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Active Reconfigurable Intelligent Surface Aided Wireless Communications

Ruizhe Long, Ying-Chang Liang, Yiyang Pei, Erik G. Larsson

arXiv:2103.00709v1cs.IT

TL;DR

The paper addresses double-fading attenuation and the large surfaces and circuit power required by passive RIS. It introduces active-load RIS for SIMO systems, jointly optimizes receive and reflect beamforming, and finds better performance than passive RIS under the same RIS power budget.

  • Problem

    Passive RIS requires many reflecting elements to offset double-fading attenuation, creating large surface size and considerable circuit power consumption.

  • Method

    The paper introduces active RIS with active loads and solves joint receive and reflect beamforming through alternating optimization using MMSE and SCA.

  • Results

    The proposed active RIS-aided system outperforms conventional passive RIS under the same RIS power budget, with optimized element counts reducing surface size.

  • Takeaways & Limitations

    Active RIS can strengthen the RIS-aided link through both incident-signal amplification and careful selection of the number of active reflecting elements.

Abstract

from arXiv · show

Reconfigurable Intelligent Surface (RIS) is a promising solution to reconfigure the wireless environment in a controllable way. To compensate for the double-fading attenuation in the RIS-aided link, a large number of passive reflecting elements (REs) are conventionally deployed at the RIS, resulting in large surface size and considerable circuit power consumption. In this paper, we propose a new type of RIS, called active RIS, where each RE is assisted by active loads (negative resistance), that reflect and amplify the incident signal instead of only reflecting it with the adjustable phase shift as in the case of a passive RIS. Therefore, for a given power budget at the RIS, a strengthened RIS-aided link can be achieved by increasing the number of active REs as well as amplifying the incident signal. We consider the use of an active RIS to a single input multiple output (SIMO) system. {However, it would unintentionally amplify the RIS-correlated noise, and thus the proposed system has to balance the conflict between the received signal power maximization and the RIS-correlated noise minimization at the receiver. To achieve this goal, it has to optimize the reflecting coefficient matrix at the RIS and the receive beamforming at the receiver.} An alternating optimization algorithm is proposed to solve the problem. Specifically, the receive beamforming is obtained with a closed-form solution based on linear minimum-mean-square-error (MMSE) criterion, while the reflecting coefficient matrix is obtained by solving a series of sequential convex approximation (SCA) problems. Simulation results show that the proposed active RIS-aided system could achieve better performance over the conventional passive RIS-aided system with the same power budget.

I. INTRODUCTION

The paper introduces active RIS for SIMO communications to address passive RIS double-fading attenuation under a constrained RIS power budget. It jointly optimizes receive and reflect beamforming, studies the number of active elements, and reports improved performance over passive RIS.

  • Motivation: Passive RIS suffers double-fading attenuation and requires many reflecting elements, increasing surface size and circuit power consumption.The cascaded transmitter–RIS and RIS–receiver channels constrain the reflected link.
  • Active RIS concept: Active RIS uses active loads to amplify incident signals while retaining RIS-style reflection without complex, power-hungry RF chains.Negative-resistance components can convert DC bias power into RF amplification.
  • Design tradeoff: Under a fixed RIS power budget, the number of active elements trades off against amplification power per element, motivating optimization of the element count.Adding elements increases circuit consumption and can reduce available amplification power.
  • Optimization: The proposed SIMO design maximizes SNR through alternating optimization of receive beamforming and the RIS reflecting coefficient matrix.MMSE provides closed-form receive beamforming, while SCA handles reflect beamforming.
  • Element-count analysis: The paper derives an optimal element count for LOS channels and extends the analysis to general channels through numerical verification.The analysis provides an upper bound on received SNR as a function of the number of reflecting elements.
  • Results: Simulation results show that properly designing the number of elements lets active RIS outperform passive RIS under the same RIS power budget.The paper positions this result as supporting more spectrum- and energy-efficient wireless communication.

