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Joint Localization and Data Detection in Ambient Backscatter Communications: Uncertainty-Preserving Inference and Cross-Frame Geometry Consensus

Xianhua Yu, Dong Li, Bowen Gu, Tianhao Liang, Tingting Zhang

arXiv:2609.37622v1eess.SP

TL;DR

Weak ambient-backscatter observations can leave competing geometry hypotheses plausible, while a staged point-estimate interface can discard ambiguity relevant to joint localization and detection. GeoFrameNet preserves candidate-level uncertainty across a frame, and CFGC-Net fuses candidate information across frames for localization; both show favorable localization comparisons within the evaluated settings.

  • Problem

    Weak channel observations can leave multiple physical geometry hypotheses plausible, and a staged point-estimate interface can discard that ambiguity before data detection.

    Source: B. Related Work and Research Gap · p. 2

  • Method

    GeoFrameNet forms a shared geometry posterior from sign-robust full-frame evidence for task-specific localization and detection, while CFGC-Net fuses frozen candidate logits and features across frames for localization.

    Source: §VI · p. 13

  • Results

    GeoFrameNet achieves lower localization RMSE than MMV-SBL at all eight evaluated SNR points, with simultaneous BER and RMSE reductions from −30 to −22.5 dB; CFGC-Net has the lowest aggregate RMSE among evaluated fusion strategies for 2, 4, and 8 frames.

    Source: §VI · p. 13

  • Takeaways & Limitations

    The results support candidate-level geometry inference for joint reception and cross-frame candidate fusion for localization under the evaluated conditions.

    Source: §VI · p. 13

    The evaluation is limited to a single-BD model with a dominant backscatter path and idealized environmental suppression; richer propagation, imperfect suppression, multiple-BD reception, and over-the-air validation remain future study.

    Source: §VI · p. 13

Abstract

from arXiv · show

We address joint continuous localization and data detection in ambient backscatter communication, where weak observations can leave competing geometry hypotheses plausible and a staged point-estimate interface can discard information about this ambiguity. We develop the \emph{Geometry-aware Frame Network (GeoFrameNet)}, which projects channel frequency responses onto a physics-derived delay--angle-of-arrival lattice and aggregates sign-robust evidence across orthogonal frequency-division multiplexing symbols to form a shared geometry posterior over physically feasible candidates. Localization uses the full posterior with candidate-specific refinement; detection combines candidate-conditioned differential logits using posterior weights renormalized over selected candidates. Bit supervision guides geometry scoring. For a fixed device, the \emph{Cross-Frame Geometry Consensus Network (CFGC-Net)} fuses frozen GeoFrameNet candidate logits and features across frames for localization while preserving frame-wise detection outputs. On an independent test set, GeoFrameNet achieves lower localization root-mean-square error (RMSE) than an all-symbol multiple-measurement-vector sparse Bayesian learning (MMV-SBL) baseline at all eight evaluated signal-to-noise ratio (SNR) points, with simultaneous bit error rate and RMSE reductions from $-30$ to $-22.5$~dB. At $-30$~dB SNR, the respective RMSEs are 3.1573 and 18.8859~m. CFGC-Net achieves the lowest aggregate RMSE among the evaluated fusion strategies for two, four, and eight frames.

I. INTRODUCTION

Joint recovery of position and data is challenging because weak ambient-backscatter observations can leave multiple delay–AoA hypotheses plausible. GeoFrameNet and CFGC-Net retain and use candidate-level geometry information across symbols and, for localization, across frames.

