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Active RIS vs. Passive RIS: Which Will Prevail in 6G?

Zijian Zhang, Linglong Dai, Xibi Chen, Changhao Liu, Fan Yang, Robert Schober, H. Vincent Poor

arXiv:2103.15154v8cs.ITeess.SPeess.SY

TL;DR

Passive RISs have limited capacity gains with strong direct links because multiplicative fading severely attenuates reflected paths. The paper proposes and verifies amplified active-RIS signal models, analyzes asymptotic performance, and designs joint beamforming and reflect precoding for MU-MISO systems. In a typical scenario, passive RISs provide a 22% sum-rate gain, whereas active RISs provide 130%.

  • Problem

    Passive RISs often achieve limited capacity gains when the direct link is strong because multiplicative fading makes reflected-link path loss much larger than direct-link path loss.

  • Method

    The paper proposes active RISs, verifies their amplification-and-noise signal model experimentally, analyzes asymptotic performance, and develops joint transmit beamforming and reflect precoding for active-RIS MU-MISO systems.

  • Results

    Passive RISs achieve a 22% sum-rate gain in a typical scenario, while active RISs achieve a 130% sum-rate gain.

  • Takeaways & Limitations

    Active RISs can overcome multiplicative fading and achieve noticeable sum-rate gains even when the direct link is strong.

Abstract

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As a revolutionary paradigm for controlling wireless channels, reconfigurable intelligent surfaces (RISs) have emerged as a candidate technology for future 6G networks. However, due to the "multiplicative fading" effect, the existing passive RISs only achieve limited capacity gains in many scenarios with strong direct links. In this paper, the concept of active RISs is proposed to overcome this fundamental limitation. Unlike passive RISs that reflect signals without amplification, active RISs can amplify the reflected signals via amplifiers integrated into their elements. To characterize the signal amplification and incorporate the noise introduced by the active components, we develop and verify the signal model of active RISs through the experimental measurements based on a fabricated active RIS element. Based on the verified signal model, we further analyze the asymptotic performance of active RISs to reveal the substantial capacity gain they provide for wireless communications. Finally, we formulate the sum-rate maximization problem for an active RIS aided multi-user multiple-input single-output (MU-MISO) system and a joint transmit beamforming and reflect precoding scheme is proposed to solve this problem. Simulation results show that, in a typical wireless system, passive RISs can realize only a limited sum-rate gain of 22%, while active RISs can achieve a significant sum-rate gain of 130%, thus overcoming the "multiplicative fading" effect.

I. INTRODUCTION

Passive RISs offer low-noise array gains but suffer multiplicative fading when the direct link is strong. The paper proposes active RISs, verifies their signal model, analyzes their performance, and develops multi-user beamforming and precoding designs.

  • Motivation: Passive RISs intelligently reflect signals to reconfigure wireless propagation, offering high array gain, low cost, low power, and negligible noise.Their potential applications include capacity improvement, coverage extension, and power savings in future 6G networks.
  • Motivation: Passive RIS capacity gains are limited when the direct link is not weak because reflected-link path loss multiplies across the transmitter-RIS and RIS-receiver links.This equivalent path loss is typically thousands of times larger than the direct-link path loss.
  • Contributions: The paper develops and experimentally verifies an active-RIS signal model that captures signal amplification and non-negligible thermal noise from active elements.Verification uses measurements from a designed and fabricated active RIS element.
  • Contributions: The paper analyzes asymptotic active-RIS performance and formulates an MU-MISO sum-rate maximization problem solved with joint transmit beamforming and reflect precoding.It also extends the design to self-interference using an interference model and alternating optimization methods.
  • Motivation: At 5/10/28 GHz, matching the reflected link to the direct link under the stated LoS geometry requires 4,034/8,067/22,587 passive RIS elements.Such large surfaces also incur high channel-estimation overhead and O(N^2) real-time beamforming complexity.
  • Active RIS concept: Active RISs amplify reflected signals through integrated reflection-type amplifiers, compensating for reflected-link path loss at the cost of additional power consumption.The architecture retains reconfigurable phase shifts while adding amplification capability.

