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Wireless Communications with Reconfigurable Intelligent Surface: Path Loss Modeling and Experimental Measurement

Wankai Tang, Ming Zheng Chen, Xiangyu Chen, Jun Yan Dai, Yu Han, Marco Di Renzo, Yong Zeng, Shi Jin, Qiang Cheng, Tie Jun Cui

arXiv:1911.05326v2eess.SPcs.IT

TL;DR

RIS-assisted wireless communications lack tractable, reliable electromagnetic models, including an experimentally validated path loss model. This paper develops free-space path loss models for different RIS scenarios from RIS physics, proposes a general formula, and verifies the models through numerical simulations.

  • Problem

    The field lacks tractable and reliable physical and electromagnetic RIS models, including an experimentally validated path loss model for RIS-assisted wireless communications.

  • Method

    The paper theoretically develops free-space path loss models for RIS-assisted wireless communications based on RIS electromagnetic and physics properties, including a general formula for different scenarios.

  • Results

    Numerical simulations verify the proposed free-space path loss models and use the general formula to summarize models across scenarios, including near- and far-field determination.

  • Takeaways & Limitations

    The proposed general formula yields the free-space path loss of RIS-assisted wireless communications in different scenarios.

Abstract

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Reconfigurable intelligent surfaces (RISs) comprised of tunable unit cells have recently drawn significant attention due to their superior capability in manipulating electromagnetic waves. In particular, RIS-assisted wireless communications have the great potential to achieve significant performance improvement and coverage enhancement in a cost-effective and energy-efficient manner, by properly programming the reflection coefficients of the unit cells of RISs. In this paper, free-space path loss models for RIS-assisted wireless communications are developed for different scenarios by studying the physics and electromagnetic nature of RISs. The proposed models, which are first validated through extensive simulation results, reveal the relationships between the free-space path loss of RIS-assisted wireless communications and the distances from the transmitter/receiver to the RIS, the size of the RIS, the near-field/far-field effects of the RIS, and the radiation patterns of antennas and unit cells. In addition, three fabricated RISs (metasurfaces) are utilized to further corroborate the theoretical findings through experimental measurements conducted in a microwave anechoic chamber. The measurement results match well with the modeling results, thus validating the proposed free-space path loss models for RIS, which may pave the way for further theoretical studies and practical applications in this field.

I. INTRODUCTION

RISs use tunable unit cells to manipulate electromagnetic waves and are being investigated for cost-effective, energy-efficient wireless communication improvements. This paper addresses missing physical models and experimental validation by developing and testing free-space RIS path-loss models.

  • RISs use externally controlled unit cells to tune electromagnetic responses including amplitude, phase, polarization, and frequency.
  • RISs can make wireless propagation environments controllable and programmable, creating opportunities for performance improvement and coverage enhancement.
  • Existing RIS research largely lacks tractable, reliable electromagnetic models and experimentally validated free-space path-loss models.
  • The paper develops physics-based free-space path-loss models that account for RIS dimensions, unit-cell radiation patterns, distances, and near-field/far-field effects.
  • Numerical simulations and measurements with three fabricated RISs in an anechoic chamber validate the proposed modeling results, which agree well with measurements.

II. PRELIMINARIES

The preliminaries define the near-field and far-field regions of RISs and introduce normalized power radiation patterns for antennas and unit cells. These concepts provide the physical quantities used in subsequent free-space path-loss modeling.

  • A. Far Field and Near Field: An RIS transmitter or receiver is in the near field when its center distance is less than 2D^2/λ; otherwise, it is in the far field.
  • B. Power Radiation Pattern and Gain: Normalized power radiation patterns describe how transmitted or received power varies with direction relative to the antenna’s peak radiation.
  • B. Power Radiation Pattern and Gain: For the example pattern, maximum gain occurs at θ = 0, where the antenna gain is 8 (9.03 dBi) under 100% radiation efficiency.
  • A. Far Field and Near Field: The paper assumes distances from each RIS unit cell exceed 5λ, so each unit cell is modeled using its far-field component and inverse-square power law.
  • B. Power Radiation Pattern and Gain: The normalized pattern is also applied to RIS unit cells when modeling free-space path loss in RIS-assisted communications.

III. FREE-SPACE PATH LOSS MODELING OF RIS-ASSISTED WIRELESS COMMUNICATIONS

This section develops a general free-space model for RIS-assisted links without the direct transmitter–receiver path, relating received power to system geometry, antenna and unit-cell radiation patterns, and RIS parameters.

