Broadband Beamforming Research Articles

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.

Target detection in a shallow water environment using a two-dimensional array.

The detection and tracking of targets in cluttered, shallow water locations have become increasingly important for both maritime security and coastal environmental monitoring. Ambient noise contributions from snapping shrimp, as well as recreational and commercial ship traffic, can limit target detection performance. Few studies have investigated the possibility of enhanced passive acoustic detection in these locations using multiple arrays. Two synchronized 24 element arrays with 300 Hz–50 kHz bandwidth were deployed at the Kilo Nalu Nearshore Reef Observatory (University of Hawaii, Honolulu, HI) in an “L” shape configuration with a vertical array within the 12 m water column and horizontal array orthogonally aligned on the seafloor. This subtropical site is located between Honolulu Harbor and a recreational boating and diving area. Broadband snapping shrimp noise, which dominates the background levels, has a diurnal variation. A series of experiments examined the feasibility of passive acoustic monitoring with array beamforming of a variety of targets including small craft, open circuit scuba divers, and a REMUS autonomous underwater vehicle. The relative performance of narrowband versus broadband beamforming techniques for detection and tracking was quantified for these targets. Moreover, the applicability of nearfield techniques, such as wavefront curvature, was also investigated. [Work supported by the DHS.]

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.

Broadband Frequency Invariant Beamformer

In the broadband signal processing, the array has different relative aperture for the different frequency bins, which results in waveform distortion. Moreover, the greater the bandwidth is, the more serious the distortion becomes. It is valuable to study the Frequency-invariant beam patterns (FIBPs) for receiving broadband signals without distortion. Based on the array dimensions, this paper will summarize some new methods to design a broadband beamformer with an FIBP. There will be two categories: One-dimensional arrays and Multi-dimensional arrays. For one-dimensional array, there are sampling rate method, minimax frequency invariant beamforming, etc. For multi-dimensional array, there are Bessel function method, Bessel function and phase mode method, and so on. Finally, we will discuss the pros and cons of every method.

Spatial-Temporal Non-Uniform Subband Broadband Beamforming

A spatial-temporal scheme based on non-uniform subband general parameter filter banks for broadband beamforming of scaled aperture array is proposed in this paper. The scaled aperture array is composed of several uniformly-spaced linear subarrays, each of which processes an octave subband signal respectively. The non-uniform subband signal is implemented by tree-structure general parameter filter banks. Each subarray broadband beamforming is carried out by a kind of tapped-delay-line (TDL) infinite-impulse-response (IIR) filters beamformer, and four subarrays share the same weights. This processing architecture based beamformer splits the broadband signal into several narrower subband ones which are processed in parallel, and subarray is operating with lower sampling rate, which contributes to decreasing the computational load significantly and improving the speed and performances as well. Simulations show that computation complexity and load of this beamformer are much lower relative to the conventional TDL broadband beamfomer.

Bandwidth selective filter for the pre-excision of narrowband interference in broadband beamformers

A novel frequency domain excision filter for use in front of broadband adaptive beamformer systems is presented. The proposed frequency domain excision filter uses image processing techniques to determine the excision threshold such that only narrowband interference is removed from the received signal. By pre-excising the received signal of narrowband interference the adaptive beamformer only has to remove partialband or broadband interferers. This frees up degrees of freedom (DoF) in the adaptive beamformer in mixed interference environments allowing for a greater interference suppression capability. The proposed pre-excision system is simulated using a constrained space-time adaptive processor as well as a constrained sub-optimal space-frequency adaptive processor. It is shown that when pre-excision is used in front of a beamformer the total number of interference sources that can be simultaneously rejected is increased as long as the beamformer's DoF are exceeded by narrowband interference.

Performance analysis of an adaptive broadband beamformer based on a two-element linear array with sensor delay-line processing

The performance of a two-element broadband beamforming structure with sensor delay-lines (SDLs) attached is studied for two adaptive implementations, in terms of the direction of the interfering signals, the inter-spacing between delay-line sensors and the length of the SDLs. Compared with the conventional broadband beamformers with tapped delay-lines (TDLs), the SDL based structure has a better performance in two aspects: its output signal to interference plus noise ratio (SINR) drops less as the inter-delay within delay-lines increases; with the same number of delays and weights it can achieve a better performance than the TDL one.

