Optimal array pattern synthesis for broadband arrays

Abstract

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.

Adaptive Complex-Coefficient 2D FIR Trapezoidal Filters for Broadband Beamforming in Cognitive Radio Systems

“…Moreover, the design method of the 2D FIR trapezoidal filter is of closed form and takes 0.05 second on average to determine the filter coefficients using the computational resources of a typical personal computer. With the same computational resources, the iterative and complicated design methods proposed for the frequencyinvariant beamformer [28,32,33] take 3-5 seconds on average to determine the beamformer weights.…”

“…Time-domain broadband beamforming methods [6,12,22,23,33] have mostly been derived from the early basic delay-and-sum concept [7] and, although they can be adapted in real time, the errors between the required exact time delays and the corresponding realized approximate time delays typically cause considerable distortion of the desired beamformed signal [17,18,22]. As a remedy, frequency-invariant broadband beamforming methods [25,26,[31][32][33] have been proposed, which extrapolate the conventional narrowband beamformer design methods at several different temporal frequencies over the desired frequency band using iterative optimization techniques. Even though these broadband frequency-invariant beamforming methods minimize distortion, the design process is typically too computationally intensive for real-time adaptive beamforming.…”

Improving beampatterns of two-dimensional random arrays using convex optimization

“…9,20 For 2D random arrays, beampatterns can be improved by adaptive beamforming 21,22 parametric methods, 8 or data-independent optimization of the shading vector as demonstrated here.…”

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

“…Many broadband pattern synthesis techniques have been utilized in the literature [3][4][5][6]. Array pattern synthesis techniques for designing of broadband FIR beam former with constant main lobe response and minimum side lobe level (SLL) have been discussed in [3][4][5].…”