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）阵列的波束赋形在期望方向最大化信号功率（阵列增益）与在非期望方向最小化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）阵列增强的波束赋形技术，除设计天线权重外，还通过天线位置优化利用新的自由度（DoF）。研究表明，通过联合优化线性MA阵列的天线位置向量（APV）与天线权重向量（AWV），在满足特定MA数量与零陷导向方向数的条件下，可在期望方向实现全阵列增益，同时在所有非期望方向完成零陷导向。本文推导了AWV与APV的闭式最优解，揭示MA阵列的最优AWV仅需对信号进行等幅相位调整。数值结果验证了MA阵列波束赋形的解析解，并证明其性能优于传统FPA阵列波束赋形技术。