In cognitive radio networks (CRNs), the computational complexity of resource allocation algorithms is a significant problem that must be addressed. However, the high computational complexity of the optimal solution for tackling resource allocation in CRNs makes it inappropriate for use in practical applications. Therefore, this study proposes a power-based pricing algorithm (PPA) primarily to reduce the computational complexity in downlink CRN scenarios while restricting the interference to primary users to permissible levels. A two-stage approach reduces the computational complexity of the proposed mathematical model. Stage 1 assigns subcarriers to the CRN's users, while the utility function in Stage 2 incorporates a pricing method to provide a power algorithm with enhanced reliability. The PPA's performance is simulated and tested for orthogonal frequency-division multiplexing-based CRNs. The results confirm that the proposed algorithm's performance is close to that of the optimal algorithm, albeit with lower computational complexity of O(M) log (M).