###### Abstract  
Concentric circular antenna arrays (CCAAs) can obtain better performance than other antenna arrays. However, high overhead and excessive sidelobes still make its application difficult. In this paper, we consider the sparse synthesis optimization of CCAAs. Specifically, we aim to turn off a specific number of antennas while reducing the sidelobe of CCAAs. First, we formulate an optimization problem and present the solution space. Then, we propose a novel evolutionary method for solving the optimization problem. Our proposed method introduces hybrid solution initialization, hybrid crossover method, and hybrid update methods. Simulation results show the effectiveness of the proposed algorithm and the proposed improvement factors. oncentric circular antenna arrays; sparse synthesis; optimization +
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In existing CCAAs, the excitation current weights of array elements are often set as uniform, as this scheme requires no further design and is easy to implement. However, these unoptimized and simple uniform CCAAs have some drawbacks that lead to their limited application in the real world. Specifically, CCAAs often contain a huge number of array elements which indeed effectively improve the transmission performance of CCAAs but cause a large overhead. Actually, in most scenarios, not all array elements need to be turned on. On the other hand, the sidelobes of uniform CCAAs are also difficult to suppress, which may generate a great deal of interference to the surrounding devices [6]. Therefore, some of the array elements of CCAAs can be turned off and some array elements can be assigned low excitation current weights, thereby completing the sparse synthesis optimization of CCAAs. The existing methods for performing sparse synthesis are based on the following types of methods. Some work has utilized deterministic optimization methods to perform sparse synthesis of various antenna arrays, such as convex optimization methods to determine which antennas need to be turned off and optimize the excitation current accordingly. However, these methods often require the relaxation of certain key constraints, leading to a degradation of the optimization performance. Several works have employed evolutionary computation to perform sparse synthesis tasks. This is due to the fact that evolutionary computation is able to solve many NP-hard problems and does not require information about the gradient of the problem. Therefore, evolutionary computation can be seen as an effective method to perform the sparse synthesis optimization of CCAAs. For instance, references [7; 8; 9] considers using moth flame optimization, a teaching-learning-based optimization algorithm, and a cuckoo search algorithm to solve the sparse synthesis optimization of CCAAs and obtain suitable results. Most of these methods only consider reducing the sidelobes or decreasing the number of active antennas as much as possible. However, aiming to keep the transmission power steady, there also is a requirement to reduce the maximum sidelobe level while switching off a fixed number of antennas. This requirement has been overlooked in the literature. Note that turning off a specific number of array elements of CCAAs while optimizing sidelobes is challenging because the structure of the decision variables will be changed. Different from these methods, we aim to turn off the specific number of antennas while reducing the sidelobe of CCAAs via a novel evolutionary algorithm in this work. Our contributions are summarized as follows. * We formulate a novel optimization problem to turn off a specific number of antennas while reducing the sidelobes of CCAAs. The problem is challenging because it involves both binary and continuous decision variables and is an NP-hard problem. * We propose an enhanced whale optimization algorithm (EWOA) to solve our formulated problem. EWOA introduces chaos theory and thereby proposes a novel hybrid solution initialization method.