Power Allocation (PA) strategies are evaluated for distributed detection in a single-hop, multiple-ring cluster. The Detection Error Probability (DEP) is affected by the observation Signal-to-Noise Ratios (SNRs), the channel SNRs, and node distances. We seek the PA maximizing the total expected deflection coefficient of the received signals at the fusion center under different constraints: a total power constraint and a per-ring power constraint. Both optimization problems are convex, so the Karush-Kuhn-Tucker conditions lead to analytical expressions for the optimal PA. The DEPs from a uniform PA and the proposed PA are compared for various observation SNRs, channel SNRs, number of nodes, and number of rings.