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PARAFAC-Based Low-Latency Angular Tracking for RIS-Assisted Sensing

Kenneth Benício, André L. F. de Almeida, Bruno Sokal, Fazal-E Asim, Gabor Fodor, A. Lee Swindlehurst

arXiv:2609.28255v1eess.SP

TL;DR

Moving-target sensing with batch tensor estimators can require collecting a full sensing window before parameter updates, delaying tracking. ATTRACT performs structure-aware, slice-wise tensor updates, and numerical results report accuracy approaching the offline baseline at high SNR with slot-wise execution on the order of 10^-2 s in the evaluated setup.

  • Problem

    Batch tensor estimators assemble pilot blocks over a sensing window before updating moving-target parameters, delaying updates and adding computational burden.

    Source: §I · p. 1

  • Method

    ATTRACT uses slicewise ALS with carried-forward factor estimates and refines delay and Doppler factors using known sensing structure within each iteration.

    Source: §I · p. 1, §III · pp. 2–3

  • Results

    ATTRACT approaches the offline ALS baseline’s accuracy at high SNR and achieves execution times on the order of 10^-2 s per slot in the evaluated setup.

    Source: §V · p. 4, §IV · p. 4

  • Takeaways & Limitations

    Sequential processing updates the target state without waiting for a complete sensing window or requiring an explicit target-motion model.

    Source: §III · p. 3, §V · p. 4

Abstract

from arXiv · show

This paper proposes adaptive tensor tracking for angular trajectories (ATTRACT), a structure-aware alternating least squares algorithm for low-latency target tracking in reconfigurable intelligent surface (RIS)-assisted sensing. The received echo is represented as a dynamic third-order PARAFAC tensor that separates angular, delay, and Doppler information. Unlike batch tensor estimators, ATTRACT processes one data slice at a time and carries forward the preceding factor estimates, avoiding the need to collect an entire sensing window before updating the target state. Its distinguishing feature is the integration of delay and Doppler structure into each iterative update through the known transmitter-RIS channel, pilot signals, and RIS configurations. Numerical results show that, for a large enough RIS, ATTRACT achieves accuracy comparable to the offline tensor baseline at high signal-to-noise ratios while reducing computational overhead and providing slot-wise estimates.

I. INTRODUCTION

Prior batch PARAFAC estimators can be accurate but delay moving-target updates while pilot blocks are collected and increase processing burden. ATTRACT combines sequential updates with the physical factor structure of RIS-assisted sensing.

I. INTRODUCTION

  • Prior batch PARAFAC/ALS/ESPRIT frameworks collect pilot blocks over a sensing window before estimation, delaying moving-target updates and increasing computational burden.Streaming tensor algorithms address sequential processing, but the stated contribution is to combine this feature with RIS sensing structure.Source: §I · p. 1
  • ATTRACT is a structure-aware, slicewise ALS algorithm for adaptive tracking of angular trajectories.Its updates use the known transmitter–RIS channel, pilot matrix, and RIS configurations to refine delay and Doppler factors within each iteration.Source: §I · p. 1
  • A dynamic third-order PARAFAC representation separates the time-varying angular response from delay- and Doppler-dependent factors, enabling updates from each new data slice.The paper compares ATTRACT with an offline ALS baseline for accuracy, angular tracking, and execution time.Source: §I · p. 1

II. SYSTEM MODEL

The system models a moving target sensed through an RIS-assisted link, with a blocked direct path and OFDM pilots transmitted across subcarriers and symbols. Stacking time-slot echo matrices produces a third-order PARAFAC tensor that separates the evolving angular response from delay and Doppler factors treated as static over the observation window.

