Finite Blocklength Fluid Antenna Systems

• Finite Blocklength Fluid Antenna Systems (FBL-FASs) are reconfigurable antennas that select the best spatial sample among densely packed ports, using short-packet transmission where metrics like BLER and OP replace asymptotic capacity.
• They employ models such as block-correlation and KL expansion to capture spatial correlation and effective channel gains while balancing analytical tractability with conservative performance estimates.
• Designs must navigate trade-offs between increased port density and switching overhead, ensuring optimal rate, energy efficiency, and reliability in delay-aware and multiuser wireless scenarios.

Finite blocklength fluid antenna systems (FBL-FASs) are fluid antenna systems analyzed under short-packet transmission, where the number of available channel uses is limited and performance is governed by block error rate (BLER), outage probability (OP), achievable rate backoff, and latency-reliability tradeoffs rather than by asymptotic capacity alone. In the FAS paradigm, a transceiver can switch among $N$ densely packed ports within a fixed aperture and use the most favorable spatial sample; in the finite-blocklength regime, this spatial reconfigurability is coupled to strong inter-port correlation, residual codeword correlation, and, in delay-aware formulations, port-switching overhead that directly reduces the effective coding length (Zhang et al., 19 Sep 2025, Zhu et al., 7 May 2026).

1. Emergence and basic system abstractions

The FBL-FAS literature emerged from two converging lines of work. One line established that fluid antenna systems can create extra spatial degrees of freedom by moving or switching the radiating element inside a fixed aperture, but that their analysis is dominated by extremely high spatial correlation across closely spaced ports (Ramirez-Espinosa et al., 2024). The other line introduced finite-blocklength FAS analysis explicitly, emphasizing that short packets invalidate asymptotic orthogonality assumptions and make BLER the primary metric in place of rate-only or capacity-only descriptions (Zhang et al., 19 Sep 2025).

A standard abstraction is a single-RF-chain device with $N$ preset ports distributed along a normalized aperture of length $W\lambda$. The effective channel is produced by max-port selection,

$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$

or, in point-to-point downlink form,

$$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$

In multiuser uplink formulations, the received signal is commonly written as

$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$

with finite blocklength $M$, Gaussian codewords, and only one active port at a time because of RF-chain limitation (Zhang et al., 19 Sep 2025, Zhang et al., 13 Nov 2025).

The research scope is already broad. Existing FBL-FAS studies cover uplink multiuser reception, point-to-point downlink HRLLC, physical layer security in short packets, UAV relaying, dependability-oriented IIoT provisioning, and uplink unsourced ISAC massive access (Zhu et al., 7 May 2026, Zheng et al., 18 Mar 2026, Zhu et al., 26 Nov 2025, Muhammad et al., 26 Jul 2025, Xu et al., 29 Jun 2026). Despite these differences, the recurring structural elements are the same: a compact aperture, strong spatial correlation, port selection, and a short-packet performance metric that depends on the distribution of the selected channel gain.

2. Spatial correlation, effective dimensionality, and channel models

Spatial correlation is the central bottleneck in FBL-FAS analysis. Because ports may be much more densely packed than $\lambda/2$, oversampling the aperture does not generate equally useful new channel states; it mostly adds correlated samples and induces performance saturation. For one-dimensional apertures, classical physically motivated models use Toeplitz covariance matrices sampled from Jakes or Clarke kernels,

$$g(n)=J_0\!\left(\frac{2\pi n W}{N-1}\right), \qquad g(n)=\operatorname{sinc}\!\left(\frac{2\pi n W}{N-1}\right),$$

but exact analysis under these full correlation matrices is intractable in the dense-port regime (Ramirez-Espinosa et al., 2024).

A major modeling step was the block-correlation approximation, which replaces the full covariance by a block-diagonal matrix

$$\widehat{\bm{\Sigma}}= \begin{pmatrix} A_1 & 0 & \cdots & 0\ 0 & A_2 & \cdots & 0\ \vdots & & \ddots & \vdots\ 0 & 0 & \cdots & A_B \end{pmatrix},$$

where each block is a constant-correlation matrix

$N$0

Its spectral motivation is that, as $N$1 with fixed aperture $N$2, the number of dominant eigenvalues of the Jakes or Clarke covariance is approximately the number of half-wavelengths in the aperture,

$N$3

which ties the effective degrees of freedom to aperture rather than to raw port count (Ramirez-Espinosa et al., 2024).

