Study Of Sparse Array Antenna Synthesis Based On Compressed Sensing And Invasive Weed Optimization

The antenna arrays have been widely used in applications of modern radio systems, such as satellite communication, sonar, radar, radio astronomy, electronic countermeasure, microwave remote sensing, and so on, due to their advantages of easy to obtain patterns with low sidelobe and high gain as well as easy to control for multi, scanning or shaped beam. The researches on sparse antenna arrays, especially on the synthesis of sparse antenna arrays, have received gowing attention since the number of antenna elements can be efficiently reduced, which means the cost and the complexity can be further reduced when antenna array implented in practical applications.This dissertation focuses on the syntheis methods of sparse antenna arrays based on compressend sensing(CS) and invasive weed optimization(IWO) in order to achieve the desired beam patterns using as few elements as possible. The main contributions and innovations of this dissertation are summarized as follows:1. An innovative methodology based on CS theory is proposed for synthesis of maximally sparse linear and planar arrays aiming to minimize the number of antenna elements. In the proposed method, the synthesis of sparse arrays can be formulated as a convex optimization problem in view of sparse signal revovery in CS by uniformly discretizing an array aperture to build an oversamplied suppositional uniform array and get the candidate positions for each antenna element, then the weighted l1-norm convex algorithm is applied to solving the synthesis problem efficiently so as to determine the corresponding spase array parameters including the number of elements, the element positions and the excitation amplitudes simultaneously. The proposed method can solve two kinds of synthesis problems flexibly, i.e. one is to match a desired reference pattern with an acceptable error, and the other is to achieve a pattern mask with constraints on peak sidelobe level(PSLL) and the first null beamwidth(FNBW). Numerical experiments well demonstrate the effectiveness and the flexibility of the proposed method. In particular, it is very computational efficient and simple to implement. Moreover, the proposed method generally has the capability to further optimize the results obtained by the existing optimization algorithms with fewer elements.2. The CS-based synthesis method is extended to the synthesis of sparse concentric ring arrays, and a novel method involving a CS approach and a determined approach together is proposed to get circularly symmetric and invariant 3-D patterns over all-azimuth directions. Specifically, based on the Bessel function approximation of the array pattern and CS theory, the synthesis of a sparse concentric current ring array can be formulated as a convex problem with the l1-norm minimized. In order to reconstruct the 3-D pattern accurately with discrete antenna elements in place of the current rings, a determined approach with or without radial amplitude weighting is proposed to define the number of elements equally distributed on each ring. The proposed method has good numerical stability and computational efficiency. Moreover, the proposed method is very flexiable and universal to the design requirements for either matching a desired pattern or satisfying a prescribed pattern mask. In addition, more elements can be saved by the proposed method in achieving the same or better results compared with other techniques. Furthermore, the proposed method is very promising in application of large aperture array synthesis.3. A hybrid algorithm based on the invasive weed optimization and the convex optimization is proposed for minimizing PSLL of sparse linear arrays with focused and/or shaped beam patterns. In this approach, IWO is adopted to produce the array(described by element positions) and convex optimization is used to determine the excitations for each produced array. Then the corresponding PSLL acts as the fitness function of IWO in order to find the optimal positions which lead to the minimum PSLL. The proposed hybrid method can easily cope with some constraints on the aperture, e.g. the minimum element spacing along with the total number of elements. Numerical experiments are conducted to validate the effectiveness, the robustness as well as the convergence of the proposed hybrid approach.4. A novel IWO-Bessel method is proposed for synthesis of sparse concentric ring arrays composed of uniformly excited elements by simultaneously optimizing the non-uniform ring radii as well as the corresponding number of elements which are equally spaced on each ring. A new relationship between the sparse ring radii and the required element number has been first derived according to the properties of Bessel function to guarantee a circularly symmetric pattern. In this way, we only need to take the ring radii as the optimization variables of IWO since the element number can be determined according to the derived relationship. Obviously, the proposed method transforms the original multiple-type-variable optimization problem to a single-type-variable optimization problem only with respect to ring radii, therefore the complexity of array synthesis and optimization can be reduced and the efficiency can be well improved. Meanwhile, numerical experiments have demonstrated that the proposed method is very efficient and flexible for synthesizing fixed beam radiating arrays and/or the scanned counterpart.