Completion Time Minimization and Robust Power Control in Wireless Packet Networks

TL;DR

This paper develops convex optimization-based methods for minimizing completion times and robust power control in wireless networks, effectively handling imperfect channel knowledge and non-convex rate regions.

Contribution

It introduces a convex formulation for completion time minimization and robust power control under channel uncertainty, applicable to various fading distributions.

Findings

Completion time minimization is formulated as a convex problem.

Robust power control is effective under log-concave fading distributions.

Average completion time is significantly reduced with optimized power control.

Abstract

A wireless packet network is considered in which each user transmits a stream of packets to its destination. The transmit power of each user interferes with the transmission of all other users. A convex cost function of the completion times of the user packets is minimized by optimally allocating the users' transmission power subject to their respective power constraints. At all ranges of SINR, completion time minimization can be formulated as a convex optimization problem and hence can be efficiently solved. In particular, although the feasible rate region of the wireless network is non-convex, its corresponding completion time region is shown to be convex. When channel knowledge is imperfect, robust power control is considered based on the channel fading distribution subject to outage probability constraints. The problem is shown to be convex when the fading distribution is log-concave in exponentiated channel power gains; e.g., when each user is under independent Rayleigh, Nakagami, or log-normal fading. Applying the optimization frameworks in a wireless cellular network, the average completion time is significantly reduced as compared to full power transmission.