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UAV Fluid-Antenna Channel Acquisition under Intra-Scan Channel Aging

Yuanhui Wu, Hao Jiang, Liang Wu, Zaichen Zhang

arXiv:2609.06537v1cs.ITmath.IT

TL;DR

Sequential UAV–FAS sounding gathers spatial information but delays transmission, so early measurements age. The paper jointly chooses feasible probe locations and scan duration using transmission-state-aligned estimation and covariance-aware probing; simulations show alignment benefits, strong covariance-IG ranking, and competitive one-slot sounding at the highest tested mobility.

  • Problem

    UAV motion changes the channel during sounding, so earlier observations may be stale at transmission and additional slots trade more measurements for greater delay.

    Source: §I · p. 1

  • Method

    The paper jointly chooses feasible blockwise probe locations and scan duration, using Dynamic-KL for transmission-state alignment, covariance IG for probing, and a local condition to compare another slot’s information with its freshness cost.

    Source: §I · p. 1

  • Results

    Temporal alignment recovers most lower-tail loss from static stacking, covariance IG ranks highest numerically among evaluated probing rules, and one-slot sounding is statistically competitive with two-slot alternatives at the highest tested mobility.

    Source: §I · p. 1, §IV · p. 4, §V · p. 5

  • Takeaways & Limitations

    Within the evaluated schedule family, increasing mobility shifts the competitive operating region toward shorter scans, supporting joint probe-placement and sounding-duration design.

    Source: §I · p. 1, §V · p. 5

    The temporal model is a first-order stationary Gauss–Markov surrogate matched at one slot, and scan time excludes switching and processing latency.

    Source: B. Mobility-induced temporal evolution · p. 2

Abstract

from arXiv · show

Sequential sounding in UAV fluid-antenna systems (FASs) provides additional spatial information but delays transmission, causing earlier channel observations to age. This paper addresses the resulting information--freshness tradeoff by jointly determining where to probe and when to stop under blockwise hardware constraints. A dynamic Karhunen--Lo\`eve estimator aligns asynchronous measurements with the transmission state, covariance information gain selects feasible probe locations, and an age-discount identity with a local one-more-slot condition characterizes the covariance-level balance between information and freshness. Paired simulations show that temporal alignment recovers most of the lower-tail reliability lost by static stacking, covariance-aware probing ranks highest numerically among the evaluated policies, and optimized one-slot sounding becomes statistically competitive with two-slot alternatives at the highest tested mobility. Within the evaluated schedule family, increasing mobility shifts the competitive operating region toward shorter scans, supporting joint probe-placement and sounding-duration design.

I. INTRODUCTION

UAV motion ages channel measurements during sequential sounding, creating a tradeoff between spatial information and freshness. The paper jointly selects probe locations and scan duration, then evaluates temporal alignment, probing rules, and mobility-dependent scan lengths.

I. INTRODUCTION

  • Prior acquisition work uses port selection, oversampling, KL inference, learned reconstruction, and spatial priors, but the closest timing-aware work fixes measured ports.The paper identifies joint feasible port selection and stopping as the unaddressed decision.Source: §I · p. 1
  • Dynamic-KL aligns asynchronous measurements with the transmission state, while covariance IG selects feasible unused ports and an age-discount condition characterizes the one-more-slot balance.Independent validation freezes task-level sounding budgets before testing.Source: §I · p. 1
  • Paired simulations find that temporal alignment recovers most lower-tail loss from static stacking, covariance IG ranks highest numerically among evaluated probing rules, and one-slot sounding is competitive at the highest tested mobility.The results support joint probe-placement and sounding-duration design, without establishing a universally monotone budget rule.Source: §I · p. 1
  • The paper formulates acquisition as jointly choosing feasible probe ports and whether another sounding slot is worth its transmission delay.The decision balances spatial information against observation freshness under block-parallel sounding.Source: §I · p. 1
  • The paper develops a block-connected UAV–FAS model, mobility evolution, transmission-time reliability objective, temporal alignment, covariance-aware probing, and a local one-more-slot condition.Its numerical evaluation separates temporal alignment, probe geometry, and sounding duration.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system models a UAV uplink to a one-dimensional fluid antenna whose candidate ports are divided into hardware-connected blocks. Each RF chain sounds one port per slot, and the channel and projected representation are shared across estimators and reliability metrics.

