A multiuser FAS-NOMA framework for short-packet communications

1 Introduction

Despite significant advancements in multiple access technologies, the increasing demand for seamless connectivity in Internet of Things (IoT) and ultra-reliable low-latency communication (URLLC) applications has posed new challenges for edge users. The rapid proliferation of IoT and URLLC applications has intensified the need for efficient spectrum utilization and reliable connectivity, particularly for cell-edge users who suffer from severe path loss and interference. While non-orthogonal multiple access (NOMA) has emerged as a promising solution to enhance spectral efficiency via power-domain multiplexing (Ding et al., 2017; Dai et al., 2018), its performance in short-packet regimes—typical of IoT/URLLC traffic—remains constrained by limited channel coherence time, imperfect successive interference cancellation (SIC), and terminal receiver complexity (Xu and Zhu, 2026). Moreover, conventional NOMA systems typically rely on fixed antenna configurations, which fail to exploit spatial diversity gains for edge users (Vega-Sanchez et al., 2024).

The concept of fluid antenna system (FAS) was first introduced by Wong and his colleagues in a series of seminal papers in 2020–2021, establishing its theoretical foundation and performance limits (Wong et al., 2020; Wong et al., 2021). Subsequent studies have deepened the understanding of FAS through spatial correlation modeling (Wong et al., 2022a), multiple access schemes (Wong and Tong et al., 2022, Wong et al., 2023), and practical antenna implementations (Wong et al., 2022b). By enabling a single radiating element to switch among multiple pre-defined ports within a compact space, FAS exploits spatial correlation diversity to combat fading without requiring multiple radio frequency chains, making it a promising candidate for next-generation wireless communication systems.

Building upon the potential of FAS, researchers have begun investigating its integration with NOMA to address the needs of multi-user layered services. Motivated by practical demands such as reliability-based communications in smart factories and function-differentiated multi-tier communications in emergency rescue scenarios, recent studies have explored FAS-assisted NOMA systems. However, existing works on FAS-NOMA remain largely limited to two-user scenarios (Zheng et al., 2024), or rely on ideal port selection assumptions and perfect SIC decoding (Zou et al., 2024), leaving the performance of FAS in multi-user short-packet communications largely under-explored. To bridge this gap, this paper proposes a multiuser FAS-assisted NOMA framework designed for short-packet edge access. The main contributions of this paper are summarized as follows:

• We propose a multi-user downlink FAS-assisted NOMA framework that extends beyond the conventional two-user setup. Using a three-user configuration as a representative example, the framework is shown to be scalable to diverse user groups in practical multi-tier communication scenarios, such as smart factories and emergency rescue operations.
• Closed-form approximations for the average block error rate (BLER) in short-packet transmissions are derived, capturing the interplay among FAS port selection, power allocation, and imperfect successive interference cancellation (SIC). These results provide design insights for latency-critical IoT/URLLC applications.
• We formulate a sum-rate maximization problem under power normalization and SIC ordering constraints, and solve it via a projected gradient descent algorithm. The per-iteration complexity is dominated by elementary operations using precomputed channel statistics, making the solution suitable for real-time implementation.

The rest of this paper is organized as follows. Section 2 describes the system model of the proposed framework. Section 3 presents the performance analysis and optimization. Section 4 provides numerical results to demonstrate the effectiveness of the proposed scheme. Finally, references concludes the paper.

2 System model

2.1 Network architecture

Consider a multi-user downlink short-packet communication system, as illustrated in Figure 1, where a base station (BS) employs non-orthogonal multiple access (NOMA) to serve multiple users. Each user is equipped with a fluid antenna system (FAS) to exploit spatial diversity for improved reception reliability. Without loss of generality, all terminals are assumed to have a single antenna; the BS adopts a conventional fixed-antenna configuration.

The users are categorized according to their channel conditions relative to the BS: a central user (CU) with the strongest channel, an intermediate cell-edge user (C E U 1) with moderate channel quality, and a distant cell-edge user (C E U 2) with the weakest channel. This three-user configuration serves as a representative scenario that can be extended to accommodate a larger number of user groups in practical multi-tier communication environments.

