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Learning Representative Port Subsets for Efficient Fluid Antenna Systems

Quan Zhou, Ming Zeng

arXiv:2610.33730v1cs.ITcs.LGmath.IT

TL;DR

Selecting among many FAS ports can require costly probing, and prior approaches mainly reduce per-realization selection costs rather than compressing the physical candidate set for reuse. The paper learns representative ports offline from training realizations and reports that this substantially reduces the candidate space with negligible utility loss. Under online observation budgets, G-BRPL is comparable to empirical greedy at substantially lower computational cost, while F-BRPL is cheaper but has slightly higher utility loss.

  • Problem

    Selecting among many candidate ports can require probing or estimating channel quality at many ports, incurring switching or signaling overhead.

    Source: §I · p. 1

  • Method

    RPL learns a reusable subset by collecting the optimal port from each offline training realization, requiring only one scan of candidate ports per realization.

    Source: §I · p. 1, §IV · p. 5

  • Results

    RPL substantially reduces the candidate-port space with negligible utility loss; under online budgets, G-BRPL is comparable to empirical greedy at substantially lower computational cost, while F-BRPL is cheaper but incurs slightly higher utility loss.

    Source: §IV · p. 5

  • Takeaways & Limitations

    Nearby physical ports can serve as low-loss proxies even when they are not exact exhaustive optima.

    Source: Appendix A · p. 5, §IV · p. 5

    The approximation analysis assumes a finite bound on |aθ,ℓ| and unit-norm uθ,ℓ vectors.

    Source: Appendix A · p. 5

Abstract

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Fluid antenna systems (FASs) provide many candidate ports, but probing all ports for each channel realization incurs substantial online overhead. We study a complementary offline problem: compress the candidate-port space once and reuse the compressed set across future channel realizations. The method collects optimal ports from sampled training realizations, requiring only one scan of the candidate ports per realization. On a DeepMIMO 7-by-7 FAS with 49 candidate ports, 120 training realizations yield 27 representative ports on average while retaining 99.995% of the channel power gain achieved by exhaustive port selection.

I. INTRODUCTION

Fluid antenna systems can incur substantial overhead when selecting among many ports, while existing approaches mainly reduce the cost of per-realization selection. This paper instead learns a reusable subset offline, motivated by spatially similar ports, and evaluates representative-port learning against other approaches.

I. INTRODUCTION

  • Probing many ports incurs switching or signaling overhead, and existing methods mainly reduce instantaneous selection cost while retaining all N physical ports for each realization.Examples include limited-observation inference, compact arrays, multi-port reception, probabilistic selection, and channel prediction.Source: §I · p. 1
  • The paper formulates offline candidate-port compression as learning a fixed physical-port subset that preserves exhaustive-selection performance across future realizations.This differs from constructing a separate shortlist for each realization.Source: §I · p. 1
  • Because some ports are optimal more often and nearby ports tend to have similar channel responses, a small reusable set may provide near-optimal quality without containing every exact optimum.The motivation relies on spatial structure in a compact FAS aperture.Source: §I · p. 1
  • RPL collects each training realization’s optimal port in one scan, with an approximation guarantee; two budgeted variants address fixed online observation budgets.The guarantee accounts for proxy approximation and finite-sample coverage under the deployment distribution.Source: §I · p. 1
  • On DeepMIMO, RPL achieves near-exhaustive utility with a small subset, beats the mean-based baseline, and remains competitive with empirical greedy at substantially lower offline computational cost.The passage describes this as empirical validation on a DeepMIMO ray-tracing environment.Source: §I · p. 1

II. REPRESENTATIVE-PORT LEARNING

The section formulates representative-port learning for a single-user SISO system with switchable ports on a compact aperture. It defines utility and seeks a fixed offline-learned subset for online selection.

II. REPRESENTATIVE-PORT LEARNING

  • The setup is a single-user SISO system with N switchable ports on a compact two-dimensional aperture, spaced by half a wavelength.Multiple-port activation can be handled analogously by treating each feasible active-port set as a configuration.Source: §II · p. 1

A. Reusable Port-Subset Formulation

  • For realization θ, port n has utility Uθ(n); experiments use |hθ(n)|², and exhaustive selection takes the maximum utility over all ports.The chosen utility is proportional to received SNR under fixed transmit power and noise, while the formulation also allows other communication utilities.Source: A. Reusable Port-Subset Formulation · p. 2
  • The objective is to learn a fixed subset A of physical ports offline and restrict online selection to A instead of probing all N ports.The deployment distribution P describes future channel realizations, and a port index refers to the same relative physical position across realizations.Source: A. Reusable Port-Subset Formulation · pp. 1–2

B. Algorithm and Online Use

RPL learns a reusable subset by collecting the optimal port from each offline training realization, then restricts online selection to that subset. Its approximation guarantee explains why the subset can work: a training optimum from the same proxy class is sufficient, and the chance of missing a class falls with more training realizations.

