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Zak-OTFS ISAC with Bistatic Sensing via Semi-Blind Atomic Norm Denoising Scheme

Kecheng Zhang, Weijie Yuan, Maria Sabrina Greco

TL;DR

This paper tackles ISAC in bistatic Zak-OTFS under doubly dispersive channels with fractional delay-Doppler shifts. It derives a discrete-time Zak-OTFS I/O model and formulates joint channel estimation and data detection as a semi-blind atomic norm denoising problem, introducing a negative-square penalty to handle discrete data. An accelerated algorithm that combines MM, APG, and IAPG is developed and proven to converge to an $\varepsilon$-stationary point; it also employs a homotopy strategy to tune the penalty. Simulations show super-resolution sensing performance and data-demodulation accuracy approaching the perfect CSI lower bound, demonstrating strong potential for practical high-mobility ISAC systems.

Abstract

Integrated sensing and communication (ISAC) through Zak-transform-based orthogonal time frequency space (Zak-OTFS) modulation is a promising solution for high-mobility scenarios. Realizing accurate bistatic sensing and robust communication necessitates precise channel estimation; however, this remains a formidable challenge in doubly dispersive environments, where fractional delay-Doppler shifts induce severe channel spreading. This paper proposes a semi-blind atomic norm denoising scheme for Zak-OTFS ISAC with bistatic sensing. We first derive the discrete-time input-output (I/O) relationship of Zak-OTFS under fractional delay-Doppler shifts and rectangular windowing. Based on this I/O relation, we formulate the joint channel parameter estimation and data detection task as an atomic norm denoising problem, utilizing the negative square penalty method to handle the non-convex discrete constellation constraints. To solve this problem efficiently, we develop an accelerated iterative algorithm that integrates majorization-minimization, accelerated projected gradient, and inexact accelerated proximal gradient methods. We provide a rigorous convergence proof for the proposed algorithm. Simulation results demonstrate that the proposed scheme achieves super-resolution sensing accuracy and communication performance approaching the perfect channel state information lower bound.

Zak-OTFS ISAC with Bistatic Sensing via Semi-Blind Atomic Norm Denoising Scheme

TL;DR

This paper tackles ISAC in bistatic Zak-OTFS under doubly dispersive channels with fractional delay-Doppler shifts. It derives a discrete-time Zak-OTFS I/O model and formulates joint channel estimation and data detection as a semi-blind atomic norm denoising problem, introducing a negative-square penalty to handle discrete data. An accelerated algorithm that combines MM, APG, and IAPG is developed and proven to converge to an -stationary point; it also employs a homotopy strategy to tune the penalty. Simulations show super-resolution sensing performance and data-demodulation accuracy approaching the perfect CSI lower bound, demonstrating strong potential for practical high-mobility ISAC systems.

Abstract

Integrated sensing and communication (ISAC) through Zak-transform-based orthogonal time frequency space (Zak-OTFS) modulation is a promising solution for high-mobility scenarios. Realizing accurate bistatic sensing and robust communication necessitates precise channel estimation; however, this remains a formidable challenge in doubly dispersive environments, where fractional delay-Doppler shifts induce severe channel spreading. This paper proposes a semi-blind atomic norm denoising scheme for Zak-OTFS ISAC with bistatic sensing. We first derive the discrete-time input-output (I/O) relationship of Zak-OTFS under fractional delay-Doppler shifts and rectangular windowing. Based on this I/O relation, we formulate the joint channel parameter estimation and data detection task as an atomic norm denoising problem, utilizing the negative square penalty method to handle the non-convex discrete constellation constraints. To solve this problem efficiently, we develop an accelerated iterative algorithm that integrates majorization-minimization, accelerated projected gradient, and inexact accelerated proximal gradient methods. We provide a rigorous convergence proof for the proposed algorithm. Simulation results demonstrate that the proposed scheme achieves super-resolution sensing accuracy and communication performance approaching the perfect channel state information lower bound.
Paper Structure (30 sections, 4 theorems, 86 equations, 8 figures, 2 algorithms)

This paper contains 30 sections, 4 theorems, 86 equations, 8 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Two-Step ISAC
  4. Parameters Estimation
  5. Contributions
  6. Zak-OTFS Signal Model
  7. General Zak-OTFS I/O Relation
  8. Specific Zak-OTFS Implementation via OFDM Framework
  9. Matrix Form I/O Relation of Zak-OTFS
  10. ISAC Scenario and Embedded Pilot Scheme
  11. Problem Formulation
  12. Atomic Norm Formulation
  13. Penalty-Based Reformulation
  14. Iterative Coordinate Descent Method for Zak-OTFS ISAC
  15. Our Proposed Algorithm
  16. ...and 15 more sections

Key Result

Lemma 1

For any fixed channel vector $\mathbf{h}$, there exists a threshold $\rho_0 > 0$ such that for all $\rho > \rho_0$, the (local) optimal solution for $\mathbf{x}_{\operatorname{dd}, d}$ in the penalty-based problem sec4_prob:penalty_model_anm is identical to that of the original discrete problem sec3

Figures (8)

  • Figure 1: An illustration of the ISAC scenario.
  • Figure 2: OFDM-based framework of windowed Zak-OTFS.
  • Figure 3: Zak-OTFS frame with embedded pilot.
  • Figure 4: Iteration performance of the proposed accelerated algorithm and ordinary algorithm.
  • Figure 5: BER performance with BPSK modulation.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Lemma 1: wu2024quantized
  • Theorem 1
  • proof
  • Lemma 2: Schmidt2011
  • Lemma 3: xu2013block