II. SYSTEM MODEL

The system model uses active-load RIS elements as low-power reflection amplifiers in a SIMO link. Active reflection introduces practical circuit limitations, including input-power sensitivity and nonlinear amplification regions.

  • Active-load operation: Each active RIS element uses active-load or negative-resistance impedance to reflect incident signals with power amplification.This permits reflection coefficients with amplitude greater than unity.
  • Reflection amplifier: Negative-resistance components such as tunnel diodes convert DC bias power into RF power for electromagnetic-level signal amplification.The tunnel-diode circuit uses suitable biasing and impedance matching to stabilize reflection gain.
  • Illustration: The paper illustrates the active reflection-amplifier concept with a tunneling reflection amplifier block diagram.The cited figure is identified as a simple block diagram.
  • Practical limitations: Tunnel-diode reflection amplifiers are sensitive to incident power and may enter a nonlinear gain region, so deployment should target linear operation when possible.In the nonlinear region, gain is nonlinear although phase can remain nearly preserved.
  • Reconfiguration: Multistate amplitude and phase control can be implemented by presetting tuned and biased tunnel-diode loads and using QAM-style controller designs.Inductors, capacitors, and biased tunnel diodes tune the required load impedances.

B. Channel Model

The channel model contains a direct Tx–Rx link and a cascaded Tx–RIS–Rx link, with the RIS dynamically controlling element-wise amplitude and phase. The model assumes block fading and available instantaneous CSI.

  • Channel structure: The RIS-aided channel consists of a forward Tx–RIS channel and a backward RIS–Rx channel, alongside the direct Tx–Rx channel.The system uses h1, h2, and G to represent these links.
  • CSI assumption: All channels are modeled with independent block fading, and instantaneous CSI is assumed available to the receiver and RIS in each fading block.The RIS uses this CSI to configure its reflecting coefficients.
  • Reflect beamforming: The RIS uses a diagonal reflecting coefficient matrix to reconfigure the incident signal through element-wise reflect beamforming.Each coefficient controls an element’s reflection amplitude and phase.
  • Active reflection constraints: Active loads allow reflection amplitudes greater than one within the assumed continuous amplitude and phase ranges.The amplitude range is [0, am,max] with am,max ≥ 1, while phase spans [0, 2π).

C. Signal Model

The signal model includes thermal noise at both the receiver and RIS, with active RIS amplification making RIS noise non-negligible and correlated at the receiver. Receive beamforming produces a scalar decoding signal and an SNR that accounts for these effects.

  • The received signal reaches the receiver through both the direct link and RIS-aided link, with transmitter signal s(n) modeled as unit-variance complex Gaussian.Thermal noise is separately represented at the receiver and RIS.
  • Active RIS amplification makes RIS-introduced noise non-negligible, enabling more accurate quantification of correlated-noise effects.This noise is usually ignored in passive-RIS analyses because it is relatively small after reflection and propagation.
  • Linear receive beamforming transforms the received vector into a scalar used to decode the transmitted signal.The receive beamforming vector is denoted by w.
  • The active RIS can increase received signal power through its reflecting coefficient matrix, but the same matrix also increases noise power.Consequently, increasing amplification alone cannot maximize received SNR.

D. Power Consumption at the RIS

The RIS power model separates circuit and amplification-related consumption for passive and active surfaces. Under a fixed active-RIS budget, supporting more active elements leaves less power for signal amplification, while active loads provide lightweight EM-level amplification.

  • Passive RIS power consumption is mainly associated with switch and control circuits, with Pc denoting per-element circuit power.
  • Active-RIS element power consumption includes output-power-independent and output-power-dependent components.The output-power-independent component includes switch, control-circuit, and DC-biasing power.
  • The output-power-dependent consumption is modeled linearly, with amplifier efficiency represented through ξ ≜ υ^-1.The model relates each element’s output power to its incident signal power.
  • The reflection-amplifier model assumes operation in its linear region, where output power increases linearly with input power.The paper states this assumption is valid for tunnel-diode-based reflection amplifiers when input power is within their operating range.
  • Active RIS performs EM-level signal amplification without complex, power-hungry RF-chain components, although active loads require additional power.Its total power consumption accounts for all identical active elements and their output-related consumption.
  • For a fixed active-RIS power budget, remaining power after supporting M active elements is allocated to incident-signal amplification.The active-load amplitude interval can extend beyond passive-RIS limits up to a predetermined maximum amplitude.

