In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted lp norm, we utilize the l p norm of the array weight ...
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In this paper, we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers (ADMM). Unlike the usual weighted lp norm, we utilize the l p norm of the array weight vector, where 0 < p < 1, as the objective function to enhance its sparsity for arbitrary array configurations. To solve the resultant nonconvex and nonlinear optimization problem, we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes, and then, the array weight vector and auxiliary variables are updated alternately via ADMM. To determine the array weight vector with the lp norm, we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives. On the other hand, we divide the objective function of auxiliary variables into multiple nonlinear subfunctions, each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two-sided constraints. Furthermore, we extend our methodology to the symmetric excitation case with symmetric array configurations. Numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations.
In this article, we devise a novel array beampattern synthesis algorithm, namely, without lobe level mask (WLLM), to avoid specifying a possibly improper or infeasible pattern mask by minimizing the ratio of the maxim...
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In this article, we devise a novel array beampattern synthesis algorithm, namely, without lobe level mask (WLLM), to avoid specifying a possibly improper or infeasible pattern mask by minimizing the ratio of the maximal sidelobe level to the minimal mainlobe level. To solve the resultant nonconvex and nonlinear fractional programming, we introduce auxiliary exponent variables to separate the numerator and denominator, and simplify each of the corresponding subproblems as a special single-variable optimization problem with a piecewise objective function and the constraints are removed via introducing unit-step functions. We also analyze the convexity or concavity of each piecewise function to compute the corresponding local minimum from which the global minimum can be obtained. Furthermore, our developed method is extended for solving the phase-only and constant modulus pattern synthesis problems. Numerical examples show that the WLLM beampattern synthesis methods can attain sufficiently low sidelobe level relative to the mainlobe level and is suitable for arbitrary array configurations.
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