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A strip-shaped sensor network is considered, where randomly placed nodes communicate cooperatively by forming an opportunistic large array (OLA). The transmission from a group of cooperating nodes to another group of nodes is modeled with a quasi-stationary Markov chain, where the transmission channel is assumed to experience lognormal shadowing and Rice fading. The distribution of received power at a node is calculated as a three-step process, which includes finding the distribution of random distance between nodes in addition to other channel impairments, that is, fading and shadowing. It is shown that, in the presence of all three channel impairments, the received power at a node follows a lognormal distribution. This approximation uses a series of steps that involves techniques such as moment matching and moment generating function (MGF). Using the underlying Markov chain properties, the one-hop success probability of the network is derived. The system performance and coverage range of the network are quantified as a function of various network parameters and node topologies. The theoretical results are validated by performing computer simulations.