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On the Secrecy Design of STAR-RIS assisted Uplink NOMA Networks

Zheng Zhang, Jian Chen, Yuanwei Liu, Qingqing Wu, Bingtao He, Long Yang

arXiv:2111.02642v1cs.IT

TL;DR

The paper addresses secure uplink NOMA transmission using STAR-RIS when eavesdropper CSI may be full or only statistical. It develops CSI-specific secrecy optimization methods and reports strong secrecy performance with practical quantization and deployment guidance.

  • Problem

    The paper addresses secure uplink NOMA transmission through STAR-RIS under full or statistical eavesdropping CSI.

  • Method

    It formulates secrecy beamforming problems and develops AHB-based algorithms, including an exact SOP expression and modified AHB design for statistical CSI.

  • Results

    Numerical results demonstrate the secrecy superiority of the proposed scheme.

  • Takeaways & Limitations

    The paper provides guidance on amplitude quantization and deploying STAR-RIS near users or the BS under adaptive-rate coding.

Abstract

from arXiv · show

This paper investigates the secure transmission in a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted uplink non-orthogonal multiple access system, where the legitimate users send confidential signals to the base station by exploiting STAR-RIS to reconfigure the electromagnetic propagation environment proactively. Depending on the availability of the eavesdropping channel state information (CSI), both the full CSI and statistical CSI of the eavesdropper are considered. For the full eavesdropping CSI scenario, we adopt the adaptive-rate wiretap code scheme with the aim of maximizing minimum secrecy capacity subject to the successive interference cancellation decoding order constraints. To proceed, we propose an alternating hybrid beamforming (AHB) algorithm to jointly optimize the receive beamforming, transmit power, and reflection/transmission coefficients. While for the statistical eavesdropping CSI scenario, the constant-rate wiretap code scheme is employed to minimize the maximum secrecy outage probability (SOP) subject to the quality-of-service requirements of legitimate users. Then, we derive the exact SOP expression under the constant-rate coding strategy and develop an extended AHB algorithm for the joint secrecy beamforming design. Simulation results demonstrate the effectiveness of the proposed scheme. Moreover, some useful guidance about the quantification of phase shift/amplitude and the deployment of STAR-RIS is provided.

I. INTRODUCTION

The introduction motivates secure uplink NOMA with STAR-RIS by combining reconfigurable full-space propagation with physical-layer security. It formulates separate designs for full and statistical eavesdropping CSI and reports secrecy, quantization, and deployment findings.

  • STAR-RIS provides 360° coverage and more flexible deployment than conventional reflecting-only RIS, which serves devices on only one side.
  • Integrating STAR-RIS with NOMA targets channel control and spectral-efficiency gains while addressing NOMA’s additional co-channel interference.
  • The paper studies uplink NOMA secrecy with an eavesdropper, considering both full and statistical eavesdropping CSI for indoor and outdoor users.
  • For full eavesdropping CSI, the design maximizes minimum secrecy capacity through joint beamforming and power optimization under SIC and STAR-RIS coefficient constraints.
  • For statistical eavesdropping CSI, the paper derives an exact SOP expression and uses an extended AHB algorithm to minimize maximum SOP.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system is an ES-mode STAR-RIS assisted uplink NOMA network with two users, a multi-antenna BS, and an eavesdropper. It models legitimate-channel beamforming, SIC decoding, and full or statistical eavesdropping CSI under quasi-static fading.

  • The model contains an indoor user, outdoor user, base station, eavesdropper, and STAR-RIS, with the BS using M antennas and other nodes using one antenna.
  • The STAR-RIS has N independently configurable elements that adjust reflected and transmitted signal amplitudes and phases in ES mode.
  • Quasi-static block fading keeps channels constant within each fading block, with Rician fading for the STAR-RIS-to-BS link and Rayleigh fading for remaining links.
  • Legitimate instantaneous CSI is assumed perfect, while full eavesdropping CSI applies to internal wiretaps and statistical CSI to external passive wiretaps.
  • The eavesdropper is conservatively assumed to decode both signals interference-free, while its statistical CSI can be estimated through long-term monitoring.
  • The BS combines superimposed uplink signals with receive beamforming and decodes them using SIC in an optimized stronger-to-weaker order.

