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Active Inference for Joint Port Selection and Pilot Allocation in Fluid Antenna Systems Under Partial CSI

Kian Fotovat, Kamran Fotovat, Zijun Wang

arXiv:2609.02642v1eess.SP

TL;DR

Fluid-antenna selection requires channel knowledge across a dense grid, although only activated ports can be observed and prior approaches do not jointly budget sensing and serving. The paper uses active inference to choose both activated ports and pilots from a spatio-temporal channel belief. It reaches 91.2% of a full-CSI genie’s sum rate while measuring 2.27% of the array.

  • Problem

    Port selection presupposes channel state information at candidate ports, but dense sampling makes full estimation expensive and prior approaches do not jointly choose what to sense and serve under an explicit budget.

    Source: §I · p. 1

  • Method

    The agent maintains a Bayesian belief over all ports using spatial correlation and AR(p) dynamics, then chooses activated ports and pilots by minimizing expected free energy.

    Source: §III · p. 3, A. Perception: Complex Kalman Belief · p. 3

  • Results

    20.16 bits/s/Hz, or 91.2% of the full-CSI genie’s sum rate, is achieved while measuring 2.27% of the 441-port array.

    Source: B. Pilot Budget · p. 4

  • Takeaways & Limitations

    Withdrawing pilots from served ports retains 18.50 bits/s/Hz, 83.7% of the genie, at m = 6.

    Source: B. Pilot Budget · p. 4

    The AR coefficients are fitted once from an assumed Doppler spectrum, and online learning of those coefficients and spatial correlation is left to future work.

    Source: §V · p. 5

Abstract

from arXiv · show

Fluid antenna systems (FAS) obtain spatial degrees of freedom by activating a few radiating ports from a dense grid of candidates, but deciding which ports to activate presupposes channel knowledge at ports that are never measured. Prior port-selection work assumes full or near-full channel state information (CSI) and treats the pilot overhead as a fixed cost. We instead formulate port selection and pilot allocation jointly as active inference. A spatio-temporal generative model -- sub-wavelength spatial correlation together with an order-p autoregressive temporal prior -- maintains a Gaussian belief over all N port channels, and the transmitter chooses both the ports it serves and the subset of them it pilots by minimizing an expected free energy that trades achievable rate against information gain and port-switching cost. Selection is greedy and submodular, at O(NM) per slot. On a 441-port grid with a hybrid front end at n_RF = 2K, the agent attains 91% of a full-CSI genie's sum rate while measuring only 2.3% of the candidate ports; pilots can then be withdrawn from ports that are still served, one fifth of them for 2% of the sum rate and two fifths for 8%. No training is required.

I. INTRODUCTION

Fluid antenna port selection depends on channel knowledge across a dense candidate grid, but only activated ports can be observed. The paper jointly chooses which ports to serve and which to pilot using active inference.

I. INTRODUCTION

  • Only activated ports can be observed, while dense sub-wavelength sampling makes estimating every candidate channel expensive.The sensing-budget problem includes deciding whether a served port needs to be measured at all.Source: §I · p. 1
  • Prior learning-based and channel-estimation approaches do not jointly choose what to sense and serve under an explicit budget.The cited approaches assume full channels as inputs, fix measured ports, or estimate and predict channels without jointly weighing measurement cost.Source: §I · p. 1
  • Active inference frames throughput as pragmatic value and pilot information as epistemic value in expected free energy.The channel at unmeasured ports is hidden, and the generative model uses spatial and temporal correlation.Source: §I · p. 1
  • Joint active inference chooses the activated ports and piloted subset, making pilot allocation a decision rather than a fixed overhead.The agent maintains a Gaussian belief over all N ports and uses greedy expected-free-energy minimization.Source: §I · p. 1
  • The per-slot design activates M of N ports but pilots only m ≤ M; unpiloted activated ports carry data using belief-based channel estimates.Both sets are selected by minimizing the same expected free energy.Source: Figure 1 · p. 2

II. FLUID ANTENNA SYSTEM MODEL

The system uses a dense fluid-antenna grid with correlated port channels and models channel evolution using an order-p autoregressive prior.

