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On Fundamental Limits for Fluid Antenna-assisted Integrated Sensing and Communications for Unsourced Random Access

Zhentian Zhang, Kai-Kit Wong, Jian Dang, Zaichen Zhang, Chan-Byoung Chae

arXiv:2504.03183v1cs.IT

TL;DR

The paper addresses massive-access ISAC settings where conventional schemes can be overwhelmed by growing user populations. It develops FAS-UNISAC using practical channel modeling and derives achievable and floor bounds for communication and sensing. The reported results show improved user capacity and sensing and communication capability associated with fluid-antenna spatial diversity.

  • Problem

    Conventional TDMA and TIN strategies can be overwhelmed as active-user populations grow, motivating improved unsourced access for ISAC.

  • Method

    The paper proposes FAS-UNISAC, derives achievable bounds and performance floors, and develops fluid-antenna communication and covariance-based sensing analyses.

  • Results

    FAS-UNISAC supports increasing user volumes and improves sensing and communication capability through fluid-antenna spatial diversity.

  • Takeaways & Limitations

    Fluid-antenna spatial diversity provides a basis for higher-resolution sensing and improved massive-access ISAC performance.

Abstract

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This paper investigates the unsourced random access (URA) problem for integrated sensing and commutations (ISAC). Recent results reveal that conventional multiple access strategies for ISAC such as treating interference as noise (TIN) and time-division multiple access (TDMA) can be easily overwhelmed and fail to support the increasingly surging number of active users. Hence, the unsourced ISAC (UNISAC) system model has emerged as a promising enabler for the future ISAC networks. To advance this work, we adopt a more realistic channel model and propose to utilize fluid antenna system (FAS) for UNISAC. The achievable performance bound and floor of the proposed FAS-UNISAC are derived to validate the great potential. Our results demonstrate that promising improvement on the available user volume and the sensing and communication capability can be obtained due to the spatial diversities inherent within fluid antenna.

I. INTRODUCTION

The paper targets massive uncoordinated access for ISAC, where conventional coordination-based schemes struggle as device populations grow. It proposes FAS-UNISAC with practical LOS/NLOS channels and derives achievable bounds, performance floors, communication analysis, and covariance-based sensing estimation.

  • A. Background: Coordination-based multiple access becomes unsuitable for massive machine-type communications as the number of devices increases.The information bits per channel use for each user approach zero as device count grows.
  • A. Background: UNISAC enables many communication and sensing users to transmit without coordination through a shared-codebook access model.Its performance is evaluated using per-user probability of error and energy-per-user under finite blocklength.
  • C. Challenges: At finite blocklength, UNISAC prioritizes supporting enormous device populations over high throughput.The motivating example delivers 100 bits over 5000 channel uses, corresponding to 0.02 bits/channel-use.
  • C. Challenges: Existing UNISAC bounds rely on LOS-only channels, while LOS/NLOS mixtures are more realistic but difficult to analyze.The paper identifies the need to explore the degrees of freedom available under mixed propagation.
  • C. Challenges: ULA-based sensing requires half-wavelength spacing, so improving accuracy by adding elements enlarges the physical array.The paper therefore considers better sensing performance within a fixed physical antenna size.
  • D. UNISAC aided by Fluid Antennas: FAS-UNISAC removes the half-wavelength placement restriction and investigates achievable bounds and performance floors under practical LOS/NLOS channels.The paper also derives a universal upper bound for FAS-based sensing.
  • D. UNISAC aided by Fluid Antennas: The proposed communication analysis relates FAS channel gain to joint communication-and-sensing detection errors.The reported relationship is inverse proportionality between joint detection errors and FAS-induced channel gain.
  • D. UNISAC aided by Fluid Antennas: The sensing model exploits covariance information to form a wider virtual receiving aperture from coherent fluid-antenna signals.This spatial-diversity mechanism is intended to improve sensing resolution.

III. PROPOSITION: ACHIEVABLE RESULTS

The proposition specifies achievable FAS-UNISAC results under communication and sensing power constraints, with performance characterized through error probabilities and joint error counts. Several quantities involving fluid-antenna spatial diversity and the random sensing codebook are determined by Monte Carlo simulation.

  • The proposed FAS-UNISAC model is evaluated under communication and sensing power constraints using the system metrics in (3).
  • The performance definitions include constraint-surpassing probability, collision-derived error, and sensing detection error.Pcons is the probability that at least one communication or sensing user surpasses its power constraint; Pcoll denotes collision-derived error, and Pmd denotes detection error.
  • Kc and Ks denote the numbers of communication and sensing detection errors, respectively.The joint metric PKs,Kc represents the probability of observing Kc communication errors and Ks sensing errors.
  • Spatial-diversity quantities for the fluid antenna include averaged channel gains and averaged differences between selected array elements.The averaged channel gains and E{|Nm − Nn|} are determined or evaluated through the stated simulation procedure.
  • The sensing codebook A contributes a largest eigenvalue γmax to the achievable-result expressions, and this value is determined by Monte Carlo simulations.The codebook is random, so its largest eigenvalue is obtained numerically.

