  Power control in a digital handset is practically implemented in a discrete
fashion and usually such a discrete power control (DPC) scheme is suboptimal.
In this paper, we first show that in a Poison-distributed ad hoc network, if
DPC is properly designed with a certain condition satisfied, it can strictly
work better than constant power control (i.e. no power control) in terms of
average signal-to-interference ratio, outage probability and spatial reuse.
This motivates us to propose an $N$-layer DPC scheme in a wireless clustered ad
hoc network, where transmitters and their intended receivers in circular
clusters are characterized by a Poisson cluster process (PCP) on the plane
$\mathbb{R}^2$. The cluster of each transmitter is tessellated into $N$-layer
annuli with transmit power $P_i$ adopted if the intended receiver is located at
the $i$-th layer. Two performance metrics of transmission capacity (TC) and
outage-free spatial reuse factor are redefined based on the $N$-layer DPC. The
outage probability of each layer in a cluster is characterized and used to
derive the optimal power scaling law
$P_i=\Theta\left(\eta_i^{-\frac{\alpha}{2}}\right)$, with $\eta_i$ the
probability of selecting power $P_i$ and $\alpha$ the path loss exponent.
Moreover, the specific design approaches to optimize $P_i$ and $N$ based on
$\eta_i$ are also discussed. Simulation results indicate that the proposed
optimal $N$-layer DPC significantly outperforms other existing power control
schemes in terms of TC and spatial reuse.
