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Active IRS Aided Multiple Access for Energy-Constrained IoT Systems

Guangji Chen, Qingqing Wu, Chong He, Wen Chen, Jie Tang, Shi Jin

arXiv:2201.12565v1cs.ITcs.ETeess.SP

TL;DR

The paper addresses multiple access for active-IRS-aided uplinks with energy-constrained IoT devices. It compares TDMA and NOMA, proposes a user-grouped hybrid TDMA-NOMA scheme, and develops an alternating-optimization algorithm. The results identify throughput tradeoffs tied to the number of IRS beamforming vectors and show practical advantages of active IRS over passive IRS.

  • Problem

    The paper asks which multiple-access scheme best maximizes throughput in active-IRS-aided, energy-constrained IoT uplinks, where the TDMA-NOMA comparison remains unresolved.

  • Method

    The paper analytically compares TDMA and NOMA, proposes a user-grouped hybrid TDMA-NOMA scheme, and solves the associated non-convex optimization using alternating optimization.

  • Results

    NOMA generally provides higher throughput with one IRS beamforming vector, whereas TDMA can potentially achieve higher throughput with multiple vectors; active IRS also extends coverage and supports multiple low-energy devices.

  • Takeaways & Limitations

    The hybrid TDMA-NOMA scheme offers flexible performance-signaling-overhead tradeoffs for any given number of IRS beamforming vectors.

Abstract

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We investigate the fundamental multiple access (MA) scheme in an active intelligent reflecting surface (IRS) aided energy-constrained Internet-of-Things (IoT) system, where an active IRS is deployed to assist the uplink transmission from multiple IoT devices to an access point (AP). Our goal is to maximize the sum throughput by optimizing the IRS beamforming vectors across time and resource allocation. To this end, we first study two typical active IRS aided MA schemes, namely time division multiple access (TDMA) and non-orthogonal multiple access (NOMA), by analytically comparing their achievable sum throughput and proposing corresponding algorithms. Interestingly, we prove that given only one available IRS beamforming vector, the NOMA-based scheme generally achieves a larger throughput than the TDMA-based scheme, whereas the latter can potentially outperform the former if multiple IRS beamforming vectors are available to harness the favorable time selectivity of the IRS. To strike a flexible balance between the system performance and the associated signaling overhead incurred by more IRS beamforming vectors, we then propose a general hybrid TDMA-NOMA scheme with user grouping, where the devices in the same group transmit simultaneously via NOMA while devices in different groups occupy orthogonal time slots. By controlling the number of groups, the hybrid TDMA-NOMA scheme is applicable for any given number of IRS beamforming vectors available. Despite of the non-convexity of the considered optimization problem, we propose an efficient algorithm based on alternating optimization. Simulation results illustrate the practical superiorities of the active IRS over the passive IRS in terms of the coverage extension and supporting multiple energy-limited devices, and demonstrate the effectiveness of our proposed hybrid MA scheme for flexibly balancing the performance-cost tradeoff.

I. INTRODUCTION

The paper studies active IRS assistance for energy-constrained IoT uplinks, where conventional passive IRS performance can be limited by path loss. It compares TDMA and NOMA and proposes a hybrid scheme to balance throughput and signaling overhead.

  • Energy-constrained IoT devices have limited information-uploading capability and require efficient multiple access for massive connectivity.
  • Passive IRS can suffer high product-distance path loss, motivating active IRS architectures that amplify incident signals with low-cost hardware.
  • Active IRS research in energy-constrained IoT systems remains limited, especially regarding performance gains under different multiple-access schemes.
  • With one IRS beamforming vector, NOMA generally achieves larger throughput than TDMA, while TDMA can potentially outperform NOMA with multiple vectors.
  • The hybrid TDMA-NOMA scheme groups simultaneous NOMA users into orthogonal time slots and applies to any given number of available IRS beamforming vectors.
  • Simulations report active-IRS advantages in coverage extension, reflecting-element requirements, and support for multiple low-energy devices.
  • The hybrid scheme significantly lowers signaling overhead with slight performance loss by selecting the number of devices per group.

