Low Peak Sidelobe Level Beamforming with Minimum Movable-Antenna Array Size

Movable antenna (MA) arrays beamforming can achieve full array gain while suppressing interference with specific structure, whereas fixed-position antenna (FPA) arrays beamforming has to consider a trade-off between these objectives. However, non-half wavelength antenna spacing can result in a high peak sidelobe level (PSLL) and delayed response due to longer movement times. In this letter, we aim to minimize PSLL through joint optimization of antenna position vector (APV) and antenna weight vector (AWV), subject to full array gain and null steering constraints. We reveal that it is essentially equal to minimize the array size, allowing us to transform the formulated non-convex problem into several equivalent problems. Specifically, we propose an approximation method for PSLL and then formulate an integer linear programming problem. Numerical results demonstrate that the proposed algorithm significantly minimizes the array size and achieves full array gain with decent PSLL compared to other benchmark schemes.