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

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.