Movable Antennas for Robust Wireless Sensing via Joint Cramér-Rao Bound and Sidelobe Minimization

2026-06-22

AI Summary

This work addresses the challenge in wireless sensing where the mean squared error of angle estimation is jointly constrained by the Cramér–Rao bound (CRB) and the sidelobe levels of the ambiguity function across varying signal-to-noise ratios (SNRs). To tackle this, the authors propose a movable antenna placement optimization method that simultaneously minimizes the CRB and the maximum sidelobe level (MSL) of the ambiguity function. By uncovering the fundamental trade-off between these two metrics, they formulate a CRB minimization framework subject to an MSL constraint and devise an optimal threshold search mechanism. Antenna positions are optimized via successive convex approximation (SCA), while a one-dimensional line search determines the MSL threshold. Compared to conventional uniform or fixed non-uniform arrays, the proposed approach significantly reduces angle estimation error across the full SNR range, achieving robust sensing performance.

Abstract

This paper presents a novel design approach for movable antenna (MA)-enabled wireless sensing systems by jointly minimizing the Cramér-Rao bound (CRB) and the maximum sidelobe level (MSL) of the ambiguity function via antenna position optimization. In particular, the mean squared error (MSE) of angle-of-arrival (AoA) estimation is decomposed into a local estimation error within the mainlobe of the ambiguity function (i.e., CRB) and an additional ambiguity error caused by its sidelobes. Since the MSE is dominated by the CRB in the high-signal-to-noise ratio (SNR) regime but by the sidelobes of the ambiguity function in the low-SNR regime, our analysis reveals a fundamental trade-off between CRB minimization and MSL minimization in the moderate-SNR regime. Specifically, minimizing the CRB prefers a narrower mainlobe, where antennas are concentrated near the two edges of the one-dimensional (1-D) movement region; whereas minimizing the MSL favors a wider mainlobe, where antennas are distributed more densely near the center of the movement region. Inspired by this and to ensure robust sensing performance across different SNR regimes, we formulate an optimization problem to minimize the CRB subject to a prescribed MSL constraint via antenna position optimization. An efficient successive convex approximation (SCA) algorithm is developed to optimize the antenna position vector (APV), and a 1-D linear search method is proposed to determine the optimal MSL threshold that minimizes the actual MSE for any given SNR. Numerical results demonstrate that the proposed scheme effectively balances the trade-off between MSL and CRB minimization, thus achieving a significantly lower AoA estimation MSE across the entire SNR range compared to conventional uniform and non-uniform fixed-position antenna (FPA) arrays.

Problem

• movable antennas
• Cramér-Rao bound
• sidelobe minimization
• angle-of-arrival estimation
• ambiguity function

Innovation

• movable antennas
• Cramér-Rao bound
• sidelobe minimization
• ambiguity function
• antenna position optimization