A. Problem Formulation for Full Eavesdropping CSI

With full eavesdropping CSI, the paper uses adaptive-rate wiretap coding and jointly optimizes transmission power, BS receive beamforming, and STAR-RIS passive beamforming. The objective is max-min secrecy capacity under power, SIC, beamforming, and coefficient constraints.

  • Adaptive-rate wiretap coding sets codeword and redundant rates from legitimate and eavesdropper channel capacities to secure transmissions.
  • The optimization maximizes the minimum secrecy capacity of the indoor and outdoor users through joint power and beamforming design.
  • The problem enforces total transmit-power, SIC decoding-order, receive-beamforming normalization, and STAR-RIS amplitude and phase constraints.
  • Both possible SIC decoding orders are solved separately, and the solution with maximum secrecy capacity is selected.

B. Problem Formulation for Statistical Eavesdropping CSI

The statistical-CSI formulation uses constant-rate wiretap coding and minimizes the maximum secrecy outage probability while jointly designing transmission, reception, and STAR-RIS parameters. The problem is difficult because of coupled variables, energy-conservation constraints, and unavailable instantaneous eavesdropping CSI.

  • B. Problem Formulation for Statistical Eavesdropping CSI: Without instantaneous eavesdropping CSI, exact eavesdropper channel capacity cannot be evaluated, so the adaptive-rate scheme is invalid.The paper therefore uses constant-rate wiretap coding with constant codeword and secrecy rates.
  • B. Problem Formulation for Statistical Eavesdropping CSI: SOP is defined as the probability that the positive rate difference between the codeword rate and eavesdropping capacity falls below the target secrecy rate.The eavesdropping capacity is represented as CE,ρ = log2(1 + γE,ρ).
  • B. Problem Formulation for Statistical Eavesdropping CSI: The objective minimizes the maximum SOP of legitimate users subject to power, coding-rate, SIC-order, and STAR-RIS coefficient constraints.The design jointly optimizes transmit power, BS receive beamforming, and STAR-RIS passive beamforming.
  • B. Problem Formulation for Statistical Eavesdropping CSI: The constant codeword-rate requirement is explicitly represented by constraint (10c).The formulation imposes Rc,ρ ≤ Cρ = log2(1 + γρ) for each user.
  • B. Problem Formulation for Statistical Eavesdropping CSI: Two-layer coupling makes these problems harder than conventional reflecting-only RIS downlink beamforming optimization.The outer layer couples three variables in the objective and constraints, while the inner layer couples transmission and reflection amplitudes.
  • B. Problem Formulation for Statistical Eavesdropping CSI: Transmission and reflection amplitudes are mutually restricted by energy conservation, further increasing optimization difficulty.This restriction is specific to the STAR-RIS design considered here.
  • B. Problem Formulation for Statistical Eavesdropping CSI: The paper first develops an AHB algorithm for the full-CSI problem and then extends it to the statistical-CSI formulation.The statistical-CSI formulation is handled by extending the preceding algorithmic framework.
  • B. Problem Formulation for Statistical Eavesdropping CSI: The full-CSI solution jointly updates STAR-RIS coefficients and BS receive beamforming, while transmit power is obtained in closed form.This establishes the algorithmic basis for the statistical-CSI extension.

B. Optimal Transmit Power Policy

With beamforming variables fixed, the problem is reduced to transmit-power optimization. For one decoding-order case, the objective is the minimum of two functions of the transmit powers.

  • B. Optimal Transmit Power Policy: With fixed {W, Ut, Ur}, problem (8) becomes an optimization over the transmit powers.The beamforming variables are held constant while deriving the power policy.
  • B. Optimal Transmit Power Policy: For uI = 1 and uO = 0, the objective is min{OI(PI, PO), OO(PO)}.The two functions characterize the relevant secrecy-rate terms under this decoding-order case.
  • B. Optimal Transmit Power Policy: The resulting power policy is derived from the partial derivatives of OI(PI, PO).These derivatives support the subsequent closed-form transmit-power analysis.

I WqIUt) + POTr(qH

The transmit-power derivation analyzes monotonicity and intersects the competing secrecy-rate terms. Under the stated feasibility conditions, the resulting policy is characterized by positive candidate solutions and SIC-imposed power limits.

