PaperlayerView exact revision on arXiv

Source-linked AI summary

Secret Key Generation Rates for Line of Sight Multipath Channels in the Presence of Eavesdroppers

Amitha Mayya, Arsenia Chorti, Rafael F. Schaefer, Gerhard P. Fettweis

arXiv:2404.16481v1eess.SP

TL;DR

Constrained IIoT devices motivate low-complexity security, and assessing SKG from RSS requires accounting for LoS multipath and possible Eve correlations. The paper derives RSS distributions by multipath resolvability and numerically estimates MI for 3GPP LoS channels. The estimates show lower MI when MPCs resolve into separate delay bins, and are used to bound SKG rates.

  • Problem

    Constrained IIoT devices need resilient, trustworthy, low-complexity security, and realistic SKG assessment must account for correlations between legitimate users and potential eavesdroppers.

    Source: §I · pp. 1–2

  • Method

    The paper derives RSS distributions according to multipath resolvability and numerically estimates MI for the 3GPP TDL-E LoS model using the LNC estimator.

    Source: §III · p. 3, §V · p. 5, §IV · p. 5

  • Results

    When MPCs resolve into separate delay bins, variance and estimated MI decrease; unresolved components yield higher variance and MI.

    Source: §V · p. 5, §IV · p. 5

  • Takeaways & Limitations

    The estimated MI provides a benchmark for upper-bounding SKG rates, and MPC resolvability is an important channel condition in those estimates.

    Source: §I · p. 2, §V · p. 5

    The numerical channel models cannot realistically account for correlations in Alice–Bob and Alice–Eve observations, so the paper evaluates MI upper bounds and leaves lower bounds for future work.

    Source: F. Achievable SKG Rates · p. 5

Abstract

from arXiv · show

In this paper, the feasibility of implementing a lightweight key distribution scheme using physical layer security for secret key generation (SKG) is explored. Specifically, we focus on examining SKG with the received signal strength (RSS) serving as the primary source of shared randomness. Our investigation centers on a frequency-selective line-of-sight (LoS) multipath channel, with a particular emphasis on assessing SKG rates derived from the distributions of RSS. We derive the received signal distributions based on how the multipath components resolve at the receiver. The mutual information (MI) is evaluated based on LoS 3GPP channel models using a numerical estimator. We study how the bandwidth, delay spread, and Rician K-factor impact the estimated MI. This MI then serves as a benchmark setting bounds for the SKG rates in our exploration.

I. INTRODUCTION

Low-complexity security is needed for constrained IIoT devices, while eavesdropper correlation can depend on multipath effects rather than distance alone. This work characterizes LoS multipath RSS and studies how channel conditions affect MI and SKG-rate bounds.

I. INTRODUCTION

  • In IIoT, constrained computation and memory motivate resilient, trustworthy, low-complexity security, and quantum security is also a stated need.Physical-layer security uses wireless-channel properties and can complement cryptographic solutions.Source: §I · p. 1
  • SKG derives a shared secret from correlated channel observations through randomness extraction, quantization, information reconciliation, and privacy amplification.The stages convert observations into bits, correct mismatches, and address potential leakage.Source: §I · p. 1
  • Reciprocal fading gives legitimate users a common randomness source during channel coherence time, while observations beyond that time are treated as uncorrelated.The passage notes that this depends on the reciprocity of the legitimate users’ channels.Source: §I · pp. 1–2
  • The half-wavelength decorrelation assumption from Jake’s model is valid only with infinite uniformly distributed scattering, motivating attention to real-world Eve correlations.The paper upper-bounds secret key rates using conditional min-entropy to ensure confidentiality.Source: §I · p. 2
  • The study characterizes LoS multipath channel distributions and examines how bandwidth, delay spread, and Rician K-factor affect MI estimated from RSS.The resulting MI is used to bound SKG rates.Source: §I · p. 2

II. SYSTEM MODEL

Alice and Bob exchange constant-modulation complex chirps in TDD while Eve eavesdrops. The model uses reciprocal LoS channels for Alice and Bob, distinct Eve channels, and filtered received signals to obtain RSS.

II. SYSTEM MODEL

  • Alice and Bob exchange constant-modulation complex chirps in time division duplex, while Eve constantly eavesdrops on the exchange.The chirp has a nearly flat, well-defined power spectral density.Source: §II · p. 2
  • Alice and Bob’s channels are approximately reciprocal, hA(t) ≈ hB(t), and differ from Eve’s channel, hE(t).Source: §II · p. 2
  • The model assumes independently distributed multipath components with LoS magnitudes following a Rician distribution.The channel response parameters include path attenuation, phase shift, and delay.Source: §II · p. 2
  • Framewise low-pass filtering with cut-off frequency Bw/2 extracts shared channel randomness from the frequency-selective multipath.The measured RSS uses the filter impulse response and time averaging.Source: §II · p. 3

III. RECEIVED SIGNAL STRENGTH DISTRIBUTION

The RSS distribution is built from received-power measurements by modeling channel attenuation and receiver noise separately, then combining their distributions.

