Coverage aspects of cooperative multi-hop line networks in composite fading environment

We consider a cooperative multi-hop line network, where a group of nodes cooperatively transmits the same message to another group of nodes, and model the transmission from one group to another as a discrete-time quasi-stationary Markov process. We derive the transition probability matrix of the Markov chain by considering the wireless channel exhibiting composite shadowing-fading. The sum distribution of the received power by multiple relays is approximated by a single log-normal random variable (RV) by using the moment generating function (MGF)-based technique. This MGF-based technique uses Gauss-Hermite integration to present the sum distribution in closed form. We quantify the signal-to-noise ratio (SNR) margin required to achieve a certain quality of service (QoS) under standard deviation of the shadowing. We also provide the optimal level of cooperation required for obtaining maximum coverage of a line network under a given QoS. Monte Carlo simulations are used to validate the analytical model.