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Sparse Channel Acquisition in Aging Fluid Antenna Systems: A Reliability-Calibrated Posterior Reconstruction Approach

Xiaokai Song, Jie Tang, Tuo Wu, Geyang Xu, Zhongqing Wu, Baiyang Liu, Kin-Fai Tong, Naofal Al-Dhahir

arXiv:2609.06376v1eess.SP

TL;DR

Aging FAS receivers must acquire useful aperture fields from sparse current observations and dense historical CSI that may be stale. This paper proposes DCP, which anchors reconstruction to current measurements and controls reuse of history; it reports improved reconstruction and selected-port rate with millisecond-level inference.

Abstract

from arXiv · show

Fluid antenna systems (FASs) exploit port-domain diversity within a compact aperture, but their gain can be lost if the receiver has to scan too many ports before data transmission. This paper studies sparse channel acquisition for aging FAS receivers, where the available information has mixed reliability: current observations are fresh but sparse, whereas historical channel state information (CSI) is dense but stale due to Doppler-induced temporal decorrelation. We formulate the problem from a communication perspective by linking aperture-field reconstruction to port-selection rate, outage, probing budget, and online inference latency. We then cast the acquisition task as reliability-calibrated posterior reconstruction, in which the sparse current observations serve as hard measurement evidence and historical CSI is reused only as soft temporal side information. The resulting reliability-controlled conditional diffusion posterior (DCP) framework conditions the denoising process on the sparse current observations, the observation mask, and the historical CSI, and refines the reverse trajectory through observation consistency, mismatch-aware temporal gating, spatial trust weighting, progressive temporal activation, and warm initialization. Analysis shows how aging and reconstruction error induce rate distortion and rate regret. Simulations across probing budgets, signal-to-noise ratios (SNRs), temporal correlations, observation patterns, ablation settings, and latency tests show consistent reconstruction gains with millisecond-level online inference latency, indicating that stale CSI can be beneficial when its strength, timing, and spatial support are explicitly controlled.

I. Introduction

The introduction frames sparse acquisition in aging FAS receivers as a reliability problem: fresh observations are sparse, while dense historical CSI may be stale. It presents DCP as a way to prioritize current measurements while controlling temporal side information, and grounds the task in correlated aperture fields and communication utility.

I. Introduction

  • Sparse probing reduces scanning latency but leaves most ports unobserved, while reliable inference of those ports remains necessary for selection.In aging receivers, dense historical CSI may mismatch the current field and bias unobserved-port estimates.Source: §I · pp. 1–2
  • Prior reconstruction work largely addresses spatial recovery from current observations, leaving joint use of sparse current measurements and stale CSI as the gap addressed here.Existing diffusion approaches generally assume a synchronized sparse snapshot or reliable side information.Source: §I · p. 2
  • DCP prioritizes sparse current observations and reuses historical CSI only where credible, using observation consistency, temporal gating, spatial trust, progressive activation, and warm initialization.The communication-oriented formulation also connects reconstruction to rate, outage, probing budget, and inference latency.Source: §I · p. 2
  • The paper links channel aging and reconstruction error to rate distortion and rate regret, and analyzes measured-port residual contraction and stale-prior bias control.Its validation spans probing budgets, SNRs, temporal correlations, observation patterns, ablations, and latency.Source: §I · p. 2

A. Two-Dimensional FAS Aperture-Field Representation

  • The aperture is represented as a two-dimensional grid of switchable positions, whose nearby ports are spatially correlated rather than statistically independent.The correlation depends on physical separation in wavelengths.Source: A. Two-Dimensional FAS Aperture-Field… · pp. 2–3

B. Channel Aging and Historical CSI

The receiver has fresh sparse measurements and dense historical CSI that carries temporal information but may differ from the current aperture field. The section models that aging and defines sparse observations as masked, noisy measurements used with the history to reconstruct the current field.