  • System model: The model considers a RIS-assisted SISO link in which the transmitter illuminates the RIS and the receiver collects the reflected signal.
  • RIS structure: The RIS comprises N rows and M columns of regularly arranged unit cells with dimensions d_x and d_y, typically at subwavelength scale.
  • System model: The geometry includes transmitter and receiver distances and angles relative to the RIS center, as well as distances and angles relative to individual unit cells.
  • General received-power model: Theorem 1 connects received signal power with transmitted power, antenna gains, unit-cell gain and size, wavelength, radiation patterns, reflection coefficients, and transmitter/receiver distances.
  • General received-power model: The general relationships among these parameters are not straightforward and require further analysis, while the model also establishes transmitter–receiver reciprocity relevant to TDD design.
  • Scenario classification: The paper develops models for RIS-assisted beamforming and broadcasting, with reflection coefficients and RIS near-field/far-field effects determining the scenario-specific analysis.

B. Far Field Beamforming Case

The far-field beamforming case assumes both terminals lie in the RIS far field and uses common-amplitude reflection coefficients to align reflected signals in phase. The resulting path loss follows a distance-squared-product scaling, while intelligent phase programming directs energy toward a desired direction.

  • Specular reflection: With identical reflection coefficients across unit cells, reflected signals can be aligned in phase at the receiver.
  • Assumptions: Both transmitting and receiving antennas are assumed to point toward the RIS center, with both terminals located in the RIS far field.
  • Path-loss scaling: The far-field free-space path loss is proportional to (d1d2)^2 and depends on the unit cells’ normalized power radiation pattern.
  • Specular reflection: Equal reflection coefficients produce specular reflection mainly toward the mirror direction, defined by θr = θt and ϕr = ϕt + π.
  • Intelligent reflection: Programming unit-cell phase shifts enables intelligent reflection toward any desired far-field direction (θdes, ϕdes).
  • Comparison: Far-field beamforming has the same path-loss scaling law for specular and intelligent reflection, and larger RISs outperform smaller RISs under the same condition.

C. Near Field Beamforming Case

The near-field beamforming case designs RIS phase shifts to focus reflected signals at a desired receiver location and derives a corresponding path-loss formula.

  • C. Near Field Beamforming Case: Near-field beamforming assumes the transmitter and/or receiver is in the RIS near field, enabling focused reflection toward a desired receiver.The RIS reflection coefficients are designed to focus the reflected signal at a specified receiver position.
  • C. Near Field Beamforming Case: Proposition 3 gives phase shifts that maximize received signal power for a desired receiver position.The resulting expression is referred to as the near-field beamforming formula.
  • D. Near Field Broadcasting Case: For a large electrically sized RIS, equal reflection coefficients produce specular near-field broadcasting over the intersection of geometric and antenna-defined solid angles.Receivers outside that intersection can hardly receive the reflected signal.
  • D. Near Field Broadcasting Case: Phase compensation based on a virtual transmitter enables intelligent reflection toward a desired broadcasting direction.The phase shifts compensate for propagation-phase differences between the real and virtual transmitters.
  • D. Near Field Broadcasting Case: In near-field broadcasting with designed phase shifts, path loss is proportional to (d1 + d2)^2 rather than the far-field dependence on d1^2d2^2.The same relationship holds when the receiver, rather than the transmitter, is in the RIS near field.

E. Path Loss Model Summary

The paper summarizes free-space path-loss models for RIS-assisted communication scenarios and uses numerical simulations with multiple RIS and antenna configurations for validation.

  • E. Path Loss Model Summary: Table I summarizes free-space path-loss models for RIS-assisted wireless communications in different scenarios.The models are derived from the general formulation and include corresponding formulas for the analyzed cases.
  • E. Path Loss Model Summary: Far-field broadcasting is not discussed because it is considered unsuitable for wireless communications.In the far field, the large path loss of individual unit-cell links makes beamforming necessary to maintain link quality.
  • E. Path Loss Model Summary: The simulations use three RISs and two antennas with parameters specified in Table II.The electrical sizes are 35λ×35.7λ for large RIS1, 17.5λ×11.9λ for large RIS2, and 1.36λ×5.44λ for the small RIS.

A. RIS-assisted Beamforming

Beamforming simulations examine specular and intelligent reflection in far- and near-field settings, showing directional control and agreement between specialized and general path-loss formulas.

