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Power control in a digital handset is practically implemented in a discretefashion 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, ifDPC is properly designed with a certain condition satisfied, it can strictlywork better than constant power control (i.e. no power control) in terms ofaverage signal-to-interference ratio, outage probability and spatial reuse.This motivates us to propose an $N$-layer DPC scheme in a wireless clustered adhoc network, where transmitters and their intended receivers in circularclusters are characterized by a Poisson cluster process (PCP) on the plane$\mathbb{R}^2$. The cluster of each transmitter is tessellated into $N$-layerannuli with transmit power $P_i$ adopted if the intended receiver is located atthe $i$-th layer. Two performance metrics of transmission capacity (TC) andoutage-free spatial reuse factor are redefined based on the $N$-layer DPC. Theoutage probability of each layer in a cluster is characterized and used toderive the optimal power scaling law$P_i=\Theta\left(\eta_i^{-\frac{\alpha}{2}}\right)$, with $\eta_i$ theprobability 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 proposedoptimal $N$-layer DPC significantly outperforms other existing power controlschemes in terms of TC and spatial reuse.

Optimal Discrete Power Control in Poisson-Clustered Ad Hoc Networks