Source-linked AI summary
Active Reconfigurable Intelligent Surface Aided Secure Transmission
Limeng Dong, Hui-Ming Wang, Jiale Bai
TL;DR
Passive RIS secure transmission is constrained by double fading, while active RIS must also control leakage because amplification benefits the eavesdropper's reflected link. The paper proposes an active RIS secure-transmission model and jointly optimizes transmitter beamforming and RIS reflection coefficients with alternating optimization. Simulations report higher secrecy rates than passive RIS and no RIS, including gains that increase with amplification and reflecting-element count.
Problem
Double fading limits passive RIS secrecy-rate gains, and active RIS amplification can also increase information leakage to the eavesdropper.
Method
The paper designs an active RIS secure-transmission system and applies alternating optimization to jointly optimize the transmitter beamformer and RIS reflecting matrix.
Results
About 13% and 48% performance gains are reported over the optimal no-RIS solution when η2 is 20dB and 40dB, respectively.
Takeaways & Limitations
Active RIS effectively relieves double fading and achieves higher secrecy-rate performance than passive RIS and no-RIS designs.
Abstract
from arXiv · showhide
Reconfigurable Intelligent Surface (RIS) draws great attentions in academic and industry due to its passive and low power consumption nature, and has currently been used in physical layer security to enhance the secure transmission. However, due to the existence of double fading effect on the reflecting channel link between transmitter and user, RIS helps achieve limited secrecy performance gain compared with the case without RIS. In this correspondence, we propose a novel active RIS design to enhance the secure wireless transmission, where the reflecting elements in RIS not only adjust the phase shift but also amplify the amplitude of signals. To solve the non convex secrecy rate optimization based on this design, an efficient alternating optimization algorithm is proposed to jointly optimize the beamformer at transmitter and reflecting coefficient matrix at RIS. Simulation results show that with the aid of active RIS design, the impact of double fading effect can be effectively relieved, resulting in a significantly higher secrecy performance gain compared with existing solutions with passive RIS and without RIS design.
I. INTRODUCTION
Prior RIS-based secure transmission improves secrecy rate but remains limited by double fading in the reflected link. This paper introduces active RIS for secure multi-antenna transmission and develops an alternating optimization method for joint design.
- Passive RIS uses phase shifts and joint beamforming optimization to enhance secure transmission by favorably combining direct and reflected signals.
- Double fading causes reflected signals to lose power through twice the large-scale fading, limiting RIS gains relative to transmission without RIS.
- Active RIS equips each reflecting element with a power amplifier, enabling simultaneous phase adjustment and signal amplification.
- Existing active RIS studies address non-secure settings, while amplification can also reduce fading toward the eavesdropper and increase information leakage.
- The paper proposes an active RIS-assisted secure design and an efficient alternating optimization algorithm that jointly optimizes the transmitter beamformer and RIS reflecting matrix.
II. CHANNEL MODEL AND PROBLEM FORMULATION
The system models an active RIS-assisted multi-antenna wiretap channel with Alice, Bob, and Eve, including amplifier-generated RIS noise and power constraints. Secrecy-rate optimization depends on jointly designed transmission and reflection coefficients.
- The wiretap system contains Alice with m antennas, an n-element active RIS, and single-antenna Bob and Eve.
- Bob's and Eve's received signals combine direct transmission, RIS-reflected transmission, amplified RIS noise, and receiver noise.
- The transmitted signal is x = ws, where w is the beamformer and s is a zero-mean, unit-variance confidential message.
- The diagonal RIS matrix Q encodes each element's amplification factor through |Q[i, i]| and phase shift through arg(Q[i, i]).
- The model assumes full channel state information and formulates a secrecy-rate optimization problem for the channel realization.
- Active RIS imposes bounded amplification rather than passive unit modulus, while the formulation includes Alice's transmit-power and RIS amplification-power budgets.
III. AO ALGORITHM FOR SR MAXIMIZATION
The proposed solution uses alternating optimization to separate the non-convex secrecy-rate problem into transmitter-beamformer and RIS-reflection subproblems.
- The alternating optimization algorithm iteratively optimizes the beamformer w with fixed Q and the reflecting matrix Q with fixed w.
- For fixed Q, the method combines semidefinite relaxation and Charnes-Cooper transformation; for fixed w, it combines semidefinite relaxation and minorization-maximization.
- A penalty-based procedure recovers a rank-1 solution after relaxation, and convergence yields a Karush-Kuhn-Tucker point for the original problem.