A. Background

  • Ambient backscatter uses a passive device’s modulated reflection of ambient RF signals, and joint recovery of its data and position can provide spatial context for IoT applications.The related detection and localization literature primarily treats the two tasks separately.Source: A. Background · p. 1, B. Related Work and Research Gap · p. 1

B. Related Work and Research Gap

  • Weak CFR observations can leave physically feasible delay–AoA hypotheses indistinguishable, while the staged receiver in fixes geometry before later symbols contribute to detection.DBPSK sign reversals also make direct coherent accumulation liable to cancel geometry evidence.Source: B. Related Work and Research Gap · p. 2

C. Proposed Approach and Contributions

  • GeoFrameNet aggregates sign-robust evidence over the full frame into a shared geometry posterior, then uses the full posterior for refined localization and renormalized candidate weights for detection.Bit loss influences geometry scoring through posterior weights, while stop-gradient blocks the detector-content path to shared candidate representations.Source: C. Proposed Approach and Contributions · p. 2
  • GeoFrameNet has lower localization RMSE than all-symbol MMV-SBL at every evaluated SNR; CFGC-Net has the lowest aggregate RMSE among evaluated fusion strategies for 2, 4, and 8 frames.GeoFrameNet also reduces BER and RMSE simultaneously from −30 to −22.5 dB.Source: C. Proposed Approach and Contributions · pp. 2–3

A. Geometry and Propagation Model

  • The single-BD ambient-OFDM system estimates continuous two-dimensional position and conveyed data; on the visible branch, an exact delay–AoA pair determines a unique position, but noisy CFR may not identify that pair.The model assumes a dominant backscatter path and frame-static geometry and channel coefficient.Source: A. Geometry and Propagation Model · p. 3

B. Frame Structure and Equivalent CFR Observation

The receiver uses the subsequent backscatter phase after environmental suppression, with one DBPSK reflection symbol per OFDM symbol. Its input is the resulting sequence of equivalent CFR matrices.

B. Frame Structure and Equivalent CFR Observation

  • Each OFDM symbol has a DBPSK reflection state, and adjacent-symbol transitions encode the information bits.The reference reflection symbol is c1 = +1.Source: B. Frame Structure and Equivalent CFR… · pp. 3–4
  • The joint receiver operates on the equivalent post-suppression CFR sequence from the subsequent N-symbol backscatter phase.Environmental response is acquired during a preceding nonbackscattering phase and suppressed before joint inference.Source: B. Frame Structure and Equivalent CFR… · p. 3, Figure 1 · p. 4
  • After suppression and division by known unit-modulus pilots, each equivalent CFR matrix contains the reflection symbol times the geometry-dependent channel response plus noise.The response is formed from array and delay steering vectors; pilot division preserves the per-entry noise variance.Source: B. Frame Structure and Equivalent CFR… · p. 4

C. Joint Inference Problem

The joint receiver maps a sequence of CFR matrices to a continuous two-dimensional position estimate and detected information bits. It must exploit frame-shared geometry without coherently canceling sign-modulated responses or discarding plausible alternatives.

C. Joint Inference Problem

  • The receiver maps the stacked N-symbol CFR observations to a continuous two-dimensional position estimate and an N−1-bit detection vector.Delay and AoA are intermediate variables induced by position, not independent receiver outputs.Source: C. Joint Inference Problem · p. 4
  • The model assumes known source and receiver positions and OFDM parameters, but unknown device position, composite path coefficient, and information bits.It also assumes a single dominant backscatter path, frame-static geometry and coefficient, synchronization, and a sufficiently long cyclic prefix.Source: C. Joint Inference Problem · p. 4
  • Because geometry is shared across symbols while bits belong to adjacent-symbol transitions, inference must combine repeated geometry evidence without cancellation and retain competing hypotheses when observations are inconclusive.The stated receiver design addresses these coupled requirements with a shared-posterior approach.Source: C. Joint Inference Problem · p. 4

A. Receiver Overview and Design Rationale

GeoFrameNet avoids fixing geometry before localization and detection by deriving a shared posterior from full-frame observations. It uses sign-robust aggregation to strengthen geometry evidence while retaining complex responses for differential detection.

