On the Lambert-W function for constrained resource allocation in cooperative networks

Abstract

In cooperative networks, a variety of resource allocation problems can be formulated as constrained optimization with system-wide objective, e.g., maximizing the total system throughput, capacity or ergodic capacity, subject to constraints from individual users, e.g., minimum data rate, transmit power limit, and from the system, e.g., power budget, total number of subcarriers, availability of the channel state information (CSI). Most constrained resource allocation schemes for cooperative networks require rigorous optimization processes using numerical methods since closed-form solutions are rarely found. In this article, we show that the Lambert-W function can be efficiently used to obtain closed-form solutions for some constrained resource allocation problems. Simulation results are provided to compare the performance of the proposed schemes with other resource allocation schemes.