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Hybrid Relay-Reflecting Intelligent Surface-Assisted Wireless Communication

Nhan Thanh Nguyen, Quang-Doanh Vu, Kyungchun Lee, Markku Juntti

arXiv:2103.03900v1eess.SP

TL;DR

RIS can be limited by passive beamforming and hardware constraints, motivating a hybrid architecture that combines reflecting elements with a few active relaying elements. The paper develops fixed and dynamic HR-RIS designs using alternating optimization and power allocation, finding improved spectral and energy efficiency over conventional RIS, with dynamic HR-RIS especially effective.

  • Problem

    Conventional RIS has limited beamforming degrees of freedom and can require large surfaces or suffer performance degradation from hardware impairments.

  • Method

    The paper combines passive reflecting elements with a few active amplify-and-forward elements and optimizes fixed and dynamic architectures using alternating optimization and power allocation.

  • Results

    HR-RIS significantly improves spectral efficiency and energy efficiency over conventional RIS, with gains supported by analytical results and simulations.

  • Takeaways & Limitations

    A small number of active elements is favored, while dynamic selection can improve performance across the supported communication conditions.

  • Takeaways & Limitations

    The study assumes ideal amplify-and-forward relaying and does not directly optimize the energy-efficiency metric.

Abstract

from arXiv · show

Reconfigurable intelligent surface (RIS) has emerged as a cost- and energy-efficient solution to enhance the wireless communication capacity. However, recent studies show that a very large surface is required for a RIS-assisted communication system; otherwise, they may be outperformed by the conventional relay. Furthermore, the performance gain of a RIS can be considerably degraded by hardware impairments such as limited-resolution phase shifters. To overcome those challenges, we propose a novel concept of hybrid relay-reflecting intelligent surface (HR-RIS), in which a single or few elements are deployed with power amplifiers (PAs) to serve as active relays, while the remaining elements only reflect the incident signals. Two architectures are proposed, including the fixed and dynamic HR-RIS. Their coefficient matrices are obtained based on alternating optimization (AO) and power allocation strategies, which enable understanding the fundamental performances of RIS and relaying-based systems with a trade-off between the two. The simulation results show that a significant improvement in both the spectral efficiency (SE) and energy efficiency (EE) with respect to the conventional RIS-aided system can be attained by the proposed schemes, especially, by the dynamic HR-RIS. In particular, the favorable design and deployment of the HR-RIS are analytically derived and numerically justified.

I. INTRODUCTION … A. Proposed HR-RIS Beamforming Architecture

The paper introduces HR-RIS, combining passive reflecting elements with a few active amplify-and-forward relays to bridge RIS and relay systems. It develops fixed and dynamic architectures whose optimized coefficients target improved spectral and energy efficiency while exposing deployment and power-consumption trade-offs.

  • I. INTRODUCTION: RIS supports mmWave and sub-6 GHz communication by steering narrow beams and optimizing independently adjustable phase shifts to make the transmitter–receiver channel more favorable.This motivates RIS as a solution for compensating high mmWave path loss and improving propagation conditions.
  • A. Related Works: Prior RIS studies analyze capacity, channel-rank enhancement, beamforming gains, phase-shifter design, and joint transmit-power and reflection-coefficient optimization across MIMO, MISO, SISO, OFDM, sub-6 GHz, and mmWave settings.These studies establish the design and performance context for the proposed hybrid architecture.
  • B. Motivations and Contributions: HR-RIS activates a single or few surface elements with RF chains and power amplifiers, enabling hybrid active-passive beamforming that modifies both signal phases and amplitudes.The remaining elements perform passive reflection, combining relaying benefits with reduced active hardware.
  • B. Motivations and Contributions: The proposed HR-RIS bridges passive RIS and active amplify-and-forward relay operation, providing insight into their fundamental spectral-efficiency and energy-efficiency trade-offs.Active processing chains can also support channel estimation, making the perfect-CSI assumption less restrictive than for passive RIS.
  • B. Motivations and Contributions: The coefficient matrices for fixed and dynamic HR-RIS are optimized through spectral-efficiency maximization using alternating optimization and power allocation, while favorable deployment and performance gains are derived analytically.With few active elements, HR-RIS increases both spectral efficiency and energy efficiency despite higher total power consumption than conventional RIS.
  • A. Proposed HR-RIS Beamforming Architecture: HR-RIS uses N elements divided into M passive reflectors and K active relays, with K = 0 yielding a conventional RIS and K = N yielding a conventional relay station.Passive elements tune phase only, whereas active elements tune both phase and amplitude and consume more processing power.
  • A. Proposed HR-RIS Beamforming Architecture: Fixed HR-RIS uses predefined active-element positions, whereas dynamic HR-RIS changes their number and positions according to propagation conditions, with the active set treated as a design parameter.Both architectures are considered in the paper.

