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Robust Movable-Antenna Position Optimization with Imperfect CSI for MISO Systems

Haifeng Ma, Weidong Mei, Xin Wei, Boyu Ning, Zhi Chen

TL;DR

This work addresses robust movable-antenna (MA) position optimization in a MISO system under imperfect CSI. It derives a closed-form worst-case received power for norm-bounded CSI errors and adopts a Bernstein-type inequality to obtain a convex, tractable lower bound on the non-outage power for Gaussian errors, showing MRT remains optimal in general. A graph-based MA-positioning algorithm is developed to maximize the effective channel norm $\|\overline{\boldsymbol{h}}(\{a_n\})\|^2$ (or the equivalent metric in the probabilistic case), enabling efficient MA placements with complexity $\mathcal{O}(NM^2)$. Numerical results demonstrate that the proposed robust MA designs can outperform FPAs even with perfect CSI in some regimes, highlighting the practical robustness and performance benefits of MA systems in imperfect CSI environments.

Abstract

Movable antenna (MA) technology has emerged as a promising solution for reconfiguring wireless channel conditions through local antenna movement within confined regions. Unlike previous works assuming perfect channel state information (CSI), this letter addresses the robust MA position optimization problem under imperfect CSI conditions for a multiple-input single-output (MISO) MA system. Specifically, we consider two types of CSI errors: norm-bounded and randomly distributed errors, aiming to maximize the worst-case and non-outage received signal power, respectively. For norm-bounded CSI errors, we derive the worst-case received signal power in closed-form. For randomly distributed CSI errors, due to the intractability of the probabilistic constraints, we apply the Bernstein-type inequality to obtain a closed-form lower bound for the non-outage received signal power. Based on these results, we show the optimality of the maximum-ratio transmission for imperfect CSI in both scenarios and employ a graph-based algorithm to obtain the optimal MA positions. Numerical results show that our proposed scheme can even outperform other benchmark schemes implemented under perfect CSI conditions.

Robust Movable-Antenna Position Optimization with Imperfect CSI for MISO Systems

TL;DR

This work addresses robust movable-antenna (MA) position optimization in a MISO system under imperfect CSI. It derives a closed-form worst-case received power for norm-bounded CSI errors and adopts a Bernstein-type inequality to obtain a convex, tractable lower bound on the non-outage power for Gaussian errors, showing MRT remains optimal in general. A graph-based MA-positioning algorithm is developed to maximize the effective channel norm (or the equivalent metric in the probabilistic case), enabling efficient MA placements with complexity . Numerical results demonstrate that the proposed robust MA designs can outperform FPAs even with perfect CSI in some regimes, highlighting the practical robustness and performance benefits of MA systems in imperfect CSI environments.

Abstract

Movable antenna (MA) technology has emerged as a promising solution for reconfiguring wireless channel conditions through local antenna movement within confined regions. Unlike previous works assuming perfect channel state information (CSI), this letter addresses the robust MA position optimization problem under imperfect CSI conditions for a multiple-input single-output (MISO) MA system. Specifically, we consider two types of CSI errors: norm-bounded and randomly distributed errors, aiming to maximize the worst-case and non-outage received signal power, respectively. For norm-bounded CSI errors, we derive the worst-case received signal power in closed-form. For randomly distributed CSI errors, due to the intractability of the probabilistic constraints, we apply the Bernstein-type inequality to obtain a closed-form lower bound for the non-outage received signal power. Based on these results, we show the optimality of the maximum-ratio transmission for imperfect CSI in both scenarios and employ a graph-based algorithm to obtain the optimal MA positions. Numerical results show that our proposed scheme can even outperform other benchmark schemes implemented under perfect CSI conditions.
Paper Structure (12 sections, 1 theorem, 21 equations, 4 figures)

This paper contains 12 sections, 1 theorem, 21 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. CSI Error Model and Problem Formulation
  5. Norm-Bounded CSI Error
  6. Gaussian Distributed CSI Error
  7. Proposed Solution to Problem (\ref{['pf1']})
  8. Proposed Solution to Problem \ref{['pf2']}
  9. Convex Approximation of Problem (\ref{['pf2']})
  10. Proposed Solution to Problem \ref{['pf2.2']}
  11. Numerical Results
  12. Conclusion

Key Result

Lemma 1

The inequality in 4.2 is satisfied if the following constraints are met,

Figures (4)

  • Figure 1: MA MISO system with imperfect CSI
  • Figure 2: Illustrations of $\mathcal{F}'(y)$ under different values of $\rho$
  • Figure 3: Illustrations of $\mathcal{F}(y)$ under different values of $\rho$
  • Figure 4: Worst-case and non-outage received SNRs versus different parameters.

Theorems & Definitions (1)

  • Lemma 1