B. Algorithm and Online Use

  • RPL finds the optimal port for each of S offline training realizations and takes their union as the reusable subset.The procedure needs only each training realization’s optimal port index, which may be obtained by exhaustive probing or another port-identification method.Source: B. Algorithm and Online Use · p. 2
  • Online, RPL evaluates channel quality only at the R ports in the learned subset and reuses the same physical subset across future realizations.The selected online port is the one with the highest utility among those evaluated.Source: B. Algorithm and Online Use · p. 2

C. Why Representative Ports Suffice

  • Theorem 1 bounds expected regret using proxy classes whose members differ in utility by at most ε for any deployment realization, with utilities bounded by B.The classes are introduced for analysis, and the expectation over the learned subset reflects its dependence on random training realizations.Source: C. Why Representative Ports Suffice · p. 2
  • If training includes an optimal port from the test optimum’s proxy class, that representative incurs at most ε utility loss; otherwise regret is at most B.For a class with optimal-port probability q_j, the probability of missing it in S training samples is q_j(1 − q_j)^S.Source: C. Why Representative Ports Suffice · p. 2
  • Exact optimal-port recovery is unnecessary: the theorem requires only a representative from the optimal port’s proxy class, and the chance of missing a class with probability q_j decays exponentially with S.This follows from nearby ports’ similar channel qualities under the stated proxy-class condition.Source: C. Why Representative Ports Suffice · p. 2

D. Computational Complexity

RPL uses O(SN) offline utility evaluations under exhaustive optimal-port identification and reduces online port evaluations from O(N) to O(R).

D. Computational Complexity

  • RPL requires O(SN) offline utility evaluations with exhaustive optimal-port identification, then reduces online port evaluations from O(N) to O(R).The corresponding costs of the baselines are summarized in Table II.Source: D. Computational Complexity · p. 2, Table II · p. 3

III. NUMERICAL RESULTS

The evaluation uses a DeepMIMO ray-tracing environment and a compact 7 × 7 FAS with 49 switchable ports. Receiver locations are sampled from a spatially nonuniform deployment distribution, and channels are synthesized from dominant propagation paths.

III. NUMERICAL RESULTS

  • Experiments use the DeepMIMO ray-tracing environment and a compact 7 × 7 FAS with N = 49 switchable ports.The same environment is used to evaluate whether representative-port learning preserves exhaustive port-selection utility.Source: §III · p. 3

A. Experimental Setup

  • The deployment distribution assigns sampling probabilities to valid DeepMIMO receiver locations using a four-hotspot Gaussian-mixture density.The spatially nonuniform distribution is motivated by clustered user distributions in wireless networks.Source: A. Experimental Setup · p. 3
  • The channel model uses the DeepMIMO v4 O1_28 scenario, transmitter set 5, receiver set 2, subcarrier 0, and a SISO link, without Doppler-induced time variation.There are 487,711 valid receiver locations available for sampling.Source: A. Experimental Setup · p. 3
  • At each reference receiver location, channels across the FAS are synthesized from the strongest L = 20 propagation paths under a far-field plane-wave approximation.The 49 ports form a centered square grid with spacing d = λ/2, and the model implies spatially smooth channel variation.Source: A. Experimental Setup · p. 3

B. Evaluation Metrics and Baselines

The evaluation compares fixed-subset selection methods on the same 1,000 i.i.d. test realizations and considers budgeted variants when RPL’s learned subset exceeds the online budget. Baselines include spatial sampling, average-utility selection, empirical greedy selection, and a limited-observation LSTM.

B. Evaluation Metrics and Baselines

  • All subset-selection methods are evaluated on the same M = 1000 i.i.d. test channel realizations.The primary metric for a candidate subset is relative utility loss; the online probing fraction is K/N.Source: B. Evaluation Metrics and Baselines · p. 3
  • When the learned RPL subset has R > K ports, budgeted variants trim it to K ports without introducing ports from outside the subset.F-BRPL chooses ports with the largest training counts as exhaustive optima, while G-BRPL iteratively adds the port with the largest marginal empirical-objective increase.Source: B. Evaluation Metrics and Baselines · p. 3
  • Reusable-subset baselines include deterministic farthest-point Uniform, Top-K Mean Utility, and Empirical Greedy, which adds the port with the largest training-set marginal objective gain until K are selected.A Chai-style LSTM observes R approximately equispaced ports and predicts utilities for all N ports; unlike RPL, it performs inference over all N.Source: B. Evaluation Metrics and Baselines · pp. 3–4
  • RPL, F-BRPL, and Top-K Mean Utility require O(SN) offline operations, compared with O(SNK) for Empirical Greedy and O(NK) for Uniform.G-BRPL is O(SN) when R ≤ K and O(SN + SRK) when R > K; online, RPL evaluates R ports, while the LSTM requires model training and port inference.Source: B. Evaluation Metrics and Baselines · p. 4

C. Utility–Overhead Tradeoff

As the online budget K grows, G-BRPL closely tracks Empirical Greedy while avoiding its iterative subset search; its near-optimal coverage rises from 0.956 to 1.0.

