Optimization of the beampattern of 2D sparse arrays by weighting

Holm, Sverre; Elgetun, Bjørnar

doi:10.1109/ultsym.1995.495805

Cited by 16 publications

(7 citation statements)

References 5 publications

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“…Both of them start leveling off at −17 to −18 dB sidelobe level. This is in the vicinity of the mean sidelobe level predicted for a random array (18) given as the inverse of the …”

Section: -D Arraysmentioning

confidence: 84%

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Sparse Sampling in Array Processing

Holm

Austeng

Iranpour

et al. 2001

Nonuniform Sampling

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Sparsely sampled irregular arrays and random arrays have been used or proposed in several fields such as radar, sonar, ultrasound imaging, and seismics. We start with an introduction to array processing and then consider the combinatorial problem of finding the best layout of elements in sparse 1-D and 2-D arrays. The optimization criteria are then reviewed: creation of beampatterns with low mainlobe width and low sidelobes, or as uniform as possible coarray. The latter case is shown here to be nearly equivalent to finding a beampattern with minimal peak sidelobes.We have applied several optimization methods to the layout problem, including linear programming, genetic algorithms and simulated annealing. The examples given here are both for 1-D and 2-D arrays. The largest problem considered is the selection of K = 500 elements in an aperture of 50 by 50 elements. Based on these examples we propose that an estimate of the achievable peak level in an algorithmically optimized array is inverse proportional to K and is close to the estimate of the average level in a random array.Active array systems use both a transmitter and receiver aperture and they need not necessarily be the same. This gives additional freedom in design of the thinning patterns, and favorable solutions can be found by using periodic patterns with different periodicity for the two apertures, or a periodic pattern in combination with an algorithmically optimized pattern with the condition that there be no overlap between transmitter and receiver elements. With the methods given here one has the freedom to choose a design method for a sparse array system using either the same elements for the receiver and the transmitter, no overlap between the receiver and transmitter or partial overlap as in periodic arrays.

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“…Both of them start leveling off at −17 to −18 dB sidelobe level. This is in the vicinity of the mean sidelobe level predicted for a random array (18) given as the inverse of the …”

Section: -D Arraysmentioning

confidence: 84%

“…This was due to the algorithm used (Remez exchange algorithm). In [18] and [19] this approach was extended from 1-D to 2-D arrays, and improved results were reported. By using the linear programming algorithm for optimization, it was possible to optimize the whole sidelobe region.…”

Section: Optimization Of Sparse Arraysmentioning

confidence: 99%

Sparse Sampling in Array Processing

Holm

Austeng

Iranpour

et al. 2001

Nonuniform Sampling

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“…9,10 Similar to Holm's method, 9,10 the maximum side lobe level for near-field beamforming pressure, that is, maximum beamforming pressure level except the main lobe region, can be minimized by finding the appropriate weighting using optimization. The normalized maximum side lobe level of nearfield beamforming pressure ␦ s can be estimated from Eq.…”

Section: Optimization Of Weights To Minimize the Maximum Side Lobementioning

confidence: 99%

“…1, [6][7][8][9][10] Reducing side lobes improves source resolution accuracy for measurements made with and without reverberation. For an equally spaced linear array, it is possible to analytically find weights that minimize side lobe level or main lobe beam width using far-field pressure measurements.…”

Section: Introductionmentioning

confidence: 99%

“…1,7,8 The side lobe level of beamformed pressure can also be reduced by finding weights to minimize the maximum side lobes using an optimization procedure. 9,10 The conventional delay-and-sum beamforming procedure can be modified to visualize sound sources based on near-field measurements. 11 This is accomplished by modifying the form of the conventional beamforming ͑CBF͒ weights such that the beamformer focuses at specific points between the face of the array and the source rather than by steering the beamformer to coherently sum source contributions from a given direction.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive near-field beamforming techniques for sound source imaging

Cho¹,

Roan²

2009

The Journal of the Acoustical Society of America

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Phased array signal processing techniques such as beamforming have a long history in applications such as sonar for detection and localization of far-field sound sources. Two sometimes competing challenges arise in any type of spatial processing; these are to minimize contributions from directions other than the look direction and minimize the width of the main lobe. To tackle this problem a large body of work has been devoted to the development of adaptive procedures that attempt to minimize side lobe contributions to the spatial processor output. In this paper, two adaptive beamforming procedures-minimum variance distorsionless response and weight optimization to minimize maximum side lobes-are modified for use in source visualization applications to estimate beamforming pressure and intensity using near-field pressure measurements. These adaptive techniques are compared to a fixed near-field focusing technique ͑both techniques use near-field beamforming weightings focusing at source locations estimated based on spherical wave array manifold vectors with spatial windows͒. Sound source resolution accuracies of near-field imaging procedures with different weighting strategies are compared using numerical simulations both in anechoic and reverberant environments with random measurement noise. Also, experimental results are given for near-field sound pressure measurements of an enclosed loudspeaker.

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Properties of the beampattern of weight- and layout-optimized sparse arrays

Holm

Elgetun

Dahl

1997

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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127

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Theory for random arrays predicts a mean sidelobe level given by the inverse of the number of elements. In practice, however, the sidelobe level fluctuates much around this mean. In this paper two optimization methods for thinned arrays are given: one is for optimizing the weights of each element, and the other one optimizes both the layout and the weights. The weight optimization algorithm is based on linear programming and minimizes the peak sidelobe level for a given beamwidth. It is used to investigate the conditions for finding thinned arrays with peak sidelobe level at or below the inverse of the number of elements. With optimization of the weights of a randomly thinned array, it is possible to come quite close and even below this value, especially for 1D arrays. Even for 2D sparse arrays a large reduction in peak sidelobe level is achieved. Even better solutions are found when the thinning pattern is optimized also. This requires an algorithm that uses mixed integer linear programming. In this case solutions with lower peak sidelobe level than the inverse number of elements can be found both in the 1D and the 2D cases.

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Optimization of the beampattern of 2D sparse arrays by weighting

Cited by 16 publications

References 5 publications

Sparse Sampling in Array Processing

Sparse Sampling in Array Processing

Adaptive near-field beamforming techniques for sound source imaging

Properties of the beampattern of weight- and layout-optimized sparse arrays

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