in unsatisfactory performance. This paper proposes a new method of array synthesis that allows the design of a robust broadband beamformer with tunable tradeoff between frequency-invariance and directivity, without the need for imposing a desired beam pattern. The latter is defined as a set of variables that do not depend on frequency and are included in the vector of variables to be optimized. To this end, a suitable cost function has been devised whose minimum can be found in closed form. Therefore, the method is analytical and computationally inexpensive. In addition, a technique that allows obtaining a beam pattern with a linear phase over frequency is described. The results show the effectiveness of the proposed method in designing robust superdirective beam patterns for linear arrays receiving far-field signals, with special attention to microphone arrays of limited aperture.

A Computationally Efficient Procedure for the Design of Robust Broadband Beamformers

Broadband beamformers using superdirective arrays are sensitive to errors in the sensor characteristics. Recently, a method that considers the probability distributions of errors to synthesize a robust optimal beamformer has been proposed. Unfortunately, the entire synthesis process may become unacceptably long due to the computational burden of the cost function. Here, we present an alternative procedure for computing the same cost function, drastically reducing such a problem.

The synthesis of robust broadband beamformers for equally-spaced linear arrays

Broadband beamforming applied to superdirective arrays is known to be highly sensitive to transducers characteristics errors. Recently, an effective method to synthesize a robust, broadband, data-independent, filter-and-sum beamformer, which considers the probability distributions of errors, has been proposed. It considers an array with arbitrary lay-out and provides a spatial directivity pattern close to the desired one. Unfortunately, the evaluation of the cost function requires a computational load and an amount of memory that increases very quickly with the transducers and the filter coefficients. As the synthesis process requires an iterative minimization, it may become unacceptably long. In this paper, an alternative procedure for evaluating the same cost function is presented, drastically reducing such problems and without introducing any approximation. The only additional constraint is on the antenna which must be an equally-spaced linear array. This procedure makes it much easier to apply the above-mentioned synthesis method to a wide panorama of practical situations.

Superdirective Wideband Array of Planar Monopole Antenna With Loading Plates

A wideband superdirective array of a two-element planar plate monopole antenna is presented. Initially, a two-element, closely spaced array of a simple rectangular planar monopole antennas is considered. Based on a relative phase shift of 100 between the two elements, over the 3-6-GHz bandwidth this antenna array provides directivity of 3.5-6.9 dB. In order to achieve a higher directivity over a wider frequency bandwidth, a pair of small parallel plates is attached to the radiating edges of the rectangular planar monopole antenna. It is shown that this antenna array with element spacing of 2 cm and a relative phase shift of 135 between the elements produces 3.1-7.5 GHz impedance bandwidth with 7.7-10.1 dB of directivity. This antenna has an efficiency of 60%-91% over the bandwidth. Simulation and experimental results are provided and discussed.

A Stochastic Approach to the Synthesis of a Robust Frequency-Invariant Filter-and-Sum Beamformer

Frequency-invariant beam patterns (FIBPs) are often required by systems using an array of sensors to process broadband signals. Although several methods have been proposed to design a broadband beamformer (typically characterized by a finite impulse response (FIR) filter for each sensor) with an FIBP, until now, the case in which the spatial aperture is shorter than the involved wavelengths has very rarely been considered. In such a case, the use of a superdirective beam pattern is essential to attaining an efficient system. In this context, robustness to array imperfections and random errors is a very crucial feature. In this paper, a method to design a robust broadband beamformer that produces an FIBP for a data-independent superdirective array is proposed and compared with other potential approaches. The method generates a far-field beam pattern that reproduces the desired profile over a very wide frequency band (also if the array is shorter than the wavelength) and is based on a stochastic approach to the direct synthesis of the FIR filters. The very simple implementation and the resulting robustness of the attained filter-and-sum beamformer to array imperfections increase the applicability of the system. This fact is particularly important in the context of a audio signal processing carried out by microphone arrays, which is the main application considered in this paper.

Eigencurrent analysis of resonant behavior in finite antenna arrays

Resonant behavior in a finite array that appears as (modulated) impedance or current-amplitude oscillations may limit the array bandwidth substantially. Therefore, simulations should predict such behavior. Recently, a new approach has been developed, called the eigencurrent approach, which can predict resonant behavior in finite arrays. A study of line arrays of either E- or H-plane-oriented strips and rings in free space and in half-spaces confirms our conclusion in earlier research that resonant behavior is caused by the excitation of one of the eigencurrents. The eigenvalue (or characteristic impedance) of this eigencurrent becomes small in comparison to the eigenvalues of the other eigencurrents that can exist on the array geometry. We demonstrate that the excitation of this eigencurrent results in an edge-diffracted wave propagating along the surface of the array, which may turn into a standing wave. In that case, the amplitudes and phases of the element impedances show the same standing-wave pattern as those of the excited eigencurrent. We demonstrate that the phase velocity of this wave is approximately equal to or slightly larger than the free-space velocity of light. Finally, we throw light on the relation between the excitation of eigencurrents with a small eigenvalue and the behavior of super directive arrays.

