In this paper, we study the receiver performance with physical layer security in a Poisson field of interferers. We compare the performance in two deployment scenarios: (i) the receiver is located at the corner of a quadrant, (ii) the receiver is located in the infinite plane. When the channel state information (CSI) of the eavesdropper is not available at the transmitter, we calculate the probability of secure connectivity using the Wyner coding scheme, and we show that hiding the receiver at the corner is beneficial at high rates of the transmitted codewords and detrimental at low transmission rates. When the CSI is available, we show that the average secrecy capacity is higher when the receiver is located at the corner, even if the intensity of interferers in this case is four times higher than the intensity of interferers in the bulk. Therefore boundaries can also be used as a secrecy enhancement technique for high data rate applications.

INTRODUCTION

With the forecasted deployment of indoor ultra-dense wireless networks, it becomes important to develop models that consider the impact of boundaries in the performance analysis [1]–[۶]. It is well-known that close to the boundary, the connection probability degrades due to isolation [1], [5], but it improves in terms of interference [2], [4]. Analytical models considering finite deployment areas have so far been used to study spatial and temporal interference aspects [2]– [۴], optimize the base station density in cellular networks [2], assess millimeter-wave network performance [6], etc. Physical layer security (PLS) without exchanging secret keys was first proposed by Wyner [7], and refers to the protection of information messages against eavesdropping with the aid of channel coding. PLS would be well-suited for devices with light computational power, e.g., in certain types of sensor networks, where conventional security techniques fail [8]. Nevertheless, the impact of boundaries on connectivity and rate with PLS has so far received limited attention. A great deal of research has adopted a type of random geometric graphs, known as the secrecy graph [9]–[۱۱], and studied the Probability Distribution Function (PDF) of the in- and out-connectivity degree with PLS, the isolation probabilities, percolation threholds, etc. Another category of research considered the impact of interference on PLS, and applied stochastic geometry to study the performance for the typical user in networks with infinite extent [12]–[۱۵]. In [12], the trade-off between the connection and the secrecy probabilities in cellular systems is studied, and in [13] it is shown that cluttered environments and blockage can be helpful in meeting secrecy constraints. In [14], secure vehicleto-vehicle communication is considered; a subset of antennas is used for beamforming towards the receiver, while the rest send jamming signals towards other directions. In [15], relays forward the data between the sensors and the sinks, and their density is optimized for maximizing the average secrecy rate.