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Reconfigurable Intelligent Surfaces in 6G: Reflective, Transmissive, or Both?

Shuhao Zeng, Hongliang Zhang, Boya Di, Yunhua Tan, Zhu Han, H. Vincent Poor, Lingyang Song

arXiv:2102.06910v1cs.ITmath.IT

TL;DR

Prior work has focused on reflective RISs, while transmissive and hybrid types have been less investigated. This paper derives a sum-rate bound for a downlink multi-user network and compares the three types across UE distributions. Its results identify conditions where hybrid RISs are inferior or outperform the other types.

  • Problem

    Prior RIS research has focused on reflective surfaces, while transmissive and hybrid RISs have received less investigation.

    Source: §I · p. 1

  • Method

    The paper derives a system sum-rate bound and analyzes reflective, transmissive, and hybrid RISs in a downlink multi-user network.

    Source: §I · p. 1

  • Results

    When both BS and UEs are far from the RIS, hybrid RISs are inferior; with sufficiently many elements, hybrid RISs outperform the other types for arbitrary UE distributions.

    Source: C. Hybrid versus transmissive · p. 4, §V · p. 4

  • Takeaways & Limitations

    RIS type selection depends on UE distribution, and sufficiently large RISs favor the hybrid type across arbitrary distributions.

    Source: A. Reflective versus transmissive · p. 3, C. Hybrid versus transmissive · p. 4

Abstract

from arXiv · show

Reconfigurable intelligent surfaces (RISs) have attracted wide interest from industry and academia since they can shape the wireless environment into a desirable form with a low cost. In practice, RISs have three types of implementations: 1) reflective, where signals can be reflected to the users on the same side of the base station (BS), 2) transmissive, where signals can penetrate the RIS to serve the users on the opposite side of the BS, and 3) hybrid, where the RISs have a dual function of reflection and transmission. However, existing works focus on the reflective type RISs, and the other two types of RISs are not well investigated. In this letter, a downlink multi-user RIS-assisted communication network is considered, where the RIS can be one of these types. We derive the system sum-rate, and discuss which type can yield the best performance under a specific user distribution. Numerical results verify our analysis.

I. INTRODUCTION

RISs shape the wireless environment through reflection, transmission, or both, but prior research has focused on reflective RISs. This letter studies a downlink multi-user network and analyzes RIS type selection under different UE distributions.

I. INTRODUCTION

  • RISs can reflect signals toward users on the BS’s side, transmit them toward users on the opposite side, or do both.The paper frames RISs as surfaces that shape the wireless environment and improve receiver signal quality.Source: §I · p. 1
  • Existing research focuses on reflective RISs, leaving transmissive and hybrid types less investigated.The cited examples concern reflective RIS-assisted networks and channel-estimation or transmission methods.Source: §I · p. 1
  • The paper derives a sum-rate upper bound and analyzes which RIS type is optimal under different UE distributions.It considers a downlink multi-user network with one BS and any of the three RIS types.Source: §I · p. 1

A. Scenario Description

  • The network has one BS and UEs in reflection and transmission zones on opposite sides of the RIS.The system model assigns one antenna to each UE and describes the RIS as reflecting or penetrating BS signals toward them.Source: A. Scenario Description · p. 1

B. Reconfigurable Intelligent Surfaces

The RIS consists of tunable sub-wavelength elements whose electromagnetic response varies with the applied PIN-diode state. The three RIS types differ in whether elements reflect, transmit, or split energy between both paths.

B. Reconfigurable Intelligent Surfaces

C. Channel Model

The channel model represents each BS-to-UE link as a sum of RIS-mediated paths. Those paths account for fading, path loss, RIS response, and the geometry of signal incidence and departure.

