Active STAR-RIS-Aided RSMA IoT Systems: Performance Analysis, Model-Based and Data-Driven Resource Allocation Frameworks

A. Research Context

• Double-fading cascaded links and near–far imbalance challenge reliability and fairness in active STAR-RIS-assisted RSMA IoT systems.Active STAR-RIS amplification is presented as mitigating double fading, while RSMA provides flexible interference management.Source: A. Research Context · p. 1

B. Literature Overview

• Existing active-mode studies leave a gap in jointly combining complete OP/EC and asymptotic analysis, fairness-oriented resource allocation, and low-overhead learning.Prior model-based designs are primarily sum-rate or energy focused, while learning-based RA mainly uses DRL.Source: C. Novelty and Contributions · p. 2, B. Literature Overview · p. 2

C. Novelty and Contributions

• The analytical framework derives closed-form OP and EC with and without direct links, asymptotic behavior, diversity order, array gain, and two energy-efficiency metrics.The energy-efficiency measures are throughput-based and spectral-based.Source: C. Novelty and Contributions · p. 3
• The fairness-oriented model-based framework jointly optimizes power allocation and rate-splitting coefficients under practical constraints using BCD and SCA.It addresses both OP and EC fairness problems.Source: C. Novelty and Contributions · p. 3
• DMNN, CMNN, and MXGB approximate optimization-based resource-allocation solutions; MXGB has the shortest execution time while remaining comparable to ground-truth benchmarks.The framework is presented as a lower-complexity route to scalable, real-time resource allocation.Source: C. Novelty and Contributions · p. 3

II. NETWORK DESCRIPTION

• The network model uses a two-user near/far RSMA configuration to isolate fairness challenges and enable tractable closed-form OP/EC analysis.The passage describes user grouping and pairing as a route to reusing the two-user framework, while joint clustering and SIC-order optimization remain future work.Source: §II · p. 4

• The framework derives closed-form OP and EC, then analyzes asymptotic behavior, diversity order, array gain, and throughput-based and spectral-based energy efficiency.Source: §III · p. 5

1) Outage Probability Analysis:

• Outage occurs when a user fails to decode either the common stream or its private stream.The framework uses the target rates for the common and private streams to define the outage condition.Source: 1) Outage Probability Analysis · p. 5
• κℓ is approximated by a generalized Gamma distribution, whose statistical characterization supports deriving the outage expression.The approximation uses shape parameters ξℓ and 1/2 and scale parameter Ω²ℓ.Source: 1) Outage Probability Analysis · p. 5
• The generalized-Gamma approximation’s KS statistic remains on the order of 10^-3 across tested STAR-RIS sizes and amplification gains.The reported residual deviation is at the finite-sample level for 10^6 Monte Carlo realizations.Source: 1) Outage Probability Analysis · p. 5

2) Asymptotic Outage Probability:

• The high-SNR asymptotic OP formulation is used to characterize the system’s diversity order and array gain.The diversity order is governed by ξℓ, while the array gain captures horizontal OP-curve placement.Source: 2) Asymptotic Outage Probability · p. 6
• Increasing STAR-RIS elements or amplification gain raises ξℓ and steepens the OP decay; when Dℓ ≠ 0, OP keeps declining at high SNR.The horizontal OP-curve placement also depends on element count, amplification gain, target data rates, and PA coefficients.Source: 2) Asymptotic Outage Probability · p. 6

1) Ergodic Capacity Analysis:

• The closed-form EC expression is written in terms of Zℓ(·), following the capacity expression for the common and private rates.The EC is described as the long-term average achievable rate supportable with negligible OP.Source: 1) Ergodic Capacity Analysis · p. 6

2) Asymptotic Ergodic Capacity:

• High-SNR EC becomes independent of average transmit SNR and is sensitive to PA and RS coefficients.The coefficients determine how power and rate resources are divided between common and private streams.Source: 2) Asymptotic Ergodic Capacity · p. 6