A. Block-connected FAS and spatial channel

B. Mobility-induced temporal evolution

The channel evolves during sounding under UAV motion, so the model tracks coefficient changes between slots and evaluates observations at transmission time. Its first-order stationary Gauss–Markov model matches one-slot correlation, while scan time excludes switching and processing latency.

B. Mobility-induced temporal evolution

  • The coefficient model uses independent slot innovations qt ∼ CN(0, Cc), with Cc as the stationary coefficient covariance and a zero-mean estimator prior.Maximum Doppler is defined as fD = vfc/c0.Source: B. Mobility-induced temporal evolution · p. 2
  • The one-slot diffuse correlation follows the Clarke/Jakes model, with maximum Doppler determined by UAV–receiver relative speed.The supplied passage introduces the correlation expression but does not include it.Source: B. Mobility-induced temporal evolution · p. 2
  • The first-order stationary Gauss–Markov surrogate matches one-slot correlation, but its L-slot correlation is ρ^L rather than the exact J0(2πf_DL Tslot).Scan time includes sounding but excludes switching and processing latency.Source: B. Mobility-induced temporal evolution · p. 2
  • At selected ports St, the observation is modeled as yt = PSt ht + nt = At ct + nt, with At = PSt U.Noise variance is calibrated once on the training split using a fixed reference set and applies across test episodes, velocities, and sounding slots.Source: B. Mobility-induced temporal evolution · p. 2

C. Reliability metric and problem formulation

The formulation evaluates transmission-time reconstruction and selected-link performance, with the empirical fifth percentile of Grel as its primary metric. It permits causal hardware-feasible schedules, while the experiments use a finite budget set and offline covariance-generated schedules.

C. Reliability metric and problem formulation

  • The primary metric is the empirical fifth percentile Q0.05(Grel) over paired episodes.The section introduces transmission-time reconstruction error before specifying this metric.Source: C. Reliability metric and problem… · p. 2
  • The supporting rate is a selected-link spectral-efficiency diagnostic, not net payload throughput, because it excludes sounding, switching, and processing overhead.Source: C. Reliability metric and problem… · p. 3
  • The experiments use a finite budget set and offline covariance-generated schedules rather than solving the unrestricted combinatorial problem.The schedule formulation allows causal hardware-feasible choices based on the known model and past observations.Source: C. Reliability metric and problem… · p. 3

A. Temporal state alignment

Dynamic-KL updates each observation at its acquisition time to estimate the channel at transmission. The recursion starts from a zero-mean prior and covariance Cc, and its Joseph covariance form preserves Hermitian positive semidefiniteness.

A. Temporal state alignment

B. Covariance-aware feasible probing

Covariance-aware probing selects feasible unused ports by the exact rank-one information gain under blockwise hardware constraints. The schedule is computed offline from covariance evolution, and its evaluation uses validation-frozen choices and paired comparisons.

B. Covariance-aware feasible probing

  • The slot objective is log-determinant reduction, a D-optimal uncertainty criterion, and each greedy step selects the eligible port with the largest exact rank-one increment.Source: B. Covariance-aware feasible probing · p. 3
  • After selection, the port’s block is closed, used ports become ineligible, and the posterior covariance receives a rank-one update.The design and Kalman correction use the same training-calibrated variance.Source: B. Covariance-aware feasible probing · p. 3
  • Covariance evolution is value-independent, so each (ρ, T) schedule is computed once offline.Source: B. Covariance-aware feasible probing · p. 3
  • The comparison varies the second-slot rule while fixing the first slot, measurement count, estimator, and paired episodes; policies choose one unused port per block without true-channel access.One-shot IG-8 designs one feasible slot by covariance IG and transmits immediately afterward.Source: B. Covariance-aware feasible probing · p. 3
  • Validation freezes the operating point before final testing, with disjoint validation and test seeds and paired conditions within each split.The finite-budget operating point is selected from the validation competitive set.Source: B. Covariance-aware feasible probing · p. 3

C. One-more-slot uncertainty condition

Earlier posteriors decay geometrically as transmission moves farther from measurement time, and the one-more-slot condition compares uncertainty reduction with the freshness cost of delayed transmission.