To enhance reception, each user is equipped with a one-dimensional (1D) FAS comprising N reconfigurable ports evenly distributed over a linear space of size W λ (λ: wavelength). Each port corresponds to a distinct physical location to which the radiating element can be switched; switching delays are assumed negligible, which is reasonable for pixel-based switchable antennas.

2.2 Channel and signal model

Based on the network architecture described above, the BS transmits a superimposed NOMA signal, as given in Equation 1:where P t denotes the total transmit power, α C U, α C E U 1, α C E U 2 are the power allocation coefficients satisfying α C U + α C E U 1 + α C E U 2 = 1, and s C U, s C E U 1, s C E U 2 represent the information symbols for the CU, C E U 1, and C E U 2, respectively, with unit energy E [ | s | 2 ] = 1.

s t = P t α C U s C U + α C E U 1 s C E U 1 + α C E U 2 s C E U 2 , (1)

Following the conventional NOMA principle, users with poorer channel conditions are allocated higher power. Without loss of generality, we set α CEU 2 ≥ α CEU 1 ≥ α CU to reflect the channel quality ordering CEU 2 ≺ CEU 1 ≺ CU.

The received signal at the selected port k of user u ∈ { CU , CEU 1 , CEU 2 } is given by Equation 2 where d u is the distance from the BS to user u, α is the path-loss exponent, η k ( u ) ∼ C N ( 0 , σ 2 ) denotes the additive white Gaussian noise (AWGN), and g k ( u ) is the small-scale fading coefficient at port k.

y k u = g k u d u − α 2 s t + η k u , (2)

The fading coefficients across different FAS ports are spatially correlated. In this work, we adopt the Jakes’ correlation model (New et al., 2023), where the correlation between the m-th and n-th ports is given by Equation 3 with σ ls 2 representing the large-scale fading power and J 0 ( ⋅ ) the zero-order Bessel function of the first kind. The correlation matrix J ∈ C N × N is defined as [ J ] m , n = J m , n. Owing to its symmetry, eigenvalue decomposition yields J = U Λ U H, where Λ = diag ( λ 1 , … , λ N ) contains the eigenvalues arranged in descending order λ 1 ≥ ⋯ ≥ λ N. Using this decomposition, the channel coefficient at port k for user u can be expressed as Equation 4 where u k , m is the ( k , m )-th entry of U, and ω m ( u ) = a m ( u ) + j b m ( u ) with a m ( u ) , b m ( u ) ∼ N ( 0,1 / 2 ) independent across m and u. This formulation captures the spatial correlation through the shared eigenbasis U and Λ, while the independent coefficients ω m ( u ) ensure distinct yet statistically equivalent channel realizations for different users.

J m , n = σ ls 2 J 0 2 π m − n W N − 1 , (3)

g k u = ∑ m = 1 N u k , m λ m ω m u , (4)

2.3 Successive interference cancellation

For notational convenience, we denote the central user (CU), the intermediate cell-edge user (C E U 1), and the distant cell-edge user (C E U 2) as u 1, u 2, and u 3, respectively, where the channel quality satisfies u 1 ≻ u 2 ≻ u 3. Accordingly, the SIC decoding procedure can be described as follows:

• The strongest user ( u 1 ) first decodes and cancels the signals of both cell-edge users (u 3 and u 2), then decodes its own signal, i.e., S I N R u 3 → u 1 → S I N R u 2 → u 1 → S N R u 1.
• The intermediate user ( u 2 ) decodes and cancels the signal of the weakest user ( u 3 ), then decodes its own signal treating the stronger user’s ( u 1 ) signal as interference, i.e., S I N R u 3 → u 2 → S I N R u 2.
• The weakest user ( u 3 ) directly decodes its own signal, treating all other users’ signals (u 2 and u 1) as interference, i.e., S I N R u 3.

