Optimal Discrete Power Control in Poisson-Clustered Ad Hoc Networks

Abstract

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 R-2. The cluster of each transmitter is tessellated into N-layer annuli with transmit power Pi 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 is an element of Theta (eta(-(a/2))(i)), with eta(i) as the probability of selecting power P-i and a as 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.