Optimal Discrete Power Control in Poisson-Clustered Ad Hoc Networks

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.