Abstract
This paper addresses the constrained multiobjective optimization problem of time-modulated sparse arrays. The synthesis objective is to find an optimal element arrangement and associated excitation strategy of sparse arrays, which realize the balance of radiation power and sideband suppression performance with minimum number of elements, and suppress side lobe level simultaneously. A novel hybrid algorithm based on orthogonal perturbation method and convex optimization (OPM-CVX) for the synthesis of time-modulated sparse antenna array is presented in this paper. In order to satisfy the main lobe beamforming and side lobe suppression of sparse arrays, the proposed method optimizes element positions with minimum array numbers by orthogonal perturbation method and optimizes excitations of array element with dynamic range ratio constraint by convex optimization. Furthermore, a trapezoidal pulse time-modulated switching function is proposed to find the balance of radiation power and sideband suppression performance. The numerical results indicate that the proposed algorithm can be an effective approach for synthesis problems of time-modulated sparse arrays.
Highlights
Lei [4] optimized the array element positions through an iterative convex optimization algorithm and realized pencil beam and low side lobe in linear and planar arrays. e shaped beam is mainly used to meet the requirements of the radiation area and the intensity of the signal in the specified direction
For side lobe and sideband suppression of sparse arrays based on time-modulated technology, the objective of this paper is to find an optimal solution for shaped beam pattern synthesis of sparse array. at is to optimize the array element position and excitation coefficient to make the pattern achieve the following goals: (a) minimize the peak side lobe level (PSLL) and peak sideband level (PSBL) under the constraint of main band; (b) minimize the number of elements; (c) make the dynamic range ratio (DRR) meet the constraint conditions. e abovementioned optimization problem can be expressed as min max θ,φ∈Ωs
Under the constraint that the main lobe pattern is consistent, two examples are presented in comparison with the results of pencil beam and flat top beam pattern obtained in [12, 15] to demonstrate the effectiveness of the proposed algorithm in suppressing the PSBL and PSLL
Summary
Poli [10] synthesized a pencil beam pattern and suppressed sideband radiation by optimizing the equivalent excitation of the time-modulated linear array. Alberto Reyna [11] synthesized rectangular and circular sparse arrays with the same aperture size and obtained flat top beam pattern and better feeding network efficiency, but the sideband level was high. D’Urso [13] proposed simulated annealing algorithm to optimize the switch-on duration time, which realized the low side lobe of sparse array with equal spacing and effectively suppressed the sideband radiation. Gassab [15] proposed an efficient mathematical method for pattern synthesis of timemodulated linear array and obtained lower side lobe and sideband than the antenna array optimized by differential evolution algorithm. The deterministic iterative algorithm has high operational stability, its optimization effect largely depends on the initial state of the array. erefore, joint optimization of parameters such as the position and excitation of an array element can usually achieve better optimization result
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