Range extension using optimal node deployment in linear multi-hop cooperative networks

This paper considers the optimal deployment of nodes in a one-dimensional multi-hop cooperative network for obtaining the maximum network coverage under a quality of service constraint. It is assumed that the total number of nodes to be deployed are fixed and the objective is to arrange the nodes in the form of clusters to obtain maximum coverage such that the end-to-end probability of making successful hops is greater than a threshold. The transmissions that originate from one cluster to another are modeled as discrete-time Markov chain and the transition probability matrix of the chain is derived. By invoking the Perron-Frobenius Theorem and studying its properties, it is shown that a smaller sized cluster of nodes provides the maximum coverage of the network if the path loss exponent is large and vice versa.