A. Passive RIS for SIMO Systems

The passive-RIS SIMO benchmark uses phase-only reflecting elements and neglects RIS noise relative to receiver noise. Its receive beamforming is MRC, and under a limited power budget the conventional design maximizes the number of elements.

  • Each passive reflecting element adjusts the incident signal phase without power amplification, so RIS-introduced noise is neglected.
  • For a fixed reflecting matrix, maximal-ratio combining is the optimal receive beamforming scheme for SNR maximization.
  • The passive-RIS design maximizes channel power gain under unit-amplitude and phase-range constraints for each reflecting element.
  • For a limited passive-RIS power budget, received SNR increases with M, so the conventional optimum maximizes the number of passive elements as M* = floor(PRIS/Pc).

B. Active RIS for SIMO Systems

The active-RIS SIMO design jointly optimizes the reflecting matrix and receive beamforming for maximum SNR under active-RIS constraints. MMSE beamforming handles amplified RIS noise, while the remaining optimization is nonconvex because the matrix affects both signal and effective noise.

  • The active-RIS problem optimizes the reflecting coefficient matrix and receive beamforming to maximize received SNR under RIS power constraints.Unlike the passive case, the formulation includes active-element amplitude and amplification-power constraints.
  • Increasing the number of active elements can strengthen the RIS-aided signal, but it leaves less power available for incident-signal amplification.The number of elements is therefore also considered an optimization variable later in the design.
  • For a fixed reflecting matrix, linear MMSE detection provides the optimal receive beamforming because it can cope with amplified RIS-noise interference.
  • With the MMSE beamformer, the equivalent channel is h = h1 + GΦh2, and the reflecting-matrix problem remains nonconvex.Both the equivalent channel and effective noise depend on Φ in the SNR objective.

IV. ALTERNATING OPTIMIZATION SOLUTION

The paper solves active-RIS joint beamforming by alternating between MMSE receive-beamforming updates and SCA-based reflect-beamforming updates. The resulting algorithm is convergent and polynomial-time solvable under the stated formulation.

  • Alternating optimization: The alternating optimization iteratively updates the RIS reflecting coefficient matrix for fixed receive beamforming and the receive beamforming for fixed RIS coefficients.This decomposes the original joint optimization into two stages.
  • Receive beamforming: For a fixed RIS reflecting matrix, the optimal receive beamforming is obtained in closed form using linear MMSE detection.The MMSE solution solves the receive-beamforming subproblem.
  • Reflect beamforming: The reflect-beamforming subproblem is a quadratic fractional program because active-RIS noise adds a denominator term, preventing direct use of conventional RIS methods and classical Dinkelbach optimization.The active RIS introduces additional noise interference that must be included in the SNR objective.
  • Reflect beamforming: The unconstrained optimal phase aligns each reflected signal for constructive combining at the receiver, while amplitudes balance forward-channel enhancement against active-RIS noise.After fixing the optimal phases, the remaining amplitude optimization uses real-valued variables.
  • SCA solution: SCA iteratively replaces the nonconvex square-root constraint with a convex upper bound and solves a sequence of convex optimization problems.The approximation uses a first-order Taylor polynomial around the current iterate.
  • Convergence and complexity: The SCA and overall alternating algorithms generate nondecreasing objective values that remain bounded under the power constraint, guaranteeing convergence.The convex subproblem can be formulated as a QCQP, and the overall algorithm has polynomial-time complexity.