C. Utility–Overhead Tradeoff

  • G-BRPL closely tracks Empirical Greedy while avoiding its O(SNK) iterative subset search; F-BRPL has slightly higher utility loss but modestly lower computational cost.Uniform is slightly better at the smallest budgets, while both budgeted RPL variants become increasingly competitive as K grows.Source: C. Utility–Overhead Tradeoff · p. 4
  • Top-(K) Mean Utility consistently incurs substantially higher relative utility loss than the other methods.Relative utility loss decreases for all methods as the online budget K increases.Source: C. Utility–Overhead Tradeoff · p. 4
  • G-BRPL coverage rises from 0.956 to 1.0 as K increases, while Empirical Greedy closely tracks RPL and Top-K Mean Utility remains around 0.877–0.899 even at K = 25.Coverage measures the frequency of achieving at least 99.5% of exhaustive-selection utility.Source: C. Utility–Overhead Tradeoff · p. 4

D. Limited-Observation Comparison

The comparison evaluates RPL against a Chai-style limited-observation LSTM at a common online observation budget, while the methods use those observations differently.

D. Limited-Observation Comparison

  • Both methods use the same number of observed ports, with relative utility loss compared against the common budget R.RPL uses its subset cardinality R as the online budget; the LSTM observes approximately equispaced ports and predicts utilities across all N ports.Source: Figure 2 · p. 4, D. Limited-Observation Comparison · p. 4
  • RPL restricts selection to its learned representative subset, whereas the LSTM infers the remaining utilities for each realization.The LSTM uses 80% of training realizations for fitting and 20% for validation, while RPL uses all S realizations to construct its subset.Source: D. Limited-Observation Comparison · p. 4

E. Offline Sample Efficiency

The offline sample-efficiency sweep varies training size S and evaluates subset-selection methods at the learned RPL subset size. Larger training sets yield larger subsets and lower relative utility loss.

E. Offline Sample Efficiency

  • As S increases, RPL enlarges its learned subset and its relative utility loss decreases.At each training size, the learned subset size R sets the online budget K = R for baseline evaluation on the same M = 1000 test realizations.Source: E. Offline Sample Efficiency · pp. 4–5, Figure 3 · p. 5
  • At S = 120, RPL retains 27.1 ± 2.9 ports on average and incurs a relative utility loss of 4.64 × 10−5.The sample-efficiency results summarize mean learned subset size and relative utility loss over 20 repetitions.Source: E. Offline Sample Efficiency · p. 5, Table III · p. 5
  • Empirical Greedy closely tracks RPL, while Top-K Mean Utility has substantially larger loss; Uniform is competitive at small S but fares less favorably as training data increase.F-BRPL and G-BRPL produce the same subset as RPL under this setup and are omitted.Source: E. Offline Sample Efficiency · pp. 4–5

IV. CONCLUSION

The conclusion presents RPL as an offline-learned reusable subset that reduces online port-selection overhead. DeepMIMO experiments show negligible utility loss, while the proxy analysis explains how nearby ports can substitute for exact optima.

IV. CONCLUSION

  • RPL learns a reusable subset of representative physical ports offline and restricts subsequent online selection to that subset.The procedure retains only the index of the optimal port from each training realization, without iterative subset optimization or model fitting.Source: §IV · p. 5
  • On a DeepMIMO-based FAS, RPL substantially reduces the candidate-port space with negligible utility loss.For fixed online budgets, G-BRPL performs comparably to Empirical Greedy at substantially lower computational cost, while F-BRPL is cheaper but incurs slightly higher utility loss.Source: §IV · p. 5
  • RPL can be combined with methods that infer the best port from limited channel observations, and contextual representative subsets are a proposed extension for changing conditions.Source: §IV · p. 5
  • Nearby physical ports can serve as low-loss proxies; if each proxy class has diameter at most δ, the bound gives ε ≤ (4π ¯A2/λ)δ.The proxy structure supports near-optimal utility even when a selected representative is not the exhaustive optimum.Source: Appendix A · p. 5
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