II. FLUID ANTENNA SYSTEM MODEL

  • The downlink system has a base station with a fluid antenna serving K single-antenna users.Source: §II · p. 2

A. Array Geometry and Activation

  • The base station activates M of N candidate ports on a sub-half-wavelength planar grid, with N ≥ M ≥ K.Only activated ports radiate and connect to the RF front end.Source: A. Array Geometry and Activation · p. 2

B. Spatio-Temporal Channel Model

  • Under the Jakes rich-scattering model, spatially correlated Rayleigh channel coefficients have covariance βkR, which is strongly rank-deficient under sub-wavelength sampling.The correlation depends on the separation between ports.Source: B. Spatio-Temporal Channel Model · p. 2
  • Channel aging is modeled with an order-p autoregression whose coefficients and innovation variance follow from the Jakes temporal autocorrelation.Setting p = 1 recovers the first-order model.Source: B. Spatio-Temporal Channel Model · p. 2

C. Pilot Allocation Under Partial CSI

The system separates port activation from pilot allocation, allowing some served ports to remain unmeasured. A belief-based precoder accounts for their channel uncertainty within the hybrid transmission architecture.

C. Pilot Allocation Under Partial CSI

  • The base station pilots a subset Qt of its activated set St, with m ≤ M, rather than necessarily piloting every activated port.The M − m activated but unpiloted ports carry data using channels supplied entirely by the belief.Source: C. Pilot Allocation Under Partial CSI · p. 2

D. Hybrid Transmission and Achievable Rate

E. Switching Cost and Problem Formulation

The design trades throughput against port switching, while achievable rate depends on channels that partial observation does not reveal.

E. Switching Cost and Problem Formulation

III. ACTIVE INFERENCE FOR PORT SELECTION AND PILOT ALLOCATION

The agent jointly chooses activated ports and pilots by minimizing expected free energy under a Bayesian belief over all ports. A complex Kalman filter maintains that belief from partial observations, using spatial and temporal channel correlations to inform unmeasured ports.

III. ACTIVE INFERENCE FOR PORT SELECTION AND PILOT ALLOCATION

  • The agent maintains a Bayesian belief over all N ports and jointly chooses activated and piloted sets by minimizing expected free energy, with communication utility defining its preferences.The utility is rate net of port switching.Source: §III · p. 3

A. Perception: Complex Kalman Belief

  • A linear-Gaussian model yields an exact Gaussian posterior maintained by a per-user complex Kalman filter, which predicts through AR dynamics and corrects the belief using pilot observations.Source: A. Perception: Complex Kalman Belief · p. 3
  • Only the m × m innovation covariance is inverted; spatial correlation and temporal prediction let pilots inform neighboring ports and preserve estimates across slots.The current-channel belief is the leading block of the stacked state belief.Source: A. Perception: Complex Kalman Belief · p. 3

B. Exact Reduced-Rank Belief

The reduced-rank representation preserves the channel model while making belief updates tractable. Expected free energy scores port and pilot choices through communication utility, uncertainty, and the information supplied by pilots.

B. Exact Reduced-Rank Belief

  • At N = 441, the exact reduced-rank factorization has r = 26 and requires 4.9 × 10^3 less arithmetic at no modelling cost.The coefficient vector is a sufficient statistic because the channel lies in the covariance range.Source: B. Exact Reduced-Rank Belief · p. 3

C. Action: Expected Free Energy

  • Expected free energy uses pragmatic and epistemic terms, with preferences for high rate and few port changes and deterministic reconfiguration cost kept in closed form.Source: C. Action: Expected Free Energy · p. 3
  • The predicted sum rate is penalized for residual belief uncertainty, which can make high-variance served ports contribute interference the precoder cannot null.Source: C. Action: Expected Free Energy · p. 3
  • The log-determinant information value discounts redundancy: a second uncertain port earns little when it is strongly correlated with an already measured port.Source: C. Action: Expected Free Energy · p. 3

D. Greedy Selection of Both Sets

The method builds the activated and piloted sets sequentially by greedy selection. Withdrawing pilots from served ports costs little down to m = 6, while greedy selection is near-optimal in the reported slot checks.

D. Greedy Selection of Both Sets

  • Greedy construction adds ports that most decrease G until |S_t| = M, then builds Q_t by maximizing information over subsets of S_t; this is sequential, not a fixed ranking.Source: D. Greedy Selection of Both Sets · p. 3
  • Withdrawing pilots from served ports costs little down to m = 6; below that, the belief can no longer cover the gap.Fig. 2 plots sum rate against pilot budget over eight channel realizations, with a 95% confidence interval.Source: Figure 2 · p. 4
  • Because the information term is monotone submodular and switching cost modular, greedy has a (1 − 1/e) guarantee on the information-driven part.Source: D. Greedy Selection of Both Sets · p. 4
  • Greedy is exactly optimal in 95% of slots and never below 0.9996 of the exhaustive optimum; each slot predicts, selects, pilots, updates, then precodes.Source: D. Greedy Selection of Both Sets · p. 4

A. Simulation Setup

The simulations show that the agent retains much of the full-CSI genie’s rate with a small pilot budget, while pilot budget also affects port switching. Results use a 441-port grid and a genie that incurs neither pilot nor switching costs.

