PaperlayerView exact revision on arXiv

Source-linked AI summary

Reconfigurable Intelligent Surfaces for Doppler Effect and Multipath Fading Mitigation

Ertugrul Basar

arXiv:1912.04080v2eess.SPcs.ITmath.IT

TL;DR

Mobile wireless links face fading and Doppler in propagation environments treated as uncontrollable. This paper investigates RIS-based methods for reconfiguring those environments and mitigating these effects. It states that Doppler can be eliminated in a specified RIS setup, while its results assume idealized specular RISs.

  • Problem

    Random propagation and interactions with surrounding objects contribute to deep fading and Doppler, challenging reliable connectivity in harsh environments.

    Source: §I · p. 1

  • Method

    The paper takes a bottom-up approach, developing RIS phase-control methods for simple and more complex propagation scenarios with interacting objects.

    Source: §I · p. 2, 1) Setup I (N ≤M) · p. 10, §VI · p. 15

  • Results

    When M = 0, the paper states that the Doppler effect can be totally eliminated through the specified RIS phase choice.

    Source: 2) Setup II (N > M) • · p. 13

  • Takeaways & Limitations

    RIS phase control can target Doppler from plain-object reflections or align reflected signals with the LOS path, depending on the setup.

    Source: 1) Setup I (N ≤M) · p. 10

    The results assume hypothetical RISs that create specular reflections with a single, very large conducting element.

    Source: §I · p. 3

Abstract

from arXiv · show

Extensive research has already started on 6G and beyond wireless technologies due to the envisioned new use-cases and potential new requirements for future wireless networks. Although a plethora of modern physical layer solutions have been introduced in the last few decades, it is undeniable that a level of saturation has been reached in terms of the available spectrum, adapted modulation/coding solutions and accordingly the maximum capacity. Within this context, communications through reconfigurable intelligent surfaces (RISs), which enable novel and effective functionalities including wave absorption, tuneable anomalous reflection, and reflection phase modification, appear as a potential candidate to overcome the inherent drawbacks of legacy wireless systems. The core idea of RISs is the transformation of the uncontrollable and random wireless propagation environment into a reconfigurable communication system entity that plays an active role in forwarding information. In this paper, the well-known multipath fading phenomenon is revisited in mobile wireless communication systems, and novel and unique solutions are introduced from the perspective of RISs. The feasibility of eliminating or mitigating the multipath fading effect stemming from the movement of mobile receivers is also investigated by utilizing the RISs. It is shown that rapid fluctuations in the received signal strength due to the Doppler effect can be effectively reduced by using the real-time tuneable RISs. It is also proven that the multipath fading effect can be totally eliminated when all reflectors in a propagation environment are coated with RISs, while even a few RISs can significantly reduce the Doppler spread as well as the deep fades in the received signal for general propagation environments with several interacting objects.

I. INTRODUCTION

The paper frames fading and Doppler in mobile communications as challenges of an uncontrollable propagation environment, then examines RISs as a way to reconfigure that environment. It introduces RIS-based mitigation methods and trade-offs while noting that its results assume idealized specular RISs.

I. INTRODUCTION

  • Deep fades, path loss, non-line-of-sight transmission, inter-symbol interference, and Doppler complicate reliable mobile connectivity in harsh propagation environments.The paper links these effects to random propagation and uncontrollable interactions between radio waves and surrounding objects.Source: §I · p. 1
  • RISs are electronically controlled electromagnetic surfaces that can modify propagation through functions such as absorption, anomalous reflection, and phase modification.They are presented as a means of making the environment an active entity in processing signals and transferring information.Source: §I · p. 2
  • RIS-assisted communication is distinguished by near-passive operation, reflection without amplification or added noise, ease of deployment, and reconfigurability.The paper identifies these characteristics as introducing communication-theoretic and system-design challenges.Source: §I · p. 2
  • The paper revisits multipath fading and Doppler mitigation with RISs, introducing methods that trade Doppler mitigation against average received-signal-strength maximization.It describes this as a bottom-up investigation from simple scenarios toward more sophisticated networks.Source: §I · pp. 2–3
  • The reported results assume hypothetical RISs that create specular reflections using a single, very large conducting element.The authors say the results can be adapted to practical RISs with many small elements, while practical application scenarios remain an open problem.Source: §I · p. 3

II. REVISITING MULTIPATH AND DOPPLER EFFECTS WITH SIMPLE CASE STUDIES

The section models a moving receiver with a direct and an object-reflected signal, focusing on short travel distances where amplitudes are nearly constant but phases vary. Their interference produces rapid envelope fluctuations and distinct Doppler components.

