An algorithm is given for placing relays at spatial positions to improve the reliability of communicated data in a sensor network. The network consists of many power-limited sensors, a small set of relays, and a receiver. The receiver receives a signal directly from each sensor and also indirectly via a single-hop relay path. The relays rebroad-cast the transmissions in order to achieve diversity at the receiver. Both amplify-and-forward and decode-and-forward relay networks are considered. Channels are modeled with Rayleigh fading, path loss, and additive white Gaussian noise. The main results of the paper are geometric descriptions of sets of locations in the plane in which sensors are assigned to given, fixed-location relays, and the analysis of system performance.
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