Secrecy Analysis of Random MIMO Wireless Networks Over <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$</tex-math> </inline-formula> Fading Channels

Abstract

In this paper, we investigate the secrecy performance of stochastic multiple-input multiple-output wireless networks over small-scale α-μ fading channels, where both the legitimate receivers and eavesdroppers are distributed with two independent homogeneous Poisson point processes. 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 and cumulative distribution functions 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.