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Due to the limited energy supplies of nodes in many applications such as wireless sensor networks, energy efficiency is crucial for extending the lifetime of these networks. This paper addresses the cooperative transmission for outage-restricted multihop wireless ad hoc networks. The source node wants to transmit messages to a single destination. Other nodes in the network may operate as relay nodes. In this paper, new multihop cooperative protocol is proposed using the space-time codes for the purpose of energy savings, subject to a required outage probability at the destination. We restrict the cooperation to nodes along a chosen route. Two efficient power allocation schemes are derived, which depend only on the statistics of the channels. Furthermore, three efficient cooperative multihop transmissions are proposed when arbitrary distributed space-time codes are used. The proposed cooperative protocols offer different degrees of energy efficiency, spectral efficiency, complexity, and signalling overhead. Compared to non-cooperative multihop routing, an energy saving of up to 72% is achievable in line networks with 3 relays and an outage probability constraint of 10-3 at the destination.