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Secure Vehicular Communications through Reconfigurable Intelligent Surfaces

Yun Ai, Felipe A. P. de Figueiredo, Long Kong, Michael Cheffena, Symeon Chatzinotas, Björn Ottersten

arXiv:2011.14899v2eess.SPcs.SYeess.SY

TL;DR

The paper examines secrecy outage in RIS-assisted vehicular communications when a passive eavesdropper is present, considering both V2V and V2I scenarios. It derives SOP expressions for those scenarios and reports improved secrecy performance with RIS assistance, while describing how RIS element count and phase shifting affect the results.

  • Problem

    The paper examines secrecy outage in RIS-assisted V2V and V2I communications under passive eavesdropping.

    Source: §I · p. 1

  • Method

    The analysis treats RIS as a relay in V2V and as the receiver in V2I, derives SOP expressions, and uses RIS-SNR statistics that avoid reliance on the CLT for small element counts.

    Source: §I · p. 1, B. V2V Communications · p. 3, C. V2I Communications · p. 4

  • Results

    In V2V, SOP improves as RIS elements increase but eventually stagnates with increasing transmit SNR, while V2I SOP improves with element count even when legitimate-link attenuation is greater.

    Source: §IV · p. 4

  • Takeaways & Limitations

    The paper reports that increasing RIS element count can improve secrecy performance in both V2V and V2I, and that imperfect phase shifting adversely affects RIS-aided performance.

    Source: §IV · p. 4

Abstract

from arXiv · show

Reconfigurable intelligent surfaces (RIS) is considered as a revolutionary technique to improve the wireless system performance by reconfiguring the radio wave propagation environment artificially. Motivated by the potential of RIS in vehicular networks, we analyze the secrecy outage performance of RIS-aided vehicular communications in this paper. More specifically, two vehicular communication scenarios are considered, i.e., a vehicular-to-vehicular (V2V) communication where the RIS acts as a relay and a vehicular-to-infrastructure (V2I) scenario where the RIS functions as the receiver. In both scenarios, a passive eavesdropper is present attempting to retrieve the transmitted information. Closed-form expressions for the secrecy outage probability (SOP) are derived and verified. The results demonstrate the potential of improving secrecy with the aid of RIS under both V2V and V2I communications.

I. INTRODUCTION

RIS can shape propagation through passive reflecting elements, while physical-layer security uses channel fading to protect communications against eavesdropping. This paper examines secrecy outage in RIS-assisted vehicular V2V and V2I settings, extending prior RIS-security work to those scenarios.

I. INTRODUCTION

  • RIS uses controlled passive reflecting elements to adapt electromagnetic waves to the propagation environment and beamform signals toward intended users.The paper describes the surface as functioning like a reconfigurable lens or mirror.Source: §I · p. 1
  • Prior work studied RIS secrecy-rate beamforming for mmWave systems, SOP for RIS-aided systems including NOMA, and average secrecy capacity in vehicular networks.The cited examples are,, and, respectively.Source: §I · p. 1
  • The paper analyzes secrecy outage under passive eavesdropping in V2V and V2I scenarios, with the RIS assisting blocked vehicles in V2V and serving as the receiver in V2I.The V2I receiver is described as infrastructure close to the RIS for robust transmission of messages to intelligent transport infrastructure.Source: §I · p. 1
  • Its contributions include analysis of two RIS configurations, results valid for small RIS element counts without relying on the central limit theorem, and accurate or exact RIS-SNR statistics.The paper also presents the statistics as potentially useful for other RIS-related analyses.Source: §I · p. 1

II. CHANNEL AND SYSTEM MODELS

The paper studies secrecy outage for RIS-assisted V2V and V2I communications using the classic Wyner wiretap model. Figure 1 illustrates the considered model.

II. CHANNEL AND SYSTEM MODELS

  • The system-model section considers secrecy outage in both RIS-assisted V2V and V2I communications.Source: §II · p. 2
  • The analysis uses the classic Wyner wiretap model.Source: §II · p. 2
  • Figure 1 illustrates the considered wiretap model for the two communication scenarios.Source: §II · p. 2

A. V2V Communications

In the V2V case, an RIS relays communication between blocked vehicles while a nearby eavesdropper listens to the source. The analysis models the RIS channels under ideal and imperfect phase shifting and develops signal statistics without requiring a large element count.

