Secrecy Analysis of Random MIMO Wireless Networks over $α$-$μ$ Fading Channels

In this paper, we investigate the secrecy performance of stochastic MIMO 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 (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.