This decoding order allows users with poorer channel conditions to experience less interference, thereby improving their reliability. Accordingly, the corresponding SINR and SNR expressions for user u i ( 1 ≤ i ≤ 3 ) are given as Equation 5:for user u 1, where ρ = P t / σ 2 denotes the transmit SNR. Similarly, for the intermediate user u 2, we have Equation 6 and for the weakest user u 3 Equation 7,

γ 1,3 = α u 3 ρ | g u 1 | 2 d u 1 − α α u 2 ρ | g u 1 | 2 d u 1 − α + α u 1 ρ | g u 1 | 2 d u 1 − α + 1 γ 1,2 = α u 2 ρ | g u 1 | 2 d u 1 − α α u 1 ρ | g u 1 | 2 d u 1 − α + 1 γ 1,1 = α u 1 ρ | g u 1 | 2 d u 1 − α , (5)

γ 2,3 = α u 3 ρ | g u 2 | 2 d u 2 − α α u 2 ρ | g u 2 | 2 d u 2 − α + α u 1 ρ | g u 2 | 2 d u 2 − α + 1 γ 2,2 = α u 2 ρ | g u 2 | 2 d u 2 − α α u 1 ρ | g u 2 | 2 d u 2 − α + 1 , (6)

γ 3,3 = α u 3 ρ | g u 3 | 2 d u 3 − α α u 2 ρ | g u 3 | 2 d u 3 − α + α u 1 ρ | g u 3 | 2 d u 3 − α + 1 . (7)

2.4 Block error rate (BLER) analysis

Based on the SIC decoding order described in the previous subsection, we now characterize the reliability performance of each user in the short-packet regime. For K users sorted in descending channel quality (user u 1 strongest, u K weakest), let ϵ i , j denote the BLER when user u i decodes the message of user u j ( j ≥ i ). According to Equation 8 in (Polyanskiy et al., 2010),where Q ( x ) = 1 2 π ∫ x ∞ e − t 2 / 2 d t, C ( γ ) = log 2 ( 1 + γ ), V ( γ ) = ( log 2 e ) 2 ( 1 − ( 1 + γ ) − 2 ), N j is the packet size (in bits) of user u j, and L the channel blocklength (in symbols).

ϵ i , j ≈ Q C γ i , j − N j / L V γ i , j / L , (8)

Consequently, the overall BLER for user u i after SIC is shown as Equation 9

ϵ i = 1 − ∏ j = i K 1 − ϵ i , j . (9)

For the proposed three-user case ( K = 3 ), the overall BLER for each user is given, respectively, by Equation 10 where the specific BLER ϵ i , j values correspond to various ( i , j ) pairs and are obtained from Equation 8.

ϵ 1 = ϵ 1,3 + 1 − ϵ 1,3 ϵ 1,2 + 1 − ϵ 1,3 1 − ϵ 1,2 ϵ 1,1 ϵ 2 = ϵ 2,3 + 1 − ϵ 2,3 ϵ 2,2 ϵ 3 = ϵ 3,3 , (10)

3 Performance analysis

3.1 Average BLER analysis

Building upon the system model established in Section 2 and the SIC decoding order described therein, we analyze the average block error rate (BLER) for the three users in the short-packet regime. The expectations are taken over all channel realizations, accounting for both the spatial correlation among FAS ports and the independent fading components. Following the linearization method for finite blocklength codes (Polyanskiy et al., 2010), the average BLER is expressed in terms of the cumulative distribution functions (CDFs) of the relevant SINRs, which are derived from the spatial correlation model in (Wong et al., 2021). The detailed derivations are presented in the following subsections.

3.1.1 Central user ( u 1 )

Following the SIC order described in Section 2, the average BLER for u 1 is obtained as Equation 11 where ϵ 1 , j denotes the instantaneous BLER when user u 1 decodes the message of user u j ( j = 1,2,3 ). According to the short-packet approximation (Zheng et al., 2024), each expectation can be approximated by Equation 12 where N j is the packet size (in bits) of user u j, L is the channel blocklength, δ N j , L, v N j , L, u N j , L are constants and F γ 1 , j ( ⋅ ) is the CDF of the instantaneous SINR γ 1 , j. The CDF incorporates the spatial correlation of the FAS ports and can be computed from the eigenvalue decomposition of the correlation matrix J as in (Wong et al., 2021).

