Conventional beamforming with fixed-position antenna (FPA) arrays has a fundamental trade-off between maximizing the signal power (array gain) over a desired direction and simultaneously minimizing the interference power over undesired directions. To overcome this limitation, this letter investigates the movable antenna (MA) array enhanced beamforming by exploiting the new degree of freedom (DoF) via antenna position optimization, in addition to the design of antenna weights. We show that by jointly optimizing the antenna positions vector (APV) and antenna weights vector (AWV) of a linear MA array, the full array gain can be achieved over the desired direction while null steering can be realized over all undesired directions, under certain numbers of MAs and null-steering directions. The optimal solutions for AWV and APV are derived in closed form, which reveal that the optimal AWV for MA arrays requires only the signal phase adjustment with a fixed amplitude. Numerical results validate our analytical solutions for MA array beamforming and show their superior performance to the conventional beamforming techniques with FPA arrays.

翻译：传统固定位置天线（FPA）阵列的波束赋形在最大化期望方向信号功率（阵列增益）与最小化非期望方向干扰功率之间存在根本性权衡。为突破这一限制，本文研究了可移动天线（MA）阵列增强波束赋形技术，除了天线权值设计外，还通过天线位置优化利用新的自由度。研究表明，在线性MA阵列中，通过联合优化天线位置矢量（APV）和天线权值矢量（AWV），可在特定MA数量与零陷导向方向数条件下，在期望方向实现全阵列增益，同时在所有非期望方向实现零陷导向。我们推导了AWV与APV的闭式最优解，表明MA阵列的最优AWV仅需在固定幅度下进行信号相位调整。数值结果验证了MA阵列波束赋形解析解的有效性，并展示了其相比传统FPA阵列波束赋形技术的优越性能。