A. Multipath Fading Due to User Movement and A Reflector

  • The model combines a direct BS–MS signal with a signal reflected from an interacting object as the mobile station travels along a straight route.The analysis uses a unity-magnitude reflection coefficient with phase π for a large, smooth surface producing specular reflection.Source: A. Multipath Fading Due to User… · p. 3
  • For a short travel distance of a few wavelengths, the two rays have nearly constant amplitudes but rapidly varying phases due to receiver motion.The section uses an unmodulated carrier and a low-pass complex-equivalent signal to study the time-varying envelope and Doppler spectrum.Source: A. Multipath Fading Due to User… · p. 3
  • At fc = 3 GHz and V = 10 m/s, the two-ray signal fluctuates rapidly, with Doppler components at −100 Hz from the LOS path and 100 Hz from the IO.The variation is more significant when d1 is smaller, and the oscillation frequency is 2fD.Source: A. Multipath Fading Due to User… · p. 4, Figure 2 · p. 4

B. Eliminating Multipath Fading Due to User Movement with an RIS

A dynamically adjusted RIS reflection phase aligns reflected and direct signals, eliminating fading and keeping received magnitude constant in the considered setup. The direct path still produces a Doppler shift, while a practical multi-element RIS can align its elements’ signals with the line-of-sight signal.

B. Eliminating Multipath Fading Due to User Movement with an RIS

  • The RIS varies its reflection phase with user movement to align the reflected signal with the direct signal and maximize received magnitude.The described reflection is unit gain, with R(t) = e^jθ(t); the phase must be adjusted dynamically over time.Source: B. Eliminating Multipath Fading Due to… · p. 4
  • Time-varying RIS reflection eliminates fading and keeps the received signal magnitude constant in the considered scenario.Fig. 4(a) shows the maximized magnitude; the direct BS signal still produces a Doppler shift, as reflected in Fig. 4(b).Source: B. Eliminating Multipath Fading Due to… · pp. 4–5, Figure 4 · p. 4
  • The direct BS signal remains outside RIS control, so this scenario retains a −fD Doppler shift despite eliminating fade patterns.Fig. 4(b) presents the Doppler spectrum for the scenarios.Source: B. Eliminating Multipath Fading Due to… · pp. 4–5, Figure 4 · p. 4
  • For a practical multi-element RIS, phase choices θ_n(t) = 2π(d_Rn(t) − d_LOS(t))/λ align element signals with the LOS signal.The analysis assumes equal path loss across elements in the far field; detailed investigation of many-element RISs is left for future work.Source: B. Eliminating Multipath Fading Due to… · p. 5

C. Increasing Fading and Doppler Effects with An RIS

RIS phase control can deliberately reshape received magnitude and Doppler behavior. In a single-reflection NLOS link without an RIS, the signal magnitude stays fixed while motion still produces Doppler.