B. System Model · C. Problem Formulation

The paper models downlink MIMO communication without a direct BS–MS link, assisted by an HR-RIS comprising relay and reflecting coefficients. It formulates spectral-efficiency maximization under active-element power and unit-modulus constraints, yielding an intractable nonconvex problem.

  • B. System Model: The system considers downlink transmission from a BS to an MS with no direct link, assisted by an HR-RIS.The direct path may be unavailable because of severe pathloss or blockage.
  • B. System Model: The BS and MS use N_t and N_r antennas, while H_t and H_r denote the BS–HR-RIS and HR-RIS–MS channels.The model specifies N_t ≥ 1 and N_r ≥ 1.
  • B. System Model: The received-signal model includes AWGN at the active relay elements and MS, with n representing the total effective MS noise.The effective noise combines relay-element noise propagated through H_r and MS noise.
  • C. Problem Formulation: The HR-RIS design problem maximizes the spectral efficiency of the assisted MIMO system subject to active-element power and coefficient constraints.The formulation includes the active elements’ transmit-power expression and a power budget.
  • C. Problem Formulation: The HR-RIS coefficient matrix is parameterized by relay/reflecting coefficients α_n on its main diagonal.The coefficient set is {α_n} = {α_1, α_2, …, α_N}.
  • C. Problem Formulation: The objective is nonconvex in {α_n}, while the feasible set is also nonconvex because of the unit-modulus constraint.These properties make problem (P0) difficult to solve optimally.
  • C. Problem Formulation: Because problem (P0) is intractable, the paper develops an efficient solution for designing the HR-RIS relay/reflection coefficients.The solution is introduced in the following section rather than derived in the formulation itself.

III. EFFICIENT SOLUTION TO (P0) · A. A Tractable Approximation of (P0) · B. Efficient Solution to (Phybrid): an AO Approach

The method first replaces (P0) with a tractable upper-bounded approximation, then solves the resulting nonconvex problem efficiently through alternating optimization by updating one HR-RIS coefficient at a time.

  • A. A Tractable Approximation of (P0): The proposed procedure approximates (P0) by replacing f0({αn}) with its upper bound f({αn}), yielding a more tractable formulation.The bound follows from substituting the preceding expressions into (7) and retains constraints (5b) and (5c).
  • A. A Tractable Approximation of (P0): The approximation becomes tighter when log2 |R| is smaller, including settings with large path loss or only a few active HR-RIS elements.With a single or few active elements, Ψ becomes very sparse, reducing log2 |R|.
  • A. A Tractable Approximation of (P0): Although f({αn}) remains nonconvex, its structure enables an efficient alternating-optimization solution.The subsequent AO procedure updates individual coefficients while holding the others fixed.
  • B. Efficient Solution to (Phybrid): an AO Approach: In each AO iteration, one coefficient αn is updated while all other HR-RIS coefficients remain fixed.The objective and active-relay power are expanded to isolate the role of αn.
  • B. Efficient Solution to (Phybrid): an AO Approach: The matrix expansions isolate αn in the objective while matrices An, Bn, and Cn become fixed once the remaining coefficients are fixed.The same decomposition identifies the dependence of Pa({αn}) on αn and treats the remaining terms as constants.
  • B. Efficient Solution to (Phybrid): an AO Approach: With other coefficients fixed, the αn-update reduces the objective to a single-variable problem involving αn.Because An is full-rank and invertible, fn(αn) can be rewritten with log2 |An| constant in αn.
  • B. Efficient Solution to (Phybrid): an AO Approach: The resulting subproblem (Pupdate) has a closed-form solution, supporting efficient practical implementation.The derivation proceeds by rewriting gn(αn).

