The Synthesis of Sparse Planar Arrays Based on Quantum Observation and Constraint Conversion

This study proposes a novel method for the synthesis of sparse planar arrays with multiple constraints including the array aperture, the number of elements, and the minimum spacing between adjacent elements. It consists of two stages: the generation of thinned arrays based on quantum observation and the optimization of element positions via constraint conversion. Firstly, a step to determine element states is introduced based on quantum observation in the generation of thinned arrays. Driven by the uncertainty of outcomes in quantum observation, all possible array layout schemes can be probabilistically represented by the individuals in the algorithm, which enhances the search performance. On the basis of the thinned array, the logistic-tent chaotic mapping is introduced to initialize the population to ensure the randomness and uniformity in the population distribution. Then, a penalty mechanism is proposed to convert the spacing constraints during position optimization into a penalty factor. Then, to find the optimal solution, the modified differential evolution algorithm is employed to optimize element positions. This approach simplifies the problem and leverages the algorithm\u2019s optimization tendency to avoid infeasible solutions. Compared with other techniques, the proposed method can more effectively utilize the degrees of freedom in element placement, and both numerical calculations and simulation results show that it can achieve better performance than existing methods, which verifies the effectiveness and reliability of the proposed method.