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Data-Aided Asynchronous OFDM Integrated Sensing and Communications: A Mean-Field Variational Bayes Approach
Van-Chung Luu, Nuria González Prelcic, Duy H. N, Nguyen
TL;DR
Practical asynchronous uplink OFDM-ISAC must handle TO and CFO while making better use of limited pilot resources. The paper proposes a data-aided mean-field VB framework that jointly estimates data, channel, sensing, and synchronization parameters, and reports improved performance across communication and sensing tasks.
Problem
Pilot-centric ISAC designs underuse data symbols, while TO and CFO complicate reliable data detection and sensing-parameter estimation.
Method
A mean-field VB receiver jointly infers transmitted symbols, multipath parameters, sensing parameters, TO, and CFO, then uses detected data as additional observations for refinement.
Results
The proposed method outperforms SAGE, SBL, AB2FM, and pilot-only VB baselines across symbol detection, channel estimation, path-parameter estimation, synchronization estimation, and localization.
Takeaways & Limitations
Detected data symbols can enhance communication and sensing estimation without sacrificing communication performance or requiring extra pilot overhead.
Abstract
from arXiv · showhide
Integrated sensing and communication (ISAC) is regarded as a key technology for sixth-generation wireless networks, allowing sensing and communication operations to jointly utilize the same spectrum and hardware infrastructure. However, in practical uplink ISAC systems, timing offset (TO) and carrier-frequency offset (CFO) introduce phase distortions across subcarriers and OFDM symbols, which can severely degrade both data detection and sensing-parameter estimation. In this paper, we propose a data-aided variational Bayesian (VB) framework for asynchronous uplink OFDM-ISAC systems. Specifically, the received signal is modeled as a sparse multipath superposition, where the transmitted data symbols, complex path gains, spatial frequencies, delay-Doppler parameters, and synchronization parameters are jointly inferred. To enable tractable inference, we develop a mean-field VB algorithm in which von Mises distributions are used for gridless updates of the angular and delay-Doppler phase parameters, while a Gamma-Gaussian prior is adopted to promote path sparsity. A key feature of the proposed framework is its data-aided sensing capability: after initial pilot-based estimation, the detected data symbols are exploited as additional observations to refine the channel and sensing parameters. This substantially increases the effective sensing resources without requiring extra pilot overhead. The simulation results demonstrate that the proposed approach achieves superior performance compared with SAGE, SBL, AB2FM, and pilot-only VB baselines in terms of symbol error rate, channel reconstruction accuracy, path-parameter estimation, TO/CFO estimation, and 3D localization accuracy. The results also demonstrate that ignoring TO and CFO leads to severe sensing degradation, highlighting the importance of synchronization-aware and data-aided receiver design for ISAC systems.
I. Introduction
The paper addresses asynchronous uplink OFDM-ISAC under synchronization mismatch and limited pilot resources by jointly inferring data, channel, sensing, and synchronization parameters. Its mean-field VB receiver uses probabilistic modeling and detected data symbols to refine estimation without additional pilot overhead.
- Motivation: TO and CFO, along with mobility and multipath propagation, create practical impairments for ISAC signal processing.
- Motivation: Pilot-centric designs underuse data-carrying symbols, although detected data can enhance sensing without additional signaling overhead.
- Contributions: The proposed mean-field VB framework jointly infers TO, CFO, propagation parameters, and transmitted data symbols in a unified receiver.
- Contributions: Unknown path gains, angles, delays, Doppler shifts, TO, and CFO receive suitable priors, including von Mises distributions for angular and phase parameters.
- Results: Simulation results show consistent outperformance over SBL, AB2FM, and SAGE across SER and channel-parameter NMSE, while data payload symbols improve estimation accuracy.
- System Model: The bistatic uplink model contains pilot and data symbols, a direct path, multiple reflected paths, and a UPA receiver.
III. Unambiguous Delay and Doppler Ranges
Delay and Doppler parameters are identified through periodic complex phase sequences. Consequently, each is uniquely recoverable only within its corresponding unambiguous interval.
- Delay and Doppler identifiability is governed by the periodicity of their associated complex exponentials.
A. Delay Ambiguity
The delay-dependent phase progression makes delays periodic and therefore potentially indistinguishable. Unique delay identification requires restricting delay to an interval of width 1/∆f.
- Two delays are indistinguishable when they generate the same phase progression over all subcarriers.
- Delay is periodic with period 1/∆f, so unique identification requires an interval of width 1/∆f.
B. Doppler Ambiguity
Doppler shifts exhibit periodicity through their phase sequence across OFDM symbols. Thus, unique Doppler identification is limited to an interval of width 1/Tsym.
- The Doppler-dependent phase term produces a Doppler periodicity across OFDM symbols.
- Unique Doppler identification is restricted to an interval of width 1/Tsym, with a common symmetric range choice.
C. Impact of Pilot Subsampling
Pilot-only initialization uses every D_f-th subcarrier, which narrows the unambiguous delay range and can make delays ambiguous before joint refinement.
- Pilot observations are subsampled every D_f-th subcarrier during initialization, changing the delay-dependent phase progression.
- Under pilot subsampling, two delays become indistinguishable when they produce the same sampled phase progression.
- The resulting delay periodicity and unambiguous delay interval are reduced relative to full-subcarrier observations.
- Pilot subsampling can therefore create initialization ambiguity when the true delay exceeds the narrowed identifiable interval.
