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Most existing studies on cooperative relay in wireless sensor networks (WSNs) concentrate on link capacity or symbol error rate (SER) constrained power allocation. We advance the study in two aspects. First, we adopt the packet error rate (PER) constraint instead of SER or link capacity constraint. Assuming non-coherent frequency shift keying (NC-FSK) modulation (used in Mica2 motes) and selection combining diversity, we derive an exact closed-form expression of PER for cooperative relay. The advantage of using the PER constraint is that it can be directly utilized by the routing protocols for end-to-end packet loss rate control. Secondly, realizing the transmission distance is usually kept short for power conservation in WSNs, instead of considering only the transmit power, we adopt a more accurate power model that also takes into account the circuit power and power amplifier efficiency, to provide more realistic results. Numerical results reveal that cooperative relay exhibits a reduction in power cost with a specified PER objective. It is also shown that there exists an optimal number of relays that achieves minimum energy consumption under a specified PER constraint.