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System-Level Gains of Dual-Band RIS: From Wireless Communication to SWIPT

Aritra Basu, Zina Mohamed, Sonia Aïssa

arXiv:2610.01526v1eess.SP

TL;DR

DBRIS integration into wireless systems remains an underexplored area. This paper evaluates DBRIS-assisted communication and SWIPT, reporting enhanced system performance compared with multiple single-band RISs in both use cases.

  • Problem

    Although DBRISs are physically feasible, their integration into wireless systems remains largely unexplored.

    Source: C. System-level Integration of DBRISs · p. 2

  • Method

    The paper formulates energy-efficiency maximization for DBRIS-assisted communication and SWIPT and applies alternating optimization to joint phase-shift design and power allocation across frequency bands.

    Source: §VI · p. 13

  • Results

    Numerical results report enhanced system performance for DBRIS compared with multiple single-band RISs in both communication and SWIPT.

    Source: A. DBRIS-Assisted Communication · p. 10, §VI · p. 13, B. DBRIS-Assisted SWIPT · p. 13

  • Takeaways & Limitations

    The findings indicate DBRIS has potential to address hardware redundancy and spatial limitations in the evaluated wireless system designs.

    Source: §VI · p. 13

Abstract

from arXiv · show

This paper introduces the integration of dual-band reconfigurable intelligent surfaces (DBRIS) in wireless system design, and investigates the ensuing performance gains in different application scenarios. This type of metasurfaces offers a compelling technology due to their reduced material usage, compact design, and multi-functional operation across multiple frequency bands compared to single-band RISs. Two representative use cases are considered to assess the achievable performance gains with the said integration, namely, DBRIS-assisted wireless communication, and DBRIS-assisted simultaneous wireless information and power transfer (SWIPT). For the first design, where the DBRIS is deployed as a relay, we focus on the energy efficiency (EE) maximization of the communication system. An alternating manifold method is proposed for the joint optimization of the source transmit power and the DBRIS phase shifting. For the second design, we investigate a DBRIS-assisted SWIPT system using a novel power splitting approach. An EE metric is defined, and an alternating optimization algorithm is developed to maximize it. Numerical results validate the advantages of the proposed design architectures as well as the proposed optimization framework. In particular, we highlight the energy efficiency gains enabled by the DBRIS as compared to operations with conventional single-frequency surfaces, in both application scenarios.

I. INTRODUCTION … D. Contributions

The introduction presents DBRIS as a way to address conventional RIS limits in multi-band networks and evaluates its integration in communication and SWIPT systems, with energy efficiency as the optimization objective.

A. Context and Motivation

  • Growing 6G connectivity demand makes energy efficiency, reduced material use, and hardware sharing central sustainability goals for wireless networks.Source: A. Context and Motivation · p. 1
  • Conventional RISs face half-space coverage, limited multifunctionality, hardware complexity, and rigid frequency selectivity that constrain multi-band operation.Source: A. Context and Motivation · p. 1
  • Other RIS variants broaden angular coverage and signal control – but remain single-band; DBRIS enables independent multi-band beamforming – with greater spectral utilization and less material use and cost.Source: A. Context and Motivation · pp. 1–2

B. Physical Realization of DBRISs

  • Reported prototypes demonstrate dual-band tunability and control, while ground planes, EBGs, shielding, and multilayer spacers mitigate inter-band coupling to preserve independent operation.Source: B. Physical Realization of DBRISs · p. 2

C. System-level Integration of DBRISs

  • System integration remains underexplored; as relays, DBRISs can create alternative LoS paths around blockages and serve multiple bands or operators, reducing material use and deployment footprint.Source: C. System-level Integration of DBRISs · p. 2

D. Contributions

  • The paper studies shared dual-band assistance for data communication and SWIPT, each involving a dual-band transmitter and two single-band receivers.Source: D. Contributions · p. 3
  • Both systems maximize energy efficiency by jointly optimizing transmit power and DBRIS phase shifts; SWIPT additionally optimizes the power-splitting ratio using alternating optimization.Source: D. Contributions · p. 3

II. DBRIS RESPONSE FUNCTION

The section describes a dual-band DBRIS architecture and its idealized propagation model, including frequency-specific reflection behavior, direct and surface-reflected paths, and assumptions used in system analysis.