Designing superdirective microphone arrays with a frequency-invariant beam pattern

Frequency-invariant beam patterns are often required in systems using an array of sensors to process broadband signals. Although several methods have been proposed to design a broadband beamformer [typically realized with a finite-impulse-response (FIR) filter for each sensor] with a frequency-invariant beam pattern (FIBP), until now the case in which the spatial aperture is shorter than the involved wavelengths has very rarely been addressed. In such a case, the use of a superdirective beam pattern is essential for attaining an efficient system. In this paper, a novel method to design a broadband beamformer that produces an FIBP for a data-independent superdirective array is proposed and compared with other potential approaches. The method generates a far-field beam pattern that reproduces the desired profile over a very wide frequency band, also if the array is shorter than the wavelength. Two steps are necessary: 1) the generation of many apodizing windows at different frequency values by a stochastic method and 2) the synthesis of the FIR filters with the Parks-McClellan technique. At the end of the design chain, the very simple implementation and the robustness of the attained broadband beamformer to array imperfections increases the applicability of the system, for instance, in audio signal processing using microphone arrays

A monopole superdirective array

In principle, the end-fire directivity of a linear periodic array of N isotropic radiators can approach N/sup 2/ as the spacing between elements decreases, provided the magnitude and phase of the input excitations are properly chosen. Thus, the directivity of a two-element array of isotropic radiators would approach a value of four, that is, 6 dB higher than that of a single isotropic radiator. We have conducted a theoretical, computational, and experimental study for a two-element superdirective array of resonant monopoles. In agreement with the theoretical and computational curves, the measured gain of the monopole array does indeed continually increase with decreasing spacing of the monopoles, provided the relative magnitudes and phases are maintained. However, for very small separation, maximum achievable gain is not reached due to the presence of ohmic loss.

Robust supergain beamforming for circular array via second-order cone programming

The phenomenon of supergain for a circular array and its robust beamforming are presented. The coplanar superdirective array gain of the circular array, although it is not so extreme as an endfire line array, outperforms a lot over that of a conventional delay-and-sum beamformer in isotropic noise fields when the inter-element spacings are much smaller than one-half wavelength. However, optimum beamforming algorithms can be extremely sensitive to slight errors in array characteristics. The performance are known to degrade significantly if some of underlying assumptions on the sensor array is violated. Therefore, white noise gain constraint is used to improve the robustness of the supergain beamformer against random errors. We show that the design of the weight vector of robust supergain beamformer can be reformulated as a form of second-order cone programming and resolved efficiently via the well-established interior point method. Results of computer simulation for a 24-element circular array confirm satisfactory performance of the approach proposed in this paper.

Performance of a superdirective line array in nonideal environments

Superdirective line arrays can provide high gains relative to their dimensions, whenever the inter-element spacing is much less than half a wavelength. However, their performance can be degraded by system noise. System noise can result from limitations in electronic components, inter-element mismatch in gain or phase, or from scatter from array components. Using state-of-the-art electronics and digital signal processing one can drastically reduce the errors due to electronic noise as well as those due to gain and phase mismatch. Thus, acoustic scatter from the array components can determine the performance limit. Since theoretical developments typically assume plane waves incident on idealized point receivers, it is not all that surprising that array performance fails to meet theoretical expectations! This is especially true if the array is merely one component within a much larger system. Nonetheless, impressive gains can still be realized from superdirective arrays even with significant departures from the idealized model. To support this observation, we present results obtained using a 0.8 m long, 5th order superdirective receiver that is part of a much larger system used to study scattering from marine sediments.

Superdirective and gradient sensor arrays

During the late 1960s and the 1970s, underwater acoustic investigators examined superdirective and gradient sensor systems in order to enhance submarine detection capabilities for surface ships and maritime aircraft. Simple gradient processing had already been used in both in-air acoustic systems (cardioid and super-cardioid microphones) as well as radio and radar applications. Superdirective techniques were known [R. L. Pritchard, J. Acoust. Soc. Am. 25, 879 (1953)] and sometimes exploited in radar systems. It was quickly demonstrated that simple gradient sensors and modest degrees of superdirective array processing were possible, although self-noise and the ability to calibrate hydrophones limited the processing gains achievable. Circular superdirective arrays were used extensively by the Defence Research Establishment Atlantic for noise directionality measurements in the frequency range 4 Hz to about 1 kHz and considered for naval ASW applications until the superiority of oil-filled conventional arrays became apparent. Nevertheless, the significant theoretical and practical development of spatial harmonic beamforming and direction finding was completed. Although much of this work was not considered classified, neither was it widely published. This presentation will review the concepts developed and progress made. Beamforming, noise mitigation and calibration issues are covered.

