  This paper addresses three issues in the field of ad hoc network capacity:
the impact of i)channel fading, ii) channel inversion power control, and iii)
threshold-based scheduling on capacity. Channel inversion and threshold
scheduling may be viewed as simple ways to exploit channel state information
(CSI) without requiring cooperation across transmitters. We use the
transmission capacity (TC) as our metric, defined as the maximum spatial
intensity of successful simultaneous transmissions subject to a constraint on
the outage probability (OP). By assuming the nodes are located on the infinite
plane according to a Poisson process, we are able to employ tools from
stochastic geometry to obtain asymptotically tight bounds on the distribution
of the signal-to-interference (SIR) level, yielding in turn tight bounds on the
OP (relative to a given SIR threshold) and the TC. We demonstrate that in the
absence of CSI, fading can significantly reduce the TC and somewhat
surprisingly, channel inversion only makes matters worse. We develop a
threshold-based transmission rule where transmitters are active only if the
channel to their receiver is acceptably strong, obtain expressions for the
optimal threshold, and show that this simple, fully distributed scheme can
significantly reduce the effect of fading.