II. DBRIS RESPONSE FUNCTION

  • The adopted super-cell DBRIS, uses two independently biased asymmetric patches per unit for simultaneous 2.5- and 3.6-GHz operation, with negligible inter-band coupling and interference.Spatially separated receivers and independent beamforming at each frequency also render inter-band interference negligible.Source: §II · p. 3
  • Its architectural advantage is comparable beamforming capability to two independent single-band RISs with lower energy and material costs, simplified control, and reduced overhead.The paper focuses on sustainability and energy-efficiency advantages rather than throughput quantification.Source: §II · p. 3
  • Each element has frequency-specific amplitude reflection coefficients and tunable phase shifts; the analysis assumes lossless elements with unit-magnitude reflection.The lower- and higher-frequency responses are represented by separate diagonal matrices across the N elements.Source: §II · p. 3
  • The electrically large DBRIS is modeled as a specular planar reflector in a two-ray model, with a direct LoS component and a dominant reflected component following geometric optics.Reflections obey Snell’s law; Figure 1 illustrates the two-ray geometry.Source: Figure 1 · p. 3, §II · p. 4
  • Under far-field conditions, N DBRIS elements yield gain of (N + 1)^2 when LoS exists or N^2 otherwise, and transmit powers at both bands require optimization.The far-field approximation treats each receiver’s aerial distance as approximately equal to its direct distance and the sum of the two reflected-path distances.Source: §II · p. 4
  • For subsequent optimization and simulations, propagation channels follow 3GPP standardized specifications to model realistic deployment conditions beyond the deterministic two-ray baseline.The deterministic formulation omits complex multipath scatterers, terrain irregularities, and mobility.Source: §II · p. 4

III. DBRIS AIDED COMMUNICATION … 1) Problem Formulation:

The communication design models an AP using a DBRIS relay to serve two receivers over separate frequency bands, then formulates energy-efficiency maximization over transmit powers and DBRIS phases. It assumes negligible inter-band interference and focuses on a two-user, ideal-equipment setting.

A. System Model

  • The dual-band AP simultaneously sends distinct signals to two single-antenna receivers, while the DBRIS reflects each signal toward its respective receiver and direct links are neglected.The receivers are spatially separated and narrowband; the AP has one antenna dedicated to each band.Source: A. System Model · p. 4, Figure 2 · p. 4
  • The model assumes far-field DBRIS operation, negligible inter-band interference, and ideal equipment; multi-user intraband interference and hardware impairments are left for future work.The analysis uses a two-user setup to study fundamental performance limits.Source: A. System Model · p. 4

1) Problem Formulation:

  • Energy efficiency is the design objective because it captures the trade-off between system throughput and total power consumption in dual-band transmission.Total power includes both transmit powers, DBRIS circuitry and elements, AP control circuitry, and receiver power.Source: 1) Problem Formulation · p. 5
  • The system sum-rate is the sum of the two receivers’ log2(1 + SNR) rates, with one rate contributed by each frequency band.The transmit powers are Ph and Pl for the high- and low-frequency links, respectively.Source: 1) Problem Formulation · p. 5
  • The formulation jointly optimizes both transmit powers and DBRIS phase matrices under an AP power budget, receiver SNR requirements, and unit-modulus phase constraints.The AP is assumed to have the required channel state information and relevant system parameters.Source: 1) Problem Formulation · p. 5
  • The fractional, non-convex EE problem is NP-hard, so the authors apply the Dinkelbach method and alternate between phase optimization and feasible power allocation.The phase matrices are optimized with transmit powers fixed, followed by power allocation with the phases fixed.Source: 1) Problem Formulation · pp. 5–6

2) Proposed Solution: · Phase Shifting Design:

The phase-shifting design alternates optimization over the high- and low-frequency phase matrices, using manifold-based updates to maintain feasible DBRIS responses. The same procedure obtains phase matrices for both operating frequencies.