Within this block model, each block contributes one dominant eigenvalue when $N$4, because

$N$5

This explains why densification eventually saturates: adding ports inside a fixed aperture does not keep increasing effective rank. The 2025 FBL block-correlation study adopts the same viewpoint and uses uniform strong local correlation $N$6 with adaptive block size $N$7 to preserve tractability for BLER and OP integrals (Zhang et al., 29 Sep 2025).

A different line of work replaces block approximation by a Karhunen–Loève (KL) expansion,

$N$8

and proves that only

$N$9

eigenmodes are needed regardless of $W\lambda$0. The same work proves via Anderson’s inequality that KL truncation always overestimates outage probability,

$W\lambda$1

so the approximation is conservative, whereas block-diagonal models are characterized there as typically optimistic because they underestimate outage (Wu, 21 Mar 2026). This distinction is important for FBL-FAS because finite-blocklength reliability analyses are highly sensitive to tail behavior.

The short-packet security literature adds a variable block-correlation model (VBCM), in which different blocks have different correlation coefficients $W\lambda$2. This model is explicitly positioned as more accurate than a constant block-correlation model for practical compact FAS deployments and yields product-form CDFs for the selected amplitude (Zheng et al., 18 Mar 2026).

3. Finite-blocklength performance metrics and analytical machinery

The defining shift from conventional FAS analysis to FBL-FAS analysis is the replacement of asymptotic capacity by BLER, OP, and finite-blocklength achievable rate. In the point-to-point HRLLC setting, with payload $W\lambda$3 bits and effective blocklength $W\lambda$4, the normal approximation is

$W\lambda$5

where

$W\lambda$6

This formulation leads to exact closed-form expressions for average BLER and average achievable rate after integrating over the post-selection SNR distribution (Zhu et al., 7 May 2026).

In multiuser uplink FBL-FAS, finite blocklength enters through non-negligible codeword correlation. Under Gaussian codewords, the average codeword correlation is approximated as

$W\lambda$7

and the maximum correlation across $W\lambda$8 pairs is characterized via extreme value theory as

$W\lambda$9

with $$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$0. These terms enter the SINR lower bound

$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$1

which in turn yields the OP threshold condition in terms of the selected channel gain (Zhang et al., 19 Sep 2025).

The early FBL-FAS BLER analysis uses Chernoff bounds and a union bound over decoding-error subsets. Conditioned on $$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$2, the resulting upper bound has the form

$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$3

with

$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$4

Averaging this expression over the PDF of the selected gain gives the statistical BLER without CSI (Zhang et al., 19 Sep 2025).

The universal-BLER-bound work generalizes this perspective by deriving a Chernoff-inequality-based BLER upper bound that is explicitly both model-aware and model-free. In model-aware form, the BLER is obtained by integrating the conditional bound against $$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$5; in model-free form, the same formula can be computed empirically from measured or simulated samples of $$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$6. This is presented as a general benchmark across several FAS architectures and several correlation models, including simple reference correlation, modified reference correlation, and a fully correlated Toeplitz model (Zhang et al., 13 Nov 2025).

Exact tractability depends heavily on the selected-gain distribution. Under block-correlation, the CDF of the selected squared gain becomes a product of Marcum-$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$7-based integrals,

$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$8

which directly feeds both BLER and outage calculations (Zhang et al., 29 Sep 2025). In the HRLLC downlink analysis, by contrast, the eigenvalue representation produces a compact exact CDF and PDF for the post-selection SNR,

$$|g_{\mathrm{FAS}}|=\max\{|g_{u,1}|,\ldots,|g_{u,N}|\},$$9

enabling closed-form averaging of the linearized $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$0-function (Zhu et al., 7 May 2026).