E ϵ 1 = E ϵ 1,3 + E 1 − ϵ 1,3 ϵ 1,2 + E 1 − ϵ 1,3 1 − ϵ 1,2 ϵ 1,1 , (11)

E ϵ 1 , j ≈ δ N j , L L ∫ v N j , L u N j , L F γ 1 , j τ d τ , (12)

3.1.2 Intermediate user ( u 2 )

Similarly, the average BLER for u 2 is given by Equation 13 with the same linearization method applied to ϵ 2,3 and ϵ 2,2.

E ϵ 2 = E ϵ 2,3 + E 1 − ϵ 2,3 ϵ 2,2 , (13)

3.1.3 Weakest User ( u 3 )

For the weakest user u 3, which performs no SIC, the average BLER is directly expressed as Equation 14 where F γ 3,3 ( ⋅ ) is the CDF of γ 3,3 defined in Equation 7.

E ϵ 3 ≈ δ N 3 , L L ∫ v N 3 , L u N 3 , L F γ 3,3 τ d τ , (14)

Note that at high SNR, the terms involving ϵ 1,3 and ϵ 1,2 will become negligible compared to ϵ 1,1; see the asymptotic analysis in Section 3.

3.2 Asymptotic behavior

To gain further insight, we examine the asymptotic behavior when the transmit SNR ρ tends to infinity. Following the approach in (Zheng et al., 2024) and exploiting the diversity gain offered by the FAS with N ports, the average BLERs simplify to polynomial forms, shown as Equation 15:where β N j , L = 2 N j / L − 1 accounts for the finite blocklength penalty and D is a constant derived from the eigenvalue distribution of the FAS correlation matrix (Wong et al., 2021). These asymptotic results reveal that each user achieves a diversity order equal to the number of FAS ports N, despite the presence of multiuser interference, confirming the effectiveness of FAS in enhancing reliability for all users in the short-packet NOMA system.

E ϵ 1 ≈ 1 D d u 1 α β N 1 , L α u 1 ρ N E ϵ 2 ≈ 1 D d u 2 α β N 2 , L α u 2 − α u 1 ρ N E ϵ 3 ≈ 1 D d u 3 α β N 3 , L α u 3 − α u 1 − α u 2 ρ N , (15)

Remark: The asymptotic expressions in Equation 15 follow the analysis framework in (Zheng et al., 2024), where the finite-blocklength approximation (including channel dispersion V ( γ ) and the Q-function) was simplified in the high-SNR regime. The dispersion term mainly contributes to a constant factor, and is absorbed into D and the short-packet penalty β N j , L = 2 N j / L − 1, without affecting the diversity order N. The detailed derivation can be found in (Zheng et al., 2024).

R u 1 = min log 2 1 + α u 3 γ u 1 α u 1 γ u 1 + α u 2 γ u 1 + 1 , log 2 1 + α u 2 γ u 1 α u 1 γ u 1 + 1 , log 2 1 + α u 1 γ u 1 (16)

R u 2 = min log 2 1 + α u 3 γ u 2 α u 1 γ u 2 + α u 2 γ u 2 + 1 , log 2 1 + α u 2 γ u 2 α u 1 γ u 2 + 1 (17)

R u 3 = log 2 1 + α u 3 γ u 3 α u 1 γ u 3 + α u 2 γ u 3 + 1 (18)

Furthermore, due to the power allocation α u 1 < α u 2 < α u 3, the SINRs for decoding weaker users at u 1 and u 2 are much larger than those for decoding their own messages. Hence, the error propagation terms ϵ 1,3 , ϵ 1,2 and ϵ 2,3 decay with SNR much faster than the final decoding terms ϵ 1,1 and ϵ 2,2, respectively. Consequently, the asymptotic BLERs for u 1 and u 2 are dominated by their own decoding steps, as reflected in Equation 15. The expressions for E [ ϵ 2 ] and E [ ϵ 3 ] also incorporate the interference from stronger users through the power differences in the denominators (e.g., α u 2 − α u 1 and α u 3 − α u 1 − α u 2), consistent with the SIC order. For the weakest user u 3, only its own decoding exists.