II. SYSTEM MODELS AND PROBLEM FORMULATIONS

The system contains multiple energy-constrained single-antenna IoT devices transmitting uplink data to a single-antenna AP with active IRS assistance. Channels are modeled as quasi-static flat-fading, and devices use their available energy during each transmission period.

  • A. System Model: An active IRS with N elements assists uplink transmission from K single-antenna IoT devices to a single-antenna AP.
  • A. System Model: Each device has a specified energy budget E_k available at the beginning of a transmission period.
  • A. System Model: Devices use their available energy to transmit their own data to the AP over the uplink.
  • A. System Model: All devices and the AP operate over the same frequency band.
  • A. System Model: The equivalent channels include IRS-to-AP, device-to-IRS, and device-to-AP links.
  • A. System Model: Wireless channels are assumed quasi-static flat-fading and remain constant within each transmission period T_max.
  • A. System Model: The model covers applications such as MEC offloading and wireless sensing with limited device energy.
  • A. System Model: Instantaneous CSI for all links is assumed available through compressive sensing or active sensors at the IRS.

B. TDMA and NOMA-based Multiple Access

The paper formulates sum-throughput maximization for TDMA and NOMA under energy, time, and active-IRS power constraints. It develops efficient algorithms and compares the schemes despite their coupled non-convex optimization structures.

  • 1) TDMA-based Scheme:: TDMA assigns orthogonal time slots to devices, with each slot using a dedicated IRS beamforming pattern.
  • 1) TDMA-based Scheme:: Each active IRS coefficient combines amplitude and phase, and its amplitude may exceed one because the IRS is active.
  • 2) NOMA-based Scheme:: NOMA lets all devices transmit simultaneously while sharing a common IRS beamforming pattern.
  • 2) NOMA-based Scheme:: At the AP, successive interference cancellation decodes users sequentially, subtracting earlier messages and treating later messages as noise.
  • 2) NOMA-based Scheme:: The NOMA formulation includes a common transmission duration and active-IRS amplification-power constraint.
  • 1) TDMA-based Scheme:: TDMA optimizes transmission times, device powers, and individual IRS beamforming under energy, total-time, nonnegativity, and amplification-power constraints.
  • The TDMA and NOMA problems are non-convex because optimization variables are coupled in their objectives and constraints.
  • The paper exploits problem structure to develop efficient algorithms and provide a fundamental performance comparison between the schemes.

III. INVESTIGATIONS ON ACTIVE IRS AIDED TDMA AND NOMA SCHEMES

The paper formulates active IRS-aided TDMA and NOMA throughput maximization problems under energy, amplification, and coupled-variable constraints. It develops iterative optimization methods that obtain locally optimal TDMA solutions and convergent NOMA solutions despite non-convexity.

  • Active IRS-aided TDMA and NOMA are studied through dedicated algorithms for their achievable sum-throughput maximization problems.
  • The TDMA formulation includes coupled variables, a non-concave objective, and the active IRS amplification-power constraint, making optimal solution difficult.
  • At the TDMA optimum, every device exhausts its available energy, so τ_kp_k = E_k.
  • The TDMA algorithm introduces slack variables and successive convex approximation, repeatedly solving convex problems until convergence to a locally optimal solution.

B. Proposed Algorithm for NOMA

The NOMA optimization couples a common IRS beamforming vector with all devices’ transmit powers, creating non-convex constraints. An alternating-optimization algorithm separates these variables and iteratively optimizes them until convergence.

  • NOMA uses one common IRS beamforming vector, which cannot be flexibly adjusted for individual devices.
  • The common-vector coupling can lock active-IRS amplification gains when all devices simultaneously transmit at maximum power.
  • Unlike TDMA, NOMA may leave some devices’ energy unused at the optimum, so the TDMA algorithm is not directly applicable.
  • A lemma shows that the optimal NOMA transmission time satisfies τ = T_max.
  • Alternating optimization divides the variables into IRS beamforming and power-control blocks, optimizing them iteratively until convergence.

1) IRS Beamforming Optimization:

The IRS-beamforming subproblem is transformed into a tractable convex optimization problem by relaxing the rank-one constraint and applying the Charnes–Cooper transformation. Alternating optimization then combines this step with power control and converges through non-decreasing objective values.