4. Port dimension, switching overhead, and optimality structure

A foundational design conclusion is that port densification is beneficial only up to a point. Under realistic spatial correlation, the gain from increasing $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$1 saturates because the effective number of independent spatial dimensions is bounded by the aperture. In the block-correlation foundation, this is expressed spectrally through the dominant-eigenvalue count and operationally through the observation that FAS gains do not increase indefinitely with port density (Ramirez-Espinosa et al., 2024). The KL work sharpens the same conclusion by showing that the effective dimensionality is controlled by $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$2, not by the raw number of ports (Wu, 21 Mar 2026).

The delay-aware HRLLC formulation makes the trade-off explicit by introducing per-port switching and estimation overhead. If $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$3 is the latency budget and $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$4 the per-port overhead, the effective coding length is

$$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$5

Hence, more ports improve diversity but linearly reduce the blocklength available for coding. The paper identifies this as the core FAS-HRLLC trade-off and proves that reliability, achievable rate, and energy efficiency are strictly unimodal in the port dimension after relaxing $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$6 to a continuous variable. Correspondingly, BLER has a unique global minimum, while rate and energy efficiency each have a unique global maximum (Zhu et al., 7 May 2026).

The same work derives explicit switching-delay thresholds separating regimes in which FAS is beneficial from regimes in which a fixed-position antenna (FPA) is preferable. In reliability terms, FAS has no worse asymptotic BLER than FPA only when the switching delay is below a derived threshold $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$7; an analogous threshold $$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$8 is obtained for rate. This formalizes the statement that FAS is not always better than FPA under finite blocklength, because switching overhead may consume too much of the packet budget (Zhu et al., 7 May 2026).

A closely related overhead-versus-diversity trade-off appears in FAS-enabled UAV relaying. There, the total energy includes transmit energy, static circuit energy, and explicit FAS switching energy; the effective transmission time is reduced by

$$\gamma_{\mathrm{FAS}}=\bar{\gamma}\max_{n\in\{1,\dots,N\}} |h_n|^2.$$9

The resulting energy efficiency is quasi-concave in $$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$0: initially, increasing the number of ports reduces required power and improves EE, but after an optimal $$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$1, the time and energy overhead of port selection dominates (Zhu et al., 26 Nov 2025). This is consistent with the HRLLC unimodality result and indicates that “maximize $$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$2” is generally not a valid design rule once finite blocklength and non-ideal switching are included.

The dependability-theoretic formulation adds a further layer to optimality. In quasi-static block fading, the FBL-FAS channel is mapped to an ON/OFF service process through a finite-blocklength decoding threshold, and mission effective energy efficiency (mEEE) becomes quasi-concave in SNR because higher power eventually gives diminishing returns once mission reliability and queueing-QoS constraints are accounted for (Muhammad et al., 26 Jul 2025).

5. Extended formulations: reliability, secrecy, relaying, and massive access

One major extension treats FBL-FAS as a temporally evolving service process rather than a per-packet selection problem. In Nakagami-$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$3 fading, new closed-form expressions are derived for the level-crossing rate (LCR) and average fade duration (AFD) of an $$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$4-port FAS. These second-order statistics are then used to define mission reliability and mean time-to-first-failure (MTTFF), with

$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$5

The same framework extends effective capacity to mission effective capacity,

$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$6

and defines mission effective energy efficiency through mEC divided by a bursty-traffic-aware power model. This line of work places FBL-FAS within statistical QoS provisioning for IIoT and URLLC rather than within isolated packet-level analysis (Muhammad et al., 26 Jul 2025).

Short-packet secrecy introduces a distinct objective: average achievable secrecy throughput (AAST). In the downlink wiretap setting with FAS-equipped legitimate and eavesdropping users, the VBCM is used to model maximum-gain statistics for both sides, and a finite-blocklength secrecy-rate approximation combines the secrecy-capacity difference with dispersion terms from the legitimate and eavesdropper channels. A central result is that the asymptotic AAST is monotonically non-decreasing in the number of legitimate-receiver ports, so the original three-dimensional optimization over transmit power, blocklength, and receiver-port number reduces to a two-dimensional grid search (Zheng et al., 18 Mar 2026).

