Analysis of an opportunistic large array line network with Bernoulli node deployment

A linear multi-hop cooperative network is considered where the relay nodes are deployed in a random fashion according to a Bernoulli random process. The transmission from one hop to another is modelled as a discrete-time Markov process while taking into account the random locations of the participating nodes along with the Rayleigh fading channel model. Quasi-stationary theory of Markov chains has been applied to study the various properties of the network under consideration, including successful probability of hops as well as network coverage. It is shown that there is a loss of one-hop success probability when the random deployment is done compared to a regular deployment. However, an additional signal-to-noise ratio margin has also been quantified for obtaining a desired quality of service and one-hop success probability.