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

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The throughput capacity of WLANs can be improved the authors 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. The authors apply this optimization framework to a multi-rate WLAN based on the IEEE 802.11g standard under Rayleigh fading. The authors 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.