B. Channel Aging and Historical CSI

  • Temporal correlation declines with Doppler and delay, so historical CSI becomes less useful as mobility or acquisition delay increases.The first-order channel model is a controlled statistical description of temporal mismatch, not an exact propagation law.Source: B. Channel Aging and Historical CSI · p. 3
  • Historical CSI comes from a source slot d slots earlier, with α_t representing additional fidelity loss from prediction, storage, scanning, calibration, or residual modeling uncertainty.Temporal decorrelation from channel evolution is already represented separately and is not applied again through α_t.Source: B. Channel Aging and Historical CSI · p. 3

C. Sparse Observation Model

D. Communication-Oriented Acquisition Objective

The acquisition objective evaluates reconstruction by its communication use: choosing a port under probing and latency constraints. The section analyzes how stale CSI distorts rate and how reconstruction error can cause rate regret or alter the selected port.

D. Communication-Oriented Acquisition Objective

  • The acquisition objective treats NMSE as a surrogate while prioritizing rate regret, outage, preservation of the best-port region, probing budget, and inference latency.The selected port is activated for data transmission, so reconstruction quality matters through its decision utility.Source: D. Communication-Oriented Acquisition… · p. 4
  • Stale-CSI rate distortion grows with temporal decorrelation, so historical CSI is treated as reliability-dependent memory rather than current measurements.This result is stated for a fixed port under the proposition’s temporal-correlation model.Source: D. Communication-Oriented Acquisition… · p. 4
  • Exact top-port recovery is guaranteed when the true strongest-to-second-strongest gain gap exceeds 2ε(2A + ε).The result connects reconstruction error bounds to the ordering of port gains.Source: D. Communication-Oriented Acquisition… · p. 4
  • Aperture-field reconstruction must preserve local peaks, not only reduce average error, because those peaks affect the final port-selection decision.This motivates combining sparse current observations, historical CSI, and an aperture-field prior.Source: D. Communication-Oriented Acquisition… · p. 4

E. Reliability-Calibrated Posterior Objective

The objective treats sparse current measurements as the priority evidence and historical CSI as reliability-weighted temporal information, alongside a learned aperture-field prior.

E. Reliability-Calibrated Posterior Objective

  • The reconstruction is formulated as posterior inference conditioned on current observations, their mask, and historical CSI, rather than one-shot deterministic regression.The posterior may be represented through sampling or a posterior-mean approximation.Source: E. Reliability-Calibrated Posterior… · p. 4
  • The mask prioritizes measured current entries and lets historical CSI regularize primarily the unmeasured aperture entries.Historical CSI is not imposed as a hard constraint; its reliability is represented by a precision field.Source: E. Reliability-Calibrated Posterior… · p. 5
  • The negative log-posterior combines a learned aperture-field prior, a current-observation likelihood, and a reliability-weighted temporal likelihood for historical CSI.The paper interprets these as prior structure, consistency with sparse current observations, and controlled reuse of stale CSI.Source: E. Reliability-Calibrated Posterior… · pp. 4–5

III. Aging-FAS Posterior Reconstruction Algorithm

The algorithm approximates the aperture-field posterior by combining learned spatial structure with sparse current measurements and reliability-controlled historical CSI. Its conditional diffusion model receives all three information sources, while temporal precision varies with sample mismatch and spatial trust.

III. Aging-FAS Posterior Reconstruction Algorithm

  • DCP solves sparse-probing reconstruction with stale CSI under latency constraints, anchoring probed ports with observation guidance and reusing historical CSI on unobserved ports under reliability control.Offline learning and online inference use the same side information.Source: §III · p. 5

A. FAS Posterior Decomposition Under Sparse Port Probing

  • The posterior score combines a learned aperture-structure term, a pull toward current-slot measured ports, and an aging-dependent historical-CSI term.These correspond to spatial regularity, fresh but sparse observations, and dense but potentially outdated CSI.Source: A. FAS Posterior Decomposition Under… · p. 5
  • A small mismatch between historical CSI and observed entries yields a large effective temporal weight, while a large mismatch suppresses that weight.The sample-wise reliability gate and spatially varying trust map use this overlap to assess whether historical aperture peaks remain informative.Source: A. FAS Posterior Decomposition Under… · p. 5