  • Earlier posterior value decays geometrically across unobserved transitions as transmission moves farther from measurement time.The covariance recursion applies across L unobserved transitions.Source: C. One-more-slot uncertainty condition · p. 3
  • The endpoint-trace test asks whether the next feasible slot's covariance reduction outweighs the freshness penalty of delaying transmission.It is not a guarantee or predictor of task-level Q0.05(Grel) improvement.Source: C. One-more-slot uncertainty condition · p. 3
  • The first locally non-beneficial extension is defined for a prescribed continuation, not as a globally optimal stopping point or universal threshold.Nonmonotone feasible sets rule out a universal single-crossing threshold; stronger aging raises the freshness term, while noise and redundant ports reduce the next-slot covariance reduction.Source: C. One-more-slot uncertainty condition · p. 3

IV. NUMERICAL RESULTS

Paired numerical evaluations isolate temporal inference, probe geometry, and sounding duration under controlled schedules. Freshness-aware estimation and covariance-aware probing improve lower-tail reliability, while the competitive sounding depth shifts shorter overall with mobility.

b) Temporal alignment under intra-scan aging

  • At ρ = 0.4, KL-LAMP gives −3.480 dB NMSE and Q0.05(Grel) = 0.170, while freshness-aware estimators remain stable as inter-slot correlation decreases.Latest-slot, AR-aided, and Dynamic-KL retained-gain fifth percentiles are 0.578, 0.586, and 0.585, respectively.Source: §IV · pp. 3–4, Figure 2 · p. 4

c) Covariance-aware probing

  • 0.6571 is IG’s retained-gain fifth percentile at ρ = 0.4, and its reported selected-link rate is highest at 2.727 bit/s/Hz.The comparison varies the second-slot rule while fixing Dynamic-KL, first-slot measurements, and paired episodes.Source: Figure 3 · p. 4, §IV · p. 4

a) Simulation setup and protocol

  • The rank-12 KL basis retains 99.59% of covariance energy, and disjoint validation and test sets keep checkpoint selection separate from final paired testing.Captions identify the controlled variable and native transmission time.Source: §IV · p. 3, Table I · p. 4

d) Mobility and sounding duration

  • 0.0608 ([0.0383, 0.0839]) is the one-shot IG-8 improvement over Original Anchor-8 at 160 km/h; it is statistically competitive with IG16-Latest and IG16-Dynamic.FinalSet-early-8 has the largest tabulated Q0.05, 0.6785, reflecting its prescribed geometry rather than an independently optimized one-shot policy.Source: Table II · p. 4, §IV · pp. 4–5
  • Eight of nine validation-frozen sounding budgets are test-competitive; the sequence favors shorter scans overall with mobility but is not strictly monotone.The sole regret is 0.0109 at 40 km/h.Source: §IV · pp. 4–5, Figure 4 · p. 5

V. CONCLUSION

The conclusion frames UAV fluid-antenna acquisition as a balance between probe placement and observation freshness. It reports covariance-IG scheduling, shorter cost-effective scans under aging, and one-shot competitiveness with two-slot schemes at 160 km/h.

  • Intra-scan channel aging creates a trade-off between probe placement and observation freshness in UAV fluid antenna systems.Source: §V · p. 5
  • Covariance-IG scheduling optimizes time-varying channel probing, while channel aging shortens the cost-effective scan window.Source: §V · p. 5
  • At 160 km/h, one-shot IG-8 achieves comparable performance to two-slot schemes as rapid aging offsets the gain of an extra slot.Future work includes aperture coupling, multi-lag channel evolution, hardware latency, and real UAV channel data.Source: §V · p. 5
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