C. Active RIS Aided MU-MISO System

This section models an active RIS aided MU-MISO downlink and analyzes its asymptotic SNR, showing how active-element amplification and associated noise shape performance.

  • System Model: An active RIS aided downlink MU-MISO system uses an M-antenna base station to serve K single-antenna users with an N-element active RIS.The system employs multi-user linear precoding at the base station.
  • System Model: The received signal model includes the direct and reflected channels, active-RIS amplification, amplified RIS noise, and user AWGN.The active RIS reflection matrix contains per-element amplification factors that may exceed one.
  • Asymptotic Analysis: The asymptotic analysis specializes to a SU-SISO system with one base-station antenna and one user, initially ignoring the direct link and using a common amplification factor.Power allocation among active elements is deferred to the MU-MISO design.
  • Asymptotic Analysis: The asymptotic active-RIS SNR depends on both the maximum base-station transmit power and the maximum active-RIS reflect power.These power limits determine which noise and channel terms constrain the asymptotic performance.
  • Asymptotic Analysis: For sufficiently large base-station power, the active-RIS asymptotic SNR is bounded by a term proportional to N and determined by the RIS-user channel gain and user-noise power.Under sufficiently large active-RIS reflect power, the bound instead becomes independent of the RIS-user channel and user-noise power.
  • Comparison Basis: The analysis compares active and passive RIS asymptotic SNRs to characterize the capacity gains of active RISs in wireless communications.The general MU-MISO system is addressed separately from the tractable SU-SISO asymptotic analysis.

B. Comparisons between Passive RISs and Active RISs

The comparison shows that active RISs can outperform passive RISs in practical element-count regimes despite introducing thermal noise, whereas passive RISs require extremely large arrays to catch up.

  • Asymptotic Scaling: Active-RIS asymptotic SNR scales proportionally to N, whereas passive-RIS asymptotic SNR scales proportionally to N^2 because active components introduce additional noise.The different scaling laws do not by themselves determine which architecture performs better at practical sizes.
  • Asymptotic Scaling: Active RISs can still achieve higher SNR gains because their denominator contains much smaller path-loss and noise products than the passive-RIS denominator.This can offset the active architecture’s loss in numerator scaling.
  • Practical Comparison: Passive RISs generally outperform active RISs only when their element count becomes unaffordably large.The paper formalizes this condition in a lemma for large N.
  • Practical Comparison: 2.5×10^6 elements are required for the passive RIS to outperform the active RIS under the stated comparison parameters.The comparison uses separate maximum base-station powers for the active and passive systems.
  • Practical Comparison: At N = 256, the passive RIS achieves γpassive ≈39.0 dB, while the active RIS achieves γactive ≈79.0 dB, about 10,000 times higher.The stated setup uses P max_BS-P = 2 W and P max_A = 1 W.
  • Practical Comparison: For N from 10 to 1000, the active-RIS user SNR is about 40 dB higher; passive performance becomes comparable at N = 2.5 × 10^6.The two element-count ranges are shown in Fig. 3.
  • Mechanism: Active RISs retain higher SNR because reflected desired signals combine coherently, while introduced noises do not and are attenuated over the RIS-user path.Thus, active components can provide higher SNR despite their additional thermal noise.

C. Impact of Distances on RIS Performances

This section studies how propagation distances and path losses affect the relative SNR performance of active and passive RISs, identifying broad conditions favoring active RISs.