A. Receiver Overview and Design Rationale

  • GeoFrameNet strengthens geometry evidence without prematurely fixing geometry, using full-frame observations and retaining alternatives when the evidence is ambiguous.Localization uses the full posterior with continuous refinement; detection renormalizes posterior weights over selected candidates, and bit supervision guides geometry scoring.Source: A. Receiver Overview and Design… · p. 4

B. Shared-Geometry Posterior Construction

  • The frame-shared geometry posterior is built over nondegenerate physically feasible candidates, while all 2048 lattice sites remain available for dense feature processing.The physical support contains 322 candidates in the considered geometry.Source: B. Shared-Geometry Posterior… · p. 5
  • Magnitude- and energy-based evidence is aggregated across symbols for geometry, while complex candidate projections are retained for differential detection.This separation avoids direct coherent averaging that may cancel components because DBPSK symbols reverse the backscatter sign.Source: B. Shared-Geometry Posterior… · p. 5
  • Candidate features combine local lattice evidence with global context over valid support, and a masked softmax produces the geometry posterior normalized over that support.The posterior retains candidate weights for both receiver tasks without an intermediate top-1 decision.Source: B. Shared-Geometry Posterior… · p. 6

C. Task-Specific Posterior Inference and Controlled Coupling

GeoFrameNet retains a full geometry posterior for localization and combines candidate-conditioned differential logits across selected hypotheses for detection. Bit loss can influence geometry scoring through posterior weights while gradient blocking limits direct detector-content feedback.

C. Task-Specific Posterior Inference and Controlled Coupling

  • Localization retains the full geometry posterior, while detection combines candidate-conditioned differential logits over the top-Ksel candidates using renormalized posterior weights.Candidates outside the selected subset remain in the posterior used for localization; Ksel is 16 in all experiments.Source: C. Task-Specific Posterior Inference… · pp. 6–7
  • The differential detector uses adjacent-symbol phase/sign relations and magnitude context, with the frame-static composite phase canceling while the differential sign carries the bit.The six-dimensional transition feature includes logarithmic magnitude terms and a normalized complex product; its third and sixth entries are algebraically identical.Source: C. Task-Specific Posterior Inference… · p. 7
  • Candidate-conditioned bit logits combine temporal features with geometry and candidate features in an 80-dimensional detector input.The temporal feature is 32-dimensional, the geometry feature is 16-dimensional, and the candidate feature is 32-dimensional.Source: C. Task-Specific Posterior Inference… · p. 7
  • Bit loss acts on final detection logits and can influence geometry scoring through posterior weights, but stopgrad blocks direct gradient flow through candidate content features.Selected top-Ksel indices are fixed during backpropagation, detector parameters still receive bit-loss gradients, and the bit loss does not update refinement-MLP parameters.Source: C. Task-Specific Posterior Inference… · p. 7

D. Continuous Refinement and Training Objective

GeoFrameNet refines candidate coordinates before forming a position estimate from the full posterior, without projecting the final estimate onto the feasible region. Its training objective jointly supervises bit and position recovery, geometry posterior scores, and candidate-specific offsets.

D. Continuous Refinement and Training Objective

  • Candidate-specific refinement reduces local lattice mismatch, while the full posterior is retained through weighted position estimation without an additional projection onto P.The refinement MLP predicts bounded delay and spatial-sine corrections, with each offset bounded by half the nominal lattice spacing before feasibility clipping.Source: D. Continuous Refinement and Training… · p. 7
  • Posterior supervision scores candidates by geometric proximity, while offset supervision targets individual refined coordinates using target weights rather than predicted posterior weights.The position-dependent posterior target is defined on valid physical candidates and is used for training, not required at inference.Source: D. Continuous Refinement and Training… · p. 8
  • The total training objective combines bit, position, delay, spatial-sine, posterior, and offset losses with respective weights 1, 2, 0.25, 0.25, 0.5, and 0.10.The delay and spatial-sine losses are auxiliary constraints derived from predicted and true positions, not independent receiver outputs.Source: D. Continuous Refinement and Training… · p. 8
  • At inference, GeoFrameNet produces position and bit outputs in one fixed-depth forward pass without an intermediate geometry point estimate.The refinement MLP maps shared candidate features to bounded delay and spatial-sine corrections.Source: D. Continuous Refinement and Training… · pp. 7–8

A. Motivation and Design Overview

Across frames, geometry is shared but payloads, composite phases, and noise differ, making direct complex-response averaging vulnerable to destructive combination. CFGC-Net fuses GeoFrameNet candidate logits and features for localization while leaving frame-wise detection outputs unchanged.