2) Solution to (Pupdate):

The solution analyzes both terms of the objective using almost-sure rank-one eigenvalue decompositions, yielding an update expression that includes the active-relaying coefficient. The resulting optimal α_n cannot be determined until A is fixed or dynamically optimized, motivating separate fixed and dynamic HR-RIS cases.

  • Objective update: The derived second-term expression differs from the conventional RIS result by the additional factor |α_n|^2 introduced by the active-relaying coefficient.The expression also uses the real part of a complex quantity, denoted R(·).
  • HR-RIS architectures: The optimal update α_n⋆ cannot yet be determined because it depends on the matrix A.The derivation therefore considers predetermined fixed A and dynamically optimized A scenarios.
  • HR-RIS architectures: These two scenarios correspond to the fixed and dynamic HR-RIS architectures, whose coefficient solutions are derived separately.The architectures are illustrated in Figs. 1(a) and 1(b), respectively.

IV. BEAMFORMING COEFFICIENT MATRIX OF FIXED AND DYNAMIC HR-RIS · A. Fixed HR-RIS Architecture

The fixed HR-RIS coefficient matrix is obtained by alternatingly updating active and reflecting-element coefficients through an iterative algorithm that converges in objective value. Its performance depends on active-element count, power budget, and channel conditions, motivating dynamic HR-RIS.

  • A. Fixed HR-RIS Architecture: The fixed HR-RIS coefficient matrix is obtained by alternatingly updating each element’s coefficient using the optimal solution of (Pupdate).Algorithm 1 initializes reflecting-element coefficients with unit modulus and iteratively updates coefficients for active and inactive elements.
  • A. Fixed HR-RIS Architecture: Algorithm 1 repeats coefficient updates until the objective converges, with convergence guaranteed because the objective is upper bounded and each subproblem is solved optimally.The resulting objective sequence is non-decreasing over iterations.
  • A. Fixed HR-RIS Architecture: Increasing the number K of active elements does not always improve fixed-HR-RIS spectral efficiency because the resulting active-element coefficients can become smaller.With limited P max, numerous active elements may yield |α⋆_n| < 1, attenuating the signal; a small K can therefore more readily provide SE gains.
  • A. Fixed HR-RIS Architecture: The fixed HR-RIS requires sufficient maximum active-element power for |α_n| > 1, specifically P max_a exceeding the aggregate ξ_n over active elements.This condition follows from the fixed-HR-RIS power allocation relationship.
  • A. Fixed HR-RIS Architecture: For fixed P max_a, lower transmitter power PBS or smaller channel gain ∥t_n∥2 produces larger power-amplifier coefficients |α⋆_n| and potentially greater performance improvement.The dependence follows from substituting ξ_n ≜ σ2 + PBS∥t_n∥2 into the coefficient expression.
  • A. Fixed HR-RIS Architecture: Fixed active-element numbers and positions limit HR-RIS beamforming gain, motivating dynamic HR-RIS as a more robust architecture intended to guarantee SE improvement.The paper states that the fixed architecture’s remarks are further numerically justified in Section VI.

B. Dynamic HR-RIS Architecture

Dynamic HR-RIS treats the number and positions of active elements as design variables, creating a cardinality-constrained SE-maximization problem. An alternating procedure jointly updates phases, active-element selection, and amplitudes, with power allocation obtained by water filling.

  • Dynamic HR-RIS formulation: Dynamic HR-RIS allows both the number and positions of active elements to be optimized, unlike the fixed architecture.The design is constrained by the maximum number of available RF-PA chains.
  • Alternating optimization: The proposed solver alternates over phase variables Θ, amplitude variables ˆΥ, and the active-element set A to obtain an efficient solution.This avoids the excessive computational cost of exhaustive search over all valid active-element combinations.
  • Dynamic amplitude design: Active elements are assigned amplitudes greater than one, while RF-PA chains are switched off when their candidate amplitudes would be below one.Passive elements retain unit modulus, whereas active-element amplitudes are determined after selecting A⋆ and allocating power.
  • Dynamic active-element and power optimization: The optimal active-element set A⋆ comprises the indices of the K largest values of ξ_n, followed by water-filling power allocation over A⋆.The quantities ξ_n are obtained during phase optimization, and the resulting powers determine the active-element amplitudes.
  • Algorithm 2: Algorithm 2 initializes unit-modulus coefficients, iterates phase updates until convergence, selects A⋆, computes amplitudes, and finally derives the dynamic HR-RIS coefficients.The procedure computes the phase-related quantities before selecting the K largest ξ_n values.

