Optimal resource allocation in wireless communication and networking

Optimal design of wireless systems in the presence of fading involves the instantaneous allocation of resources such as power and frequency with the ultimate goal of maximizing long term system properties such as ergodic capacities and average power consumptions. This yields a distinctive problem structure where long term average variables are determined by the expectation of a not necessarily concave functional of the resource allocation functions. Despite their lack of concavity it can be proven that these problems have null duality gap under mild conditions permitting their solution in the dual domain. This affords a significant reduction in complexity due to the simpler structure of the dual function. The article discusses the problem simplifications that arise by working in the dual domain and reviews algorithms that can determine optimal operating points with relatively lightweight computations. Throughout the article concepts are illustrated with the optimal design of a frequency division broadcast channel.