Given a wireless network where each link undergoes small-scale (Rayleigh) fading, we consider the problem of routing a message from a source node to a target node while minimizing energy or power expenditure given a fixed time budget, or vice versa. Given instantaneous channel state information, we develop tight hyperbolic bounds on the quantities of interest and solve the related optimizations in closed form or via lightweight computations. If only average channel state information is available, probabilistical performance measures must be introduced. We therefore develop another set of bounds that supports resource-optimal routing with a guaranteed success probability. Our results rest on novel formulations and solution methods for hyperbolic convex programs and, more generally, nonlinear multicriterion combinatorial optimization.
['Matthew Brand', 'Andreas F. Molisch']
Delay-Energy Tradeoffs in Wireless Ad-Hoc Networks with Partial Channel State Information