  • I WqIUt) + POTr(qH: Under feasibility conditions, OI is increasing in PI and OO is increasing in PO.These monotonicity properties support the stated power-policy construction.
  • I WqIUt) + POTr(qH: The optimal power policy for uI = 1 and uO = 0 is stated in Proposition 1.Its closed-form expression uses the discriminant ΔO.
  • I WqIUt) + POTr(qH: OI(PI, PO) decreases with PO, whereas OO(PO) increases with PO.Their opposing monotonicity determines whether the optimum occurs at an intersection or a boundary.
  • I WqIUt) + POTr(qH: When an intersection exists, the minimum secrecy-rate objective is maximized where OI(PI, P*O) = OO(P*O).The intersection is selected within the feasible interval from 0 to PO,max.
  • I WqIUt) + POTr(qH: When no intersection exists, OO(PO) remains below OI(PI, PO), so the optimum is determined by OO(PO).The corresponding optimal PO is then obtained from the boundary analysis.
  • I WqIUt) + POTr(qH: The SIC decoding-order constraint also limits PO through the received-beamforming and STAR-RIS terms.This constraint is incorporated into the feasible power range.
  • I WqIUt) + POTr(qH: Although the quadratic equation yields two candidates, monotonicity guarantees a unique positive solution.The result is used to complete the transmit-power derivation.

C. Overall Algorithm

Algorithm-2 alternates beamforming updates and closed-form power updates while tracking the minimum security capacity. Its objective is guaranteed to converge to a suboptimal solution over non-decreasing iterations.

  • C. Overall Algorithm: The convergence test uses the minimum security capacity and a predefined accuracy threshold across alternating, outer, and inner iterations.The parameters lA, louter, and linner count the respective iteration layers.
  • C. Overall Algorithm: Algorithm-2 alternates Algorithm-1 beamforming updates with transmit-power updates and records the minimum security capacity at each iteration.The initialization sets PI(n), PO(n), and Rs,min(n) before the alternating process begins.
  • C. Overall Algorithm: Proposition 2 guarantees that the proposed AHB algorithm converges to a suboptimal solution over non-decreasing iterations.The proof is given in Appendix B.
  • C. Overall Algorithm: The optimal transmit powers are updated by closed-form expressions, so Algorithm-2’s main complexity depends on Algorithm-1.The interior-point solution of problem (24) determines the dominant computational cost.

IV. PROPOSED SOLUTION FOR STATISTICAL EAVESDROPPING CSI

For statistical eavesdropping CSI, the paper derives an exact SOP expression and extends AHB to jointly optimize beamforming, STAR-RIS coefficients, and transmit power. Simulations show the analytical SOP is accurate, while the indoor user has worse secrecy performance than the outdoor user because of stronger eavesdropping links.

  • A. Exact SOP Expression of IU and OU: The exact SOP derivation models the relevant fading coefficients as independent zero-mean Gaussian variables and establishes the independence of the resulting channel components.
  • A. Exact SOP Expression of IU and OU: The extended statistical-CSI solution derives an exact SOP expression for the indoor and outdoor users and evaluates its analytical accuracy.The derivation uses Gaussian channel components and an exponential distribution for the eavesdropper effective-channel power.
  • A. Exact SOP Expression of IU and OU: The analytical SOP in (35) accurately matches numerical SOP results for both users under random STAR-RIS phase shifts and amplitudes.The comparison uses M = 8, N = 24 and Rc,ρ − Rs,ρ = 1 bps/Hz, with other parameters fixed as in Table I.
  • A. Exact SOP Expression of IU and OU: The indoor user has worse secrecy performance than the outdoor user because it is closer to the eavesdropper and experiences stronger eavesdropping links.

B. Joint Beamforming and Power Optimization

The statistical-CSI optimization is decomposed into beamforming and transmit-power subproblems, solved by an extended alternating procedure. The method jointly updates beamforming variables and STAR-RIS coefficients, then applies a closed-form power policy, with convergence and complexity characterized.