3.3 Sum-rate analysis

To complement the reliability analysis in Section 3.1, we evaluate the achievable sum-rate of the proposed system from a throughput-oriented perspective. The derivations follow the finite blocklength capacity formulation (Polyanskiy et al., 2010) and incorporate the FAS channel model established in Section 2.

3.3.1 Achievable Rates

Based on the SIC decoding order defined in Section 2, the achievable rates for the three users are thus expressed as the formulas, i.e., Equations 16-18, shown at the top of this page.

In the sum-rate expressions, γ u i = ρ | g FAS ( u i ) | 2 d u i − α for i = 1,2,3, with ρ denoting the transmit SNR. The FAS channel gain | g FAS ( u i ) | is defined as Equation 19 where the port coefficients g k ( u i ) follow the spatial correlation model in Equation 4 (Wong et al., 2021).

3.3.2 Sum-Rate and Finite Blocklength correction

The total sum-rate is shown as Equation 20

R sum = R u 1 + R u 2 + R u 3 . (20)

In the high-SNR regime ( ρ → ∞ ), the sum-rate simplifies to Equation 21 highlighting the role of power allocation in determining the multiplexing gains.

R sum ≈ log 2 α u 3 α u 1 + α u 2 + log 2 α u 2 α u 1 + log 2 α u 1 γ u 1 , (21)

For short-packet transmissions, the achievable rate is adjusted by the channel dispersion (Polyanskiy et al., 2010), as shown in Equation 22:where V ( γ ) = ( log 2 e ) 2 1 − ( 1 + γ ) − 2, L is the blocklength, ϵ i is the target BLER, and Q − 1 ( ⋅ ) is the inverse Gaussian Q-function. The corresponding sum-rate under finite blocklength is R sum fb = ∑ i = 1 3 R u i fb.

R u i fb = R u i − V γ u i L Q − 1 ϵ i , i = 1,2,3 , (22)

3.4 Sum-rate maximization via gradient descent

Using the sum-rate expressions derived in Section 3.3, we formulate the power allocation problem to maximize the total throughput under power normalization and SIC ordering constraints, which is solved via projected gradient descent.

3.4.1 Problem formulation

Let α = [ α u 1 , α u 2 , α u 3 ] T denote the power allocation vector. The sum-rate maximization problem is stated as Equation 23 subject to Equations 24, 25. where the individual rates R u i are given in Equations 16-18. The constraints ensure the feasibility of SIC by allocating higher power to users with poorer channel conditions.

max α R sum α = R u 1 + R u 2 + R u 3 (23)

α u 1 + α u 2 + α u 3 = 1 , (24)

0 < α u 1 < α u 2 < α u 3 , (25)

Remark: Although the finite-blocklength rate expression Equation 22 is used for performance evaluation, the optimization problem is formulated with the infinite-blocklength sum rate in Equation 20 because the channel dispersion term does not significantly affect the optimal power allocation. This simplification has been numerically verified and is common in former literature.

3.4.2 Gradient computation

To apply gradient-based optimization, we compute the partial derivatives of R sum with respect to each power coefficient. Using the expressions above, the gradients are derived as Equations (26–28).

3.4.2.1 Partial derivative with respect to α u 1

∂ R sum ∂ α u 1 = γ u 1 ln 2 1 + α u 1 γ u 1 ⏟ from R u 1 − α u 2 γ u 2 2 ln 2 1 + α u 1 γ u 2 1 + α u 1 + α u 2 γ u 2 ⏟ from R u 2 − α u 3 γ u 3 2 ln 2 1 + α u 1 + α u 2 γ u 3 1 + α u 1 + α u 2 + α u 3 γ u 3 ⏟ from R u 3 . (26)