II. SYSTEM MODEL

  • The model assumes a blocked direct line-of-sight path, so the sensing echo uses the RIS-assisted link between the transmitter and moving target.The transmitter uses a uniform planar array and a diagonal RIS with unit-modulus response.Source: §II · p. 1
  • OFDM pilot observations across subcarriers and symbols form a per-slot echo matrix with delay-, angular-response-, and Doppler-dependent factors.The delay factor includes the pilot and transmitter–RIS channel structure; the angular factor contains the time-varying response and complex channel coefficient.Source: §II · p. 2
  • Stacking the per-slot matrices over time yields a third-order PARAFAC tensor that separates the evolving angular response from delay and Doppler factors treated as static over the observation window.The proposed algorithm recursively updates factors and estimates the angular state from the current slice.Source: §II · p. 2

III. PARAFAC-BASED ADAPTIVE TENSOR TRACKING FOR ANGULAR TRAJECTORIES

ATTRACT fits a dynamic PARAFAC model by processing each current data slice and carrying forward preceding factor estimates. It enforces known delay and Doppler structure within ALS updates, then uses ESPRIT to extract physical parameters.

III. PARAFAC-BASED ADAPTIVE TENSOR TRACKING FOR ANGULAR TRAJECTORIES

  • Each new slice is processed using preceding factor estimates, with adaptive ALS updating factors for the current observation rather than refitting the accumulated tensor.The dynamic fitting formulation separates the evolving angular response from delay- and Doppler-dependent factors treated as static over the observation window.Source: §III · pp. 2–3
  • The described subproblems yield slot-wise updates.Source: §III · p. 3
  • Known sensing structure refines delay and Doppler factors within the ALS loop instead of treating all factor entries as independent unknowns.The method uses the ST–RIS channel matrix G, assumed available from prior estimation, and known RIS configurations for the structured updates.Source: §III · p. 3
  • The unstructured delay-factor update resolves the N matched Kronecker columns, but cannot uniquely recover the N^2−N cross-column terms.The rank deficiency also prevents unique estimation of all columns of X̂τ,t.Source: §III · p. 3
  • After ALS converges, ESPRIT estimates delay and Doppler, while the reconstructed echo supports estimation of the time-varying complex channel coefficient.The channel gain is computed as the sample mean of element-wise ratios between the received and reconstructed slices.Source: §III · pp. 2–3

IV. NUMERICAL RESULTS

ATTRACT’s accuracy gap relative to offline ALS narrows as SNR approaches 20 dB, and its accuracy improves with more reflecting elements in the evaluated configurations. It tracks a directional shift more closely in the reported example and produces slot-wise estimates with execution time on the order of 10^-2 seconds per slot.

IV. NUMERICAL RESULTS

  • The evaluation uses 1000 Monte Carlo runs in a far-field monostatic OFDM scenario with a diagonal RIS and random pilot signals.The reported configuration uses T = 32 time slots, M = 256 symbols, and Q = 16 subcarriers.Source: §IV · pp. 3–4
  • As SNR approaches 20 dB, ATTRACT’s accuracy gap with offline ALS narrows; increasing reflecting elements degrades offline accuracy but improves ATTRACT’s in the evaluated configurations.The paper attributes the more favorable accuracy–complexity tradeoff to reusing preceding estimates and imposing known delay and Doppler structure.Source: §IV · p. 4
  • At SNR 15 dB with N = 4, ATTRACT follows the angular trajectory more closely than offline ALS in the example with an azimuth-trend step at t = 13.Offline ALS exhibits outliers, including at t = 16.Source: §IV · p. 4
  • ATTRACT’s execution time is on the order of 10^-2 s per slot, and sequential updates do not require waiting until the sensing window ends.The paper distinguishes this data-collection delay from processing time.Source: §IV · p. 4

V. CONCLUSION

ATTRACT combines slicewise adaptive ALS with delay- and Doppler-factor refinement from the known sensing configuration for low-latency RIS-assisted angular tracking. It approaches offline-baseline accuracy at high SNR while achieving execution times on the order of 10^-2 s per slot in the evaluated setup.

  • ATTRACT integrates slicewise adaptive ALS with delay- and Doppler-factor refinement based on the known sensing configuration.Source: §V · p. 4
  • By processing each new observation slice, ATTRACT updates the target state without assembling a full sensing window or requiring an explicit motion model.Source: §V · p. 4
  • At high SNR, ATTRACT approaches the offline baseline’s accuracy in the evaluated setup.Source: Figure 2 · p. 4, §V · p. 4
  • ATTRACT achieves execution times on the order of 10^-2 s per slot; Fig. 3 compares angular tracking and execution time at 15 dB with N = 4.Source: Figure 3 · p. 4, §V · p. 4
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