A. V2V Communications

  • A source vehicle communicates with a blocked destination through an N-element RIS, while an eavesdropper near the source overhears the transmission.Vehicles are modeled with single antennas for simplicity.Source: A. V2V Communications · p. 2
  • The received destination signal is modeled through the RIS, whose diagonal reflection matrix combines the source-to-RIS and RIS-to-destination channel gains.The channel vectors are expressed using link amplitudes and phases, with independent Rayleigh-distributed amplitudes for each RIS hop.Source: A. V2V Communications · p. 2
  • With perfect CSI at the RIS, ideal phase shifting is assumed to maximize the destination's instantaneous SNR.Source: A. V2V Communications · p. 2
  • The analysis approximates the destination-SNR statistics without the CLT, addressing small N and independent, non-identically distributed channel amplitudes across the two RIS links.The passage notes that the CLT approximation becomes inaccurate when N is not large and that the two propagation links are different.Source: A. V2V Communications · p. 2
  • The imperfect-phase case considers uniformly distributed phase errors, while the source-to-eavesdropper link is modeled as double-Rayleigh fading.The double-Rayleigh model represents cascaded scattering around the two vehicles' local environments.Source: A. V2V Communications · pp. 2–3

B. V2I Communications

In the V2I scenario, the RIS is deployed beside the infrastructure RF receiver and the pair is treated as one receiver. The destination-SNR statistics use an accurate approximation where an exact closed form is unavailable for more than two elements.

B. V2I Communications

  • The V2I infrastructure receiver comprises an RIS and RF receiver close enough that their mutual channel attenuation is ignored in the analysis.The RIS and RF receiver are treated together as a single receiver.Source: B. V2I Communications · p. 3
  • For the destination SNR, the received-signal statistic is equivalent to a SIMO system with equal-gain combining, whose exact closed-form solution is unavailable for N greater than two.Source: B. V2I Communications · p. 3
  • The paper presents a close approximation for the destination-SNR PDF and CDF and gives the eavesdropper-SNR PDF and CDF for V2I.Source: B. V2I Communications · p. 3

A. Secrecy Outage Probability (SOP)

The section defines instantaneous secrecy rate from the main-link and eavesdropper SNRs, then uses a fixed target rate to define secrecy outage.

A. Secrecy Outage Probability (SOP)

B. V2V Communications

For V2V, the paper gives SOP expressions for perfect RIS phase shifting and uniformly distributed phase-estimation error, and also describes an alternative Mellin-transform evaluation.

B. V2V Communications

  • For independent γD and γE, Parseval’s formula for the Mellin transform provides an alternative evaluation of SOP.The Mellin transform notation uses an integration path L1 from c − j∞ to c + j∞.Source: B. V2V Communications · p. 3
  • Lemma 1 gives the V2V SOP for perfect RIS phase shifting.Source: B. V2V Communications · p. 3
  • Lemma 2 gives the V2V SOP when RIS phase-estimation error is uniformly distributed.Source: B. V2V Communications · p. 3
  • The V2V material identifies Fig. 3 as SOP versus transmit power Ps and notes a case with varying numbers of RIS elements.The supplied passages do not state the plotted outcome.Source: Figure 3 · p. 4, B. V2V Communications · p. 4

C. V2I Communications

For V2I, the paper presents an SOP evaluation under independent destination and eavesdropper SNRs and points to Appendix D for its proof.

C. V2I Communications

IV. NUMERICAL RESULTS AND DISCUSSIONS

Numerical results show that adding RIS elements improves secrecy outage performance in both V2V and V2I. In V2V, increasing transmit SNR eventually stops helping, while the V2I large-N trend depends on distance rather than transmission power.

IV. NUMERICAL RESULTS AND DISCUSSIONS

  • Under V2V and V2I, adding RIS elements improves SOP; V2V gains eventually stagnate with transmit SNR, while the V2I large-N log-SOP slope depends on distance, not power.The V2I result is shown in Fig. 4.Source: Figure 4 · p. 4, §IV · p. 4
  • The gap between perfect and random RIS phase shifting marks the upper and lower secrecy-outage limits, respectively, and shows the adverse effect of imperfect phase shifting.Increasing N can improve the V2V performance bound that further transmit-power increases cannot raise.Source: §IV · p. 4

APPENDIX A: PROOF OF PROPOSITION 1

  • A is approximated by a Gamma random variable whose shape and scale match its first two moments; squaring it yields the statistics of γ_D.The moment-matching step equates the first and second moments of A and the Gamma approximation.Source: Appendix A · pp. 4–5

APPENDIX B: PROOF OF PROPOSITION 2

  • The V2V received-signal distance is modeled as N random-walk steps with lengths r_n, products of independent non-identically distributed Rayleigh variables; Kluyver’s result supports the exact γ_D PDF and CDF.The random-step directions are uniform.Source: Appendix B · p. 5

APPENDIX C: PROOF OF LEMMA 1

Appendix C derives the exact SOP using a bivariate Fox H-function representation. Appendix D obtains the closed-form SOP for the V2I scenario.

APPENDIX C: PROOF OF LEMMA 1

  • The SOP is rewritten as a double contour integral and expressed exactly as a bivariate Fox H-function.The derivation uses Mellin transforms and represents the relevant Meijer G-functions through contour integrals.Source: Appendix C · p. 5

APPENDIX D: PROOF OF LEMMA 2

  • For V2I, expanding the incomplete Gamma function and rewriting the resulting integral leads to the closed-form SOP in Lemma 2.The derivation also uses a series representation of [(1 + x)^Θ − 1]^k and Meijer G-functions.Source: Appendix D · p. 5
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