  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.
