A convex optimization based beampattern synthesis method with antenna selection is proposed for linear and planar arrays. Conjugate symmetric beamforming weights are used so that the upper and non-convex lower bound constraints on the beampattern can be convex. Thus, a mainlobe of an arbitrary beamwidth and response ripple can be obtained. This method can achieve completely arbitrary sidelobe levels. By minimizing a re-weighted objective function based on the magnitudes of the elements in the beamforming weight vector iteratively, the proposed method selects certain antennas in an array to satisfy the prescribed beampattern specifications precisely. Interestingly, a sparse array with fewer antennas (compared to other methods) is produced. This method can design non-uniformly spaced arrays with inter-element spacings larger than one half-wavelength, without the appearance of grating lobes in the resulting beampattern. Simulations are shown using arrays of up to a few hundred antennas to illustrate the practicality of the proposed method.

Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization

Aninvestigation oftheeffects ofsystemandmediumperturbations, andthedeviations ofsignal field statistics fromusual assumptions, on theperformance ofadaptive arraysispresented. Theemphasis isplaced on thedetermination ofthesensitivity oftheadaptive processorstoperturbations, rather thanitsoverall performance in arepresentative background. Thenumerical results arelimited to CW signals, andafrequency domainelement spaceadaptive beamformerismodeledforthemajority oftheresults. Representative comparative results including frequency domainbeamspace,time domainelement space,andmatched arrayprocessorsarealsogiven.

https://ieeexplore.ieee.org/iel5/7/4102094/04102106.pdf

Effects ofPerturbations on thePerformance of Optimum/Adaptive 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.

Optimal array pattern synthesis for broadband arrays.

We discuss fast implementations of primal-dual interior-point methods for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, a class of problems that are widely encountered in control and signal processing applications. By exploiting problem structure we achieve a reduction of the complexity by several orders of magnitude compared to general-purpose semidefinite programming solvers.

Interior-Point Algorithms for Semidefinite Programming Problems Derived from the KYP Lemma

Robust beamforming is a challenging task in a number of applications (radar, sonar, wireless communications, etc.) due to strict restrictions on the number of available snapshots, signal mismatches, or calibration errors. We present a new approach to adaptive beamforming that provides increased robustness against the mismatch problem as well as additional control over the sidelobe level. We generalize the conventional linearly constrained minimum variance cost function by including a regularization term that penalizes differences between the actual and the target (ideal) array responses. By using the so-called epsi-insensitive loss function for the penalty term, the final cost function adopts the form of a support vector machine (SVM) for regression. In particular, the resulting cost function is convex with a unique global minimum that has traditionally been found using quadratic programming (QP) techniques. To alleviate the computational cost of conventional QP techniques, we use an iterative reweighted least-squares (IRWLS) procedure, which also converges to the SVM solution. Computer simulations demonstrate an improved performance of the proposed SVM-based beamformer, in comparison with other recently proposed robust beamforming techniques

Robust Array Beamforming With Sidelobe Control Using Support Vector Machines

We present algorithms for the solution of two problems in array pattern synthesis. The first is the design of nonuniform arrays with a desired magnitude response. The second is that of robust design, i.e., design in the presence of uncertainties. Constraints such as power limitation can be addressed with both problems. The algorithms that we present are based on semidefinite programming, for which efficient software is readily available. We present examples that illustrate the effectiveness of our approach.

Optimal array pattern synthesis using semidefinite programming

We present a new technique to solve array pattern synthesis problems by using semidefinite programming. We first formulate (or reformulate) the array design problems into semidefinite programming problems, and then use the recently developed efficient numerical algorithms and software to compute the numerical solution of antenna array weights. Using this approach, we can directly solve not only the standard synthesis problems for nonuniform arrays, but also the synthesis problems for arrays having power restrictions and uncertainties. Numerical examples are presented to illustrate our approach.

A wireless system (30) minimizes nulls within the wireless system while simultaneously providing diversity. The system uses time or frequency offset on signals input to an antenna (40, 50, 60, 100) to minimize interference in regions of beam overlap. Additionally, polarization diversity can be introduced using Butler Matrices (69, 70) in conjunction with array elements (102-128) to enhance the interference reduction. As a result, the wireless system has increased capacity and coverage due to an enhanced signal to interference ratio in the areas of beam overlap (O1-O3).

Method and system for minimizing overlap nulling in switched beams

We present algorithms for the solution of two prob- lems in array pattern synthesis. The first is the design of nonuni- form arrays with a desired magnitude response. The second is that of robust design, i.e., design in the presence of uncertainties. Con- straints such as power limitation can be addressed with both prob- lems. The algorithms that we present are based on semidefinite programming, for which efficient software is readily available. We present examples that illustrate the effectiveness of our approach. Index Terms—Array pattern synthesis, semidefinite program- ming.

Jason Jiangnan Chen

Papers

Optimal array pattern synthesis using semidefinite programming

Optimal array pattern synthesis using semidefinite programming

Method and system for minimizing overlap nulling in switched beams

Optimal Array Pattern Synthesis Using

Verfahren und system zur minimierung der überlappungsnullung in geschalteten strahlen