Mismatch Analysis and Cooperative Calibration of Array Beam Patterns for ISAC Systems

TL;DR

This paper tackles calibration-induced sensing degradation in ISAC systems by introducing a cooperative beam-pattern calibration framework that emphasizes angle estimation accuracy over traditional beam-pattern similarity. It develops a novel, differentiable loss based on a KL-divergence–driven pseudo-true parameter to quantify sensing performance under model mismatch, and proposes REL and AEL losses to enable gradient-based optimization. The method supports distributed calibration across multiple UEs (cooperative calibration) and demonstrates that joint optimization of the codebook ${f W}$ and gain matrix ${oldsymbol{ emovebrace}}$ yields substantial angle-error reductions, validated with real-world chamber measurements in both 2D and 3D scenarios. The results show angle estimation improvements from $1.01^ 0$ to $0.11^ 0$ (2D) and from $5.19^ 0$ to $0.86^ 0$ (3D), and the cooperative framework achieves near-centralized performance with reduced communication overhead, highlighting practical applicability for 6G ISAC systems.

Abstract

Integrated sensing and communication (ISAC) is a key technology for enabling a wide range of applications in future wireless systems. However, the sensing performance is often degraded by model mismatches caused by geometric errors (e.g., position and orientation) and hardware impairments (e.g., mutual coupling and amplifier non-linearity). This paper focuses on the angle estimation performance with antenna arrays and tackles the critical challenge of array beam pattern calibration for ISAC systems. To assess calibration quality from a sensing perspective, a novel performance metric that accounts for angle estimation error, rather than beam pattern similarity, is proposed and incorporated into a differentiable loss function. Additionally, a cooperative calibration framework is introduced, allowing multiple user equipments to iteratively optimize the beam pattern based on the proposed loss functions and local data, and collaboratively update global calibration parameters. The proposed models and algorithms are validated using real-world beam pattern measurements collected in an anechoic chamber. Experimental results show that the angle estimation error can be reduced from {$\textbf{1.01}^\circ$} to $\textbf{0.11}^\circ$ in 2D calibration scenarios, and from $\textbf{5.19}^\circ$ to $\textbf{0.86}^\circ$ in 3D calibration ones.

Figures (11)

• Figure 1: Illustration of the considered cooperative beam calibration scenario. Local calibrated array beam patterns are obtained from cooperative UEs and then fused globally.
• Figure 2: The photo of the RIS pattern measurements in the anechoic chamber.
• Figure 3: Visualization of beam pattern measurements collected from the chamber: (a) 3D beam pattern for scanning angle at $[-20^\circ, -20^\circ]$; (b) Visualization of 2D beam patterns ($11$ codewords) when elevation angle is $0^\circ$; (c) Visualization of 3D beam patterns ($6 \times 11$ codewords, and the red cross indicates ideal beamforming angle).
• Figure 4: Visualization of the reconstructed 2D beam patterns ($\bar{\varphi}=-20^\circ$).
• Figure 5: Visualization of the reconstructed 3D beam patterns.