C. Throughput-based and Spectral-based Energy Efficiencies

• The two EE metrics distinguish successfully delivered bits per consumed power from long-term achievable spectral efficiency per unit power.Throughput-based EE accounts for users’ outage probabilities, while spectral-based EE uses ergodic capacities.Source: C. Throughput-based and Spectral-based… · pp. 6–7
• Increasing β_RΣ² enhances beamforming gain but also raises overall power consumption, making careful parameter optimization important for energy efficiency.PA and RS factors also affect the common- and private-stream rates in the EE numerators.Source: C. Throughput-based and Spectral-based… · p. 7
• More STAR-RIS elements or higher amplification gain can trade hardware against power to meet reliability targets, while EE is unimodal in average SNR.The passive mode is reported as preferable at low-to-moderate SNR; at high SNR, fairness depends on resource allocation rather than transmit power.Source: C. Throughput-based and Spectral-based… · p. 7

IV. MODEL-BASED RESOURCE ALLOCATION FRAMEWORK

• The analysis identifies reliability and capacity fairness among users as distinct resource-allocation objectives.The model-based framework considers user outage fairness and user capacity fairness.Source: §IV · p. 7

1) Problem Formulation:

• The outage-fairness objective minimizes the worst-user OP by jointly optimizing PA coefficients α and RS coefficients τ under system constraints.The formulation targets reliability imbalance associated with heterogeneous near- and far-user channels.Source: 1) Problem Formulation · p. 7
• The optimization is nonconvex because of its max-min structure, nonlinear variable coupling, and Υ(·,·) in the OP expressions.The formulation uses ϱ = 10^-3 to prevent division by zero and ensure numerical stability.Source: 1) Problem Formulation · p. 7

2) Proposed Solution:

• The proposed solution introduces θ to bound the maximum user OP and substitutes an asymptotic OP approximation to form a surrogate objective.The PA block uses convexification steps, including first-order Taylor expansions and auxiliary variables to bound terms.Source: 2) Proposed Solution · p. 7
• The method recasts the outage-fairness problem as a convex optimization problem solvable with CVX and an SDP solver.The constraints are transformed from the original formulation and intermediate approximation constraints.Source: 2) Proposed Solution · p. 8
• Because the reformulated problem remains nonconvex through coupled variables, BCD alternates between tractable PA and RS subproblems until convergence.The two blocks update the PA coefficients α and RS coefficients τ in turn.Source: 2) Proposed Solution · p. 8
• The RS block remains nonconvex after simplification, so a bound at the previous feasible point is used to convexify a constraint.The recast RS problem is then solved using CVX with an SDP solver.Source: 2) Proposed Solution · p. 8

3) Overall Algorithm, Convergence, and Complexity:

• Each outage-fairness iteration solves the RS and PA blocks alternately, then returns their final coefficients when the objective converges.The algorithm initializes variables in their feasible regions and evaluates the objective before repeating the updates.Source: 3) Overall Algorithm, Convergence, and… · p. 8
• The objective sequence is bounded below, and the stated convergence analysis concludes that the algorithm converges.The argument relies on marginal optimality from alternating solutions of the RS and PA blocks.Source: 3) Overall Algorithm, Convergence, and… · p. 8
• Total outage-fairness complexity is O(I0(C1 + C2)), where I0 is the number of outer iterations and C1 and C2 are the RS- and PA-block costs.The block costs use interior-point complexity expressions with n1 = 7, n2 = 8, and convergence accuracies ϵ1 = ϵ2 = 10^-6.Source: 3) Overall Algorithm, Convergence, and… · p. 8

1) Problem Formulation:

• Near users typically achieve higher ergodic capacity, so the optimization balances users’ long-term achievable rates by jointly tuning power-allocation and rate-splitting coefficients.The objective is to reduce the capacity gap between users.Source: 1) Problem Formulation · p. 9

2) Proposed Solution:

• The non-convex capacity-fairness problem is converted into a convex one using successive convex approximation.An auxiliary variable lower-bounds each user’s ergodic capacity, while the constraints include QoS thresholds for common- and private-stream rates.Source: 1) Problem Formulation · p. 9, 2) Proposed Solution · p. 9
• The convexified problem can be solved with CVX and an SDP solver, and near/far-pair groups extend to K users with the same per-group reformulation.A full single-cell K-user model with one shared common stream and cross-user private-stream interference requires re-derived surrogate bounds and joint clustering/SIC-ordering optimization, and is left for future work.Source: 2) Proposed Solution · p. 9

A. ML-Based Resource Allocation Applications

• Offline-trained models approximate the optimization-based resource-allocation policy, replacing repeated online optimization with fast inference.The workflow connects analytical expressions to model-based solutions, which generate labels used to train DMNN, CMNN, and MXGB models.Source: A. ML-Based Resource Allocation… · p. 10

1) Dataset Generation:

• Two supervised datasets use model-based outage- and capacity-fairness solutions as labels; together they contain 500,000 samples, split 80% for training and 20% for testing.Input features and output labels are normalized to [0, 1].Source: 1) Dataset Generation · pp. 10–11

2) Description of Machine Learning Models:

• DMNN jointly predicts five resource-allocation outputs from system inputs using a feedforward network trained by backpropagation to minimize mean squared error.The described architecture has 10 input neurons and five output neurons.Source: 2) Description of Machine Learning… · p. 11
• CMNN serves as a convolutional baseline for low-dimensional tabular inputs, while MXGB decomposes multi-output regression into independently trained single-target boosting models.The stated results favor MXGB over both neural architectures in the accuracy–latency tradeoff; the implementation uses one XGBoost model per target.Source: 2) Description of Machine Learning… · p. 11

C. Real-Time Inference Phase

• Given a new system configuration, the trained DMNN, CMNN, or MXGB directly outputs resource-allocation parameters through a learned mapping.This replaces iterative optimization with a single forward inference, reducing computational complexity and execution latency.Source: C. Real-Time Inference Phase · p. 12
• The reported millisecond-scale latency measures simulated algorithmic inference, not validated end-to-end deployment.It excludes STAR-RIS control and reconfiguration latency, control signaling, and RF front-end effects; the paper identifies hardware or over-the-air validation as future work.Source: C. Real-Time Inference Phase · p. 12

D. Computational Complexity Analysis

• Inference complexity is measured in FLOPs, while dataset generation and model training are offline costs amortized over subsequent inferences.The paper treats forward inference as the cost governing real-time operation.Source: D. Computational Complexity Analysis · pp. 12–13

1) Graphical Validation of Assumption 1 and Active-Passive STAR-RIS Comparison:

• 10^-11 bps/Hz: the SI-induced rate-loss upper bound is negligible under the stated practical gain conditions, corroborating the overlap of SI-aware and SI-neglected curves.The reported bound applies for SI power of -80 dBm and source power of at least 30 dBm.Source: 1) Graphical Validation of Assumption… · pp. 13–14, Figure 6 · p. 13
• Active STAR-RIS operation considerably improves OP and EC over passive operation; OP keeps declining at high SNR, while EC saturates as desired signal and inter-message interference scale together.Analytical and simulation results show excellent agreement.Source: Figure 6 · p. 13, 1) Graphical Validation of Assumption… · p. 14

2) Impact of Direct Links:

• Direct links enhance OP and EC, but their improvement is smaller than the gain attributed to active STAR-RIS operation.The near user has a steeper high-SNR OP slope and lower OP, while both users’ EC saturates at a floor whose gap reflects asymmetric power-allocation and rate-splitting.Source: 2) Impact of Direct Links · p. 14, Figure 7 · p. 14

3) Impact of STAR-RIS Elements and Amplification Gain:

• Both OP and EC improve as STAR-RIS element count and amplification gain increase, with OP continuing to fall and EC tending to saturate at high values.Analytical curves closely match simulations across the parameter range.Source: 3) Impact of STAR-RIS Elements and… · pp. 14–15, Figure 9 · p. 15

4) On Performance of Energy Efficiencies:

