We develop a stochastic model to characterize the effects of correlated shadow fading on a linear cooperative multi-hop wireless network. A one-dimensional network of equally-spaced nodes is considered, where a group of nodes transmits cooperatively to another group of nodes under large-scale fading effects. The transmission from one level to another is modeled as a Markov process and the transition probability matrix of the Markov chain is derived, which depends upon the underlying distribution of the received power. The received power is modeled as a log-normal random variable and its distribution is derived by using Fenton-Wilkinson's approach. The eigen-decomposition of the transition matrix provides insightful information about the network coverage and various other parameters. We quantify the values of signal-to-noise ratio margin required to get a desired coverage distance under a given quality of service and standard deviation of shadowing constraints. The accuracy of the model is validated by matching both the simulation and analytical results.
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