A. Motivation and Design Overview

  • The shared geometry across frames contrasts with frame-specific payloads, composite phases, and noise, so direct complex-CFR averaging can combine destructively.Averaging final Cartesian estimates instead discards candidate-level geometry information before fusion.Source: A. Motivation and Design Overview · p. 8
  • CFGC-Net fuses candidate logits and features from frozen GeoFrameNet passes across frames for localization, while preserving every frame-wise detection output.Mean logits provide a parameter-free reference, while averaged features support consensus-score correction and frozen continuous refinement.Source: A. Motivation and Design Overview · p. 8

B. Candidate-Level Cross-Frame Consensus

CFGC-Net averages corresponding candidate logits and features across frames, then uses a feature-based residual correction to the mean-logit consensus reference. It forms localization from a truncated selected-candidate posterior.

B. Candidate-Level Cross-Frame Consensus

  • Axial convolutions exchange information along the delay and wrapped spatial-sine candidate dimensions, and a pointwise map produces one residual logit per candidate.The corrected consensus score adds the learned residual to the mean geometry logit through a learned scalar gate.Source: B. Candidate-Level Cross-Frame Consensus · p. 8
  • The trainable consensus module learns a feature-based residual correction to the parameter-free mean-logit reference.Corresponding candidate logits and 64-dimensional features are averaged across frames; averaged features are arranged on a delay–AoA lattice for axial refinement.Source: B. Candidate-Level Cross-Frame Consensus · p. 8
  • The cross-frame estimator retains the 16 largest valid corrected logits and forms its position estimate from the resulting truncated posterior.Unlike single-frame localization, it uses a posterior restricted to the selected support.Source: B. Candidate-Level Cross-Frame Consensus · p. 8
  • Candidate-level fusion enhances cross-frame localization while preserving all frame-wise detection outputs.The architecture caption identifies localization fusion and unchanged frame-wise detection as the distinct outputs.Source: Figure 3 · p. 9

C. Continuous Position Estimation and Training Objective

CFGC-Net fuses frozen GeoFrameNet candidate information across frames for localization while retaining the original frame-wise detection outputs. Its evaluation uses a shared device position across frames and tests frame counts of two, four, and eight.

C. Continuous Position Estimation and Training Objective

A. Simulation Setup

  • The device position is uniformly sampled over a 20 m by 20 m area, excluding locations within 0.5 m of either endpoint.The source and receiver are at (0, 0) m and (20, 0) m.Source: A. Simulation Setup · p. 9
  • The simulator generates post-suppression channel responses with complex AWGN directly, and training, validation, and test data use disjoint random seeds.Environmental acquisition and suppression are not simulated explicitly.Source: A. Simulation Setup · p. 9
  • Single-frame SNR comparisons reuse the same 300 test frames, while multi-frame tests use 300 groups per SNR with nested prefixes of eight-frame groups.Within each multi-frame group, device position and path-loss magnitude are shared, but payloads, phases, and noise realizations vary across frames.Source: A. Simulation Setup · p. 10

B. Baselines and Evaluation Metrics

GeoFrameNet improves single-frame localization RMSE over MMV-SBL at all evaluated SNRs, with simultaneous BER and RMSE reductions at weak SNR. The evaluation also compares detection and localization baselines using paired test samples.

