A general wireless networking problem is formulated whereby end-to-end user rates, routes, link capacities, transmit-power, frequency, and power resources are jointly optimized across fading states. Even though the resultant optimization problem is generally nonconvex, it is proved that the gap with its Lagrange dual problem is zero, so long as the underlying fading distribution function is continuous. The major implication is that separating the design of wireless networks in layers and per-fading state subproblems can be optimal. Subgradient descent algorithms are further developed to effect an optimal separation in layers and layer interfaces.
Bibliographical noteFunding Information:
Manuscript received February 01, 2008; revised September 21, 2009. Date of current version August 18, 2010. The work in this paper was prepared through collaborative participation in the Communications and Networks Consortium supported by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The material in this paper was presented in part at the CISS 2008, Princeton, NJ, March 2008.
- Lagrangian duality
- wireless networking