  • B. Joint Beamforming and Power Optimization: The joint optimization separates beamforming from transmit-power optimization, alternating between stationary beamforming solutions and closed-form optimal power updates.The beamforming step optimizes receive beamforming and STAR-RIS variables, while the power step uses the policy derived in Proposition 3.
  • B. Joint Beamforming and Power Optimization: The beamforming subproblem uses rank-one penalties and convex reformulations to optimize the reflection/transmission and receiving-beamforming variables.
  • B. Joint Beamforming and Power Optimization: The optimal transmit-power policy is obtained when the QoS constraint is active while satisfying the successive-interference-cancellation decoding-order constraint.
  • B. Joint Beamforming and Power Optimization: The extended AHB algorithm is guaranteed to converge to a suboptimal solution over non-increasing iterations.
  • B. Joint Beamforming and Power Optimization: The overall algorithm has complexity expressed using the alternating, outer-layer, inner-layer, optimization-variable, and SOC-constraint dimensions.The cited complexity expression includes l_A, l_outer, l_inner, p = 2N^2 + M^2 + 8, and q = N^2 + 1.

V. SIMULATION RESULTS

Simulations evaluate convergence, coding and quantization effects, baseline comparisons, STAR-RIS size, and deployment location. The results show improved secrecy with STAR-RIS-assisted NOMA and provide design guidance for system configuration.

  • Algorithm convergence: Both proposed algorithms converge to stable solutions, and larger BS antenna count M increases minimum secrecy capacity while reducing the iteration count.Increasing M adds spatial degrees of freedom and improves per-iteration optimization despite increasing computational complexity.
  • Baseline comparisons: STAR-RIS-assisted NOMA achieves higher secrecy performance than conventional RIS schemes, NOMA outperforms OMA, and random phase/amplitude performs worst.The explanations attribute these trends to STAR-RIS's additional propagation-control degrees of freedom, NOMA's shared time-frequency resource block, and the inability of random control to exploit passive gain.
  • STAR-RIS size: Secrecy performance increases as the number of STAR-RIS reflection/transmission elements N grows, because larger N provides more passive beamforming design space.Under statistical eavesdropping CSI, STAR-RIS also provides more gains than conventional RIS.
  • CSI-dependent comparisons: With full eavesdropping CSI, STAR-RIS-OMA outperforms C-RIS-NOMA, whereas with statistical CSI it performs worse because uncertainty changes which spatial or multiplexing gains dominate.Full CSI enables accurate eavesdropping-channel adjustment, while statistical CSI makes spatial gains more influential.
  • Quantization effects: 3-bit quantization reaches 98.07% of continuous transmission-rate performance, while 4-bit quantized secrecy rate reaches 97.54%.Phase shifts dominate transmission-rate control, whereas secrecy requires more accurate joint phase-shift and amplitude control to balance legitimate and wiretap links.
  • STAR-RIS deployment: Adaptive-rate coding favors deploying STAR-RIS near users or the BS, whereas constant-rate coding favors placement far from both for channel suppressing.The two recommendations reflect channel strengthening under full CSI and channel suppression under statistical CSI.

VI. CONCLUSION

The paper proposes a STAR-RIS assisted uplink secrecy framework with separate beamforming optimizations for full and statistical eavesdropping CSI. Numerical results show secrecy superiority and provide guidance on quantization resolution and STAR-RIS placement.

  • For full eavesdropping CSI, the AHB algorithm jointly optimizes receive and passive beamforming with a closed-form optimal transmit-power policy.
  • For statistical eavesdropping CSI, the method derives an exact SOP expression and designs a modified AHB algorithm for secrecy beamforming.
  • The proposed scheme achieves the best secrecy performance over other baseline schemes.
  • Amplitude quantization has little impact on quantization performance, whereas secrecy transmission significantly increases the required quantization resolution.
  • STAR-RIS placement should favor users or the BS for adaptive-rate coding, but be far from both for constant-rate coding to respectively enhance or degrade cascaded channels.

APPENDIX A: PROOF OF LEMMA 2

The appendix proves structural properties of the optimal receiving beamforming solution using convexity, duality, and KKT conditions. It also establishes monotonic objective improvement and convergence of the alternating algorithm, while noting that the converged solution is generally suboptimal.

  • The proof uses strong duality and KKT conditions to characterize the optimal receiving beamforming matrix and its associated multipliers.
  • The dual formulation requires a positive multiplier to avoid an unbounded feasible solution space.
  • KKT conditions imply that the optimal receiving beamforming matrix lies in the null space structure determined by the optimal dual matrix.
  • Each alternating update does not decrease the minimum secrecy-rate objective, producing a bounded monotonic sequence over the compact feasible set.
  • The AHB algorithm therefore converges, but because the alternating variables constrain one another, its converged solutions are usually suboptimal.
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