This paper investigates the performance of multi- antenna spatial diversity in the overlaid wireless ad hoc network. We apply the more practical stochastic geometry tools to model the network. Then we derive closed-form expressions for the outage probability of two coexisting networks employing two basic diversity techniques, the maximum ratio combining (MRC) and the transmit antenna selection (TAS). Monte Carlo simulations verify the accuracy of our expressions, based on which, we further evaluate these two basic diversity schemes from the newly developed perspectives of transmission capacity and overlaid network. We explore the gain source for the transmission capacity of the overlaid network over that of a single network. Our work shows that employing low complexity diversity schemes at either transmit or receive side can significantly improve the overall transmission capacity requiring little or no feedback.