Optimal Throughput-Distance Relationship in Multi-Relay Wireless Data Networks

In a multi-rate wireless data network, the data rate is a function of the distance from the Access Point (AP). To extend the coverage range of the data network and to increase the throughput to a target terminal outside the AP coverage range, relay nodes are inserted between the AP and the target terminal. Therefore, for a given throughput-distance relationship, and a given distance between the access point and the target receiver, there must be a minimum number of nodes that provides the maximum throughput to the target receiver. In this paper we present an analytical method to determine the optimal performance bounds, the minimum number of relays and the optimal deployment for a multi-hop multi-rate wireless data network, given that a target receiver located at a specific distance from the access point. The analytical solution is presented in the form of two theorems and their proofs. We apply the theorems to a general analytical model for the throughput distance relationship and compare the analytical model results with those of a network simulator.