B. Aperture-Field Prior Conditioned on FAS Side Information

  • The conditional denoiser receives historical CSI, sparse current observations, and the observation mask, distinguishing measured, missing, and temporal side information.The condition tensor uses two real-imaginary channels for each CSI input and one channel for the mask.Source: B. Aperture-Field Prior Conditioned on… · p. 5
  • A two-dimensional U-Net-style denoiser uses time embeddings and skip connections, with conditioning at every reverse step to preserve measured values and decision-relevant local aperture structure.The framework learns complete aperture-field distributions offline and uses the current observations, mask, and historical CSI to guide online posterior sampling.Source: B. Aperture-Field Prior Conditioned on… · p. 5, Figure 1 · p. 6, Figure 2 · p. 6

C. Measured-Port Anchoring

Measured-port anchoring limits drift from the freshest current-slot evidence, while historical CSI is reused according to mismatch, spatial trust, and reverse-step timing.

C. Measured-Port Anchoring

  • Likelihood-gradient correction and direct fusion jointly limit drift at measured entries, leaving the learned prior to reconstruct the remaining aperture.Observed ports serve as hard evidence, while the diffusion prior controls unmeasured regions.Source: C. Measured-Port Anchoring · p. 6

D. Reliability-Controlled Reuse of Historical CSI

  • DCP estimates temporal reliability from pilot disagreement and controls historical-CSI reuse through sample-wise gating, spatial trust weighting, and progressive scheduling.Historical CSI is useful only when consistent with the current slot, because stale peaks can bias port ranking.Source: D. Reliability-Controlled Reuse of… · p. 6
  • Small mismatch keeps the temporal gate near its maximum, whereas large mismatch drives it toward its minimum and weakens temporal correction.The gate therefore reuses historical CSI aggressively only when observed ports indicate that the old aperture pattern still resembles the present one.Source: D. Reliability-Controlled Reuse of… · p. 7
  • Spatial trust gives greater temporal weight to regions consistent with current observations and less to mismatched regions, accommodating aging that affects only part of the aperture.Temporal regularization activates only after a reverse-sampling threshold, allowing early steps to establish present-slot structure from the prior and sparse observations first.Source: D. Reliability-Controlled Reuse of… · p. 7

E. Low-Latency Sampling for Online FAS Receivers

The online sampler uses reliability-controlled warm initialization and skipped DDIM steps to balance inference speed and reconstruction accuracy for port activation.

E. Low-Latency Sampling for Online FAS Receivers

  • A large temporal gate initializes sampling near a noisy historical field, while a small gate falls back to standard random initialization.The warm start is intended to provide a more informative initialization when historical CSI is reliable.Source: E. Low-Latency Sampling for Online FAS… · p. 7
  • Skipped-step DDIM sampling offers a runtime–accuracy tradeoff for latency-sensitive online aperture-field reconstruction.Inference delay must remain small relative to channel coherence time and the probing overhead reduced by sparse acquisition.Source: E. Low-Latency Sampling for Online FAS… · p. 7
  • The reported experiments use one posterior sample and 25 DDIM steps, with online cost O(SCnet), where S is retained steps and Cnet is one denoiser evaluation.More samples reduce sampling variance but increase latency.Source: E. Low-Latency Sampling for Online FAS… · p. 7

IV. Theoretical Validation of DCP

The analysis interprets DCP guidance as reliability-calibrated fusion: current observations anchor measured ports, while historical CSI guides unmeasured ports according to its reliability. It also describes the sampler’s sequential guidance as a low-cost approximation to this fusion rule.