  • 1) Specular Reflection in the Far Field Beamforming Case:: In far-field specular reflection, both large RIS1 and the small RIS reflect incident signals specularly.The reflected power becomes more concentrated as the RIS electrical size increases.
  • 1) Specular Reflection in the Far Field Beamforming Case:: The far-field specular-reflection formula matches the general formula for large RIS1.This validates the corresponding far-field beamforming path-loss model.
  • 2) Intelligent Reflection in the Far Field Beamforming Case:: Designed phase shifts steer reflected signals toward desired directions for both large RIS1 and the small RIS.The received signal power is maximized in the desired direction.
  • 2) Intelligent Reflection in the Far Field Beamforming Case:: The phase-designed far-field formula agrees with the general formula for intelligent reflection.The agreement validates the far-field intelligent-reflection path-loss model.
  • 3) Intelligent Reflection in the Near Field Beamforming Case:: Near-field beamforming successfully focuses the reflected signal toward a desired receiver even when the transmitter is in the RIS near field.As distance increases, the near-field formula fits the far-field formula more closely.
  • 3) Intelligent Reflection in the Near Field Beamforming Case:: The near-field beamforming path loss approaches the far-field dependence as both distances increase, including for the small RIS.The reported convergence is not related to RIS size.

B. RIS-assisted Broadcasting

Broadcasting simulations validate specular and intelligent near-field path-loss models, identify the near/far-field transition, and extend validation to measurements with three metasurfaces.

  • 1) Specular Reflection in the Near Field Broadcasting Case:: Near-field specular reflection illuminates a specific receiver region defined by the intersection of geometric and transmitting-antenna solid angles.The near-field broadcasting formula fits the general formula for several transmitter distances.
  • 1) Specular Reflection in the Near Field Broadcasting Case:: As the transmitter distance increases, the general-formula curve transitions from the near-field broadcasting curve toward the far-field curve.For large RIS1, the curves nearly overlap at d1 = 28 m.
  • 1) Specular Reflection in the Near Field Broadcasting Case:: The redefined far-/near-field boundary is obtained by equating the far-field and near-field formulas.For large RIS1, the resulting boundary is Lbound = 28.77 m.
  • 2) Intelligent Reflection in the Near Field Broadcasting Case:: Intelligent near-field broadcasting uses phase design to direct reflected signals toward desired directions.The design supports simultaneous broadcasting toward two desired directions with large RIS2.
  • 2) Intelligent Reflection in the Near Field Broadcasting Case:: The near-field broadcasting formula matches the general formula for both large RIS1 and large RIS2 scenarios.These agreements validate the path-loss model for near-field intelligent broadcasting.
  • Validation: Numerical simulations verify the summarized free-space path-loss models and the proposed field-boundary criterion.The criterion determines whether the transmitter or receiver is in the RIS near or far field.
  • Experimental Validation: Experimental measurements use a microwave anechoic chamber and three fabricated metasurfaces to validate the proposed path-loss models.The metasurfaces act as RISs in different measurement scenarios.

A. Measurement Setup

The study measures RIS-assisted free-space path loss in a microwave anechoic chamber using configurable metasurfaces, horn antennas, and controlled transmitter–RIS–receiver distances. Measurements cover specular and intelligent reflection, near-field broadcasting, and far-field beamforming scenarios, and generally agree with the proposed formulas.

  • Measurement system: The anechoic-chamber setup suppresses multipath and blocks the direct transmitter–receiver path so the received signal mainly comes from RIS reflection.Two perpendicular aisles allow flexible variation of d1 and d2, with the metasurface placed at their junction.
  • Reflection scenarios: The two aisles meet the metasurface at 45°, producing specular reflection for most measurements, while a separate experiment implements intelligent reflection into two directions.The antenna and metasurface polarization directions are horizontally matched.
  • RIS configurations: 28.77 m, 4.8 m, and 0.866 m are the far-field boundaries Lbound for large RIS1, large RIS2, and the small RIS, respectively.These boundaries enable near-field measurements for the two large RISs and far-field measurements for the small RIS within the approximately 6 m × 5 m chamber.
  • Measurement results: The near-field large-RIS measurements agree with the general and near-field broadcasting formulas, with path loss proportional to (d1 + d2)2 for specular reflection.For intelligent reflection, the two measured path trends match theory with approximately 3 dB difference.
  • Measurement results: The far-field small-RIS measurements agree with the general and far-field formulas, with approximately 2 dB difference and path loss proportional to (d1d2)2.The small RIS is evaluated in the specular-reflection far-field beamforming case.
  • Measurement limitations: Small position deviations can lower measured received power because they shift the RIS reflected-beam direction away from the measurement path.A few degrees of azimuth deviation can cause a 2∼3 dB decrease in measured received power.