V. HOW MANY RES DOES AN ACTIVE RIS NEED?

The number of active RIS elements must be selected jointly with per-element amplification power because increasing element count reduces available amplification power. Under the LOS analysis, the optimum is determined by the larger of two thresholds and performs well under Rayleigh fading.

  • Design tradeoff: Active-RIS design has a tradeoff between the number of reflecting elements and the amplification power allocated to each element.More elements can improve signal combining, but the power budget leaves less power for amplification.
  • LOS analysis: The analysis assumes a single-antenna receiver, ignores the direct link for optimizing element count, and models both RIS subchannels as LOS channels with fixed phase shifts.The direct link is independent of the number of elements in this analysis.
  • LOS analysis: For the LOS model, equal amplification gain across active elements satisfies the relevant equality condition because all elements have the same large-scale pathloss.The optimal phase is selected as θ_m = −(ω_h2,m + ω_g,m).
  • Optimal element count: When the amplification-power constraint is active, SNR increases with M up to M1 and decreases beyond M1; under the alternative active constraint, it increases up to M2.These two regimes determine the candidate optimum.
  • Optimal element count: The optimal active-RE count is M⋆ = max{M1, M2}, with the integer choice taken from ⌊M⋆⌋ and ⌈M⋆⌉.This is the stated LOS solution for maximizing active-RIS SNR.
  • Scope and validation: The LOS result represents an upper bound on achievable SNR, while the optimized LOS-based element count retains good performance under more general fading channels.Numerical results verify this extension for Rayleigh fading.

VI. SIMULATION RESULTS

The simulations evaluate active-RIS SNR, algorithm convergence, achievable rate, and RIS placement under specified channel and power-budget settings. Results show that performance depends on jointly balancing amplification, correlated noise, RE count, transmit power, and RIS location.

  • SNR and convergence: The SISO received SNR rises with RE amplitude until an optimum, then decreases as RIS-correlated noise grows faster than amplified signal power.When the direct link is blocked, increasing amplitude continues to improve SNR, highlighting the need for amplitude optimization.
  • SNR and convergence: The proposed alternating optimization algorithm converges quickly, reaching a stable achievable rate within around 8 iterations for different (M, N) RIS configurations.The convergence experiment uses pt = 23 dBm, Pout = 10 dBm, and maximum amplitude gain amax = 40 dB.
  • Transmit power and amplification: At low transmit power, amplification-budget curves are nearly identical, whereas higher transmit power activates the constraint and limits achievable-rate gains.A larger amplification power budget provides better performance at higher transmit power, requiring amplification gain to be reconfigured accordingly.
  • RE count and channels: Under the same RIS power budget, achievable rate first increases and then decreases with RE count; the active RIS reaches optimal performance with 13 or 20 REs, versus 100 passive REs.The peak reflects the tradeoff between adding REs and retaining power for amplification, and the LOS-derived optimal M remains effective under Rayleigh fading.
  • RIS location: The active RIS maintains better achievable rate than the passive RIS across RIS locations and benefits from placement closer to the receiver.Its amplification can compensate for weaker incident signals near the receiver, reducing the impact of double-fading attenuation.

VII. CONCLUSION

The proposed active RIS-aided SIMO system uses power-amplifying reflecting elements to improve efficiency with fewer REs and jointly optimizes receive and reflect beamforming under an RIS power budget.

  • VII. CONCLUSION: Active RIS enables spectrum- and energy-efficient SIMO communication with fewer reflecting elements by amplifying incident signals.Its active loads enhance the reflected signal while preserving low-power operation.
  • VII. CONCLUSION: The design formulates joint receive and reflect beamforming to maximize received SNR under the RIS power budget constraint.
  • VII. CONCLUSION: An alternating optimization algorithm updates receive beamforming using MMSE and reflect beamforming using sequential convex approximation.The two beamforming components are optimized iteratively to address the nonconvex problem.
  • VII. CONCLUSION: The study also examines how the number of reflecting elements affects the active RIS-aided system.
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