Improving beampatterns of two-dimensional random arrays using convex optimization

Abstract

Sensors are becoming ubiquitous and can be combined in arrays for source localization purposes. If classical conventional beamforming is used, then random arrays have poor beampatterns. By pre-computing sensor weights, these beampatterns can be improved significantly. The problem is formulated in the frequency domain as a desired look direction, a frequency-independent transition region, and the power minimized in a rejection-region. Using this formulation, the frequency-dependent sensor weights can be obtained using convex optimization. Since the weights are data independent they can be pre-computed, the beamforming has similar computational complexity as conventional beamforming. The approach is demonstrated for real 2D arrays.

Sonar Model Based Matched Field Signal Processing

“…Results from measurements with a bistatic sonar experimental setup are presented in (Kolev et al 2009), (Kolev et al 2010). The interest for developing adaptive beamforming methods is as with uniform but also with non-uniform and random sparse (ad-hoc) arrays with distance between nodes bigger than a half-wavelength (Hodgkiss, 1981, Gerstoft, P & Hodgkiss, 2011. MFP methods are subject to development for application in these underwater networks.…”

A Pareto Elite Selection Genetic Algorithm for Random Antenna Array Beamforming With Low Sidelobe Level

“…The scope has now been extended to include arbitrarily placed antenna elements too, which form a random antenna array (RAA) [8][9][10][11][12][13]. An RAA consists of randomly placed antenna elements over a specified radius, which collectively forms an array for beamforming purposes.…”

“…Since the usually scattered sensor nodes' position cannot be changed, the array formed to beamform is random by nature and beamforming has to be achieved using these randomly placed elements. Seismic, ocean and air acoustic also applies non-spatially perturbed RAAs [10].…”

“…However, most works focus on SLL reduction for either arrays with uniform element arrangement [18][19][20][21][22], or on RAAs that fall into the first classification, namely the spatially perturbed RAA [10,12,14,15,20,23,24]. Literatures available on SLL reduction proposals for spatially unperturbed RAAs are fairly limited.…”

“…A popular method in the literature to reduce the SLL in antenna arrays is by strategically placing the elements according to a set of pre-calculated optimum positions using optimization algorithms such as Genetic Algorithms (GA) [14,20,21], Particle Swarm Optimization [14,20,21,26], Differential Evolution [27][28][29][30][31] and convex optimization [10,12]. The position of the elements in the array is optimized via iterative procedures until the cost function of the algorithm, which is the PSLL, is minimized.…”