  • Distance and Path Loss: The comparison focuses on how BS-RIS and RIS-user distances influence the SNR gains of active and passive RISs through their path losses.The analysis uses a far-field spherical-wave propagation model.
  • Distance and Path Loss: The model uses reference-distance loss L0, link distances dt and dr, and path-loss exponents α and β to characterize the two RIS links.The paper states typical values L0 = −30 dB and α, β ranging from 2 to 4.
  • Conditions Favoring Active RISs: Under the assumed power split σ2_A = P max/2, a lemma gives the condition under which an active RIS can outperform a passive RIS for large N.The total radiation power is denoted by P max.
  • Conditions Favoring Active RISs: With dt = 20 m, L0 = −30 dB, α = β = 2, P max = 2 W, σ2 = −100 dBm, and N = 1024, active RISs can outperform passive RISs across nearly the whole communication region.The stated conclusion follows from the distance condition derived from the path-loss model.
  • Multi-User Extension: The section also formulates sum-rate maximization for an active-RIS aided MU-MISO system and introduces joint transmit beamforming and reflect precoding.These formulations provide the multi-user setting associated with the distance-based SNR analysis.

A. Sum-Rate Maximization Problem Formulation

The sum-rate problem jointly optimizes base-station beamforming and active-RIS precoding under both power constraints, using alternating optimization with fractional programming.

  • A. Sum-Rate Maximization Problem Formulation: The MU-MISO formulation defines each user’s SINR from the equivalent direct-plus-reflected channel and the desired, interference, and noise terms.The formulation is built from the received-signal model and user-specific channel quantities.
  • A. Sum-Rate Maximization Problem Formulation: The active RIS reflect power includes amplified noise power, unlike the base-station transmit power, which includes only desired signal power.This additional noise-related consumption is included in the active-RIS power constraint.
  • A. Sum-Rate Maximization Problem Formulation: The optimization is difficult because the variables are non-convex and coupled, with additional active-RIS power allocation, interference, and amplified-noise constraints.These active-RIS features complicate joint beamforming design.
  • A. Sum-Rate Maximization Problem Formulation: The proposed algorithm initializes the base-station beamforming vector and RIS precoding matrix, then iteratively updates auxiliary variables, beamforming, precoding, and sum-rate until convergence.The algorithm returns optimized w, Ψ, and Rsum.
  • B. Proposed Joint Beamforming and Precoding Scheme: Fractional programming decouples the sum-of-logarithms and fractional terms so that multiple variables can be optimized separately.The reformulation introduces auxiliary variables ρ and ϖ.
  • B. Proposed Joint Beamforming and Precoding Scheme: Alternating optimization updates ρ, ϖ, w, and Ψ; when each update is optimal, the method obtains a locally optimal solution as Rsum converges.The paper summarizes these updates in Algorithm 1.
  • B. Proposed Joint Beamforming and Precoding Scheme: With fixed auxiliary variables, the beamforming and RIS-precoding subproblems are reformulated as QCQPs and solved using Lagrange multipliers.The multiplier searches use a two-dimensional grid for w and binary search for Ψ.
  • B. Proposed Joint Beamforming and Precoding Scheme: The RIS-precoding QCQP uses a Lagrange multiplier selected to satisfy the active-RIS power constraint’s complementary-slackness condition.The resulting precoding solution is obtained from the equivalent problem formulation.

V. SELF-INTERFERENCE SUPPRESSION FOR ACTIVE RISS

This section extends joint beamforming and precoding design to active RIS systems operating in full-duplex mode, where self-interference must be modeled and suppressed.

  • Full-duplex active RISs experience practical self-interference that must be incorporated into joint beamforming and precoding design.The section first models this interference and then formulates a suppression-oriented optimization problem.

A. Self-Interference Modeling

The section models feedback-type self-interference in active RISs and explains how the resulting equivalent precoding matrix modifies the channel model and optimization problem.

