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Extending the lifetime of wireless sensor networks and reducing their energy consumption mandate the development of effective and efficient communication strategies. In this paper, we propose a novel scheme for extending network lifetime via joint power allocation and optimal cluster head (CH) selection under strict constraints on outage probability at the destination. Particularly, we develop a novel definition of network lifetime so as to capture the time beyond which the target outage probability QoS at the destination cannot be attained any longer. Using this definition, we develop a CH selection scheme which allows a group of sensors to choose the optimal CH so as to minimizes the cluster transmit power, subject to a desired outage constraint. Then, we devise a multi-hop transmission scheme using optimal power allocation at the CHs to send the data received from the sensors to the destination, via intermediate CHs, while optimizing the network lifetime. The proposed algorithm allows to find the power allocation at all hops (in-cluster and at the CH tier). Simulation results assess the performance and characteristics of the proposed approach under various path loss and outage probabilities, in a Rayleigh fading environment.