IV. COMMUNICATION: OPTIMIZATION AND ANALYSIS

The communication analysis decomposes error sources, relates joint detection errors to averaged channel variance, and characterizes how fluid-antenna spatial diversity improves channel responses.

  • Error analysis: Communication and sensing errors are decomposed into collision, consistency, and missed-detection components.The derivation defines the overall error from Pcons, Pcolli, and Pmd, then introduces the corresponding detection framework.
  • Collision errors: Certain collision cases need not cause errors, so the collision expression is treated as an upper bound.The paper notes that recent work has shown some collision cases may be harmless.
  • Channel diversity: The joint error probability PKs,Kc is inversely proportional to the averaged variance of the channel response.This relationship connects communication-and-sensing reliability to channel variability induced by the antenna configuration.
  • Port selection: Selecting ports with larger channel responses can provide an array-response gain for the activated elements.The analysis assumes optimal port selection from the available ports and identifies the resulting gain as a consequence of spatial diversity.
  • Channel diversity: Fluid-antenna spatial diversity creates location-dependent channel-response fluctuations, unlike the unit-modulus LOS-only model.The LOS/NLOS components overlap and produce response fluctuations across ports, whereas LOS-only responses retain identical element-wise modulus.

V. SENSING: OPTIMIZATION AND ANALYSIS

The sensing analysis establishes an upper bound for angle-of-arrival estimation by validating a pessimistic high-interference model for the irregular fluid-antenna array.

  • Upper-bound analysis: The pessimistic sensing model yields an MSEAOA upper bound under a high-interference assumption.The section also explains how fluid-antenna spatial diversity optimizes the sensing model and supports an analytical solution.

A. Scalability of Pessimistic Sensing Model

The pessimistic ULA angle-of-arrival estimation model remains applicable to the fluid-antenna setting under the stated fixed-size and LOS-only comparison.

  • Array models: ULA uses uniformly divided elements with half-wavelength spacing, while FAS randomizes exponent indices through element-selection strategies.The FAS formulation replaces fixed array-index structure with randomized activated-element indices.
  • Estimation procedure: The receiver estimates θ_i from different g^T results associated with the randomized fluid-antenna configuration.The resulting estimation deviations are compared within the pessimistic model.
  • Model scalability: FAS and ULA use the same antenna-size constraint, W = (M−1)2.The comparison keeps the physical antenna-size condition identical across the two array models.
  • Model scalability: The LOS-only FAS and ULA models have the same estimation-deviation expression because their random shifting factors do not affect the distribution.The terms e^jπ(M−1) cos θ_i and e^j2Wπ cos θ_i leave the relevant distribution unchanged.

B. Sensing Optimization Model

The sensing optimization converts covariance information from randomized fluid-antenna activations into a virtual difference-co-array model, then selects ports to maximize degrees of freedom.

  • Optimization objective: The pessimistic model uses spatial diversity to derive an upper bound on sensing estimation error.The subsection assumes independent noise and develops the optimization around the virtual AOA estimation model.
  • Difference co-array construction: Randomized index differences define a difference co-array N = {N_m − N_n}, from which an activated subset N_sub is selected.The covariance matrix contains the index-difference factor, motivating the DCA construction.
  • Virtual sensing model: Activating M elements can produce a virtual sensing signal of dimension M^2 × 1 with more unique DCA elements than activated ports.Matrix vectorization maps the covariance observation into a virtual array whose subset cardinality can exceed the number of active elements.
  • Virtual sensing model: The virtual AOA model has a wider receiving aperture than the original model because M^2 > M.This widened aperture is a direct consequence of the covariance-based virtual representation.
  • DOF optimization: A maximum DOF of N_sub in the order of M(M −1) + 1 is obtained when nonzero difference weights have minimal redundancy.When w(x) > 1, the DOF decreases, so port selection directly controls the observed-signal degrees of freedom.

C. Port Selection for FAS

The section selects fluid-antenna ports using minimum-redundancy principles and derives a compressive-sensing-based sensing-error upper bound. Direct MUSIC processing is unavailable for the coherent virtual array, while smoothing and matrix reconstruction incur degrees-of-freedom loss.

