[Paper Review] STAR-RIS-Assisted Full-Space Angle Estimation via Finite Rate of Innovation

Ziming Liu, Tao Chen+2 more|arXiv (Cornell University)|Feb 2, 2026

Advanced Wireless Communication Technologies0 citations

TL;DR

This paper develops a gridless, FRI-based full-space DOA estimation framework for STAR-RIS aided sensing, addressing two practical STAR-RIS configurations (element-wise uniform and nonuniform ES) and recovering angles via annihilating filters with proximal gradient optimization.

ABSTRACT

Conventional sensor architectures typically restrict angle estimation to the half-space. By enabling simultaneous transmission and reflection, simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) can support full-space angle detection. This paper develops a fullspace angle estimation framework by leveraging a finite rate of innovation (FRI) model enabled by STAR-RIS. We distinguish two practical STAR-RIS configurations: (i) an element-wise uniform setting, where all metasurface elements share identical energy-splitting (ES) coefficients and phase differences, and (ii) a nonuniform ES setting, where the phase difference is common across elements while the ES coefficients vary element-wise to increase design flexibility. For each regime, we formulate the corresponding FRI-based signal model and derive the Ziv-Zakai bound (ZZB) for angle estimation. To recover the underlying FRI sampling structure, we develop a proximal-gradient algorithm implemented via alternating projections in matrix space and establish its convergence. Exploiting the recovered FRI structure, we construct an annihilating filter whose zeros encode user angles, enabling gridless estimation via polynomial root finding. Numerical results demonstrate that the proposed methods operate reliably across both configuration regimes and achieve improved angle estimation performance with low overhead.

Motivation & Objective

• Motivate full-space DOA estimation in STAR-RIS-enabled sensing to overcome hemispherical limitations of conventional RIS.
• Formulate FRI-based signal models under two practical STAR-RIS configurations (uniform ES and nonuniform ES).
• Develop gridless angle recovery algorithms leveraging annihilating filters and structured Hankel matrices.
• Provide recovery guarantees and theoretical performance bounds for DOA estimation (ZZB).
• Validate the proposed methods through simulations showing robustness and efficiency across regimes.

Proposed method

• Model the STAR-RIS as reflection and transmission matrices with element-wise ES and phase constraints under two regimes (uniform ES; nonuniform ES).
• Transform the multiuser STAR-RIS data into a multichannel line-spectrum form and apply FRI for gridless DOA recovery via annihilating filters.
• For uniform ES, exploit a rank-one structured sensing form and recover DOAs by solving AF equations after denoising via a proximal-gradient method with alternating projections.
• For nonuniform ES, use a single-row block Hankel construction and adapt the alternating-projection framework to handle the resulting block-matrix structure with convergence guarantees.
• Derive the ZZB to characterize fundamental angle-estimation limits.
• Outline an algorithm (Algorithm 1) combining PGD, Hankel/rank projections, and polynomial root finding to extract DOAs.

Figure 1: Schematic diagram of the STAR-RIS-assisted system.

Experimental results

Research questions

• RQ1 How can STAR-RIS achieve true full-space angle estimation by leveraging reflection-transmission coupling?
• RQ2 How to formulate and solve a gridless, FRI-based DOA estimation problem under element-wise uniform ES and nonuniform ES STAR-RIS configurations?
• RQ3 What are the theoretical performance limits (ZZB) for DOA estimation in STAR-RIS aided sensing?
• RQ4 Can a proximal-gradient with alternating projections reliably recover the FRI structure from slot-varying measurements and enable accurate angle reconstruction?
• RQ5 How do the proposed methods perform in terms of accuracy and overhead across the two practical STAR-RIS regimes?

Key findings

• The proposed FRI-based framework enables gridless DOA estimation for full-space STAR-RIS configurations in both regimes.
• An annihilating-filter approach encodes user angles as polynomial roots, enabling direct angle recovery.
• A proximal-gradient method with alternating projections recovers denoised FRI samples under both regimes, with convergence guarantees for the nonuniform ES case.
• Ziv–Zakai bound is derived to characterize the fundamental DOA-estimation performance limits.
• Numerical experiments show reliable operation and improved estimation performance with low overhead across both uniform and nonuniform ES settings.

(a) Scenario 1