• Throughput-based and spectral-based EE rise initially with average SNR, then decline as power consumption dominates after throughput and spectral efficiency saturate.Passive STAR-RIS achieves higher peak EE than active STAR-RIS, which has better OP and EC but requires amplification power.Source: 4) On Performance of Energy Efficiencies · p. 15, Figure 10 · p. 15

5) Impact of Imperfect CSI:

• With CSI imperfection level ς≤0.2, OP and EC remain close to the perfect-CSI case; larger errors cause gradual degradation.The iCSI model preserves per-link average power and reduces to perfect CSI when ς=0.Source: 5) Impact of Imperfect CSI · p. 15

6) Impact of Residual SI and Nonlinear Amplification:

• For δ≤δsat, residual SI and nonlinear amplification leave OP and EC close to ideal behavior; above δsat, accumulated SI and distortion noticeably degrade performance.A rigorous analytical treatment of these impairments is left for future work.Source: 6) Impact of Residual SI and Nonlinear… · p. 16

1) Convergence Behavior of Algorithm 1:

• Algorithm 1 produces a non-increasing objective sequence and converges to a local optimum within fewer than 30 iterations across eight drops.The convergence curves are described as reliable and consistent across the trials.Source: 1) Convergence Behavior of Algorithm 1 · p. 16

2) Optimal Hyperparameters and FLOPs Comparison:

• MXGB has the lowest inference complexity among the compared models, while the selected hyperparameters balance prediction accuracy and computational efficiency.The hyperparameter search uses finite, practically motivated spaces, so its configurations are locally optimal rather than guaranteed global optima.Source: 2) Optimal Hyperparameters and FLOPs… · p. 16, Table III · p. 16

3) Outage Probability Fairness Performance:

• Optimal RA jointly adjusts PA and RS coefficients to narrow the near/far OP gap and improve both users, unlike fixed RA, where the far user has higher OP.The imbalance is more pronounced in the moderate-SNR regime.Source: 3) Outage Probability Fairness… · pp. 16–17

5) ML-based RA Performance and Average Execution Time Comparison:

• MXGB consistently achieves the lowest inference time for both fairness problems, at less than 1 ms, while maintaining performance comparable to optimization-based benchmarks.The execution-time comparison covers different STAR-RIS element counts; the trained ML methods remain in the millisecond range across configurations.Source: Table IV · p. 17, 5) ML-based RA Performance and Average… · p. 17

4) Ergodic Capacity Fairness Performance:

• Optimal RA alleviates the fixed-configuration EC imbalance by raising the far user’s EC while slightly reducing the near user’s, yielding a more equitable distribution without compromising overall rate.Source: 4) Ergodic Capacity Fairness Performance · p. 17

5) ML-based RA Performance and Average Execution Time Comparison:

• All three ML frameworks achieve nearly identical fairness performance; predicting RA configurations and then computing EC is more reliable than directly predicting EC.The passage attributes similar fairness results to relatively small variance between predicted RA configurations and ground-truth values.Source: 5) ML-based RA Performance and Average… · p. 17

6) Generalization and Out-of-Distribution Resilience:

• At unseen SNRs of 51, 53, and 55 dB—outside the 0–50 dB training range—all three models’ predictions closely track ground-truth optimal RA configurations.Source: 6) Generalization and… · p. 17

A. Concluding Remarks

• The study combines OP/EC analysis, fairness-oriented joint PA and RS optimization, and ML models that approximate optimization solutions with lower computational complexity.The analysis covers direct-link and no-direct-link scenarios, asymptotic metrics, diversity order, array gain, and throughput-based and spectral-based EE tradeoffs.Source: A. Concluding Remarks · p. 18

B. Open Challenges and Future Research Directions

• A full single-cell K-user treatment remains open; dimension- and geometry-varying learning settings require further model or feature changes, and end-to-end real-time operation still needs hardware validation.The future-work discussion also identifies high-gain impairment analysis and an EE-aware joint optimization scheme as research directions.Source: B. Open Challenges and Future Research… · p. 18