C. Channel Model

  • The BS-to-UE channel matrix H has entries h(s,k), the channel gain from BS antenna k to UE s, and the direct link is assumed blocked.Each link is composed of MN RIS-mediated channels, one through each RIS element.Source: C. Channel Model · p. 2
  • Each RIS-mediated channel includes fast fading, path loss, and the RIS response.Small-scale fading coefficients have mean zero and variance one and are assumed independent across RIS-based channels.Source: C. Channel Model · p. 2
  • The RIS channel response depends on whether the BS and UE are on the same side of the RIS or separated by it.The model also accounts for the incident angle through a cosine term; departure angle has no influence on one RIS-based channel.Source: C. Channel Model · p. 2
  • The path-loss model includes wavelength, antenna gain, a path-loss exponent, and RIS element radiation patterns.The patterns describe arrival from a BS antenna and departure toward a UE.Source: C. Channel Model · p. 2
  • The small-scale fading distribution may be arbitrary.Hardware-related constants are included in the channel model.Source: C. Channel Model · p. 2

III. ANALYSIS ON SUM RATE

The analysis uses an upper bound on capacity to compare RIS types, with channel statistics and power allocation specified for the comparison. It derives conditions under which performance varies with UE distribution and RIS size.

III. ANALYSIS ON SUM RATE

  • When the number of RIS elements is large and phase shifts are deterministic, the channel gain follows a complex normal distribution.The proof invokes the central limit theorem for independently identically distributed small-scale fading across RIS elements.Source: §III · p. 2
  • The system capacity is upper bounded, and that bound is tight when the eigenvalues of HHH are equal.The paper notes this condition can be obtained by optimizing phase shifts to maximize the effective rank of H [11].Source: §III · pp. 2–3
  • As the number of transmission-zone UEs increases, transmissive sum rate rises while reflective sum rate declines.The comparison uses the capacity upper bound as its performance metric and assumes equal UE-to-RIS distances.Source: §III · p. 3
  • For transmissive or reflective RISs, users on the unsupported side receive no power, while supported users share power equally.For hybrid RISs, power is allocated equally within each side, with the allocation between sides optimized.Source: §III · p. 3
  • The type-selection analysis assumes equal distances from UEs in both zones to the RIS; unequal distances are left for future work.Long-term performance is evaluated using path loss rather than instantaneous small-scale fading for power allocation.Source: §III · p. 3

A. Reflective versus transmissive

As the number of UEs in the transmission zone increases, transmissive sum-rate rises while reflective sum-rate falls. Under the stated isotropic-pattern condition, their performance crosses at a unique UE distribution.

A. Reflective versus transmissive

  • As ST increases, transmissive sum-rate increases while reflective sum-rate decreases.The transmissive trend is shown by the derivative of CT over (1, S −1); the reflective trend is stated alongside it.Source: A. Reflective versus transmissive · p. 3
  • With approximately isotropic RIS power radiation patterns, the reflective and transmissive types have a unique equal-performance UE distribution.The comparison considers the endpoint relationships CT(1) − CR(1) ≤ 0 and CT(S −1) − CR(S −1) ≥ 0.Source: A. Reflective versus transmissive · p. 3
  • The transmissive type outperforms the reflective type when ST exceeds their unique equal-performance UE distribution.The crossover follows from the opposite monotonic trends of the two sum-rates.Source: A. Reflective versus transmissive · p. 3
  • The hybrid comparison is divided around the UE distribution where reflective and transmissive performance is equal.The analysis compares the hybrid type with whichever of the reflective and transmissive types has the higher sum-rate.Source: A. Reflective versus transmissive · p. 3

B. Hybrid versus reflective

Under a sufficiently high received SNR, the reflective–hybrid rate difference decreases as ST increases. Which type performs better depends on the endpoint comparisons and the UE distribution.

B. Hybrid versus reflective

  • Under sufficiently high received SNR, the derivative of reflective sum-rate is much larger than that of hybrid sum-rate.The condition is that each UE's received SNR with the hybrid RIS is sufficiently high.Source: B. Hybrid versus reflective · p. 3
  • The reflective–hybrid sum-rate difference decreases with ST.The argument uses the high-SNR derivative relationship and the decrease of reflective sum-rate with ST.Source: B. Hybrid versus reflective · pp. 3–4
  • If reflective exceeds hybrid at ST=1 and the endpoint difference at the reflective–transmissive crossover is negative, reflective leads at low ST while hybrid leads above S(a)T.The stated comparison applies when CR(1) − CH(1) ≥ 0 and Ceq − CH(S(c)T) < 0.Source: B. Hybrid versus reflective · p. 4
  • When reflective is already below hybrid at ST=1, the reflective–hybrid difference cannot become positive at the crossover because it decreases with ST.The paper identifies a unique UE distribution where reflective and hybrid performance is equal when such a crossover applies.Source: B. Hybrid versus reflective · p. 4

