  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.
