Synthesis of Large Sparse Sensor Arrays Utilizing Relaxed-Intensified Exploration Algorithm (RIEA) for Optimal UAVs Beamforming

In this study, we present a novel relaxed-intensified exploration algorithm (RIEA) to synthesize large-aperture sensor arrays producing good array sparsity and optimal weight vector of the sparse sensor arrays for sensing unmanned aerial vehicles (UAVs) in airspace. The proposed algorithm is based on the compressed-sensing framework integrated with a kind of relaxed-intensified optimization thought, which comprises two core stages: the relaxed optimization stage and the intensified reoptimization stage. The relaxed-intensified exploration algorithm (RIEA) is tailored to accelerate array synthesis efficiency and promote global optimization. For the proposed algorithm, the ability to approach the global convergence is embodied in two key stages. The first stage aims to generate an optimal sparse sensor array with arbitrary upper mask constraints, whose upper mask is slightly relaxed to expand the solution space for further enhancing the array sparsity. Meanwhile, direction dimension reduction is further conducted to relax the radiating direction matrix for reducing massive computational cost. For the intensified reoptimization stage, the “relaxed” upper mask is first readjusted back to the strictly constrained strength and the weight vector of the designed sparse sensor array in the previous stage is then further optimized to approach the global optimal solution. Finally, the presence of element pattern for an individual sensor and array beam-scanning capability are also considered and investigated in synthesizing the sparse sensor arrays for precise positioning and sensing of UAVs. Several representative examples of the small/large-aperture sparse sensor arrays are performed to demonstrate the superiority, effectiveness, and robustness of the proposed RIEA.