  • Nanosecond processing delay makes active-RIS self-interference feedback-type rather than colored Gaussian noise.This differs from full-duplex relays, whose longer processing delay produces interference from symbols in adjacent timeslots.
  • With self-interference, the reflected-signal model reaches a steady state when det(I_N − ΦH) is nonzero.The output is described as a standard self-feedback loop under the no-self-excitation condition.
  • The equivalent RIS precoding matrix becomes (I_N − ΦH)^−1Φ instead of the ideal-case matrix Ψ.When H is zero, this equivalent matrix reduces to the diagonal matrix Φ.
  • Replacing Ψ with (I_N − ΦH)^−1Φ incorporates self-interference into the beamforming optimization while leaving w, ρ, and ϖ optimizations unchanged.The resulting focus is optimization of Φ.
  • The inverse involving Φ makes the equivalent channel difficult to optimize directly, so a first-order Taylor approximation is introduced.The approximation (I_N − ΦH)^−1 ≈ I_N + ΦH requires sufficiently weak self-interference.
  • The suppression algorithm takes the ideally optimized precoding vector, self-interference matrix, and user channels as inputs, then iteratively updates φ, φ′, and ζ.The penalty coefficient is initialized at 10^-3 and doubled after each iteration.
  • The approximated model replaces each user’s RIS precoding vector with an equivalent vector involving φ and the self-interference coupling term.The text identifies this equivalent vector as φ + diag(φ)H_H_kφ for user k.

C. Proposed Self-Interference Suppression Scheme

The proposed scheme addresses a difficult non-ideal self-interference optimization by alternating updates with a gradually increasing penalty, then scales the result to satisfy the active-RIS power constraint.

  • The proposed suppression scheme solves the self-interference design problem for active RIS aided systems.It is introduced specifically to preserve communication performance under self-interference.
  • The non-ideal optimization is difficult because its objective is generally non-convex, quartic, and coupled through a non-standard quadratic term.These properties arise from the asymmetric, indefinite self-interference matrices.
  • Alternating optimization inspired by ADMM and SUMT temporarily convexifies subproblems and imposes agreement between auxiliary variables.The penalty coefficient increases iteratively, and the penalized problem becomes equivalent to the original as ζ approaches infinity.
  • For fixed ζ, alternating minimization updates φ and φ′ through convex quadratic subproblems.As the penalty grows, the converged variables satisfy φ′ = φ.
  • A positive scaling factor τ is applied after optimization to enforce the active-RIS power constraint.Binary search selects τ so that the active-RIS power reaches the required bound.

VI. CONVERGENCE AND COMPLEXITY

The paper establishes convergence properties for both proposed algorithms and characterizes their computational complexity through the costs of their variable updates and iteration counts.

  • Convergence Analysis: Algorithm 1 converges to a local optimum because its objective is monotonically non-decreasing and upper-bounded by power constraints.Each update optimally solves its corresponding subproblem.
  • Convergence Analysis: Algorithm 2 converges to a local optimal point with φ = φ′ and q(φ, φ′) = f(φ).Its penalized objective decreases monotonically for each penalty coefficient, while increasing ζ enforces equality of the auxiliary variables.
  • Computational Complexity Analysis: Algorithm 2’s complexity is mainly determined by the closed-form updates of φ and φ′.The total complexity includes the iteration count I_s required for convergence.

VII. VALIDATION RESULTS

The validation results experimentally verify the active RIS signal model by measuring reflection gain and noise power with a fabricated active RIS element. The measurements confirm substantial amplification and the predicted near-linear relationship between amplified noise power and reflection gain.

  • Experimental validation: The fabricated active RIS element and measurement platforms validate the proposed signal model’s amplification and noise components.The experiments focus on reflection gain and noise introduced by the active element.
  • Reflection gain measurement: The reflection gain G is measured as a function of signal frequency f for different pump-source input powers Pp.The pump source reconfigures the reflection gain, which is measured using a vector network analyzer.
  • Reflection gain measurement: More than 25 dB reflection gain is measured at Pp = 18.24 dBm, confirming substantial amplification by the active RIS element.At Pp = 0, the measured gain falls to −6 dB, mainly because of losses in the circulator and transmission lines.
  • Noise power measurement: The measured noise power Gσ2_s increases nearly linearly with G, verifying the active RIS noise model.The noise measurements use a spectrum analyzer and examine different operating frequencies.
  • Noise power measurement: At f = 2.3601 GHz, the spectral density of σ2_v is about −160 dBm/Hz, approximately 15 dB higher than the input-noise reference.The difference is attributed to amplification by the noise factor and additional noise from active components in the measurement equipment.

