A Lagrangian Approach for the Optimal Placement of Wireless Relay Nodes in Wireless Local Area Networks

The throughput capacity of WLANs can be improved by a carefully designed relay infrastructure. In this work, we propose an optimization formulation based on Lagrangian relaxation and a subgradient algorithm to compute the best placement of a fixed number of relay nodes (RNs) in a WLAN. We apply this optimization framework to a multi-rate WLAN based on the IEEE 802.11g standard under Rayleigh fading. We then study the expected throughput capacity of a WLAN with relay infrastructure and investigate how the optimal placement of RNs is affected by the number of RNs, path-loss characteristics, and the traffic pattern. Our numerical results show that, in some network scenarios, more than 120% performance gain can be achieved when RNs are strategically installed in the network. Furthermore, we also show that for a wide range of system parameters, optimally placed RNs can significantly increase the network throughput capacity over random placement.