We consider an ad hoc network in which each multi-antenna transmitter sends independent streams
 to multiple receivers in a Poisson field of interferers. We provide the outage probability and 
transmission capacity scaling laws, aiming at investigating the fundamental limits of 
Space Division Multiple Access (SDMA). We first show that super linear capacity scaling with 
the number of receive/transmit antennas can be achieved using dirty paper coding. 
Nevertheless, the potential benefits of multi-stream, multi-antenna communications fall off 
quickly if linear precoding is employed, leading to sublinear capacity growth in the case of 
single-antenna receivers. A key finding is that receive antenna array processing is of vital 
importance in SDMA ad hoc networks, as a means to cancel the increased residual interference 
and boost the signal power through diversity.