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Movable-Antenna Array Enhanced Beamforming: Achieving Full Array Gain with Null Steering

Lipeng Zhu, Wenyan Ma, Rui Zhang

Abstract

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.

Movable-Antenna Array Enhanced Beamforming: Achieving Full Array Gain with Null Steering

Abstract

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.
Paper Structure (7 sections, 3 theorems, 16 equations, 5 figures, 1 table)

This paper contains 7 sections, 3 theorems, 16 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation and Transformation
  3. Antenna Position Optimization
  4. Numerical Results
  5. Conclusion
  6. Proof of Lemma \ref{['Lemma_KInterf']}
  7. Proof of Theorem \ref{['Theorem_NMA']}

Key Result

Lemma 1

For $K=1$, an APV satisfying the SVO condition eq_SV_ort and constraint eq_problem2_b always exists for any $N \geq 2$.

Figures (5)

  • Figure 1: Illustration of the linear MA array and the steering angles.
  • Figure 2: An example of the optimal APV for $N=8$.
  • Figure 3: Comparison of the beam patterns between MA and FPA arrays assuming digital beamforming for the FPA array, with $N=8$, $K=3$, $\theta_{0}=90^{\circ}$, $\theta_{1}=30^{\circ}$, $\theta_{2}=82^{\circ}$, and $\theta_{3}=100^{\circ}$.
  • Figure 4: Comparison of the beam patterns between MA and FPA arrays assuming analog beamforming for the FPA array, with $N=8$, $K=3$, $\theta_{0}=90^{\circ}$, $\theta_{1}=10^{\circ}$, $\theta_{2}=55^{\circ}$, and $\theta_{3}=160^{\circ}$.
  • Figure 5: Beam gains of the MA and FPA arrays over the desired direction $\theta_{0}=90^{\circ}$ versus undesired direction $\theta_{1}$, with $N=8$ and $K=1$.

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Theorem 1