Phase Shifting Design:

  • The phase-shifting problem is solved by alternating between optimizing Φh with Φl fixed and optimizing Φl with Φh fixed.The two subproblems are formulated after mathematical manipulation.Source: Phase Shifting Design · p. 6
  • Each DBRIS element response lies on the complex circle S1, with phase shifts constrained to [0, 2π); the manifold structure is cited as.The unit-modulus constraints apply to both frequency responses.Source: Phase Shifting Design · p. 6
  • The phase variables are updated with Riemannian gradient steps and a retraction operator that maps updated variables back to the manifold.The gradient and back-projection can be computed iteratively.Source: Phase Shifting Design · p. 6
  • A barrier term penalizes constraint violations, and gradient and back-projection updates run for Kmax iterations or until convergence.The barrier is incorporated into the modified objective function.Source: Phase Shifting Design · p. 6
  • The procedure is repeated at operating frequency fl to obtain the optimal low-frequency phase-shift matrix Φopt_l.The phase matrices are designed for fixed transmit powers Ph and Pl.Source: Phase Shifting Design · p. 6
  • Algorithm 1 generates channel data and repeats gradient descent and manifold updates, then applies the phase-design steps to Φl.The algorithm stops when its stated threshold is met or k reaches Kmax.Source: Phase Shifting Design · p. 6

Power Allocation Strategy:

The power-allocation strategy approximates non-convex QoS constraints with convex Taylor-series lower bounds, then uses alternating optimization and Dinkelbach iterations to maximize energy efficiency.

Power Allocation Strategy:

  • Taylor-series expansions convert the non-convex QoS constraints into convex approximations, with SNR constraints lower-bounded as described in [38, Eq. (12)].The approximated SNR constraints are used in subsequent sections as well.Source: Power Allocation Strategy · pp. 6–7
  • Because the variables η, P_h, and P_l remain interlinked, the method applies an alternating technique after transforming the objective with Dinkelbach’s method.For a given η_t, the algorithm solves the power-allocation problem and updates η until convergence or the iteration limit.Source: Power Allocation Strategy · p. 7

l + PDBRIS + PAP + PUE

The power-allocation objective is made tractable with DC programming and solved iteratively for fixed phase shifts. The iterations use a stated convergence threshold or maximum-iteration limit.

l + PDBRIS + PAP + PUE

  • For fixed A_h and A_l, or fixed elements of Φ_h and Φ_l, f(p) is a concave-minus-convex function that is tractable with DC programming.The passage states that problem (25) can be solved using iterative DC programming techniques.Source: l + PDBRIS + PAP + PUE · p. 7
  • Algorithm 3 calculates f_j(p_j), then repeats solving (25) using CVX for fixed Φopt_h and ηt, sets p_j = p_opt, calculates f_j(p_j), and updates j to j + 1.Source: l + PDBRIS + PAP + PUE · p. 7
  • The iterations stop when |f^j(p^j) − f^{j−1}(p^j)| ≤ ϑ3 or j = Jmax.Algorithm 3 then outputs the power allocation p^j.Source: l + PDBRIS + PAP + PUE · p. 7

C. Complexity Analysis … B. Utility Function Maximization

The paper analyzes the complexity of the DBRIS-assisted communication-system optimization and specifies a dual-band SWIPT architecture whose energy-efficiency utility jointly accounts for information rate, harvested energy, and power consumption.

C. Complexity Analysis

  • Algorithm 1 has complexity O(KmaxN), Algorithm 2 has overall complexity O(Tmax), and Algorithm 3 has complexity O(Jmax).Algorithm 1’s cost includes channel and matrix initialization; Algorithm 2’s convex subproblem is solved in O(1) per iteration, and Jmax is Algorithm 3’s iteration limit.Source: C. Complexity Analysis · p. 7

A. System Model 

  • DBRIS-assisted SWIPT assigns the lower frequency band to wireless power transfer and the higher band to information transmission, enabling simultaneous energy and information transfer over distinct bands.The lower band is leveraged for improved wireless power-transfer efficiency and higher harvested energy at the target device.Source: A. System Model  · pp. 7–8
  • The lower-band WPT assignment is preferred because it reduces propagation loss and improves RF-to-DC conversion efficiency.Higher-frequency WPT can amplify parasitic losses, worsen rectifier nonlinearities, and complicate impedance matching, increasing hardware complexity and reducing energy-harvesting performance,.Source: A. System Model  · p. 7
  • Unlike RIS-aided SWIPT studies limited to a single operating band, this design uses DBRIS for simultaneous energy transfer and information transmission; the model can be extended to multi-user scenarios.The considered system has a common AP and two spatially separated receivers, and uses the channel model described in section III.Source: A. System Model  · pp. 7–8
  • The SWIPT energy-efficiency utility captures the trade-off among achievable information rate, harvested energy, and transmit power, and the joint maximization considers all three objectives,.The metric is described as widely adopted in SWIPT literature.Source: A. System Model  · p. 8
  • The harvested energy is modeled with a practical sigmoid-based nonlinear energy-harvesting model,.Its parameters include the power-splitting factor ς and maximum harvested energy Emax at circuit saturation; the model also identifies received SNR γh and harvested power PlAl.Source: A. System Model  · p. 8
  • The weighted utility uses objective weights wh, wl, and wp, while total system power is PP = Ph + Pl + PDBRIS + PAP + PUE.The component power terms are defined in section III.Source: A. System Model  · p. 8

