## 1 Introduction  
Electronic warfare is an important form of modern warfare. Jammers interfere with communication systems by emitting electromagnetic waves, affecting the quality of communication and reducing combat effectiveness [1, 2, 3, 4, 5, 6]. The increase in the dimensions of combat has put forward higher requirements for the coordination between equipment. This has made coordinated electronic jamming a development trend in electronic warfare. Coordination between jammers can extensively play to their respective advantages and minimize the impact of the shortcomings of individual jammers on the entire jamming system. Distributed beamforming has been widely used in coordinated jamming due to its high directivity and flexibility. This technology uses the coordination between array elements to optimize the main beam and half-power beamwidth and suppress sidelobes to achieve higher-quality power transmission [7, 8, 9]. These papers studied the impact of frequency and phase errors between nodes on beam efficiency. They used phase prediction models to estimate errors, track the drift of signals, and implement beam correction through probabilistic adaptive direction adjustment techniques. They proposed average received power and the amount of information exchange as evaluation indicators of the model's overall performance. UAVs carry array elements due to their high mobility to achieve more efficient energy transmission [10]. Based on a nonlinear energy harvesting model, this paper proposed an energy efficiency maximization problem, which mainly involves the optimization of analog beamforming, trajectory planning, and transmission power control. The authors simplified the complex three-dimensional uniform linear array and designed a convex optimization iterative algorithm, which improved the convergence speed of the algorithm and achieved beam concentration. In addition to adjusting the positions of nodes to change the phase, directly adjusting the signal's phase can gather more energy in the target area. The author proposed a phase adjustment algorithm in [11], similar to the Fresnel zone plate focusing principle. The far-field transmitter is constructively superimposed in the target area. Experiments have shown that the proposed method can produce a high-energy beam in the target area. Under far-field conditions, distributed arrays form plane waves. However, the node spacing in coordinated jamming is usually greater than half a wavelength, which does not meet the far-field conditions. In such cases, sparse arrays have been proposed to solve this problem. The nodes in sparse arrays are composed of highly directional sub-arrays. These nodes aim at the target to implement precise jamming and can adjust the position and transmission power of the nodes according to the size of the area and the characteristics of the target. Under the limited transmission power of the nodes, by optimizing the beam of the sparse array, effective jamming can be achieved over a larger area [12; 13; 14]. These papers introduced matrix mapping to transform the strictly constrained optimization problem into a non-constrained problem with only upper and lower limits. Based on the genetic algorithm, the differential evolution of nodes is realized, and multiple beampattern matching is achieved by optimizing the positions of nodes and the phase of excitation current. The paper in [15] studied the configuration of arrays in regular and irregular networks, aiming to reduce the number of sub-arrays while maintaining the sensitivity of the system. Experiments have shown that the effective area of the same number of sub-arrays in regular networks is more significant than that in irregular networks. In [16], an asymmetric mapping method was proposed, which contrasts with traditional symmetric matrix mapping. Under the constraints of aperture, the number of sub-arrays, and the spacing of sub-arrays, the authors constructed two distinct mapping functions to optimize the array layout.