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An analytical framework to evaluate the performance of a dense energy-efficient wireless sensor network (WSN) enabling environment monitoring is developed in this paper. We address the estimation of a target multidimensional process by means of samples that are captured by nodes randomly and uniformly distributed and transmitted to a collector through a self-organizing clustered network. The WSN performance is defined in terms of both process estimation error and network lifetime. A new contention-based medium access control (MAC) protocol is introduced to reduce retransmissions. The impact of the proposed MAC strategy on the energy budget is shown.