Throughput-optimal multihop wireless network operation entails a key physical-layer
optimization problem: maximizing a weighted sum of link rates, with weights given by the
differential queue backlogs. This emerges in joint back-pressure routing and power control,
which is central in cross-layer wireless networking. We begin by showing that the core
problem is not only nonconvex, but also NP-hard. This is a negative result, which however
comes with a positive flip side: drawing from related developments in the digital subscriber …

Cross-layer design and operation of wireless networks has attracted significant interest in
the last decade, yet some basic problems in the area remain unsolved. In this paper, we
consider the joint routing and power control problem, and specifically how to choose
transmission powers at the physical layer to maximize stable end-to-end throughput at the
network layer for a multi-hop wireless network. This is the back-pressure power control
(BPPC) problem. Earlier work had recognized that BPPC is a non-convex problem, and …