V. POWER CONSUMPTION ANALYSIS · A. Fixed HR-RIS Architecture

The fixed HR-RIS power model assumes fixed numbers of active and passive elements and accounts for amplifier, element, circuit, and base-station power consumption. Its total consumption incorporates both dynamic and static power components.

  • A. Fixed HR-RIS Architecture: The fixed HR-RIS contains K active elements and M passive reflecting elements, which remain fixed in the system model.
  • A. Fixed HR-RIS Architecture: The total power consumption of the fixed HR-RIS-aided MIMO system is modeled from the system’s component power expenditures.
  • A. Fixed HR-RIS Architecture: The model includes BS and active-element power amplifier efficiencies, denoted by τBS and τa, respectively.
  • A. Fixed HR-RIS Architecture: It incorporates Pa for active elements and Pp for the power required by each passive reflecting element.
  • A. Fixed HR-RIS Architecture: The fixed HR-RIS circuit power term, P fix.c,H, represents the total circuit consumption of the fixed HR-RIS-aided MIMO system.
  • A. Fixed HR-RIS Architecture: BS and active relay elements each contribute dynamic RF-chain power and static overhead to the total consumption.For the BS, static overhead includes baseband processing, power supply, and cooling; analogous dynamic and static terms are defined for active relay elements.

B. Dynamic HR-RIS Architecture · C. Conventional RIS Architecture · VI. SIMULATION RESULTS

The dynamic HR-RIS adapts its active and passive element counts to the power budget, while conventional RIS uses only passive elements; simulations evaluate their power consumption under specified array, channel, and phase-resolution assumptions.

  • B. Dynamic HR-RIS Architecture: Dynamic HR-RIS varies its active and passive element counts according to P_max, with passive elements numbering N−|A⋆| after Algorithm 2.The active set A⋆ contains elements whose amplitudes exceed one.
  • B. Dynamic HR-RIS Architecture: Dynamic HR-RIS power consumption includes switch power for N switches and a circuit-power term for the dynamic architecture.Each switch consumes P_SW, and the circuit term is denoted P_dyn,c,H.
  • C. Conventional RIS Architecture: Conventional RIS has no active relay elements and instead uses N=M+K passive reflecting elements.Its total power includes circuit consumption P_c,RIS and the passive-element term NP_p.
  • C. Conventional RIS Architecture: Compared with conventional RIS, fixed and dynamic HR-RIS incur power increases that grow linearly with K and |A⋆|, respectively.This comparison assumes P_passive ≪ P_a,dynamic.
  • VI. SIMULATION RESULTS: Simulations model ULAs at the BS and MS, a UPA with N elements at the HR-RIS, and half-wavelength inter-element spacing.The BS is fixed at (0,0), while HR-RIS and MS locations vary in the two-dimensional setup.
  • VI. SIMULATION RESULTS: Channels use distance-dependent path loss and Rician fading, combining deterministic LoS and Rayleigh NLoS components.The Rician factor controls the transition from Rayleigh fading to LoS, and the channel matrices include the square root of path loss.
  • VI. SIMULATION RESULTS: The default setup uses β0=−30 dB, path-loss exponents {2.2,2.8}, noise power −80 dBm, 2-bit phase shifts, and 100 channel realizations.The default coordinates are {x_MS,y_MS,x_H}={40,2,51} m and Rician factors are {κ_t,κ_r}={∞,0}.