B. Simulation Results for Joint Beamforming and Precoding Design

Simulations evaluate the proposed joint beamforming and precoding design for active and passive RIS-aided MU-MISO systems under weak and strong direct-link conditions. They compare optimized active and passive RIS schemes with random phase shifts and no RIS across distance and total-power settings.

  • Simulation setup: Two scenarios model weak and strong direct BS-user links, while BS-RIS and RIS-user channels use the strong-link path-loss model.Ricean fading is used for all channels with κ = 1.
  • Simulation setup: The total power consumption is constrained to P max = 10 dBm for fair comparison between active and passive RIS systems.The active RIS maximum reflect power excludes hardware static power.

2) Coverage performance of active RISs:

Across coverage, power, element-count, and self-interference evaluations, active RISs provide larger gains than passive RISs, including when direct links are strong. Their advantage depends on controlling self-interference, while requiring substantially less power for comparable performance.

  • Coverage performance: Active RISs achieve much larger sum-rate gains than passive RISs when the direct link is strong.At L = 300 m in scenario 2, passive RIS provides a 22% gain, whereas active RIS achieves 130%.
  • Coverage performance: Active RISs require less total power than passive RISs to achieve the same sum-rate.At P max = 30 dBm for the passive-RIS system, the active-RIS system requires 7 dBm in scenario 1 and 12 dBm in scenario 2.
  • Simulation setup: The simulations evaluate sum-rate against RIS-element count and active-RIS self-interference factor under the coverage-performance setup.Figures 10 and 11 respectively vary N and δ, using the setup described for the power-consumption and element-count evaluations.
  • Coverage performance: Increasing the number of RIS elements improves both systems, but produces larger sum-rate increases for active RISs.From N = 100 to 900, active RIS gains are 15.32 bps/Hz in scenario 1 and 14.78 bps/Hz in scenario 2, versus 7.21 and 3.28 bps/Hz for passive RISs.
  • Impact of self-interference: Self-interference has little impact below δ < −50 dB but increasingly degrades active RIS performance as it strengthens.At δ = −35 dB, suppression compensates for losses of 14.72 bps/Hz in scenario 1 and 18.52 bps/Hz in scenario 2.

APPENDIX A PROOF OF LEMMA 2

The appendix rewrites the received-signal model to expose noise from the active RIS and the user, then formulates constrained SNR maximization. It uses phase alignment and large-element asymptotics to derive the active-RIS SNR and compare it with passive RIS performance.

  • Signal model: The rewritten downlink model separates the received signal, active-RIS noise, and user noise.The active-RIS contribution is represented through the term labeled as noise introduced by the active RIS, while z is user noise.
  • Optimization: The user-SNR maximization is constrained by maximum transmit power at the BS and maximum reflect power at the active RIS.The appendix identifies these two power limits before deriving the optimal solution with the Lagrange multiplier method.
  • Optimization: The optimal RIS phase choice aligns the reflected paths through n = ∠f_n − ∠g_n for every element.This phase configuration is substituted into the constrained SNR problem to obtain the maximum achievable active-RIS SNR.
  • Asymptotic analysis: Taking N →∞ and applying the law of large numbers yields the asymptotic SNR expression for active RISs.The appendix substitutes the resulting asymptotic equations into the finite-element SNR expression.
  • Passive-versus-active comparison: The appendix compares the achievable SNRs of passive and active RISs and derives a condition from γ_passive ≥ γ_active.It distinguishes the maximum BS transmit powers for active-RIS and passive-RIS systems in this comparison.
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