A. Algorithm for optimizing w given Q
With RIS coefficients fixed, beamformer optimization is relaxed into a semidefinite problem and solved through transformation, penalization, and rank-1 recovery. The resulting procedure has monotonic convergence and recovers an optimal beamformer.
- Algorithm for optimizing w given Q: For fixed Q, the beamformer subproblem is transformed using semidefinite relaxation, with S = wwH and the rank(S) = 1 constraint initially omitted.
- Algorithm for optimizing w given Q: Charnes-Cooper transformation converts the relaxed quasiconcave problem with convex constraints into a form that can be optimized using a CVX solver.
- Algorithm for optimizing w given Q: The penalty formulation enforces rank one through tr(˜S) − λmax(˜S) ≤ 0 and uses a subgradient approximation of λmax(˜S).
- Algorithm for optimizing w given Q: Algorithm 1 updates the penalty parameter when progress stalls and terminates when the trace–maximum-eigenvalue gap reaches the target accuracy.
- Algorithm for optimizing w given Q: The objective sequence is nonincreasing during the penalty iterations, guaranteeing monotonic convergence under the stated optimization procedure.
- Algorithm for optimizing w given Q: After convergence, the method obtains an optimal rank-1 solution and recovers the beamformer as w = umax(S).
B. Algorithm for optimizing Q given w
With w fixed, the algorithm optimizes the RIS reflecting matrix through SDR, MM-based approximation, and penalty-based rank-1 recovery. The resulting V yields a first-order KKT solution for the Q subproblem.
- The Q subproblem is reformulated using v = q* and an SDR variable V representing the RIS reflecting coefficients.The entries of q are the diagonal elements of Q.
- Because P8 remains non-convex, MM iteratively optimizes a relaxed problem using a surrogate objective function.The surrogate is constructed from a first-order Taylor-based bound.
- After each relaxed optimization, a penalty-based procedure recovers a rank-1 solution when V is not rank-1.The recovered solution is used as the next initial point for the MM iterations.
- Once V is optimized, the original RIS matrix is reconstructed as Q = diag((umax(V) λmax(V))[1 : n]).
- The SDR+MM procedure alternates optimization and rank-1 recovery until the objective change satisfies |C(k+1)(V) − C(k)(V)| ≤ ǫ3.The final V is reported as a first-order optimal KKT point of P8.
C. Convergence and complexity of the algorithm
The bounded AO algorithm is guaranteed to converge monotonically, and convergence yields a KKT solution for the original joint optimization problem. Its dominant subproblem costs scale cubically with the RIS dimension.
- The AO algorithm has guaranteed monotonic convergence because both w and Q are bounded by the constraints.At convergence, it obtains a KKT point for the original problem P1.
- The computational complexity is about O(n3) for optimizing w given Q and O((n + 1)3) for optimizing Q given w.
IV. SIMULATION RESULTS
Simulations compare active RIS with passive RIS and no RIS under channel and power settings specified for the evaluation. Active RIS achieves substantially higher secrecy-rate performance and converges monotonically under the tested algorithm settings.
- SR versus PT: With PT varied, passive RIS improves SR by about 3% over no RIS, whereas active RIS gains about 13% at η2 =20dB and about 48% at η2 =40dB.The comparison uses m = 4, n = 10, and PI =40dBm.
- Power and efficiency: At PT =40dBm and η2=20dB, RIS amplification uses only about 4dBm while producing a 13% performance gain compared with passive RIS.The RIS amplification-power constraint is reported inactive, while the individual amplification-factor constraint is active.
- SR versus reflecting elements: As n increases from 10 to 60, passive RIS SR rises by about 15%, whereas active RIS rises by less than 36% at η2 =20dB.At n = 60, passive RIS reaches about 8.6 SR, while active RIS reaches 9.0 already at n = 10 with η2 =20dB.
- Convergence: The AO and MM algorithms converge monotonically; MM requires 2 to 3 iterations and AO requires 4 to 8 iterations to reach the target accuracy of 10^-3.Larger m and n enable larger SR after convergence under the tested settings.
V. CONCLUSION
The paper studies active RIS-assisted secure transmission, using simultaneous phase and amplitude adjustment to address the non-convex secrecy-rate optimization problem. Simulations show that active RIS relieves double fading and outperforms passive RIS and no-RIS approaches.
- Active RIS simultaneously adjusts signal phase and amplitude to enhance secure wireless transmission.
- An alternating optimization algorithm jointly optimizes the transmitter beamformer and RIS reflecting coefficient matrix.
- Active RIS effectively relieves the double-fading effect in the reflection link.
- The proposed algorithm greatly boosts secrecy-rate performance compared with passive-RIS and no-RIS algorithms.