C. Increasing Fading and Doppler Effects with An RIS

  • 18 dB received-power variation is possible by co-phasing and out-phasing multipath components, while the normalized Doppler spectrum remains unchanged in this setup.Fig. 5 depicts the minimized received magnitude and Doppler spectra across scenarios.Source: C. Increasing Fading and Doppler… · p. 5, Figure 5 · p. 5
  • RIS phase adjustment can add Doppler components at desired shifts of 200 Hz and 400 Hz, producing faster fading in the received complex envelope.The described phase setting can increase the Doppler spread and reduce coherence time.Source: C. Increasing Fading and Doppler… · p. 5, Figure 6 · p. 5
  • Random RIS phases produce about 5 dB magnitude variation over a sampling distance of λ/32 m, although their effect on the Doppler spectrum is not very significant.The phase is selected randomly between 0 and 2π in each time interval.Source: C. Increasing Fading and Doppler… · p. 6, Figure 7 · p. 6

A. NLOS Transmission without An RIS

  • Without an RIS, a single reflected NLOS signal has fixed magnitude but retains a Doppler shift of fD due to mobile-station movement.The model assumes the direct link is blocked and other multipath components are absent.Source: A. NLOS Transmission without An RIS · p. 6, §III · p. 6

B. NLOS Transmission with An RIS

In a blocked-LOS link, adjusting the RIS reflection phase can eliminate Doppler without changing received magnitude. The multiple-reflector case without RIS control combines three Doppler components, yielding faster and more hostile fading.

B. NLOS Transmission with An RIS

  • With no direct BS–MS transmission, setting the RIS phase to compensate Doppler can eliminate the effect while leaving received-signal magnitude unchanged.The illustrated spectrum places the adjusted received signal at 0 Hz.Source: B. NLOS Transmission with An RIS · p. 6

IV. DOPPLER AND MULTIPATH FADING EFFECTS: CASE STUDIES WITH MULTIPLE REFLECTORS

  • The multiple-reflector analysis extends the models to networks with several interacting objects and examines RIS capabilities for fading and Doppler mitigation.Source: §IV · p. 6, Figure 10 · p. 7

A. Direct Signal and Two Reflected Signals without any RISs

B. Direct Signal and Two Reflected Signals with One or Two RISs

With one RIS and two reflected paths, phase selection trades received-signal strength against Doppler spread and fading. Out-phasing the uncontrollable reflection can nearly remove the fade pattern, while an optimal phase maximizes the envelope magnitude at each time.

1) One RIS

  • Method 1 aligns the RIS reflection with the stronger LOS path, yielding a high time-average envelope magnitude at the cost of faster variation and a larger Doppler spread.It removes the 100 Hz spectral component, but two components and a noticeable fade pattern remain because of the uncontrollable IO 2 reflection.Source: 1) One RIS · pp. 7–8
  • Method 2 aligns the RIS reflection with IO 2, increasing the relative 50 Hz component and producing more severe fading through destructive interference with the LOS signal.The paper also identifies this setting as a possible way to degrade an eavesdropper’s signal quality.Source: 1) One RIS · p. 8
  • Out-phasing the plain-IO reflection with Method 3 nearly mitigates fading and reduces Doppler spread, but residual variation remains when the paths have different lengths.For the illustrated setup, Method 3 reduces fade severity while retaining the same minimum magnitude at a lower time average.Source: 1) One RIS · pp. 8–9, Figure 12 · p. 8
  • For the considered setup, the optimal reflection phase maximizes the complex-envelope magnitude at every time, while Method 1 closely approximates its phase behavior with only minor magnitude degradation.Method 3 instead reduces fade severity while ensuring the same minimum magnitude, at the cost of a lower time average.Source: 1) One RIS · pp. 8–9, Figure 14 · p. 9

2) Two RISs

With two RISs, the authors co-phase both reflected signals with the LOS signal. This produces a constant-amplitude complex envelope and minimizes Doppler spread to a single component at −fD Hz.

2) Two RISs

  • Co-phasing the two RIS reflections with the LOS signal produces a constant-amplitude envelope and minimizes Doppler spread to a single component at −fD Hz.The RIS phases are set to align both reflected signals with the LOS path.Source: 2) Two RISs · p. 9

C. Two RISs without a LOS path

The general multiple-object analysis compares RIS phase strategies across cases with and without a LOS path, and with differing numbers of RIS-equipped and plain objects. The results show that RIS phase control can reduce deep fades and Doppler variation, with the balance between envelope magnitude and variation depending on the method and setup.