IV. Variational Bayesian Inference
The proposed mean-field VB algorithm jointly estimates data, multipath channel parameters, and residual synchronization parameters to support data-aided sensing under TO and CFO.
- The inference framework jointly estimates transmitted data symbols, multipath channel parameters, and residual synchronization parameters.
- The algorithm derives tractable update rules for all latent variables in the probabilistic model.
- Joint inference enables data-aided sensing despite timing-offset and carrier-frequency-offset impairments.
A. Background on VB
Variational Bayes approximates an generally intractable posterior with a tractable distribution, and the mean-field assumption yields coordinate-wise updates.
- VB approximates the posterior p(x | y) with a distribution q(x) from a chosen variational family.
- The variational objective is equivalent to maximizing the evidence lower bound, or ELBO.
- The mean-field assumption factorizes the approximation so each latent-variable factor can be updated separately.
- Coordinate-ascent variational inference monotonically increases the ELBO and converges to a local optimum.
B. Proposed Variational Bayesian Inference Algorithm
The proposed algorithm applies mean-field VB to a sparse multipath OFDM-ISAC model, jointly updating data, channel, spatial, delay-Doppler, and synchronization variables.
- The unknown noise precision γ is inferred jointly with transmitted symbols, path gains, delay-Doppler parameters, spatial frequencies, and synchronization parameters.
- The channel is reconstructed from path-specific array responses and updated path parameters during inference.
- The received signal is modeled through a probabilistic factorization involving observations, data symbols, path parameters, synchronization variables, and noise precision.
- A sparse Gamma-Gaussian prior is imposed on path-related variables to support sparse multipath estimation.
- Von Mises approximations provide gridless updates for spatial-frequency variables and their expected steering vectors.
- The algorithm initializes paths from pilot observations, then iteratively updates data symbols, synchronization, spatial frequencies, delay-Doppler phases, path parameters, and noise precision.
V. Simulation Results
Simulations evaluate data detection, channel reconstruction, and parameter estimation across SNR for the proposed method and four baselines. The proposed data-aided refinement consistently improves performance across communication, channel, path, angular, delay, timing, velocity, and CFO metrics.
- Data detection: All considered methods achieve reliable data detection, while the proposed method attains slightly lower SER than the baselines.Joint channel refinement and symbol detection improve the reliability of both channel estimation and data detection.
- Channel reconstruction: The proposed method substantially improves channel reconstruction NMSE after incorporating detected data symbols into the refinement stage.The improvement is approximately 10 dB over the pilot-only case.
- Path-gain estimation: The proposed JED-VB method substantially improves complex path-gain estimation and consistently outperforms SAGE and SBL.Pilot-only VB performs comparably to SAGE and SBL because all exploit statistical inference over sparse multipath structure.
- Angular estimation: The proposed method achieves the best azimuth- and elevation-angle estimation performance over the entire SNR range.Von Mises posterior approximations support efficient gridless angular updates, while detected data provide additional observations during refinement.
- Delay and timing estimation: The proposed method consistently outperforms all baselines for path-delay and timing-offset estimation across the considered SNR range.Data-aided refinement exploits detected symbols as additional observations; AB2FM performs worse especially at moderate and high SNR.
- Velocity and CFO estimation: The proposed method achieves the best velocity and CFO estimation performance over the entire SNR range.For CFO, VB-based methods continue improving with SNR while baselines show saturation; data-aided refinement further reduces estimation error.
A. 3D Target Position Estimation
The paper derives a 3D target-position estimation procedure from estimated angular and delay information, then evaluates moving-target position and velocity recovery under synchronization compensation. Ignoring TO and CFO causes substantial localization and velocity-estimation errors.
- Position-estimation procedure: The target position is estimated from the UE and BS positions, estimated target direction, and bistatic excess delay.The direction is obtained from estimated azimuth and elevation, while the excess delay is measured relative to the direct UE-BS path.
- Simulation results: At SNR = 10 dB, TO and CFO compensation enables accurate recovery of moving-target position and velocity.The comparison is presented in Fig. 11 for 3D position and velocity estimation.
- Simulation results: Ignoring TO and CFO makes the estimated target states deviate significantly from the true states.Residual timing and frequency offsets therefore produce severe localization and velocity-estimation errors.
VI. Conclusion
The conclusion presents a unified variational-Bayesian receiver for asynchronous uplink OFDM-ISAC that jointly estimates communication, channel, sensing, and synchronization variables. Data-aided refinement improves communication and sensing performance, while synchronization-aware processing is necessary for reliable localization and velocity estimation.
- Conclusion: The proposed framework jointly estimates transmitted symbols, multipath channel parameters, and residual TO and CFO.It combines channel estimation, synchronization, and data detection within one VB framework.
- Conclusion: The framework uses separable UPA steering responses and von Mises distributions for efficient gridless angular-parameter estimation.The conclusion identifies this modeling choice as an efficiency-enabling component of the method.
- Conclusion: Detected data symbols are used as additional observations in a data-aided refinement stage to improve communication and sensing performance.This refinement follows the initial joint inference framework.
- Conclusion: The method outperforms SBL, SAGE, AB2FM, and pilot-only VB across SER, channel NMSE, parameter estimation, and TO/CFO estimation metrics.The reported comparison also covers sensing-related performance across multiple evaluated metrics.
- Conclusion: Neglecting TO and CFO significantly impairs localization accuracy and velocity estimation.The conclusion uses this result to underscore synchronization-aware receiver design for ISAC.