4) On the Sensitivity of Phase Regulation to the Incident Angle:

The section examines incident-angle sensitivity, RIS power consumption, and the paper’s overall validation of electromagnetic path-loss models. It reports that the tested RIS is highly incident-angle sensitive, while experiments broadly support the models and leave small-scale fading for future study.

  • Incident-angle sensitivity: If the reflection coefficient depends on the incident angle, RIS-assisted channel reciprocity may no longer hold.The reciprocity result assumes Γn,m is not sensitive to changes in incident angle θt.
  • Incident-angle sensitivity: The used RIS is highly sensitive to the incident angle, based on measured control-voltage–phase-shift relationships.The measurements are plotted in Fig. 17 for the small RIS under different incident angles.
  • Power consumption: Varactor-diode RIS power consumption is described as almost zero because unit-cell diode current is negligible during operation.PIN-diode RIS consumption instead depends on the states of their unit cells.
  • Power consumption: 0.33 mW/unit cell is the measured power consumption of a PIN-diode unit cell in the on state.The calculation uses 0.7 V, 0.8 A, and 50×34 unit cells, giving PRIS = 0.33Non mW.
  • Power consumption: The controller consumes about 0.72 W for the small RIS and about 10 W for large RIS2, in addition to RIS unit-cell consumption.The reported controller power depends on circuit design and the number of output control signals.
  • Conclusions: Measurements in different scenarios match the modeling results well, validating the proposed free-space path-loss models.The models are intended to support understanding of large-scale fading, link-budget calculation, and performance analysis.
  • Conclusions: Small-scale fading and other fading factors remain an important direction for future generalization of the paper.The conclusion explicitly identifies small-scale fading as requiring further study.

APPENDIX A-PROOF OF THEOREM 1

The appendix derives Theorem 1 from the incident and reflected fields of individual RIS unit cells. It combines energy conservation, antenna apertures, propagation phases, and coherent superposition to obtain received power and its far-field specialization.

  • Unit-cell fields: The incident power at each unit cell is related to the receiving-antenna aperture and the transmitter-to-cell distance.The derivation introduces the incident electric field and cell position before calculating reflected power.
  • Unit-cell fields: Energy conservation sets reflected unit-cell power equal to incident power multiplied by the squared reflection-coefficient magnitude.The reflection coefficient is parameterized by controllable amplitude An,m and phase φn,m.
  • Received field: The receiver’s reflected field is obtained for each unit cell, and the total field is the superposition of all unit-cell contributions.The received signal power is then expressed using the receiving-antenna aperture.
  • General formula: Theorem 1 follows by substituting the derived incident-field, reflected-field, and received-power expressions into the general formula.This establishes the general received-power expression used for subsequent scenarios.
  • Far-field specialization: When all unit cells share reflection coefficient Aejφ, the phase terms reduce to geometric progressions in the far-field derivation.Far-field transmitter and receiver positions are parameterized by d1, d2, and their angular coordinates.
  • Far-field specialization: The far-field received signal power is obtained from the geometric-progression result and is maximized when the transmitter and receiver directions satisfy reciprocal angular conditions.The maximizing condition is θr = θt and ϕr = ϕt + π.

APPENDIX C-PROOF OF PROPOSITION 2

The appendix derives the far-field intelligent-reflection expression by incorporating programmable unit-cell phase shifts into the general RIS received-power formula. The resulting power is maximized when the incident, reflected, and programmed phase gradients satisfy directional matching conditions.

  • Intelligent-reflection derivation: For far-field intelligent reflection, substituting Γn,m = Aejφn,m into the general expression incorporates each unit cell’s programmable phase shift.The phase-shift terms enter the spatial summation governing the received signal.
  • Intelligent-reflection derivation: The received power is obtained by summing the resulting geometric progression across the RIS unit cells.This produces the far-field intelligent-reflection formula used in the proposition.
  • Maximization condition: The intelligent-reflection power is maximized when the angular phase-gradient components plus δ1 and δ2 each equal zero.The conditions are sin θt cos ϕt + sin θr cos ϕr + δ1 = 0 and sin θt sin ϕt + sin θr sin ϕr + δ2 = 0.
  • Maximization condition: For a desired receiver position, substituting the programmable reflection coefficient into the general formula yields the corresponding maximizing phase condition.The derivation presents this condition in equations (11) and (12).
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