3.4.2.2 Partial derivative with respect to α u 2

∂ R sum ∂ α u 2 = γ u 2 ln 2 1 + α u 1 + α u 2 γ u 2 ⏟ from R u 2 − α u 3 γ u 3 2 ln 2 1 + α u 1 + α u 2 γ u 3 1 + α u 1 + α u 2 + α u 3 γ u 3 ⏟ from R u 3 . (27)

3.4.2.3 Partial derivative with respect to α u 3

∂ R sum ∂ α u 3 = γ u 3 ln 2 1 + α u 1 + α u 2 + α u 3 γ u 3 ⏟ from R u 3 . (28)

The gradient vector is thus expressed as ∇ R sum ( α ) = ∂ R sum ∂ α u 1 , ∂ R sum ∂ α u 2 , ∂ R sum ∂ α u 3 T.

Note that the rate expressions in Equations 16-18 involve the min operator, which is non-differentiable at points where two arguments are equal. However, for continuous channel realizations and power allocation coefficients, the probability of encountering such exact equality during numerical optimization is practically zero. Hence, the rate function is differentiable almost everywhere, and the partial derivatives in (26)–(28) effectively correspond to the gradient of the active (minimizing) term. In the unlikely event of a tie, the presented formulas still provide a valid subgradient, and the projected gradient descent algorithm converges to a stationary point under standard subgradient theory.

3.4.3 Projected gradient descent algorithm

The optimization proceeds via projected gradient ascent. The algorithm is initialized with the fixed allocation α ( 0 ) = [ 0.1 , 0.3 , 0.6 ], which serves as the baseline. At iteration t, the update is expressed as Equation 29 where η t > 0 is the step size, and the projection operator P is defined as P ( a ) = sort ( max ( a , 0 ) ) ∑ sort ( max ( a , 0 ) ), which enforces the constraints ∑ i = 1 3 α u i = 1 and α u 1 < α u 2 < α u 3. The step size η t is adaptively adjusted by a backtracking line search (Armijo condition) to ensure monotonic improvement, so that the optimized sum rate never falls below the baseline.

α t + 1 = P α t + η ∇ R sum α t , (29)

3.4.4 Convergence and complexity

R sum ( α ) is continuously differentiable with a Lipschitz-continuous gradient over the compact feasible set (Boyd and Vandenberghe, 2004). Hence, the projected gradient method converges to a stationary point with a sublinear convergence rate O ( 1 / t ). The computational complexity per iteration is dominated by evaluating the three partial derivatives, which involves only elementary operations and the precomputed γ u i values, making the algorithm suitable for real-time power control in practical systems.

Numerical results are provided in the following section.

4 Numerical results

In this section, we evaluate the performance of the proposed multi-user FAS-NOMA framework through Monte Carlo simulations. The system parameters are set in accordance with practical short-packet communication scenarios as follows: number of FAS ports N = 4, blocklength L = 100 symbols, packet sizes N u 1 = 80 bits, N u 2 = 60 bits, N u 3 = 40 bits, path-loss exponent α = 3.9, distances d u 1 = 5 m, d u 2 = 10 m, d u 3 = 15 m, FAS size W λ = 5 λ, and power allocation coefficients α u 1 = 0.1, α u 2 = 0.3, α u 3 = 0.6 for the fixed scheme. The spatial correlation among FAS ports follows the Jakes’ model, and each user selects the port with the maximum channel gain.

4.1 Average BLER performance

Figure 2 depicts the average BLER of the three users based on Equations 10, 15 for different numbers of FAS ports, namely, N = 3, 4, and 5, along with a comparison to conventional single-antenna reception. The solid curves represent the simulation results for the proposed FAS-NOMA scheme, while the dashed curves correspond to the high-SNR asymptotic approximations. As can be observed, increasing the number of FAS ports N consistently improves the BLER performance for all users, demonstrating the diversity gain of FAS. The asymptotic curves correctly capture the diversity order (slope) for each N, and the conventional single-antenna scheme exhibits considerably higher BLER, especially for the cell-edge users. The consistency between the simulation and asymptotic results validates the theoretical analysis.

