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This paper presents an analysis of the performances of the Aloha protocol combined with the preamble sampling technique. This protocol is intended for low power sporadic communications in an ad hoc wireless network of sensors. The delay performances and the resulting power consumption and lifetime are computed analytically. The benefits of using CSMA instead of Aloha are indicated. The lifetime that can be expected by a node with a single alkaline LR6 battery is given for the different protocols in function of the interval between successful transmissions. Lifetime of years can be expected using Aloha with preamble sampling if the traffic is low. This protocol can be used to transmit sporadic data traffic or the signaling traffic needed to synchronize a network into a TDMA schedule.