Secrecy Analysis of Random MIMO Wireless Networks over $\alpha$-$\mu$ Fading Channels

TL;DR

This paper analyzes the secrecy performance of stochastic MIMO wireless networks over $\alpha$-$\mu$ fading channels, deriving key secrecy metrics for various user orderings and providing insights into the effects of network parameters.

Contribution

It introduces new analytical expressions for secrecy metrics in MIMO networks over $\alpha$-$\mu$ fading, considering both nearest and best user cases, and explores the impact of network parameters.

Findings

Closed-form expressions for COP, PNZ, and ergodic secrecy capacity.

Maximal number of best-ordered users under secrecy constraints.

Effects of fading parameters and network densities on secrecy performance.

Abstract

In this paper, we investigate the secrecy performance of stochastic MIMO wireless networks over small-scale $\alpha$-$\mu$ fading channels, where both the legitimate receivers and eavesdroppers are distributed with two independent homogeneous Poisson point processes (HPPPs). Specifically, accounting for the presence of non-colluding eavesdroppers, secrecy performance metrics, including the connection outage probability (COP), the probability of non-zero secrecy capacity (PNZ) and ergodic secrecy capacity, are derived regarding the $k$-th nearest/best user cases. The index for the $k$-th nearest user is extracted from the ordering, in terms of the distances between transmitters and receivers, whereas that for the $k$-th best user is based on the combined effects of path-loss and small-scale fading. In particular, the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the composite channel gain, for the $k$-th nearest and best user, are characterized, respectively. Benefiting from these results, closed-form representations of the COP, PNZ and ergodic secrecy capacity are subsequently obtained. Furthermore, a limit on the maximal number of the best-ordered users is also computed, for a given secrecy outage constraint. Finally, numerical results are provided to verify the correctness of our derivations. Additionally, the effects of fading parameters, path-loss exponent, and density ratios are also analyzed.