UAV relaying introduces heterogeneous propagation conditions and a two-hop reliability bottleneck. In the FAS-enabled UAV framework, the UAV-to-user hop is approximated by the maximum of scaled independent Nakagami-$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$7 branches,

$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$8

which yields closed-form BLER expressions for LoS-dominant rural scenarios and probabilistic LoS/NLoS urban scenarios. The high-SNR asymptotic analysis identifies the diversity order of the FAS-enabled second hop as

$$\boldsymbol{y}= g_{i,k}\boldsymbol{x}_i+\sum_{u\neq i}^{U}g_{u,k}\boldsymbol{x}_u+\boldsymbol{\eta},$$9

At system level, however, the end-to-end BLER can exhibit an error floor because the first hop becomes the bottleneck even when the second hop is strengthened by FAS (Zhu et al., 26 Nov 2025).

Massive unsourced access extends the concept beyond conventional BLER and outage formulations. In uplink unsourced ISAC, a transmitter-side FAS is used to improve the effective uplink channel gain before a multi-stage receiver performs SOMP-based activity detection, MMSE channel estimation, ESPRIT AOA estimation, channel-refinement via angular sparsity, and alternating SIC. The performance metrics are per-user probability of error (PUPE) and AOA mean-square error, and the reported numerical result is a 40 dB capacity gain over traditional TDMA at 1000 active users (Xu et al., 29 Jun 2026). This setting is finite-blocklength in resource allocation and decoding structure, even though it is not framed as a closed-form FBL coding theorem.

6. Misconceptions, limitations, and open directions

A recurring misconception is that any accurate FAS outage model is already a finite-blocklength theory. The literature does not support that equivalence. The block-correlation paper provides outage probability analysis, equivalent-independent-antenna interpretations, and saturation laws, but explicitly does not derive finite-blocklength formulas, normal approximations, or Polyanskiy-type coding-rate expressions (Ramirez-Espinosa et al., 2024). The KL-expansion work likewise provides outage analysis, ergodic-rate characterization, and conservative truncation guarantees, but explicitly does not introduce finite-blocklength quantities such as codeword length $M$0, FBL packet error probability, or $M$1-type backoff terms (Wu, 21 Mar 2026). Both are best understood as channel-modeling and outage-analysis foundations for FBL-FAS rather than as direct FBL coding results.

A second misconception is that more ports are always better. The correlation literature shows that the effective degrees of freedom scale with aperture, not indefinitely with port count (Ramirez-Espinosa et al., 2024, Wu, 21 Mar 2026). The HRLLC study proves that BLER, rate, and energy efficiency are unimodal in the port dimension once switching delay is included (Zhu et al., 7 May 2026). The UAV-relay work reaches a parallel conclusion from an energy-overhead perspective (Zhu et al., 26 Nov 2025). The secrecy study is an exception only in its own asymptotic objective: there, AAST is monotonically non-decreasing in the legitimate receiver’s port number for fixed $M$2 and $M$3 under the adopted formulation (Zheng et al., 18 Mar 2026).

A third point of contention concerns approximation philosophy. Block-diagonal and variable block-correlation models are valued for tractability, and Gauss–Laguerre quadrature is reported to be more accurate than Taylor-expansion-based simplifications in the strongly correlated regime $M$4 (Zhang et al., 29 Sep 2025). By contrast, the KL line argues that block-correlation models can introduce optimistic performance bias, whereas KL truncation gives a conservative outage overestimation guaranteed by Anderson’s inequality (Wu, 21 Mar 2026). This is not a contradiction so much as a difference in design objective: tractable average-case approximation versus reliability-safe upper bounding.

The stated open issues are also concrete. Existing studies identify the block-correlation model as still an approximation of the full Toeplitz structure, assume a single active port due to RF limitation, focus on uplink-only or single-antenna BS settings in several formulations, and often omit non-ideal hardware effects such as mutual coupling or switching impairments beyond explicit switching-delay models (Zhang et al., 29 Sep 2025, Zhu et al., 7 May 2026). In unsourced ISAC, FAS is currently deployed only at the transmitter, with future work explicitly aimed at FAS deployment at both transmitter and receiver (Xu et al., 29 Jun 2026). A plausible implication is that future FBL-FAS theory will increasingly combine conservative low-dimensional channel representations, such as KL truncation, with explicit finite-blocklength reliability approximations, delay-aware overhead models, and broader multiuser or multi-hop architectures.