1) Problem Formulation: · 2) Proposed Solution:

This section formulates DBRIS-assisted SWIPT around a utility function the authors identify as first used for this system, then develops a Dinkelbach-based alternating optimization solution.

1) Problem Formulation:

  • The authors identify applying the utility function to evaluate DBRIS-assisted SWIPT as a first for this system.The function is used to assess the proposed system design's energy efficiency.Source: 1) Problem Formulation · p. 8
  • The formulation includes a minimum harvested-energy requirement and unit-modulus constraints on both DBRIS phase-shift coefficients.The minimum energy level is set by the harvesting device's requirement.Source: 1) Problem Formulation · p. 8
  • The Dinkelbach transformation converts the fractional objective into a subtractive form, the difference between its numerator and a scaled quasi-denominator.This reformulation is used to make the fractional optimization more tractable.Source: 1) Problem Formulation · p. 8

2) Proposed Solution:

  • The solution alternates between transmit-power allocation and DBRIS phase-shift optimization, with both subproblems framed as disciplined convex-concave programming.Source: 2) Proposed Solution · p. 8
  • Harvested energy is re-expressed as an equivalent data rate to reflect its later use for uplink transmission; conversion efficiency ηcon, between 0 and 1, ensures unit consistency.The efficiency depends on the RF-to-DC circuitry and harvesting-module hardware.Source: 2) Proposed Solution · p. 8

1) Problem Formulation:

  • Because the problem is non-convex, fixed objective weights are varied to trace the Pareto-optimal trade-offs; the weights sum to unity to facilitate convergence.Choosing weights for specific operational objectives is outside the paper's scope.Source: 2) Proposed Solution · p. 8

2) Proposed Solution:

  • For fixed transmit powers and ζ, manifold optimization tunes the phase shifts using Riemannian gradients and retraction until convergence.The gradient is computed on the modified objective, which includes a penalty, then projected back onto the manifold.Source: 2) Proposed Solution · p. 9

Power Splitting Factor Design:

The design optimizes the power-splitting factor and, given that factor and the optimized phase-shift matrices, determines the high- and low-band transmit powers.

Power Splitting Factor Design:

  • The power-splitting factor ς is the optimization target, and the resulting problem can be solved with convex tools such as CVX.The supplied passage does not include the full optimization formulation.Source: Power Splitting Factor Design · p. 9
  • Given ηsw, the optimized ς, and phase-shift matrices Φh and Φl, the power allocation strategy obtains Ph and Pl using iterative DC programming with CVX.The algorithm begins by generating channel data and setting t = 0.Source: Power Splitting Factor Design · p. 9

C. Complexity Analysis · V. PERFORMANCE EVALUATION · A. DBRIS-Assisted Communication

The analysis gives Algorithm 4 a complexity of O(TmaxKmaxN), then evaluates DBRIS-assisted systems under communication and SWIPT settings. In the communication results, DBRIS improves energy efficiency (EE) over dual-SBRIS configurations and outperforms the tested algorithm baselines.

C. Complexity Analysis

  • Algorithm 4 has overall computational complexity O(TmaxKmaxN), dominated by manifold optimization of DBRIS phase shifts at O(KmaxN).Power-splitting-factor and power-allocation updates each solve a low-dimensional convex problem with O(1) complexity.Source: C. Complexity Analysis · p. 9

V. PERFORMANCE EVALUATION

  • The evaluation varies key operating parameters for communication and SWIPT, using 500 channel realizations and operation frequencies of 3.6 GHz and 2.5 GHz.The stated bandwidth is 100 KHz for both use cases.Source: §V · pp. 9–10
  • The SBRIS baseline uses two separate controllers with fixed static power, while the comparison assumes ideal continuous phase-shifting surfaces.The drive-circuit power is held the same as for DBRIS; discrete phase-resolution hardware limits are omitted.Source: §V · p. 10