C. Two RISs without a LOS path

  • For two RISs without a LOS path, carefully adjusted reflection phases can totally eliminate the Doppler effect.The paper gives phase settings for each RIS in this case.Source: C. Two RISs without a LOS path · p. 9

D. The General Case with Multiple IOs and the Direct Signal

  • The general model has N RIS-coated and M plain interacting objects, with Doppler shifts depending on mobile speed and each reflected signal’s arrival angle.The authors assume the rays remain parallel during the short movement interval and use a reflection coefficient of −1 for plain objects.Source: D. The General Case with Multiple IOs… · pp. 9–10

1) Setup I (N ≤M)

  • For Setup I, the methods either align RIS reflections with the LOS path or assign RISs to plain IOs to reduce their reflections; the latter strategies search over C(M, N)N! assignments.Method 2 selects the assignment maximizing received magnitude, whereas Method 3 selects to minimize envelope variation over time.Source: 1) Setup I (N ≤M) · p. 10
  • In Setup II, where N > M, Method 2 searches RIS assignments to plain IOs while aligning remaining RISs with the LOS path; Method 3 assigns M RISs to the plain IOs and aligns the rest with the LOS path.The permutation selection considers P(N, M) possibilities for Method 2.Source: 1) Setup I (N ≤M) · p. 10
  • With N = 0, M = 10, the received signal has many Doppler components and severe deep fades; with N = 10, M = 0, aligning all RIS reflections to the LOS path gives a constant envelope and the maximum-magnitude benchmark.The latter case provides full control of the propagation environment in the considered setup.Source: 1) Setup I (N ≤M) · p. 11, Figure 17 · p. 11
  • In Setup I, Methods 2 and 3 reduce fade patterns more effectively than Method 1, with Method 3’s improvements most noticeable; for N = 7, M = 3 it nearly removes the three plain-IO Doppler components and yields an approximately constant envelope.Method 1 favors higher average magnitude, Method 2 offers a compromise, and Method 3 minimizes peak-to-peak variation, with slight average-magnitude degradation for Methods 2 and 3.Source: 1) Setup I (N ≤M) · pp. 11–12, Figure 20 · p. 12
  • For the Setup I comparisons, increasing the number of RISs reduces peak-to-peak envelope variation, especially for Methods 2 and 3; those methods slightly degrade the time-average magnitude.Method 1 can be preferred for maximizing the time-averaged magnitude, though the authors state that a complete mathematical proof is highly intractable.Source: 1) Setup I (N ≤M) · p. 12

E. The General Case with Multiple IOs and without the Direct Signal

For multiple interacting objects without a LOS path, the paper adapts its RIS-control methods to use the strongest available reflected path as the alignment reference. When there are more RISs than plain objects, the remaining RISs are aligned with the strongest RIS path for each assignment.

E. The General Case with Multiple IOs and without the Direct Signal

  • The no-LOS general case models N RISs and M plain interacting objects, whose reflections contribute to the received signal.The section applies the methods introduced for the corresponding LOS case with slight modifications.Source: E. The General Case with Multiple IOs… · p. 12
  • Without a LOS path, Method 1 aligns the available RISs to the strongest path, which may come from an RIS or a plain object and has the shortest radio path distance..Source: E. The General Case with Multiple IOs… · p. 12
  • When N > M, after selecting a permutation, the method aligns the strongest of the remaining N − M RISs as the reference and aligns the other N − M − 1 RISs to it.When M ≥ N, Methods 2 and 3 assign all N RISs to plain-object reflections as in the LOS case.Source: E. The General Case with Multiple IOs… · p. 12

1) Setup I (M ≥N) •

Setup I describes three RIS phase-selection methods for aligning reflected paths and estimating received samples.