C. Hybrid versus transmissive

The preferred RIS type depends on the UE distribution and network geometry, but with sufficiently many elements the hybrid type is best for any UE distribution. When both BS and UEs are far from the RIS, hybrid is inferior to a single-function type.

C. Hybrid versus transmissive

  • The hybrid–transmissive sum-rate difference increases with ST, while the detailed effects of ST and ST = S −1 on their performance are omitted.The paper summarizes the optimal-type conditions in Table I, with T, R, and H denoting transmissive, reflective, and hybrid.Source: C. Hybrid versus transmissive · p. 4
  • RIS element count and the BS–RIS and RIS–UE distances can change which RIS type is optimal.The paper identifies these parameters as affecting the relationships among the compared sum-rates.Source: C. Hybrid versus transmissive · p. 4
  • For a given number of RIS elements, hybrid is always inferior to reflective or transmissive when both BS and UEs are far from the RIS.Source: C. Hybrid versus transmissive · p. 4
  • When MN > E0^2max(ER,ET), the hybrid type is better than both alternatives for any UE distribution.The threshold combines the conditions for hybrid to outperform the transmissive and reflective types.Source: C. Hybrid versus transmissive · p. 4

V. SIMULATION RESULTS

Simulations support the derived sum-rate bound and show that RIS performance depends on UE distribution and RIS size.

V. SIMULATION RESULTS

  • The simulation uses a 12-antenna BS transmitting at 43 dBm, with RIS element power-radiation parameters ϵr = 1 and ϵt = 0.95.The stated setup also uses a 0.1 m wavelength and −96 dBm noise variance.Source: §V · p. 4
  • The simulated capacity is upper-bounded by the theoretical bound for all three RIS types, and the gap is small enough to justify using the bound as a performance metric.The simulated data rate is based on 100 Monte Carlo simulations.Source: §V · p. 4
  • As the number of UEs in the transmission zone increases, reflective capacity decreases while transmissive sum-rate increases; at 200 m for both distances, hybrid is inferior to either type.When both the UEs and BS are closer to the RIS, the hybrid advantage over the other types becomes more significant.Source: §V · p. 4
  • With more RIS elements, the hybrid advantage grows because it schedules more UEs, and above a sufficiently large element count it outperforms the other types for any UE-zone size.The reported comparison varies RIS size and the number of UEs in the transmission zone.Source: §V · p. 4

VI. CONCLUSION

The conclusion identifies two deployment-dependent outcomes: hybrid RISs can be inferior at large distances, but superior beyond an element-count threshold.

VI. CONCLUSION

  • When both the BS and UEs are far from the RIS, the hybrid type is inferior to either the reflective or transmissive type.The conclusion also states that when both distances are 200 m, hybrid is inferior to the other two types.Source: §VI · p. 4
  • Once the number of RIS elements exceeds the derived threshold, the hybrid type is better than the other types for any UE distribution.Source: §VI · p. 4
  • The paper concludes from analysis and simulation of a downlink network with one BS and multiple UEs.Source: §VI · p. 4

APPENDIX A PROOF OF REMARK 2

The appendices provide an approximation-based argument for Remark 2 and a distance-based comparison supporting Proposition 4.

APPENDIX A PROOF OF REMARK 2

  • The proof approximates E1 and E2 as zero under near-equal reflection and transmission power; its E2 approximation also assumes ST/S < 1 and sufficiently high received SNR.Source: Appendix A · p. 5

APPENDIX B PROOF OF PROPOSITION 4

  • For large BS–RIS and UE–RIS distances, the proof argues that the hybrid type is inferior to the transmissive type because the distance-dependent term makes CH − CT < 0.Source: Appendix B · p. 5

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