Experimental performance analysis of a superdirective line array

Superdirective line arrays can provide a significant array gain from a structure that is relatively small in terms of acoustic wavelengths. However, system imperfections, electronic noise and acoustic scatter from the array structure can degrade their performance. An acoustic calibration of a six-element line array, 0.8 m in length, has been performed over the frequency range 1 to 4 kHz in order to investigate the performance of a real array. The data is used to identify the angular variation of the hydrophone outputs and the phase difference between hydrophone pairs. These angular responses are analyzed in terms of a modal series in order to quantify the variations and help identify the source of perturbations. The effects of imperfections are also investigated by synthesising superdirective arrays of order 1 to 5 and monitoring how the array gain varies for both deterministic signals and ambient acoustic noise. These results are compared with theoretical predictions. Further evidence of the variation in performance is gained by comparing the output of different implementations of lower order arrays, synthesized from subsets of the full array. The results indicate the influences that the array structure may have on the performance of the array.

Measured performance of an endfire superdirective line array in littoral water

Superdirective line arrays can provide high gains whenever the interelement spacing is much less than half a wavelength. In practice these arrays have fallen short for two reasons: First, performance degrades appreciably in the presence of uncorrelated system noise. Second, the optimum array weights are specific to the form of the noise field and the choice of these weights is often sensitive to deviations from that noise field. Furthermore, since the process involves computing signal differences between hydrophones, the signal to noise ratio (SNR) degrades as the steering angle approaches broadside. In spite of these drawbacks, a superdirective array can provide substantial improvement over a conventional array in specific instances. For example, the present application requires an endfire array of limited extent (1 m in length) and wide bandwidth (1–5 kHz) making a conventional array impractical. Moreover, improvements in array hardware have substantially reduced uncorrelated system noise, and increased computer speed makes it reasonable to process data using several weighting schemes. In this paper, the superdirective array will be described and its measured performance will be compared to theoretical predictions.

Automatic identification of sound source direction based on neural networks

Automatic identification of sound sources direction is still an unsolved problem in contemporary teleconferencing systems. Speech signals coming from various directions not only interfere with the target signal but also can obscure it. People have difficulty in understanding speech with background noise, high reverberation, and/or with many concurrent speakers. Source identification system should allow tracking a target speaker automatically without much delay in order to avoid picking up concurrent speakers by the same microphone channel. In literature one can find two approaches to this problem. One of them is a classical approach to this problem based on delay-summation algorithms, superdirective arrays and adaptive algorithms, and nonlinear frequency domain microphone array beamformers, etc. The second solution to this problem was proposed among others by the authors in their previous studies, namely, they applied Artificial Neural Networks (ANNs) for the purpose of the automatic sound source localization. In this paper a method for automatic detection of sound source was studied. Both standard feed-forward ANNs and Recurrent Neural Networks were employed for that purpose. Comparison of the results obtained is given. Conclusions are also derived. [Research sponsored by the Committee for Scientific Research, Warsaw, Poland, Grant No. 8 T11D 00218.]

Generalized Gaussian quadratureapplied to an inverse problem in antenna theory*

We discuss the linear inverse problem of determining the currentdistribution (weighting function) for a line source antenna fromits directivity pattern. The relationship between the two is afinite Fourier transform and we use its singular functions toexpand the directivity pattern. These singular functions are theprolate spheroidal wavefunctions (PSWFs). We point out that thetruncation of this expansion, advocated by Rhodes to control thesuperdirective ratio, is a way of regularizing the inverseproblem. We discuss the problem of trying to improve theresolution by narrowing the main lobe of the directivitypattern.Given that the line source is a mathematical abstraction, inorder to make a physical device with the given directivitypattern one needs to discretize the line source. To do this weshow that the PSWFs form a Tchebycheff system, which allows usto calculate exactly integrals involving these functions via ageneralized Gaussian quadrature rule. This quadrature rule thengives the appropriate set of element positions and weights forthe equivalent discrete array.We show how superdirective arrays fit into the frameworkdiscussed in this paper and finally we look at a couple ofdiscrete arrays for which the beam pattern has a narrowed mainlobe.

Superdirective linear arrays with uniform amplitudes

Linear arrays of isotropic elements with equal amplitudes are examined for superdirective possibilities. Such arrays with alternating signs are evaluated and compared with maximum directivity arrays. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 28–31, 1999.

Superdirective radiation from finite gratings of rectangular grooves

In this paper, the superdirective property of arrays comprising a finite number of rectangular grooves is studied by using the modal approach, which is a simple but powerful technique for analyzing these gratings. Numerical results show that when a specific characteristic mode of the structure referred to as the /spl pi/ mode is excited, the intensity of the field scattered in the specular direction exhibits a maximum, which becomes sharper and narrower as the number of grooves is increased. The far-field patterns exhibit superdirectivity at these resonant frequencies as evidenced by their beamwidths that are narrower than those expected from apertures of comparable size. The model-based parameter estimation (MBPE) technique has been employed to help locate extremely narrow resonances that are characteristic of superdirective arrays and its usefulness has been demonstrated.

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.