A. DBRIS-Assisted Communication

  • DBRIS consistently outperforms dual-SBRIS configurations across the considered power budgets, while EE rises with reflecting-element count and AP transmit power.DBRIS with N = 70 achieves the highest EE across the transmit-power range; the reported advantage is attributed to hardware sharing.Source: A. DBRIS-Assisted Communication · p. 10, Figure 3 · p. 10, Figure 4 · p. 10
  • The proposed algorithm outperforms the optimized-phase and random-phase baselines, with random phase performing worst.The comparison attributes beamforming and array gain to phase alignment, and amplitude scaling to power allocation.Source: A. DBRIS-Assisted Communication · p. 10, Figure 5 · p. 11
  • EE is highest when the DBRIS is near the AP or receivers, and is reduced when it is midway between them.The comparison fixes DBRIS-to-obstacle separation at T = 5 m; the passage attributes the trend to constructive reflections and path loss.Source: A. DBRIS-Assisted Communication · p. 10, Figure 6 · p. 11
  • Algorithm 2 converges to optimal phase shifts and power allocations within seven iterations for both system models.The comparison is with a baseline using two SBRISs.Source: A. DBRIS-Assisted Communication · p. 11, Figure 7 · p. 11
  • The results characterize DBRIS as an alternative to multiple SBRISs that offers enhanced EE alongside reduced hardware complexity and deployment cost.The passage also identifies lower material use and cost savings in manufacturing, installation, and operation.Source: A. DBRIS-Assisted Communication · p. 11

B. DBRIS-Assisted SWIPT · VI. CONCLUSION

The SWIPT results show that DBRIS can improve utility over two SBRISs, while performance depends on surface size, placement, power budget, and utility weights. The conclusion presents alternating optimization for DBRIS-assisted communication and SWIPT as an energy-efficiency approach, and identifies multi-user and hardware studies as future work.

B. DBRIS-Assisted SWIPT

  • The proposed AO algorithm outperforms the Optimized Phase and Random Phase baselines, with Random Phase worst because phase has greater influence than amplitude for DBRIS.The cited comparison is for the DBRIS-assisted SWIPT system.Source: B. DBRIS-Assisted SWIPT · p. 12, Figure 9 · p. 12
  • Utility rises with transmit-power budget and initially with DBRIS size, but can saturate or decline beyond N = 50 at Pmax = 30 dB and 40 dB.The passage attributes the decline to logarithmically growing sum-rate versus linear per-element biasing and control costs; SWIPT also dynamically allocates AP power between communication and WPT bands, and utility varies less than communication EE across element counts and AP–DBRIS distances.Source: B. DBRIS-Assisted SWIPT · pp. 12–13, Figure 10 · p. 12
  • Utility peaks when the DBRIS is near the AP or end receivers and diminishes near the midpoint, where combined path loss weakens received signals.This placement comparison holds the DBRIS–obstacle distance T at 5 m; stronger reflections and improved harvested energy explain the endpoint gains.Source: B. DBRIS-Assisted SWIPT · pp. 12–13, Figure 11 · p. 12
  • Across tested cases, DBRIS achieves higher SWIPT utility than two same-size SBRISs, with gains from serving users at different frequencies and increasing element count.The DBRIS advantage is also attributed to simplified power needs and reduced hardware overhead, including eliminated extra circuitry; its curves converge within a few iterations and reach a ceiling set by the transmit-power budget.Source: B. DBRIS-Assisted SWIPT · pp. 11, 13, Figure 8 · p. 11, Figure 12 · p. 13
  • Prioritizing data rates with wh = 0.5, wl = 0.4, wp = 0.1 yields the highest utility, whereas wp = 0.8 degrades performance.All tested weight configurations converge within a few iterations, demonstrating the optimization process’s efficiency and the role of weights in performance trade-offs.Source: B. DBRIS-Assisted SWIPT · p. 13, Figure 13 · p. 13

VI. CONCLUSION

  • The conclusion reports that alternating optimization jointly addresses phase shifts and power allocation across bands for energy-efficiency maximization in DBRIS-assisted communication and SWIPT.Numerical results showed performance gains over multiple SBRISs; future work includes multi-user extensions, other use cases, testbed-based mutual-coupling models, and hardware impairments.Source: §VI · p. 13
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