IV. Theoretical Validation of DCP

  • The analysis supports per-step fusion, contraction of measured-port residuals, and suppression of stale-CSI bias on unobserved entries, without claiming global optimality.Its scope is guidance properties tied to FAS acquisition, rather than a global optimality result.Source: §IV · p. 7

A. Per-Step Reliability-Calibrated Fusion

  • The algorithm computes mismatch, a temporal gate, a spatial trust map, and a warm start before iterating denoising, observation anchoring, and reliability-controlled historical-CSI correction.It then propagates the state through DDIM steps and outputs the reconstructed aperture field.Source: A. Per-Step Reliability-Calibrated… · p. 8
  • The surrogate objective keeps estimates near the denoiser output, enforces current observations, and reuses historical CSI only on unobserved ports.The resulting unique minimizer fuses denoiser predictions with current observations at measured ports and reliability-weights historical CSI on unmeasured ports.Source: A. Per-Step Reliability-Calibrated… · p. 8

B. Measured-Port Stability and Stale-CSI Bias Control

The analysis examines measured-port stability and stale-CSI bias control, then gives the sampler’s computational implications and the scope of its experimental aging protocol.

B. Measured-Port Stability and Stale-CSI Bias Control

  • The observation-guidance update contracts residuals on measured ports for 0 < µ < 2, keeping currently sounded ports as reference points during reconstruction.Direct fusion further reduces drift by replacing or averaging measured components with sparse current observations.Source: B. Measured-Port Stability and… · p. 8
  • When g_min is small, the stale-CSI bias bound on unobserved entries decreases as observed historical mismatch increases.The sample-wise gate and spatial trust map suppress bias when historical CSI is inconsistent with current observations, reducing the risk of outdated aperture peaks distorting port ranking.Source: B. Measured-Port Stability and… · pp. 8–9

C. Computational Implication

  • With L = 1 and S = 25, online complexity is dominated by 25 denoiser evaluations, while reliability-control modules add only lower-order elementwise operations.The reported dominant complexity is O(LSCnet), and methods using similar steps and backbones are expected to have similar deployment costs with a small additional reliability-control cost.Source: C. Computational Implication · p. 9

A. Data Construction and Aging Protocol

  • Evaluation uses a controlled synthetic 16 × 16, 256-port aperture protocol to isolate sparse probing, temporal correlation, and historical-CSI mismatch rather than replace ray-tracing or measured-channel campaigns.Unless otherwise specified, the SNR is 15 dB and diffusion sampling uses 25 DDIM steps.Source: A. Data Construction and Aging Protocol · p. 9

B. Compared Methods and Fairness Rules

DCP combines conditional diffusion with reliability-controlled use of current observations and historical CSI. Across probing budgets and observation SNRs, it leads the reported NMSE and selected-port rate comparisons, with the clearest advantage under sparse probing.

B. Compared Methods and Fairness Rules

  • DCP is the full proposed design; DUPP tests inference-only historical-CSI reuse, DUNP removes historical reuse, and GP-ST fuses current observations and temporal side information through a Gaussian-process prior.OMP, SBL, and LMMSE provide model-driven sparse-recovery and covariance-based linear-estimation comparisons.Source: B. Compared Methods and Fairness Rules · p. 9

C. Evaluation Metrics

  • Evaluation separates full-field fidelity (NMSE), decision-relevant selected-port utility (average achievable rate), and online deployment cost (per-sample inference time).The rate metric uses a transmission SNR of 5 dB.Source: C. Evaluation Metrics · pp. 9–10

D. Parameter Interpretation

  • The parameter guidance tunes observation anchoring for measurement reliability, temporal gating and spatial trust for aging, then warm-start settings on held-out validation data.The selected settings are kept fixed during the corresponding test sweeps.Source: D. Parameter Interpretation · p. 10

VI. Numerical Results

  • The numerical evaluation covers reconstruction accuracy, selected-port rate, robustness, and online complexity across probing, SNR, temporal correlation, historical delay, and historical-prior noise.It also assesses latency overhead.Source: §VI · p. 10