B. Baselines and Evaluation Metrics

  • Single-frame comparators include all-symbol Grid-LS and MMV-SBL and first-symbol FS-SBL; cross-frame baselines average positions or candidate logits without trainable fusion.MMV-SBL processes all 64 symbols with shared support and geometry variables.Source: B. Baselines and Evaluation Metrics · p. 10
  • Localization uses 300 estimates and 5-m outage; cross-frame RMSE and outage are summarized by geometric and arithmetic means across SNR, respectively, with paired intervals scoped to fixed receivers.The intervals describe test-sample variability, not independent training runs or simultaneous confidence statements across SNRs.Source: B. Baselines and Evaluation Metrics · p. 10

1) Data Detection:

  • 0.348995 vs 0.454339 BER at −30 dB: GeoFrameNet reduces BER by 23.2% relative to MMV-SBL, with both BER and RMSE lower from −30 to −22.5 dB.The BER values are for GeoFrameNet and MMV-SBL, respectively.Source: Figure 4 · p. 10, 1) Data Detection · p. 10
  • At −20 dB, MMV-SBL’s lower empirical BER is not statistically resolved, while GeoFrameNet retains a statistically resolved BER advantage over Grid-LS.The GeoFrameNet-minus-MMV-SBL BER difference has a paired 95% confidence interval of [−5.82 × 10−4, 2.22 × 10−3].Source: 1) Data Detection · pp. 10–11

2) Continuous Localization:

  • 3.1573 m vs 18.8859 m at −30 dB: GeoFrameNet’s RMSE is lower than MMV-SBL’s at all eight SNR points, an 83.3% reduction at −30 dB.At −22.5 dB, the respective GeoFrameNet and MMV-SBL RMSEs are 1.0771 and 3.3255 m.Source: Figure 5 · p. 11, 2) Continuous Localization · p. 11

1) Data Detection:

  • At −15, −10, and −5 dB, all three receivers have zero observed errors, which does not establish zero true BER or BER equivalence.These observations place all three receivers in a near-zero-error regime on this finite test set.Source: 1) Data Detection · p. 11

3) Localization Error Tail:

Across the evaluated frame counts, CFGC-Net leads the fusion strategies in aggregate localization RMSE; GeoFrameNet also reduces large errors, with ablations showing distinct roles for receiver components. The findings are scoped to a single-BD model with a dominant backscatter path and idealized environmental suppression.

3) Localization Error Tail:

  • At −30 dB, GeoFrameNet’s 5-m outage is 0.0900 versus 0.7600 for MMV-SBL; at −27.5 dB, the respective probabilities are 0.0267 and 0.3367.The 5-m outage reductions complement the reported RMSE gains by measuring errors beyond a fixed threshold.Source: 3) Localization Error Tail · p. 11, Figure 6 · p. 11

D. Mechanism Ablation

  • At −20 dB, first-symbol geometry raises BER from 0.0047 to 0.0868 and RMSE from 1.073 to 5.509 m; hard top-1 raises BER to 0.0858 and RMSE to 1.328 m.These are separately trained first-symbol controls and inference-time hard top-1 interventions, respectively.Source: D. Mechanism Ablation · p. 11, Figure 7 · p. 12
  • At −20 dB, blocking the bit-loss gradient through posterior weights raises BER to 0.0130, about 2.8 times GeoFrameNet’s value, while RMSE changes modestly to 1.106 m.This control retains full-frame aggregation, and its larger relative effect is on detection rather than localization.Source: D. Mechanism Ablation · p. 11
  • Removing continuous offsets leaves bit decisions unchanged but increases RMSE to 1.256 m at −20 dB.The inference-time intervention isolates continuous refinement’s localization role in the selected trained model.Source: D. Mechanism Ablation · p. 11, Figure 7 · p. 12

E. Cross-Frame Localization Performance

F. Runtime and Model Size

  • GeoFrameNet requires 1.199 ms/frame and uses 407,812 active inference parameters; CFGC-Net adds 24,770 trainable consensus parameters for 432,582 total.Grid-LS is the fastest evaluated implementation; precision, batching, and implementation differences limit interpretation of timing gaps as implementation-independent complexity.Source: F. Runtime and Model Size · p. 12, Table II · p. 12

VI. CONCLUSION

  • Under the evaluated conditions, GeoFrameNet has lower localization RMSE than MMV-SBL at all eight SNR points, and CFGC-Net has the lowest aggregate RMSE for F ∈ {2, 4, 8}.The findings are limited to a single-BD model with a dominant backscatter path and idealized environmental suppression.Source: §VI · p. 13

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