On the Beneficial Role of a Finite Number of Scatterers for Wireless Physical Layer Security

TL;DR

This paper demonstrates that a limited number of scatterers in a wireless environment can enable perfect secrecy against passive eavesdroppers without channel state information, highlighting the beneficial role of physical multipath effects.

Contribution

It introduces the concept that a finite number of scatterers can ensure perfect secrecy in wireless channels, providing explicit analysis for two scatterers and the impact of increasing scatterers.

Findings

Zero outage probability of secrecy capacity within certain SNR ranges.

Explicit relationship between SNRs, secrecy rate, and scattering parameters for two scatterers.

Increasing scatterers can still achieve perfect secrecy if the dominant component is strong.

Abstract

We show that for a legitimate communication under multipath quasi-static fading with a reduced number of scatterers, it is possible to achieve perfect secrecy even in the presence of a passive eavesdropper for which no channel state information is available. Specifically, we show that the outage probability of secrecy capacity (OPSC) is zero for a given range of average signal-to-noise ratios (SNRs) at the legitimate and eavesdropper's receivers. As an application example, we analyze the OPSC for the case of two scatterers, explicitly deriving the relationship between the average SNRs, the secrecy rate $R_s$ and the fading model parameters required for achieving perfect secrecy. The impact of increasing the number of scatterers is also analyzed, showing that it is always possible to achieve perfect secrecy in this scenario, provided that the dominant specular component for the legitimate channel is sufficiently large compared to the remaining scattered waves.