Design of Robust Broadband Beamformers With Passband Shaping Characteristics Using Tikhonov Regularization

Broadband beamformers are known to be highly sensitive to the errors in microphone array characteristics, especially for small-sized microphone arrays. This paper proposes an algorithm for the design of robust broadband beamformers with passband shaping characteristics using Tikhonov regularization method by taking into account the statistics of the microphone characteristics. To facilitate the derivation, a weighted least squares based broadband beamforming algorithm with passband shaping characteristics is also proposed, while keeping a minimal stopband level. Unlike the existing criteria for broadband beamforming for microphone arrays, the proposed approaches fully exploit the degrees of freedom in weighting functions of the criteria used to design broadband beamformers. By doing so, efficient and flexible broadband beamforming can be achieved with the desired passband shaping characteristics. In addition, this paper also shows that the robust broadband beamforming using the statistics of the microphone characteristics recently proposed (Doclo and Moonen, 2003 and 2007) belongs to the class of white noise gain constraint-based techniques, which gives an insight into the nature of the state-of-the-art approach. The performance of the proposed beamforming algorithms is illustrated by the design examples and is compared with the existing approaches for microphone arrays.

A Robust Broad-Band Beamformer with Spatial and Frequency Derivative Constraints

In this paper, we propose a set of constraints for adaptive broad-band beamforming in the presence of angular errors. We first present spatial and frequency derivative constraints (SFDC) for the design of the quiescent beamformer response. With the wavelet-based blocking matrices, the proposed generalized sidelobe canceller (GSC) preserves the desired signal, and it is less sensitive to the broad-band noise. To make this beamformer more robust to the directional mismatch, we add a pseudo-interference algorithm in the weight adaptive process. Analysis and simulation results demonstrate that the angular beamwidth is insensitive to the input signal-to-noise ratio (SNR).

Waveguide invariant focusing for broadband beamforming in an oceanic waveguide

The performance of broadband sonar array processing can degrade significantly in shallow-water environments when interference becomes angularly spread due to multipath propagation. Particularly for towed line arrays near endfire, elevation angle spreading of multipath interference often results in masking of weaker sources of interest. While adaptive beamforming in a series of narrow frequency bands can suppress coherent multipath interference, this approach requires long observation times to estimate the required narrowband covariance matrices. To form wideband covariance matrices which can be estimated with less observation time, plane-wave focusing methods have been used to avoid interference covariance matrix rank inflation. This paper extends wideband focusing to the case of coherent multipath interference. The approach presented here, called waveguide invariant focusing (WIF), exploits a robust relationship for the frequency dependence of horizontal wave number differences. Unlike matched-field methods, WIF does not model multipath wave fronts but rather makes the interference appear to occupy the same rank-one subspace across frequency. This permits formation of wideband covariance matrices without interference rank inflation. Simulation experiments in a realistic ocean environment indicate that adaptive beamforming using WIF covariance matrices can provide a significant array gain improvement over conventional adaptive methods with limited observation time.

Design and Analysis of Broadband Beamspace Adaptive Arrays

A beamspace adaptive planar array for broadband beamforming is proposed based on the frequency invariant beamforming technique. A detailed analysis is provided for both the linear arrays and the planar arrays, where two conditions are imposed: the beams should exhibit a good frequency invariant property and be linearly independent. These two conditions are not independent and there is a tradeoff between them. To improve the interference cancellation capability of the array, we may need to sacrifice the frequency invariant property to some degree for more linearly independent beams. A sufficient condition for the linear independence of the beams is derived with a DFT matrix based design proposed. Simulation results verified our analysis and the proposed method.

Optimal array pattern synthesis for broadband arrays

Broadband beamformers with constant mainlobe response over the frequency of interest are desirable in many applications including underwater acoustics, ultrasonics, acoustic imaging and communications, and so on. Solutions to this problem have been presented for specific array geometry often requiring a larger number of sensors. And the array pattern synthesis error minimization is employed for the whole field of view, which leads to suboptimal designs. In this paper, a broadband array pattern synthesis approach to designing time-domain constant mainlobe response beamformer is proposed. By imposing constraints both on the mainlobe spatial response variation over frequency and on the sidelobes of the beamformer, several optimization criteria are presented and the corresponding convex second-order cone programming implementations are given. In this approach, no preliminary desired beampattern is required and the beam responses variation minimization is employed only in the mainlobe region and not in the sidelobe regions, which improves the beamformer mainlobe synthesis accuracy. Equally, one can obtain lower sidelobes at the same mainlobe synthesis accuracy. This approach is applicable to arrays with arbitrary geometry. Simulation and experimental results are presented to illustrate the effectiveness of this approach. Performance comparisons of the proposed beamformers and the existing beamformer are also provided.