  • Port selection: MRA searches port combinations with least redundancy to maximize the degrees of freedom of the virtual array.Favourable ports are obtained through exhaustive search because MRA lacks explicit algebraic solutions.
  • Coherent-signal processing: Direct MUSIC processing cannot solve the coherent signal after virtual DCA array conversion.Smoothing or matrix reconstruction can enable subspace search but causes degrees-of-freedom loss.
  • Compressive sensing: Compressive sensing preserves full degrees of freedom for the virtual DCA array with an appropriate sensing codebook.The resulting formulation supports an upper-bound search.
  • Sparse estimation: The sensing model is rewritten as a sparse linear regression problem with an unknown coefficient vector and vectorized noise.The sparse solution is constrained by a prescribed deviation tolerance.
  • Error bound: The MSEAOA upper bound is obtained using γmax, the largest eigenvalue of AHA.The estimation error bound is derived through the Lasso formulation and subsequent substitutions.

VI. PERFORMANCE LOWER BOUND

The performance lower bound is an optimistic bound based on idealized error assumptions. It combines collision-derived communication error with a single-user sensing CRLB and imposes averaged capacity constraints.

  • Lower-bound definition: The optimistic bound targets the potential minimum MSEAOA and PUPE under ideal assumptions.It considers collision-derived error for communication and the single-user CRLB for sensing.
  • Capacity constraints: The channel matrix GFAS and diagonal matrix Ψ enter averaged channel-capacity and sum-rate constraints for the multiantenna system.The capacity constraints determine the number of transmitted bits, with error-free transmission possible below averaged capacity according to Shannon's theorem.
  • Error assumptions: PUPE in the lower-bound formulation includes only collision-derived error, while MSEAOA uses the single-user CRLB.These assumptions define the sensing and communication performance floor.

VII. NUMERICAL RESULTS

The numerical results validate the analytical sensing bound and show that FAS-UNISAC supports more users and generally requires less energy than benchmark schemes. They also identify sensing-codebook eigenvalues as a remaining design limitation.

  • CS estimation: The simulated CS algorithms are all upper-bounded by the analytical estimation result, validating the proposed FAS-UNISAC achievability analysis.The comparison includes MP, CoSaMP, and ROMP under FAS and ULA channel models.
  • CS estimation: The analytical upper bound is lower than ULA-codebook estimation, indicating the potential of high-resolution FAS.
  • Achievable results: At 1400 active users, FAS-UNISAC approaches the LOS-UNISAC performance lower bound, while TDMA and TIN become overwhelmed.
  • Achievable results: FAS-UNISAC and UNISAC maintain capacity as the number of users increases, with fluid-antenna spatial diversity improving system performance.
  • Energy efficiency: The required E/N0 decreases faster for FAS-UNISAC than LOS-UNISAC as receiving antennas increase, except that FAS-UNISAC is slightly worse at M = 3.
  • Limitation: The sensing-codebook eigenvalue γmax can become extremely large at small M, causing performance loss and leaving optimal codebook design unresolved.For M = 3 and N = 90, γmax = 1.5471 × 10^3.

APPENDIX A DERIVATIONS ON PKs,Kc

Appendix A derives the joint error probability by separating correctly and incorrectly detected signals and modeling the residual interference statistically. The derivation uses concentration and optimization steps to obtain an inverse relationship between error probability and noise variance.

  • Probability derivation: The joint error probability is related to the averaged channel variance through the derived probability calculation.
  • Error decomposition: The received signal is separated into correctly detected codewords and an erroneous-signal term modeled as complex Gaussian noise.The residual term follows CN(0, σ^2) under the stated i.i.d. array-response assumption.
  • Bounding steps: The derivation applies the Chernoff bound and minimizes a quadratic denominator at λ1 = 1/(2σ^2).
  • Result: The resulting error probability P(ζAe,Aa) is inversely proportional to σ^2.

APPENDIX B k-SPARSE VECTOR ESTIMATION UNDER LASSO MODEL

Appendix B analyzes k-sparse estimation under a Lasso model with a covariance-based sensing codebook. It replaces ordinary strong convexity with restricted strong convexity and derives an upper bound using the one-sparse estimation setting.

  • Model: The Lasso model estimates a K-sparse vector β from v = Aβ + n_z using sensing codebook A ∈ C^(M^2×N).The setup requires N ≫ K and M^2 ≥ K, while the codebook must provide the desired estimation resolution.
  • Convexity condition: When N > M^2, A^HA can be rank-deficient, so the convex objective is not strongly convex and cannot guarantee a unique minimum.
  • Convexity condition: Restricted strong convexity on the cone C(S, 3) supplies the condition used for high-dimensional estimation.The cone is defined by a constraint relating the ℓ1 norms on S and its complement.
  • Upper bound: For the one-sparse case, fixing γ = 1 yields a tight Lasso estimation upper bound because the bound decreases as γ increases.
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