Performance Analysis of Linear Cooperative Multi-Hop Networks Subject to Composite Shadowing-Fading

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 shadowing is modeled as a log-normal random variable (RV) and the multipath fading as a Rayleigh RV, where the multiplicative model for the mixture distribution known as Suzuki (Rayleigh-lognormal) distribution has been considered. The sum distribution of the multiple Suzuki RVs is approximated by a single log-normal 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. Two topologies for linear network are considered and the performance of each topology under various system parameters is provided. The analytical results have been validated by matching with the simulation results.