  • The IRS beamforming subproblem is difficult because its objective has a fractional form and includes a rank-one constraint.
  • Relaxing the rank-one constraint and applying the Charnes–Cooper transformation yields a linear convex optimization problem.
  • The relaxed problem has the same optimal value as the original problem, and an optimal rank-one solution can be recovered through the stated construction and SVD.
  • For fixed IRS beamforming, the power-control subproblem is solved separately using convex optimization techniques.
  • The AO algorithm alternately optimizes IRS beamforming and power control, with a non-decreasing objective value that guarantees convergence.

C. Active IRS Aided TDMA Versus NOMA

The paper compares active IRS-aided TDMA and NOMA under different numbers of available beamforming vectors, then introduces a hybrid TDMA-NOMA scheme. The hybrid design uses grouping to trade throughput against signaling overhead and includes both TDMA and NOMA as special cases.

  • Active IRS Aided TDMA Versus NOMA: With one available IRS beamforming vector, active IRS-aided NOMA achieves no smaller sum throughput than TDMA.
  • Active IRS Aided TDMA Versus NOMA: NOMA can obtain larger active-IRS amplification gains because its energy-constrained devices generally transmit at lower powers than under TDMA.
  • Active IRS Aided TDMA Versus NOMA: TDMA can outperform NOMA when multiple IRS beamforming vectors are exploitable, because it can harness more favorable time selectivity.
  • General Hybrid TDMA-NOMA Scheme: The hybrid scheme partitions devices into groups, using orthogonal time slots across groups and NOMA within each group.
  • General Hybrid TDMA-NOMA Scheme: Setting the group count L = K gives TDMA, while L = 1 gives NOMA; varying L supports any available number of IRS beamforming vectors with controllable overhead.

B. Proposed Solution for Problem (34)

The proposed alternating-optimization framework addresses the non-convex hybrid TDMA-NOMA problem by alternating between resource allocation and IRS beamforming. Numerical results compare TDMA and NOMA and show that TDMA benefits from multiple dedicated IRS beamforming vectors when the signaling overhead is acceptable.

  • Problem formulation: The hybrid problem is more challenging because its variables are coupled and its objective is non-concave.The formulation couples τ_l and p_kl in a constraint and has a non-concave objective.
  • Alternating optimization: The algorithm partitions the variables into {τ_l, p_kl} and {v_l}, then updates these two blocks alternately.This extends the alternating-optimization framework to multiple groups with distinct IRS beamforming vectors.
  • Resource allocation: After the change of variables e_kl = τ_l p_kl, the resource-allocation subproblem becomes convex and can be solved efficiently with standard solvers.The transformed objective is concave and all constraints are convex.
  • IRS beamforming: The IRS-beamforming subproblem separates across groups into L independent subproblems solvable with a Charnes-Cooper transformation-based SDP technique.The separation follows because variables for different groups are separable in both the objective and constraints.
  • TDMA and NOMA comparison: For K ≥2, TDMA always outperforms NOMA, with a widening gap as K increases because dedicated beamforming vectors provide more adjustment freedom.NOMA throughput increases slowly or remains nearly constant as more devices share one IRS beamforming vector.
  • TDMA and NOMA comparison: TDMA may therefore be preferable for active IRS systems, although it incurs extra signaling overhead.The numerical study evaluates the throughput tradeoff between the two access schemes.

B. Performance Comparison for Active IRS or Passive IRS

The numerical comparisons show that active IRS systems generally achieve higher throughput and broader coverage than passive IRS systems, especially with few IRS elements or low device energy. However, active IRS performance depends strongly on deployment location, and poor placement can make it inferior to passive IRS.

  • IRS architecture comparison: Active IRS throughput increases monotonically with the number of IRS elements, and active NOMA can outperform passive TDMA despite using one beamforming vector.The comparison contrasts one active beamforming vector with K passive beamforming vectors.
  • IRS architecture comparison: 10 bps/Hz requires 10 active-IRS elements instead of 90 passive-IRS elements.The active architecture reduces the required element count by increasing each element’s amplification coefficient.
  • Energy-constrained operation: Active IRS significantly improves throughput over passive IRS when each device has low available energy, supporting multiple low-energy devices.The improvement is attributed to larger allowed amplification coefficients when the incident signal is weaker.
  • Coverage and distance: Active IRS extends transmission coverage, and its throughput decreases more slowly with AP-device-cluster distance than passive IRS throughput.This behavior is reported for both TDMA and NOMA systems.
  • IRS deployment: Active IRS placement is critical: moving it farther from the AP can sharply reduce throughput, and improper placement can make active IRS performance worse than passive IRS.The reported bottleneck is the IRS-AP link when the IRS is too close to the devices.

