Synthesis of Large-Scale Planar Isophoric Sparse Arrays Using Iterative Least Squares With Nonredundant Constraints (ILS-NRC)

This article presents a novel method to efficiently synthesize large-scale planar isophoric sparse arrays (ISAs), aiming to achieve low sidelobe levels (SLLs). This method tackles the challenge of layout optimization by framing it as a constrained least squares problem and iteratively refining the solution. To accelerate the synthesis process, two key strategies are implemented. First, the method defines the objective function as minimizing the discrepancy between the resulting array pattern and an adaptive reference pattern. This innovative choice obviates the need for introducing numerous sidelobe constraints, streamlining the optimization problem significantly. Second, the method incorporates a redundancy elimination technique. This technique involves calculating the theoretical limits for the achievable minimum spacing and aperture, allowing for the selective retention of only the nonredundant positional constraints. This step further reduces the optimization’s computational complexity. Several numerical examples are conducted for different applications. Comparative studies with the iterative convex optimization method show the proposed method’s efficiency advantages. In addition, a full-wave analysis of a microstrip patch antenna array verifies the method’s effectiveness in real array cases.