1) Setup I (M ≥N) •

  • Method 1 aligns the RIS phases to the strongest path, whether that path comes from an RIS or a plain interacting object.The selected strongest path determines the phase rule, with the corresponding RIS held at zero phase when it is the strongest path.Source: 1) Setup I (M ≥N) • · p. 12
  • Method 2 follows its earlier procedure for M ≥ N, obtaining each permutation's received-signal sample r_n(t0) from (21).Source: 1) Setup I (M ≥N) • · p. 13
  • Method 3 likewise follows its earlier procedure for M ≥ N, obtaining each permutation's received-signal sample r_n(t0) from (21).Source: 1) Setup I (M ≥N) • · p. 13

2) Setup II (N > M) •

For N > M, the paper describes permutation-based RIS phase selection and reports how the methods perform without a LOS path. It also considers zero-LOS operation and practical RIS constraints.

2) Setup II (N > M) •

  • For Method 2, each permutation selects the strongest RIS among those not assigned to eliminate IO reflections, then aligns the remaining RIS phases.The selected permutation determines the RIS sets targeting IOs and remaining for alignment.Source: 2) Setup II (N > M) • · p. 13
  • Method 3 follows Method 2's procedures but uses a different procedure to determine the optimum permutation.Source: 2) Setup II (N > M) • · p. 13
  • Without a LOS path, all methods provide similar time-average envelope magnitude, while Methods 2 and 3 eliminate deep fades and Method 1 loses its average-magnitude advantage.The comparison covers the two stated setups, N = 3, M = 7 and N = 7, M = 3.Source: Figure 22 · p. 13, 2) Setup II (N > M) • · p. 13
  • When M = 0, Doppler can be totally eliminated because there is no LOS path; when N = 0, none of the methods applies.Source: 2) Setup II (N > M) • · p. 13
  • The proposed methods are heuristic; determining ultimately optimum RIS angles is beyond scope, and the global optimum appears intractable.Source: 2) Setup II (N > M) • · p. 13

A. Realistic RISs

  • A practical RIS with -1 dB reflection amplitude and phase range -150° to 140° slightly degrades envelope magnitude and shape; discrete phase shifts may degrade it further.Source: Figure 23 · p. 14, A. Realistic RISs · p. 14

B. Imperfect Knowledge of Doppler Frequencies

The paper examines Doppler-estimation errors and discrete-time RIS phase updates as practical constraints on fading mitigation. It reports that update speed becomes more demanding as Doppler frequency rises.

B. Imperfect Knowledge of Doppler Frequencies

  • The central processing unit needs Doppler-frequency knowledge for incoming rays to coordinate Methods 1–3 across multiple RISs.Source: B. Imperfect Knowledge of Doppler… · p. 14
  • With Doppler-estimation errors, U = 1 Hz caused no major envelope degradation, but U = 4 Hz caused significant distortion; Methods 2 and 3 appeared more reliable, though the system remained highly sensitive.The error model uses independent, identically distributed uniform errors in [-U, U], while the LOS Doppler shift is assumed perfectly known.Source: B. Imperfect Knowledge of Doppler… · p. 14

C. High Mobility & Discrete-Time RIS Phases

VI. CONCLUSIONS AND FUTURE WORK

  • The paper concludes that real-time tuneable RISs can eliminate or mitigate movement-induced multipath fading, with trade-offs between fade elimination and envelope magnitude.Amplitude/phase modulation and more practical path-loss and propagation models are identified as future research directions.Source: §VI · p. 15

APPENDIX

The appendix derives a condition for maximizing the received complex-envelope magnitude by tuning the RIS reflection phase. It uses a three-signal magnitude identity and groups the phase-dependent terms to obtain the condition.

APPENDIX

  • The received-envelope magnitude is maximized with respect to the RIS phase ξ1(t) = 2πfDt + θ1(t).The envelope includes the line-of-sight signal and two reflected signals.Source: APPENDIX · p. 15
  • A trigonometric identity expresses the magnitude of the sum of the line-of-sight and two reflected signals using their magnitudes and pairwise phase differences.Source: APPENDIX · p. 16
  • After dropping phase-independent terms, the derivation groups terms with θ1(t) and uses the harmonic addition theorem to obtain a maximizing condition.The appendix then states that the condition can be satisfied and completes the proof.Source: APPENDIX · p. 16

Related papers

Loading 1912.04080v2…