Physical Layer Security in <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math> </inline-formula>-Tier Heterogeneous Cellular Networks Over Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$ </tex-math> </inline-formula> Channel During Uplink and Downlink Phases

Abstract

In this paper, we study the physical layer security performance under K-tier heterogeneous cellular network during both downlink and uplink phases. Especially, Nakagami-m fading is used to capture the characteristics of line-of-sight (LoS) propagation. Using stochastic geometry tool, tractable expressions of connection probability are derived accordingly. Upper-bound expression of secrecy probability is derived through only considering the closest eavesdropper, whose rationality is validated theoretically. While lowerbound expression of secrecy probability is derived through using Jensen's inequality. Moreover, we demonstrate the effects of parameter setting upon network connection and secrecy performances through numerical simulation. For example, Rayleigh fading and LoS scenario (an extreme Rician case) can be regarded as special cases of this paper through properly setting m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> value. Connection probability is insensitive to BS density during downlink phases, while it is an increasing function of BS density during the uplink phase. We also find that connection probability is an increasing function of m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> value. Secrecy probability is insensitive to m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> value, while it is an increasing function of BS density during both downlink and uplink phases.