Title :
Synthesis of Sparse Arrays With Frequency-Invariant-Focused Beam Patterns Under Accurate Sidelobe Control by Iterative Second-Order Cone Programming
Author :
Yanhui Liu ; Liang Zhang ; Longfang Ye ; Zaiping Nie ; Qing Huo Liu
Author_Institution :
Dept. of Electron. Sci., Xiamen Univ., Xiamen, China
Abstract :
It is shown in this communication that the problem of synthesizing a frequency-invariant (FI) beam pattern with as few elements as possible can be transformed into a sequence of weighted I1 optimizations under multiple convex constraints. The objective of the weighted I1 optimization is to minimize the number of radiating elements. For the filter-and-sum beamforming structure, this is equivalent to minimizing the number of filters, each with a set of optimized coefficients. The multiple constraints are adopted to individually control the mainlobe and sidelobe pattern characteristics, so as to preserve the FI property in the mainlobe region while satisfying a given upper bound in the sidelobe region. The WNG constraint can also be incorporated into the proposed method to enhance the synthesis robustness. This method can be easily implemented by iterative second-order cone programming (SOCP), and only few iterations are required to reach the convergence. A set of examples for the synthesis of FI patterns with uniform sidelobe level (SLL) or multiple nulls, scannable FI patterns, and the synthesis of FI pattern for an arc array with directive elements, is presented to validate the effectiveness and advantages of the proposed method. The element saving is about 23.3%-50% for the test cases.
Keywords :
array signal processing; convex programming; iterative methods; FI beam pattern; FI property; WNG constraint; arc array; directive elements; filter minimization; filter-and-sum beamforming structure; frequency-invariant-focused beam patterns; iterative SOCP; iterative second-order cone programming; mainlobe pattern characteristic; multiple-convex constraint; radiating element minimization; sidelobe control; sidelobe pattern characteristic; sparse array synthesis; synthesis robustness; weighted I1 optimization; Apertures; Broadband communication; Frequency synthesizers; Optimization; Robustness; Upper bound; White noise; Broadband sparse array; filter-and-sum beamforming; frequency-invariant (FI) beam pattern; reweighted $ell_1$ optimization; reweighted l1 optimization; second-order cone programming (SOCP);
Journal_Title :
Antennas and Propagation, IEEE Transactions on
DOI :
10.1109/TAP.2015.2478908