A. Improvement in SE of the Proposed HR-RIS

The proposed HR-RIS schemes substantially improve spectral efficiency over conventional RIS, particularly at low BS transmit power, while dynamic HR-RIS is generally more robust and effective than fixed HR-RIS. These gains require only a small number of active elements and persist across deployments and surface sizes, although they diminish at high BS power or larger surfaces.

  • A. Improvement in SE of the Proposed HR-RIS: The proposed schemes perform very close to exhaustive-search optima in the small N = 4, K = 1 system, supporting the effectiveness of their AO-based designs.Exhaustive search is omitted for larger systems because of excessive computational and time complexity.
  • A. Improvement in SE of the Proposed HR-RIS: With N = 50 and K = 1, HR-RIS improves SE over random- and AO-optimized conventional RIS, while small active-element power is sufficient for substantial gains.The comparison uses Nt = 32, Nr = 2, and P_a^max = {−10, 0, 10} dBm, with the HR-RIS and AO-based RIS optimized using the same AO method.
  • A. Improvement in SE of the Proposed HR-RIS: HR-RIS achieves significant SE improvements over conventional RIS, especially at low PBS, while dynamic HR-RIS generally provides the larger gain.With P_a^max = 0 dBm, fixed and dynamic HR-RIS save more than 10 dBm and 15 dBm, respectively, in BS transmit power; at P_a^max = −10 dBm and PBS ≥35 dBm, gains become comparable to conventional RIS.
  • A. Improvement in SE of the Proposed HR-RIS: Across K and all considered scenarios, dynamic HR-RIS attains higher or equal SE than AO-based RIS, whereas fixed HR-RIS can degrade after peaking at small or moderate K.Dynamic HR-RIS can deactivate underpowered active elements, preserving conventional reflecting behavior and making it more robust than fixed HR-RIS.

B. Power Consumption and EE of the HR-RIS Schemes

The HR-RIS schemes achieve substantially higher EE than conventional RIS at low and moderate PBS, while their EE becomes comparable at high PBS. Dynamic HR-RIS preserves EE more robustly by adapting active elements, making a small active-element count favorable for spectral and energy efficiency.

  • EE comparison: HR-RIS achieves much higher EE than conventional RIS at low and moderate PBS, while HR-RIS and RIS have comparable EE at high PBS.The EE improvement follows the SE improvement observed for the same schemes.
  • Power consumption: Dynamic HR-RIS reduces power by deactivating active elements when P_max,a = −10 dBm is insufficient to amplify signals across many elements, preserving SE while approaching RIS power consumption.For small K, HR-RIS requires only reasonably additional power to obtain significant SE improvement.
  • EE versus active elements: The fixed HR-RIS EE rapidly decreases as K increases, whereas dynamic HR-RIS remains comparable to AO-based RIS at large K when P_max,a = −10 dBm.At small K, both HR-RIS architectures have the same or much higher EE than AO-based RIS.
  • Design implications: A spectral- and energy-efficient HR-RIS should use a small number of active elements, while dynamic HR-RIS limits EE loss when favorable PBS, P_max,a, or K conditions are absent.This conclusion follows jointly from the EE and SE results across the considered configurations.

VII. CONCLUSION

The paper proposes HR-RIS as a semi-passive architecture that improves SE and EE over conventional RIS and bridges RIS with active relaying. Its analysis favors few active elements and identifies implementation and relay-model challenges for future work.

  • Contributions: HR-RIS significantly improves spectral and energy efficiency over conventional RIS through semi-passive beamforming with a few power-adjusting elements.The proposed architecture includes fixed and dynamic variants, with dynamic active-element selection and water-filling power allocation.
  • Design insights: Using numerous active elements does not guarantee SE or EE improvement, so HR-RIS should employ few active elements to limit power consumption.The largest improvements occur at low or moderate transmitter power and increase when the transmitter-to-surface distance is greater.
  • Future work: Practical HR-RIS implementation remains challenging, particularly for the assumed full-duplex amplify-and-forward relay and efficient reconfigurable arrays.The paper also identifies energy-efficiency-oriented system optimization and channel estimation using active components as future directions.
  • Future work: The analysis assumes ideal amplify-and-forward components without processing delays, leaving practical delays and decode-and-forward relaying for future study.These assumptions make the active components behave similarly to passive reflection in processing latency.
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