Remark: The dashed asymptotic curves are derived from the leading-order term E [ ϵ ] ∝ ρ − N. They are intended to illustrate the diversity order (slope) rather than to provide a precise approximation at moderate SNR. Due to finite-blocklength effects, channel dispersion, and path loss, higher SNR (e.g., beyond 60 dB) is required for the asymptotic expressions to closely match the simulation results. The divergence observed at 40–45 dB is within the expected range and does not affect the conclusion on the diversity order.

Based on the NOMA power allocation constraints, Figures 3–8 show the three-dimensional surface plots and contour maps of the average BLER for the three users versus the power allocation coefficients. These figures visually illustrate the impact of power allocation on the average BLER, thereby facilitating the identification of the optimal power allocation region for each user. In particular, based on the contour analysis of the power allocation coefficient α 2, the following observations can be made for the two cell-edge users. To achieve a lower BLER for the closer edge user (C E U 1), α 2 should be set above approximately 0.3. In contrast, for the more distant edge user (C E U 2), a lower BLER is obtained when α 2 is around 0.2. The actual choice of α 2 can be tailored according to the specific requirements of the communication scenario, allowing a flexible trade-off between the reliability of the two edge users.

4.2 Throughput performance: Infinite vs. finite blocklength

Figure 9 compares the achievable rates under infinite blocklength (Shannon capacity) and finite blocklength with target BLER ϵ = 1 0 − 3. The solid lines correspond to the infinite-blocklength case, while the dashed lines show the finite-blocklength rates. As expected, the finite-blocklength rates are lower due to the channel dispersion penalty. For instance, at SNR = 60 dB, the sum rate decreases from approximately 3.96 bps/Hz (infinite blocklength) to about 2.70 bps/Hz (finite blocklength), which matches the theoretical loss V / L Q − 1 ( ϵ ). This observation highlights the importance of accounting for the finite blocklength effect in short-packet communications, such as those in URLLC and IoT scenarios.

4.3 Sum-rate maximization via power optimization

Figure 10 compares the sum rate achieved by the fixed power allocation α = [ 0.1 , 0.3 , 0.6 ] with that obtained by the proposed projected gradient descent algorithm. The algorithm is initialized with the fixed allocation and employs a backtracking line search satisfying the Armijo condition, which guarantees that the optimized sum rate is never lower than the baseline. The parameters of the algorithm are set as follows: maximum number of iterations T = 200, initial learning rate η 0 = 0.1, backtracking factor c = 0.5, and Armijo parameter α Armijo = 1 0 − 4. As observed, the optimized allocation consistently outperforms or matches the fixed allocation across the entire SNR range. In the low-to-moderate SNR region, the gain is substantial. This demonstrates that adaptive power control effectively balances interference and rate trade-offs when the SNR is limited. At higher SNRs, the gap gradually narrows as the fixed allocation becomes nearly optimal, yet the optimized curve remains slightly above or equal to the baseline. The results confirm the robustness and effectiveness of the proposed optimization framework.

The numerical results confirm that the proposed FAS-assisted NOMA framework offers a flexible and effective solution for short-packet edge access. By exploiting the spatial diversity of FAS and jointly optimizing power allocation, the system achieves a favorable trade-off between reliability and throughput, making it well-suited for URLLC and IoT applications.

5 Conclusion

In this paper, we have proposed a multi-user downlink framework that integrates FAS with NOMA for short-packet edge access, extending the conventional two-user scenario to a generalized three-user model scalable to practical multi-tier communication environments. Simulation results validate the theoretical analysis, demonstrating that the proposed framework achieves a diversity order of N and improves edge-user reliability while maintaining favorable throughput, particularly in the low-to-moderate SNR regime. These findings confirm that the combination of FAS and NOMA offers a promising solution to meet the stringent reliability and latency requirements of short-packet applications such as URLLC and IoT.

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Footnotes

Edited by: George Alexandropoulos, National and Kapodistrian University of Athens, Greece

Reviewed by: Boyi Tang, University College London, United Kingdom

Noor Waqar, University College London, United Kingdom