A technique is presented to characterize the Signal-to-Interference-plus-Noise Ratio (SINR) of a representative link with a multiantenna linear Minimum-Mean-Square-Error receiver in a wireless network with transmitting nodes distributed according to a doubly stochastic process, which is a generalization of the Poisson point process. The cumulative distribution function of the SINR of the representative link is derived assuming independent Rayleigh fading between antennas. Several representative spatial node distributions are considered, including networks with both deterministic and random clusters, strip networks (used to model roadways, e.g.), hard-core networks and networks with generalized path-loss models. In addition, it is shown that if the number of antennas at the representative receiver is increased linearly with the nominal node density, the signal-to-interference ratio converges in distribution to a random variable that is non-zero in general, and a positive constant in certain cases. This result indicates that to the extent that the system assumptions hold, it is possible to scale such networks by increasing the number of receiver antennas linearly with the node density. The results presented here are useful in characterizing the performance of multiantenna wireless networks in more general network models than what is currently available.