In this paper, a new cooperation structure for spectrum sensing in cognitive radio networks is proposed which outperforms the existing commonly-used ones in terms of energy efficiency. The efficiency is achieved in the proposed design by introducing random interruptions in the cooperation process between the sensing nodes and the fusion center, along with a compensation process at the fusion center. Regarding the hypothesis testing problem concerned, first, the proposed system behavior is thoroughly analyzed and its associated likelihood-ratio test (LRT) is provided. Next, based on a general linear fusion rule, statistics of the global test summary are derived and the sensing quality is characterized in terms of the probability of false alarm and the probability of detection. Then, optimization of the overall detection performance is formulated according to the Neyman-Pearson criterion (NPC) and it is discussed that the optimization required is indeed a decision-making process with uncertainty which incurs prohibitive computational complexity. The NPC is then modified to achieve a good affordable solution by using semidefinite programming (SDP) techniques and it is shown that this new solution is nearly optimal according to the deflection criterion. Finally, effectiveness of the proposed architecture and its associated SDP are demonstrated by simulation results.