Joint Transceiver Design for MIMO Channel Shortening

Channel shortening equalizers can be employed to shorten the effective impulse response of a long intersymbol interference (ISI) channel in order, for example, to decrease the computational complexity of a maximum-likelihood sequence estimator (MLSE) or to increase the throughput efficiency of an orthogonal frequency-division multiplexing (OFDM) transmission scheme. In this paper, the issue of joint transmitter-receiver filter design is addressed for shortening multiple-input multiple-output (MIMO) ISI channels. A frequency-domain approach is adopted for the transceiver design which is effectively equivalent to an infinite-length time-domain design. A practical space-frequency waterfilling algorithm is also provided. It is demonstrated that the channel shortening equalizer designed according to the time-domain approach suffers from an error-floor effect. However, the proposed techniques are shown to overcome this problem and outperform the time-domain channel shortening filter design. We also demonstrate that the proposed transceiver design can be considered as a MIMO broadband beamformer with constraints on the time-domain multipath length. Hence, a significant diversity gain could also be achieved by choosing strong eigenmodes of the MIMO channel. It is also found that the proposed frequency-domain methods have considerably low computational complexity as compared with their time-domain counterparts.

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved

The Experimental System PALES: Signal Separation with a Multibeam-System Based on a Rotman Lens

The experimental system PALES is described: a multi-functional array antenna in the X band with broadband beamforming by a Rotman lens. Studies that have been conducted about possible broadband antenna elements have implied the use of flared-notch antennas (Vivaldi antennas), which are specified in the paper. A short description of the Rotman lens design used is given. The receiver branch of the PALES system, the applied signal model, and different broadband array-processing methods, which can be applied to the received signals of a multibeam system, are discussed. To separate broadband signals with a small angular separation, the ICA (independent component analysis) method shows superior performance compared to ML (maximum likelihood) estimation, based on superresolution by the STCM (steered covariance matrix) method.

Convex optimization based time-domain broadband beamforming with sidelobe control

An approach to time-domain broadband beamforming with sidelobe control is proposed. The array response is expressed as a linear function of the finite impulse response filters tap weights. The filters are designed by minimizing beamformer output power while maintaining the distortionless response in the direction of the desired signal and guaranteeing the sidelobes to be below some given threshold values. Norm constraint on tap weights is also imposed to improve the robustness of the beamformer. Computationally efficient convex formulation for the beamformer design problem is derived using second-order cone programming. Simulation results demonstrate the satisfactory performance of the proposed approach.

Active control of passive acoustic fields: Passive synthetic aperture/Doppler beamforming with data from an autonomous vehicle

The maneuverability of autonomous underwater vehicles (AUVs) equipped with hull-mounted arrays provides the opportunity to actively modify received acoustic fields to optimize extraction of information. This paper uses ocean acoustic data collected by an AUV-mounted two-dimensional hydrophone array, with overall dimension one-tenth wavelength at 200-500 Hz, to demonstrate aspects of this control through vehicle motion. Source localization is performed using Doppler shifts measured at a set of receiver velocities by both single elements and a physical array. Results show that a source in the presence of a 10-dB higher-level interferer having exactly the same frequency content (as measured by a stationary receiver) is properly localized and that white-noise-constrained adaptive beamforming applied to the physical aperture data in combination with Doppler beamforming provides greater spatial resolution than physical-aperture-alone beamforming and significantly lower sidelobes than single element Doppler beamforming. A new broadband beamformer that adjusts for variations in vehicle velocity on a sample by sample basis is demonstrated with data collected during a high-acceleration maneuver. The importance of including the cost of energy expenditure in determining optimal vehicle motion is demonstrated through simulation, further illustrating how the vehicle characteristics are an integral part of the signal/array processing structure.

Generalized Broadband Beamforming Using a Modal Subspace Decomposition

We propose a new broadband beamformer design technique which produces an optimal receiver beam pattern for any set of field measurements in space and time. The modal subspace decomposition (MSD) technique is based on projecting a desired pattern into the subspace of patterns achievable by a particular set of space-time sampling positions. This projection is the optimal achievable pattern in the sense that it minimizes the mean-squared error (MSE) between the desired and actual patterns. The main advantage of the technique is versatility as it can be applied to both sparse and dense arrays, nonuniform and asynchronous time sampling, and dynamic arrays where sensors can move throughout space. It can also be applied to any beam pattern type, including frequency-invariant and spot pattern designs. A simple extension to the technique is presented for oversampled arrays, which allows high-resolution beamforming whilst carefully controlling input energy and error sensitivity.

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.