A. Simulation Setup

  • The setup uses K=3 users, N=441 ports on a 21×21 grid, M=10 activations, and n_RF=6; the full-CSI genie is a bound that pays neither pilots nor switching.Results average the second half of 40 slots after the belief has settled.Source: A. Simulation Setup · p. 4

B. Pilot Budget

  • At m=M=10, the agent reaches 20.16 bits/s/Hz, 91.2% of the genie, while measuring only 2.27% of the 441-port grid.The remaining channels are inferred from spatial correlation and the temporal model.Source: B. Pilot Budget · p. 4
  • At m=6, rate is 18.50 bits/s/Hz (83.7% of the genie), but falls to 14.86 (67.2%) at m=4 and 9.65 (43.6%) at m=2.With m=2, two measurements cannot keep the r=26 modes in step with the channel, and prediction error outruns the AR model.Source: B. Pilot Budget · p. 4
  • At m=6, removing the epistemic weight lowers rate from 83.7% to 66.0% of the genie; the ηsw=4 sweep also compares policies driven to zero reconfiguration.The ablation varies βw while holding the other components fixed.Source: Figure 3 · p. 5
  • At m=6, the objective is 12.06 (95.9% of m=M’s 12.58) with 40% fewer pilots; switching ranges from 1.01 ports per slot at m=2 to 7.58 at m=M.The agent is less willing to reconfigure when it cannot certify that an unmeasured port is worth the switch.Source: B. Pilot Budget · pp. 4–5

C. The Switching Cost

The switching weight controls reconfiguration, but rate need not improve as movement is penalized. Under partial CSI, retaining ports can also preserve estimation quality, while sufficiently costly switching makes the full-CSI genie worse on the reconfiguration-aware objective.

C. The Switching Cost

  • Raising ηsw from 0 to 4 reduces reconfigured ports from 18.89 per slot to none, while sum rate changes by only 0.89 bits/s/Hz.An array that never moves is within 2.7% of one that moves constantly.Source: C. The Switching Cost · p. 5
  • Rate peaks at ηsw=1 (18.50 bits/s/Hz), above ηsw=0 (17.61), because retained ports accumulate posterior precision while replacements start from prediction alone.Under partial CSI, some reluctance to move is an information policy, not only a hardware concession.Source: C. The Switching Cost · p. 5
  • For ηsw>0.27 bits/s/Hz per port, the agent beats the full-CSI genie on the objective, despite the genie’s 3.64 bits/s/Hz raw-rate lead.The genie reconfigures 15.34 ports per slot; the agent reconfigures none in this comparison.Source: C. The Switching Cost · p. 5

D. Does the Epistemic Term Earn Its Place?

The epistemic term improves rate even when switching is held equal, and its rate-favoring weight is interior. The reported hybrid setup uses 2K RF chains; online learning of Doppler and spatial correlation remains out of scope.

D. Does the Epistemic Term Earn Its Place?

  • At βw=0.25, rate reaches 18.50 bits/s/Hz versus 14.60 at βw=0; at equal zero reconfiguration, the epistemic agent leads by 4.30 bits/s/Hz.Mean posterior variance across all N ports falls from 0.72 to 0.37 in the equal-switching comparison.Source: D. Does the Epistemic Term Earn Its… · p. 5
  • βw≈0.25 maximizes rate; beyond it, switching saturates near 12 ports per slot and rate falls to 74% of the genie by βw=2.At βw=0.05, the ηsw=1 objective is 17.94 against 12.06, but reconfiguration is only 0.08 ports per slot.Source: D. Does the Epistemic Term Earn Its… · p. 5

E. Hybrid Transmission

  • With n_RF=6=2K rather than M=10, hybrid loss versus a fully digital front end is below 0.001 bits/s/Hz at every pilot budget, with 40% fewer RF chains.Source: E. Hybrid Transmission · p. 5

V. CONCLUSION

  • 91.2% of the full-CSI genie’s sum rate is achieved while measuring 2.3% of candidate ports, and the reconfiguration-aware objective beats the genie above a switching price of 0.27 bits/s/Hz per port.Both sets are selected greedily against a monotone submodular epistemic value at O(NM + Mm) per slot.Source: §V · p. 5
  • The AR coefficients are fitted once from an assumed Doppler spectrum; online learning of time-varying fD and learning spatial correlation R remain future work.Source: §V · p. 5
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