C. Performance Evaluation for Hybrid MA Schemes

The evaluation examines user grouping and the hybrid TDMA-NOMA scheme, showing that grouping choice has little effect while increasing the number of groups improves throughput with modest overhead costs. The active IRS and hybrid scheme provide favorable performance–overhead tradeoffs compared with passive-IRS alternatives.

  • Impact of User Grouping: Random user grouping can be applied with negligible performance loss, while exhaustive grouping optimization becomes time-consuming and computationally expensive as K grows.The grouping-search burden is especially relevant in larger-device systems.
  • Hybrid MA Performance: The hybrid scheme’s sum throughput increases as the number of user groups L increases because more IRS beamforming vectors can exploit favorable time selectivity.The evaluation varies the number of IRS elements and user groups.
  • Hybrid MA Performance: The performance gap between L = 6 and L = 12 is less than 5%, while setting two devices per group reduces signaling overhead by 50%.The number of IRS beamforming coefficients sent to the IRS controller is LN.
  • Hybrid MA Performance: The hybrid TDMA-NOMA scheme lowers signaling overhead at the cost of slight performance loss, balancing the performance–overhead tradeoff.The scheme is designed for flexible operation across available IRS beamforming vectors.
  • Active Versus Passive IRS: Active-IRS NOMA significantly outperforms passive-IRS TDMA while maintaining lower signaling overhead, supporting the active architecture’s practical advantages.The reported advantages include higher throughput and lower signaling overhead than the conventional passive IRS.
  • Active Versus Passive IRS: Numerical results show that active IRS extends coverage, reduces the required number of reflecting elements, and supports multiple low-energy IoT devices.The hybrid scheme is presented as a practical approach for large IoT networks.

APPENDIX A: PROOF OF LEMMA 1

The appendix proves Lemma 1 by constructing a feasible alternative solution and comparing its throughput with the assumed optimum. The contradiction establishes the stated optimality property.

  • Proof of Lemma 1: The constructed solution achieves a higher objective value than the assumed optimum, contradicting optimality.The comparison focuses on the throughput contributions of the affected devices.
  • Proof of Lemma 1: The proof assumes an optimal solution and constructs a new feasible solution while preserving the other devices’ variables.The construction changes the transmit power, time allocation, and beamforming variables associated with selected devices.
  • Proof of Lemma 1: Because the alternative solution remains feasible and improves throughput, the assumed optimal solution must satisfy the lemma’s scheduling condition.The proof verifies feasibility through the problem constraints before comparing objective values.

APPENDIX B: PROOF OF PROPOSITION 1

The proof compares reformulated TDMA and NOMA optimization problems, using convexity, KKT conditions, and feasible-solution mappings to establish their optimal-value relationship. It also characterizes the optimal NOMA allocation through a common received SNR and identifies when TDMA is strictly better.

  • Problem reformulation: The proof introduces paired reformulations of the TDMA and NOMA problems before restoring their original constraints.These formulations provide the basis for comparing the two schemes’ optimal values.
  • NOMA optimality: The reformulated NOMA problem is convex, and its KKT conditions yield a unique optimal received SNR shared by all devices.The uniqueness follows from the monotonicity of the auxiliary function Γ(Υ_k).
  • NOMA optimality: Each device depletes its available energy at the optimal solution of the reformulated NOMA problem.This property supports constructing a corresponding TDMA solution.
  • Throughput comparison: A feasible NOMA solution can be transformed into a TDMA solution with the same received SNR, establishing that the TDMA optimum is no smaller.The construction uses the stated feasibility relations and an arithmetic-geometric-mean inequality.
  • Throughput comparison: TDMA is strictly better than NOMA when the sufficient strictness condition in the proof holds; otherwise, the optimal values can be equal.The proof concludes the comparison through the corresponding optimal-value inequalities.
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