This paper is concerned with the power allocation problem in a transmit diversity wireless system with mean channel gain information. For a given set of mean channel gains between nodes, the aim is to find the power allocation and corresponding network topology that minimizes the total transmit power for nodes involved in the cooperative communications between the source and the destination, where all of the transmitters use single omnidirectional antennas. Specifically, the selection of store-and-forward relays deploying Alamouti-type distributed space-time coding along a multihop connection is proposed for a network with randomly distributed nodes and Rayleigh fading. By adapting the transmission power, the proposed data forwarding and processing schemes control the selection of relay nodes utilizing space time coding to minimize the total energy required to transmit the information. In addition to addressing the geometric analysis of the power-efficient topology problem, this paper also focuses on finding computationally efficient algorithms for the selection of relay nodes which will result in a topology formation requiring close to minimum energy.
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