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Efficient and reliable subcarrier power allocation in orthogonal frequency-division multiplexing (OFDM)-based cognitive radio networks is a challenging problem. Traditional waterfilling approach is inefficient for such networks due to the strict requirements on the interference generated to the primary users (PUs). In this paper, we present a solution to an energy-efficient resource allocation problem which maximizes the cognitive radio (i.e., secondary) link capacity taking into account the availability of the subcarriers (and hence the reliability of transmission by cognitive radios) and the limits on total interference generated to the PUs. We consider an energy-aware capacity expression by taking into account another factor called subcarrier availability. Optimizing such an expression saves valuable resources such as battery life by selectively allocating power to underutilized subcarriers. Based on a risk-return model, we formulate a convex optimization problem which incorporates a linear average rate loss function in the optimization objective to include the effect of subcarrier availability. Due to the complex structure of the optimal solution, we propose three suboptimal schemes, namely, the step-ladder, nulling, and scaling schemes. We compare the performances of optimal and suboptimal algorithms with the performance of a classical waterfilling scheme. We conclude that waterfilling, unable to satisfy the interference criterion, performs the worst amongst all the schemes considered in this paper.