Energy-efficient routing and link adaptation for 2d wireless relay networks in the wideband regime

We discuss the globally optimal energy-efficient design of a 2D relay network. Different from the existing routing protocols on energy saving, which finds the minimal energy route for a given data rate, the proposed algorithm jointly optimizes routing and data rate to maximize energy efficiency (EE) defined as the achievable data rate per power consumption. We propose a low-complexity algorithm to circumvent the huge complexity of the exhaustive search for the network EE maximization and prove its global optimality. Moreover, the proposed algorithm is implemented in a distributed fashion because each relay needs to send its routing information only to the relays in its adjacent tiers, which significantly reduces the signaling overhead of the centralized implementation. Our analysis on the worst-case complexity in a fading channel shows that the complexity of the proposed algorithm increases linearly while that of the exhaustive search increases exponentially as the tier index increases. Simulation results confirm that the proposed algorithm outperforms the existing routing protocols on energy saving and achieves the globally optimal network EE at a significantly lower complexity than the exhaustive search.