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 no power control (i.e., users use the same constant power) 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 on the plane ℝ². 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 ith 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 ∈ Θ(η_i^-(α/2)), with η_i as the probability of selecting power Pi and α as the path loss exponent. Moreover, the specific design approaches to optimize Pi and N based on η_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.