An overview of beamforming from a signal-processing perspective is provided, with an emphasis on recent research. Data-independent, statistically optimum, adaptive, and partially adaptive beamforming are discussed. Basic notation, terminology, and concepts are included. Several beamformer implementations are briefly described. >

Beamforming: a versatile approach to spatial filtering

Array processing involves manipulation of signals induced on various antenna elements. Its capabilities of steering nulls to reduce cochannel interferences and pointing independent beams toward various mobiles, as well as its ability to provide estimates of directions of radiating sources, make it attractive to a mobile communications system designer. Array processing is expected to play an important role in fulfilling the increased demands of various mobile communications services. Part I of this paper showed how an array could be utilized in different configurations to improve the performance of mobile communications systems, with references to various studies where feasibility of apt array system for mobile communications is considered. This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them. This paper brings together almost all aspects of array signal processing.

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Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations

Adaptive beamforming algorithms can be extremely sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise, while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint. Moreover, this scaling is equivalent to a projection onto the quadratic constraint boundary so that the usual favorable properties of projection algorithms apply. This leads to a simple, effective, robust adaptive beamforming algorithm in which all constraints are satisfied exactly at each step and roundoff errors do not accumulate. The algorithm is then extended to the case of a more general quadratic constraint.

Robust adaptive beamforming

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.

On robust Capon beamforming and diagonal loading

A short historical overview of matched-field processing (MFP) is followed by background material in both ocean acoustics and array processing needed for MFP. Specific algorithms involving both quadratic and adaptive methods are then introduced. The results of mismatch studies and several algorithms designed to be relatively robust against mismatch are discussed. The use of simulated MFP for range, depth and bearing location is examined, using data from a towed array that has been tilted to produce an effective vertical aperture. Several experiments using MFP are reviewed. One successfully demonstrated MFP at megameter ranges; this has important consequences for experiments in global tomography. Some unique applications of MFP, including how it can exploit ocean inhomogeneities and make tomographic measurements of environmental parameters, are considered. >

An overview of matched field methods in ocean acoustics

In this paper a class of linear constraints, also termed as derivative constraints, which is applicable to broad-band element space antenna array processors, is presented. The performance characteristics of the optimum processor with derivative constraints are demonstrated by computer studies involving two types of array geometries, namely linear and circular arrays. As a consequence of derivative constraints, the beam width in the look direction can be made as broad as desired and the beam spacings can be selected without fear of substantial signal suppression in the event of signal arrivals between beams. However, this increased beam width is achieved at the price of reducing array gain.

Derivative constraints for broad-band element space antenna array processors

A new set of linear constraints for designing broad-band time domain element space antenna array processors is presented. The set of linear constraints is used to ensure that a desired look-direction response of the processor over a frequency band of interest can be closely approximated. The design technique is posed in such a way that three types of presteering can be handled: no presteering, coarse presteering, and exact presteering. The elimination of presteering time delays or the possibility to use coarse presteering is an attractive feature in a digital implementation of antenna array processors. The relationship that the new processor has to other broad-band processors is also established. Furthermore, the approach enables various types of errors and mismatches between signal model and actual scenario to be incorporated in the problem formulation.

Meng Er

Papers

Derivative constraints for broad-band element space antenna array processors

A new set of linear constraints for broad-band time domain element space processors