A. Main Reconstruction Results

  • DCP maintains the lowest NMSE and highest average achievable rate as observed ports increase from 20 to 140, with its clearest advantage in sparse probing.At larger budgets, SBL approaches DCP in achievable rate, which is tied to preserving a near-optimal high-gain port rather than minimizing full-field NMSE.Source: Figure 3 · p. 10, 1) Effect of Probing Budget · p. 10, Figure 4 · p. 11

1) Effect of Probing Budget:

  • DCP’s simultaneous NMSE and rate gains indicate improvements in both aperture reconstruction and the decision-relevant structure used for port activation.The reported probing-budget comparison finds the clearest advantage in the sparse-probing regime.Source: 1) Effect of Probing Budget · p. 10

2) Effect of SNR:

  • Across −10 to 30 dB observation SNR, all methods’ NMSE decreases as observations become cleaner, and DCP remains best throughout.At low SNR, noisy pilots limit reconstruction; at high SNR, errors are dominated by unobserved ports and model mismatch.Source: 2) Effect of SNR · pp. 10–11, Figure 5 · p. 11

VI. Numerical Results

  • Methods using historical CSI improve as temporal correlation increases, while DUNP is comparatively insensitive; DCP uses history selectively according to agreement with current observations.At low correlation, stale CSI can introduce bias; at high correlation, it becomes a stronger predictor for unobserved ports.Source: 3) Effect of Temporal Correlation · p. 11

3) Effect of Temporal Correlation:

The experiments examine how temporal reliability controls affect reconstruction, whether DCP generalizes across probing patterns, and what its online deployment costs. Results support adapting historical-CSI use to its reliability rather than treating it uniformly.

3) Effect of Temporal Correlation:

  • As temporal correlation changes, the mismatch gate and spatial trust map suppress unreliable historical CSI and strengthen temporal reuse when the side information is more reliable.The test spans five temporal-correlation intervals from ρt ∈[0.75, 1.00] at 15 dB SNR.Source: 3) Effect of Temporal Correlation · p. 11, Figure 6 · p. 11

B. Mechanism Validation

  • DCP-full remains best across historical delays, while its advantage over the no-prior variant narrows as CSI becomes staler; all variants degrade with delay.The hard-prior variant deteriorates most severely, consistent with reducing the role of historical CSI as temporal decorrelation increases.Source: B. Mechanism Validation · p. 11, Figure 7 · p. 12

2) Effect of Historical-Prior Noise:

3) Historical-Prior Ablation:

  • DCP-full achieves the lowest NMSE at every tested budget, while the hard-prior variant performs worst, supporting controlled rather than uniform reuse of stale CSI.Posterior-prior injection and warm initialization help use informative temporal structure; gating and spatial trust weighting limit unreliable guidance.Source: Figure 9 · p. 12, 3) Historical-Prior Ablation · p. 12

4) Robustness to Observation Pattern:

  • DCP exhibits only limited NMSE variation across Uniform, Random, and Greedy observation patterns under the same sparse budget.Conditioning on the observation mask informs the denoiser which ports are observed and supports adaptation to different spatial supports.Source: 4) Robustness to Observation Pattern · p. 12, Figure 10 · p. 12

VII. Conclusion

  • DCP improves reconstruction and selected-port achievable rate under limited probing and imperfect historical CSI, with millisecond-level inference and negligible added FLOP/memory cost over diffusion baselines.The reported rate results also indicate better preservation of decision-relevant high-gain ports for current-slot activation.Source: §VII · p. 13
  • The conclusion recommends neither discarding historical CSI nor enforcing it as a hard prior, but reusing it according to its current reliability.Future work will consider measured channels, multi-slot memory, adaptive probing, and direct communication-utility optimization.Source: §VII · p. 13

C. Complexity and Online Deployment

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