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Antenna arrays with shaped patterns have drawn significant attention for their wide applications in radar, sonar and communication systems. The combination of genetic algorithm (GA) and fast Fourier transform (FFT) has been used to synthesise shaped pattern of antenna array's factor without considering coupling effects. In this work, the GA-FFT method is generalised by integrating with a new virtual active element pattern (AEP) expansion method which approximates each AEP as the radiation pattern by exciting several equally spaced virtual elements surrounding the real element position. The generalised GA-FFT can be applied for the shaped pattern synthesis of unequally spaced linear arrays including mutual coupling and platform effect. Several synthesis examples with different pattern shapes and different antenna structures are given to demonstrate the effectiveness, accuracy and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

It is shown in this paper that the problem of reducing the number of elements for multiple-pattern arrays can be solved by a sequence of reweighted l1 optimizations under multiple linear constraints. To do so, conjugate symmetric excitations are assumed so that the upper and lower bounds for each pattern can be formulated as linear inequality constraints. In addition, we introduce an auxiliary variable for each element to define the common upper bound of both the real and imaginary parts of multiple excitations for different patterns, so that only linear inequality constraints are required. The objective function minimizes the reweighted l1-norm of these auxiliary variables for all elements. Thus, the proposed method can be efficiently implemented by the iterative linear programming. For multiple desired patterns, the proposed method can select the common elements with multiple set of optimized amplitudes and phases, consequently reducing the number of elements. The radiation characteristics for each pattern, such as the mainlobe shape, response ripple, sidelobe level and nulling region, can be accurately controlled. Several synthesis examples for linear array, rectangular/triangular-grid and randomly spaced planar arrays are presented to validate the effectiveness of the proposed method in the reduction of the number of elements. [ABSTRACT FROM AUTHOR]

The matrix pencil method (MPM) has been used to reduce the number of elements in the linear antenna array with a pencil-beam pattern. This work extends the MPM-based synthesis method to the synthesis of shaped-beam patterns by using the forward-backward matrix pencil method (FBMPM). The FBMPM-based synthesis method places a necessary restriction on the poles which correspond to element positions, and consequently obtains more accurate synthesis results, particularly for the synthesis of asymmetric patterns. Numerical examples show the effectiveness and advantages of the proposed method in the reduction of the number of elements for shaped-beam patterns. [ABSTRACT FROM AUTHOR]

Abstract-The synthesis of a nonuniform antenna array with as few elements as possible has considerable practical applications. This paper introduces a new non-iterative method for linear array synthesis based on the matrix pencil method (MPM). The method can synthesize a nonuniform linear array with a reduced number of elements, and can be also used to reduce the number of elements for linear arrays designed by other synthesis techniques. In the proposed method, the desired radiation pattern is first sampled to form a discrete pattern data set. Then we organize the discrete data set in a form of Hankel matrix and perform the singular value decomposition (SVD) of the matrix. By discarding the non-principal singular values, we obtain an optimal lower-rank approximation of the Hankel matrix. The lower-rank matrix actually corresponds to fewer antenna elements. The matrix pencil method is then utilized to reconstruct the excitation and location distributions from the approximated matrix. Numerical examples show the effectiveness and advantages of the proposed synthesis method. [ABSTRACT FROM AUTHOR]