III. RECEIVED SIGNAL STRENGTH DISTRIBUTION

  • RSS denotes received-power measurements, whose variation reflects frequency-selective channel attenuation and receiver noise.Source: §III · p. 3
  • Channel attenuation and receiver noise are treated as independent processes, with their power distributions combined to obtain the received-power distribution.Source: §III · p. 3
  • The passage evaluates Alice’s RSS distribution and states that Bob’s and Eve’s distributions are similar under the LoS channel model.Source: §III · p. 3

A. Channel Power Distribution When Multipaths Cannot be Resolved

When multipath components arrive within a signal period, they cannot be individually resolved; the resulting multipath amplitude has a Rician distribution.

A. Channel Power Distribution When Multipaths Cannot be Resolved

B. Channel Power Distribution When All Multipaths Resolve Separately

When multipath components resolve separately, the received amplitude follows a Rician model with variance parameter σ². Its normalized power is described by a non-central chi-square distribution.

B. Channel Power Distribution When All Multipaths Resolve Separately

C. Channel Power Distribution for Hybrid Resolution of Multipaths

The hybrid-resolution model groups multipath components into delay bins, with the first bin containing the direct path and the remaining bins represented separately. The channel distribution combines the first-bin and remaining-bin distributions using a Welch-Satterwaite approximation and convolution.

C. Channel Power Distribution for Hybrid Resolution of Multipaths

D. Noise Power Distribution

Noise power is modeled as a distribution that depends on the number of receiver samples. That sample count is determined by the receiver sampling rate and frame resolution.

D. Noise Power Distribution

E. Total Power Distribution

The total RSS power distribution is formed by combining the channel-power and noise-power distributions through convolution. The paper illustrates this construction for unresolved, separately resolved, and hybrid multipath cases.

E. Total Power Distribution

F. Achievable SKG Rates

The section bounds achievable SKG rates using mutual information (MI), but evaluates the MI numerically because the joint distributions are out of scope. It reports upper bounds and leaves lower-bound evaluation for future work.

F. Achievable SKG Rates

  • The MI between Alice and Bob is used as a quantity bounding the secret-key rates.The section introduces the MI between the random variables A and B.Source: F. Achievable SKG Rates · p. 5
  • The joint Alice–Bob and Alice–Eve probability densities and their MI integral are out of scope, so numerical estimators are used.The marginal densities are obtained, and the Eve marginal is assumed to match the Alice and Bob marginals.Source: F. Achievable SKG Rates · p. 5
  • Channel-model simulations cannot realistically account for Eve’s correlation with Alice and Bob, so the analysis evaluates MI upper bounds and defers lower bounds.The passage identifies Eve’s MI with Alice and Bob as strongly dependent on observation correlations.Source: F. Achievable SKG Rates · p. 5

IV. NUMERICAL ESTIMATION

Numerical MI estimates for the 3GPP TDL-E LoS channel show that bandwidth, delay spread, and SNR affect MI, while K-factor has little impact. The results link these trends to how multipath components resolve into receiver delay bins.

IV. NUMERICAL ESTIMATION

  • The study simulates the 14-path TDL-E LoS profile and estimates MI with the local non-uniformity correction estimator across bandwidth, delay-spread, and K-factor settings.A complex chirp waveform is convolved with the channel impulse responses, noise is added, and filtered received powers are used for the SKG protocol.Source: §IV · p. 5
  • For constant 50 ns delay spread and 30 dB K-factor, MI decreases as bandwidth increases, then remains constant after 300 MHz as MPCs resolve into different delay bins, yielding constant variance.Source: §IV · p. 5
  • At 200 MHz bandwidth and 30 dB K-factor, lower delay spreads yield higher MI; beyond 150 ns, MI remains constant as all multipath components are resolved and variance stays constant.Source: §IV · p. 5
  • Increasing SNR increases MI, while increasing bandwidth or delay spread decreases it; for a given delay spread, MI remains constant across K-factors.The authors attribute the K-factor result to reciprocity: Alice and Bob observe similar K-factors, which they describe as shared, nonrandom information.Source: §IV · p. 5
  • MI, the upper bound for the evaluated SKG rate, depends on filterbank bandwidth, delay spread, SNR, and how multipath components resolve at the receiver.The authors conclude that users must be channel-aware to implement SKG and evaluate its rates.Source: §IV · p. 5

V. CONCLUSION

The conclusion attributes MI changes to multipath resolvability: increasing bandwidth and delay spread reduces MI, while K-factor itself has no impact. The work evaluates upper bounds and identifies eavesdropper-correlation effects on lower bounds as future work.

V. CONCLUSION

  • MI decreases as bandwidth and delay spread increase, but is unaffected by K-factor; unresolved paths increase RSS-distribution variance and MI, whereas separately resolved paths decrease both.The conclusion describes numerical MI evaluation for the TDL-E model and identifies bandwidth and delay spread of the receiver filterbank as determining multipath resolution.Source: §V · p. 5
  • Figure 5 fixes K at 30 dB and varies bandwidth at 50 ns delay spread in the top panel, or delay spread at 200 MHz bandwidth in the bottom panel.The plotted estimates use different SNRs.Source: Figure 5 · p. 6
  • Figure 6 fixes SNR at 33 dB and compares K-factor settings for varying bandwidth in the top panel and varying delay spread in the bottom panel.The top panel holds delay spread at 50 ns; the bottom holds bandwidth at 200 MHz.Source: Figure 6 · p. 6
  • The analysis leaves evaluation of lower SKG-rate bounds under eavesdropper correlation for future work.The conclusion says the work aims to extend its analysis to experimental datasets as well.Source: §V · pp. 5–6
Loading 2404.16481v1…